Answer:
a) ΔL = 80mm
b) h = 600 - 10w mm
Step-by-step explanation:
a. From the time when 7 L have been removed to the time when 15 L have been removed, the change in the volume has been 8L and how the height of the water decreases 10mm per liter removed, then the acumulate change in the height of water has been (8lt)(10mm/lt) = 80 mm
b) If w liters have been removed, then the change in the height of water is (10mm/lt)(wlt) = 10w mm and thus the water's height at this precise point in time is 600 - 10w mm
Mindy divides a rectangular piece of fabric into a equal-sized pieces for to suing projects for project a she will need she will use 1/2 of the fabric for Project B she will use 1/4 of the fabric draw a model to show how the fabric was divided and which piece will be used what unit fraction represents one of the pieces write an equation to find how much of the fabric will not be used let F represent the fraction of leftover fabric what is the answer?
Answer:F=A-(A/2+A/4)
=> F=1/4
Step-by-step explanation:
Let A represent the initial quality of rectangular fabric.
Half of A was used for the sewing project
Quarter of the left over was used for project B
Hence a quarter of unused fabric(F) will be left.
To illustrate the effects of driving under the influence (DUI) of alcohol, a police officer brought a DUI simulator to a local high school. Student reaction time in an emergency was measured with unimpaired vision and also while wearing a pair of special goggles to simulate the effects of alcohol on vision. For a random sample of nine teenagers, the time (in seconds) required to bring the vehicle to a stop from a speed of 60 miles per hour was recorded.
Subject 1 2 3 4 5 6 7 8 9
Normal, Xi 4.47 4.24 4.58 4.65 4.31 4.80 4.55 5.00 4.79
Impaired, Yi 5.77 5.67 5.51 5.32 5.83 5.49 5.23 5.61 5.6
(a) Whether the student had unimpaired vision or wore goggles first was randomly selected. Why is this a good idea in designing the experiment?
(b) Use a 95% confidence interval to test if there is a difference in braking time with impaired vision and normal vision where the differences are computed as "impaired minus normal. "Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.
Answer:
a) If we design the experiment on this way we can check if we have an improvement with the method used.
We assume that we have the same individual and we take a value before with the normal impaired condition and the final condition is the normal case.
b) [tex]-0.96-2.306\frac{0.359}{\sqrt{9}}=-1.24[/tex]
[tex]-0.96+2.306\frac{0.359}{\sqrt{9}}=-0.69[/tex]
The 95% confidence interval would be given by (-1.24;-0.69)
Step-by-step explanation:
Part a
If we design the experiment on this way we can check if we have an improvement with the method used.
We assume that we have the same individual and we take a value before with the normal impaired condition and the final condition is the normal case.
Part b
For this case first we need to find the differences like this :
Normal, Xi 4.47 4.24 4.58 4.65 4.31 4.80 4.55 5.00 4.79
Impaired, Yi 5.77 5.67 5.51 5.32 5.83 5.49 5.23 5.61 5.6
Let [tex]d_i = Normal -Impaired[/tex]
[tex] d_i : -1.3, -1.43, -0.93, -0.67,-1.52, -0.69, -0.68, -0.61, -0.81[/tex]
The second step is calculate the mean difference
[tex]\bar d= \frac{\sum_{i=1}^n d_i}{n}=-0.96[/tex]
The third step would be calculate the standard deviation for the differences, and we got:
[tex]s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =0.359[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\bar d \pm t_{\alpha/2}\frac{s_d}{\sqrt{n}}[/tex] (1)
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=9-1=8[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,8)".And we see that [tex]t_{\alpha/2}=2.306[/tex]
Now we have everything in order to replace into formula (1):
[tex]-0.96-2.306\frac{0.359}{\sqrt{9}}=-1.24[/tex]
[tex]-0.96+2.306\frac{0.359}{\sqrt{9}}=-0.69[/tex]
So on this case the 95% confidence interval would be given by (-1.24;-0.69)
Random selection for first testing condition (impaired or unimpaired) was used to avoid order effects. The confidence interval on whether braking times under impaired and unimpaired conditions were significantly different can be determined using a paired t-test and if the interval includes zero, we can say that there is no significant difference.
Explanation:(a) Random selection of whether the student had unimpaired or impaired vision was a good idea because it helps to prevent any order effects. An order effect occurs if the order in which the tests are performed can influence the results. For example, if the unimpaired test was always done first, the driver might be more cautious in the second test as they have learned from the first test.
(b) The confidence interval for a difference between two means (in this case the braking times) can be calculated with a paired t-test. We will compare the average of differences (impaired vision braking time - normal vision braking time) to zero, assuming that they follow a normal distribution.
The formula to calculate the confidence interval for paired data is:
(Avg(D) - (t * StdDev(D) / sqrt(n)), Avg(D) + (t * StdDev(D) / sqrt(n)))
Where Avg(D) is the average of the differences, StdDev(D) is the standard deviation of the differences, n is the sample size (9 in this case), and t is the t-value from the t-distribution table (which will be 2.306 considering 95% confidence for 8 degrees of freedom).
After calculating you'll get the confidence interval for the differences. If this interval includes zero, we can say there is no significant difference for the braking time under impaired and unimpressed conditions using the 95% confidence interval.
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Luis hizo un viaje en el coche en el cual consumio 20 l de gasolina. el trayecto lo hizo en dos etapas en la primera consumio 2/3 de la gasolina que tenia en el deposito y en la segunda, la mitadque le quedaba. ¿cuanta gasolina habia en el deposito?
Answer: [tex]24\ liters[/tex]
Step-by-step explanation:
Let be "x" the amount of gasoline in liters that the car's tank had at the beginning of the trip.
1. In the first part of the trip the amount of gasoline the car used can be expressed as:
[tex]\frac{2}{3}x[/tex]
2. After the first part of the trip, the remaining was:
[tex]x-\frac{2}{3}x=\frac{1}{3}x[/tex]
3. In the second part of the trip the car used [tex]\frac{1}{2}[/tex] of the remaining. This is:
[tex](\frac{1}{3}x)(\frac{1}{2})=\frac{1}{6}x[/tex]
4. The total amount ot gasoline used in this trip was 20 liters.
5. Then, with this information, you can write the following equation:
[tex]\frac{2}{3}x+\frac{1}{6}x=20[/tex]
6. Finally, you must solve for "x" in order to find its value. This is:
[tex]\frac{2}{3}x+\frac{1}{6}x=20\\\\\frac{5}{6}x=20\\\\5x=120\\\\x=24[/tex]
Describe your research question, and explain its importance. Describe how you would use the four-step hypothesis test process to answer your research question. Explain how using a t test could help you answer your research question.
Answer:
See explanation below
Step-by-step explanation:
Data given and notation
First we need to find the sample mean and deviation from the data with the following formulas:
[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
[tex]\bar X[/tex] represent the sample mean
[tex]s[/tex] represent the sample standard deviation
[tex]n[/tex] sample size
[tex]\mu_o [/tex] represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We have three possible options for the null and the alternative hypothesis:
Case Bilateral
Null hypothesis:[tex]\mu = \mu_o[/tex]
Alternative hypothesis:[tex]\mu \neq \mu_o[/tex]
Case Right tailed
Null hypothesis:[tex]\mu \leq \mu_o[/tex]
Alternative hypothesis:[tex]\mu > \mu_o[/tex]
Case Left tailed
Null hypothesis:[tex]\mu \geq \mu_o[/tex]
Alternative hypothesis:[tex]\mu < \mu_o[/tex]
We assume that w don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) and the value obtained is assumed as [tex]t_o[/tex]
Calculate the P-value
First we need to find the degrees of freedom:
[tex] df=n-1[/tex]
Case two tailed
Since is a two-sided tailed test the p value would be:
[tex]p_v =2*P(t_{df}>|t_o|)[/tex]
Case Right tailed
Since is a one-side right tailed test the p value would be:
[tex]p_v =P(t_{df}>t_o)[/tex]
Case Left tailed
Since is a one-side left tailed test the p value would be:
[tex]p_v =P(t_{df}<t_o)[/tex]
Conclusion
The rule of decision is this one:
[tex]p_v >\alpha[/tex] We fail to reject the null hypothesis at the significance level [tex]\alpha[/tex] assumed
[tex]p_v <\alpha[/tex] We reject the null hypothesis at the significance level [tex]\alpha[/tex] assumed
A piece of paper in the shape of an equilateral triangle with side length 3 and a circular piece of paper with radius 1 are glued together so that their centers coincide. How long is the outer perimeter of the resulting 2-dimensional shape?
Answer:
Outer perimeter of the resulting 2-dimensional shape will be 18.84 units
Step-by-step explanation:
From the figure, we could see
AE = FB = 1
And minor arc EF
=> [tex]\frac{2 \pi (1) }{6}[/tex]
=>[tex]= \frac{2 \pi}{ 6}[/tex]
=>[tex]= \frac{ \pi}{ 3}[/tex]
So by symmetry the perimeter is
=>[tex]3(2 + \frac { \pi}{3} )[/tex]
=>[tex]3(\frac {6 \pi}{3} )[/tex]
=>[tex]6 \pi[/tex]
=> [tex]6 \times 3.14[/tex]
=> 18.84 units
Answer:
6+pi or 9.14
Step-by-step explanation:
What are the factors of the polynomial function?
Good evening ,
Answer:
(x-1) ; (x+3) and (x+5).
Step-by-step explanation:
Since 1 , -3 , -5 are roots of the polynomial function
then the factors of f are:
(x-1) ; (x+3) and (x+5).
:)
9. 10. To solve 2x x 2 11 x = 8 x 2 2x , Ren multiplied both sides by the least common denominator. Which statement is true? A. 2 is an extraneous solution. B. 7 2 is an extraneous solution. C. 0 and 2 are extraneous solutions. D. This equation does not contain any extraneou
Answer:
2 is the extraneous solution
Step-by-step explanation:
Given equation is
[tex]\frac{2x}{x-2} -\frac{11}{x} =\frac{8}{x^2-2x}[/tex]
Factor the denominator
[tex]\frac{2x}{x-2} -\frac{11}{x} =\frac{8}{x(x-2)}[/tex]
LCD is x(x-2), multiply all the fractions by LCD
[tex]2x \cdot x-11(x-2)=8[/tex]
[tex]2x^2-11x+22= 8[/tex], subtract 8 from both sides
[tex]2x^2-11x+14=0[/tex]
factor the left hand side
[tex]2x^2-7x-4x+14= 0[/tex]
[tex]x(2x-7)-2(2x-7)=0[/tex]
[tex](x-2)(2x-7)=0[/tex]
x-2=0, so x=2
2x-7=0, [tex]x=\frac{7}{2}[/tex]
when x=2, then the denominator becomes 0 that is undefined
So 2 is the extraneous solution
The question is asking which statement is true regarding the potential extraneous solutions after solving an algebraic equation by multiplying both sides by the least common denominator. To determine if a solution is extraneous, it must be checked against the original equation. Without the specific manipulations made by Ren, we cannot assess the given options.
Explanation:To solve the equation 2x x 2 11 x = 8 x 2 2x, Ren multiplied both sides by the least common denominator to eliminate the fractions and then used algebraic techniques to find the solutions for x. We know that when we have an equation of the form (ax + b)x = 0, there are two multiplicands, and we can set each equal to zero to solve for x. This leads to two solutions.
After solving, we need to check each solution by substituting it back into the original equation to confirm whether or not the solution is extraneous. An extraneous solution is one that does not satisfy the original equation after simplification. Checking is important as it ensures that the proposed solutions indeed make the original equation an identity, such as 6 = 6.
Without the specific equation after Ren's manipulations, we cannot evaluate the statements A, B, C, or D directly. However, we can understand that extraneous solutions arise when certain steps in solving an equation (like squaring both sides or multiplying by a variable expression) introduce results that are not true for the original equation.
In a student government election, 7,000 students cast a vote for the incumbent, 900 vote for the opponent, and 100 cast a protest vote. What was the ratio of the incumbent”s votes in the total number of votes?
-Jarvis
Answer:
The ratio of the incumbent”s votes in the total number of votes = 7:8
Step-by-step explanation:
Given:
Number of students who cast vote for the incumbent = 7,000
Number of students who cast vote for the opponent = 900
Number of protest votes = 100
To find ratio of the incumbent”s votes in the total number of votes.
Solution:
Total number of votes cast = [tex]7000+900+100=8000[/tex]
Number of votes for incumbent = [tex]7000[/tex]
Ratio of incumbent”s votes in the total number of votes can be calculated as:
⇒ [tex]\frac{\textrm{The incumbent's votes}}{\textrm{Total number of votes}}[/tex]
⇒ [tex]\frac{7000}{8000}[/tex]
Simplifying to simplest fraction by dividing numerator and denominator by 1000.
⇒ [tex]\frac{7000\div1000}{8000\div1000}[/tex]
⇒ [tex]\frac{7}{8}[/tex]
Thus, ratio of the incumbent”s votes in the total number of votes = 7:8
Which of the following represents the slope of the line?
Help ASAP
Answer:option 3 is the correct answer.
Step-by-step explanation:
Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis
change in the value of y = y2 - y1
Change in value of x = x2 -x1
y2 = final value of y
y 1 = initial value of y
x2 = final value of x
x1 = initial value of x
From the graph given,
y2 = 3
y1 = 1
x2 = 0
x1 = - 1
Slope = (3 - 1)/(0 - - 1)
Slope = 2/1 = 2
Question 3 (1 point)
What is the midpoint of E (9, 7) and F (-1, 5)?
Question 3 options:
(4, 6)
(10, 2)
(5, 1)
(8, 12)
Answer:
The answer to your question is (4, 6)
Step-by-step explanation:
Data
E ( 9 , 7 )
F ( - 1, 5)
Formula
[tex]Xm = \frac{x1 + x2}{2}[/tex]
[tex]Ym = \frac{y1 + y2}{2}[/tex]
Substitution and simplification
[tex]Xm = \frac{9 -1}{2}[/tex]
[tex]Xm = \frac{8}{2}[/tex]
Xm = 4
[tex]Ym = \frac{7 + 5}{2}[/tex]
[tex]Ym = \frac{12}{2}[/tex]
Ym = 6
Result
(4 , 6)
Blaire walked around her garden in the morning and saw that 18 of her tomato plants had tomatoes ready to pick. If this was 90% of her tomato plants, how many tomato plants does Blaire have altogether?
Blaire has 20 tomato plants altogether.
Step-by-step explanation:
Given,
Tomatoes plants ready to pick = 18
This represents 90% of total tomato plants.
Let,
x be the original number of tomato plants.
90% of x = 18
[tex]\frac{90}{100}*x=18[/tex]
[tex]0.9x=18[/tex]
Dividing both sides by 0.9
[tex]\frac{0.9x}{0.9}=\frac{18}{0.9}[/tex]
[tex]x=20[/tex]
Blaire has 20 tomato plants altogether.
Keywords: percentage, division
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please help
with my geomtry homework
Answer:
Therefore, HL theorem we will prove for Triangles Congruent.
Step-by-step explanation:
Given:
Label the Figure first, Such that
Angle ADB = 90 degrees,
angle ADC = 90 degrees, and
AB ≅ AC
To Prove:
ΔABD ≅ ΔACD by Hypotenuse Leg theorem
Proof:
In Δ ABD and Δ ACD
AB ≅ AC ……….{Hypotenuse are equal Given}
∠ADB ≅ ∠ADC ……….{Each angle measure is 90° given}
AD ≅ AD ……….{Reflexive Property or Common side}
Δ ABD ≅ Δ ACD ….{By Hypotenuse Leg test} ......Proved
Therefore, HL theorem we will prove for Triangles Congruent.
Shear strength measurements for spot welds have been found to have standard deviation 1 0 pounds per square inch (psi). If 100 test welds are to be measured, what is the approximate probability that the sample mean will be within 1 psi of the true population mean.
Answer:
[tex]P(\mu -1< \bar X <\mu +1)=0.6826[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Let X the random variable that represent the Shear strength of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(\mu,10)[/tex]
Where [tex]\mu[/tex] and [tex]\sigma=10[/tex]
And let [tex]\bar X[/tex] represent the sample mean, the distribution for the sample mean is given by:
[tex]\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})[/tex]
On this case [tex]\bar X \sim N(\mu,\frac{10}{\sqrt{100}})[/tex]
We are interested on this probability
[tex]P(\mu -1<\bar X<\mu +1)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
If we apply this formula to our probability we got this:
[tex]P(\mu -1<\bar X<\mu +1)=P(\frac{\mu- 1-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{\mu +1-\mu}{\frac{\sigma}{\sqrt{n}}})[/tex]
[tex]=P(\frac{\mu -1-\mu}{\frac{10}{\sqrt{100}}}<Z<\frac{\mu +1-\mu}{\frac{10}{\sqrt{100}}})=P(-1<Z<1)[/tex]
And we can find this probability on this way:
[tex]P(-1<Z<1)=P(Z<1)-P(Z<-1)[/tex]
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
[tex]P(-1<Z<1)=P(Z<1)-P(Z<-1)=0.8413-0.1587=0.6826[/tex]
The probability that the sample mean will be within 1 psi of the true population mean is approximately 68.2%, according to the properties of a normal distribution and the central limit theorem.
Explanation:This is a problem of standard deviation and probability in relation to the sample mean. This type of problem can be solved by knowing the properties of a normal distribution.
The central limit theorem states that if we have a large enough sample, the distribution of the sample mean will approximate a normal distribution regardless of the distribution of the population.
For this scenario, where the true population mean is unknown, the standard deviation of the sampling distribution (also known as the standard error) can be calculated as the original standard deviation (10 psi) divided by the square root of the sample size (100 test welds in this case), hence 10 ÷ √100 = 1 psi.
Then, to find the probability that the sample mean is within 1 psi of the true population mean, we can refer to the Z-table (a standard normal distribution table) to find the corresponding probability for z = ±1 (because the z-score for ±1 standard error from the mean is ±1). This value is approximately 68.2%
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A hardware store rents vacuum cleaners that customers may use for part or all of a day, before returning. The store charges a flat fee plus an hourly rate. Choose the linear function f for the total rental cost of a vacuum cleaner.
In the context of renting a vacuum cleaner for an hourly rate plus a flat fee from a hardware store, the total rental cost can be represented as a linear function. If we consider the flat fee to be $31.50 and the hourly rate to be $32, the function would be f(x) = 31.50 + 32x, where x is the rental duration in hours.
Explanation:The question pertains to a linear function, which is a fundamental concept in algebra and represents a straight line when graphed. Such a function is typically expressed in the form y = mx + b, where m and b are constants, y is the dependent variable, and x is the independent variable.
In the context of the question, the total rental cost for a vacuum cleaner from the hardware store can be a linear function if it involves both a fixed cost (the flat fee) and an hourly rate charge. Specifically, the flat fee can be represented as the constant b, which will be added to regardless of the number of hours the vacuum cleaner has been rented.
On the other hand, the hourly rate charge is the variable cost that alters in relation to the rental duration and can be shown as m times x. Thus, if we consider the flat fee to be $31.50 and the hourly rate to be $32 (as in the reference), the total rental cost function, f, can be formulated as follows: f(x) = 31.50 + 32x
In this equation, x stands for the number of hours the vacuum cleaner is rented. Consequently, by substituting the rental duration into the equation, it would be feasible to compute the total rental cost.
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If the sum of two positive integers is 24 and the difference of their squares is 48, what is the product of the two integers?(A) 108(B) 119(C) 128(D) 135(E) 143
Answer:
143
Step-by-step explanation:
Denote by x and y such integers. The hypotheses given can be written as:
[tex]x+y=24, x^2-y^2=48[/tex]
Use the difference of squares factorization to solve for x-y
[tex]48=x^2-y^2=(x-y)(x+y)=24(x-y)\text{ then }x-y=2[/tex]
Remember that
[tex](x+y)^2=x^2+2xy+y^2[/tex]
[tex](x-y)^2=x^2-2xy+y^2[/tex]
Substract the second equation from the first to obtain
[tex](x+y)^2-(x-y)^2=4xy[/tex]
Substituting the known values, we get
[tex]4xy=24^2-2^2=572\text{ then }xy=\frac{572}{4}=143[/tex]
The sum of the two integers is 24, and the difference of their squares is 48. By setting up a system of equations, we find the integers are 13 and 11. The product of these integers is 143.
Explanation:We are given the sum of two positive integers is 24 and the difference of their squares is 48. Let's denote the integers as x and y, with x being the larger integer. So, we have:
x + y = 24 (Equation 1)x^2 - y^2 = 48 (Equation 2)We can factor Equation 2, which is a difference of squares, into (x + y)(x - y) = 48. Using the fact that x + y = 24 (from Equation 1), we can substitute into this to get 24(x - y) = 48, which simplifies to x - y = 2. Now we have a system of equations:
x + y = 24x - y = 2Adding these two equations, we get 2x = 26, so x = 13. Subtracting the second equation from the first, we get 2y = 22, so y = 11. Now to find the product of the two integers, we multiply x and y together: 13 * 11 = 143.
Therefore, the product of the two integers is 143.
By [n][n] we denote the set {1,…,n}. A function f:[m]→[n] is called monotone if f(i) \leq f(j)f(i)≤f(j)whenever i < ji
Answer:
There are a total of [tex] { 6 \choose 3} = 20 [/tex] functions.
Step-by-step explanation:
In order to define an injective monotone function from [3] to [6] we need to select 3 different values fromm {1,2,3,4,5,6} and assign the smallest one of them to 1, asign the intermediate value to 2 and the largest value to 3. That way the function is monotone and it satisfies what the problem asks.
The total way of selecting injective monotone functions is, therefore, the total amount of ways to pick 3 elements from a set of 6. That number is the combinatorial number of 6 with 3, in other words
[tex] {6 \choose 3} = \frac{6!}{3!(6-3)!} = \frac{720}{6*6} = \frac{720}{36} = 20 [/tex]
Your watch beeps every 15 seconds, and your moms watch beeps every 25 seconds. If they beep together at 3:00 pm, at what time will they beep together for the 20th time?
Answer:
The two watches will beep together for 20th time at 3:25 pm.
Step-by-step explanation:
My watch beeps every 15 seconds and mom's watch beeps every 25 seconds.
Thus both the watches beep at the same time at an interval of 75 seconds.
75 is the smallest multiple of 15 and 25.
They beep together at 3 pm and when they beep together for the 20th time , we have to add 20 times the time taken for both the watches to beep together.
This time interval = 20 [tex]\times[/tex] 75 = 1500 seconds = 25 minutes.
The two watches will beep together for 20th time at 3:25 pm.
Consider the following code segment: primes = {2, 3, 5, 7} odds = {1, 3, 5, 7} Which line of code will result in x containing {1}? a. x = primes.difference(odds) b. x = odds.difference(primes) c. x = primes.intersection(odds) d. x = odds.intersection(primes)
Answer:
a. x = primes.difference(odds)
Step-by-step explanation:
Given the list of numbers primes and odds, the list x is made subtracting odds to primes. To do that in a object oriented language you use: x = primes.difference(odds) which is equivalent to x = primes - odds
The correct line of code that will result in x containing {1} is option b: x = odds.difference(primes). This provides the set of elements in the 'odds' set that are not in the 'primes' set, which is {1}.
Explanation:The question revolves around the concept of set operations in mathematics. Specifically, it focuses on the difference and intersection operations between two sets named primes and odds. To find the set containing only the number {1}, we should look for the difference between the odds and primes sets because 1 is in the odds but not in the primes.
Answer option a, x = primes.difference(odds), would result in a set that contains elements present in primes but not in odds, which would be {2}. However, that's not what we are looking for.
Answer option b, x = odds.difference(primes), is correct. It would result in a set containing elements that are in odds but not in primes, which is exactly {1}.
Answer options c and d, which refer to the intersection of the two sets, would result in the set {3, 5}, which are elements common to both primes and odds, and therefore not the correct answer.
For visual representation, you could draw a Venn diagram with two circles, one for primes containing {2, 3, 5, 7} and another for odds containing {1, 3, 5, 7}. The number 1 would be in the part of the odds circle that does not overlap with the primes circle.
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write a polynomial function with the given zeros x= -2,1,4
Answer:
With the given zeros x=-2,1,4 the polynomial function is [tex]x^3-3x^2-6x-8[/tex]
Step-by-step explanation:
Given zeros are x=-2,1,4
Now to find the polynomial function:
With the given zeros we can write it as below:
x=-2 implies that x+2=0
x=-1 implies that x-1=0
x=4 implies that x-4=0
Then we can the zeros or factors by (x+2)(x-1)(x-4)
Now expanding the zeros or factors:
[tex](x+2)(x-1)(x-4)[/tex]
[tex](x+2)(x-1)(x-4)=(x^2-x+2x-2)(x-4)[/tex] ( multiply each term with each term of another factor)
[tex]=(x^2+x-2)(x-4)[/tex] ( adding the like terms)
[tex]=x^3-4x^2+x^2-4x-2x+8[/tex] ( multiply each term with each term of another factor)
[tex]=x^3-3x^2-6x+8[/tex] ( adding the like terms)
[tex](x+2)(x-1)(x-4)=x^3-3x^2-6x+8[/tex]
Therefore the polynomial function is [tex](x+2)(x-1)(x-4)=x^3-3x^2-6x+8[/tex]
With the given zeros x=-2,1,4 the polynomial function is [tex]x^3-3x^2-6x-8[/tex]
Kira goes running Kira goes running Monday, Wednesday, and Friday of each week. Each Monday she runs 2.5 miles, each Wednesday she runs 5.75 miles, and each Friday she runs 7.75 miles. How many total miles does she run in 9 weeks?
Kira runs a total of 144 miles in 9 weeks.
Step-by-step explanation:
Given,
Distance covered on Monday = 2.5 miles
Distance covered on Wednesday = 5.75 miles
Distance covered on Friday = 7.75 miles
Total distance covered per week = 2.5+5.75+7.75 = 16 miles
Total distance in 9 weeks = Distance per week * 9
Total distance in 9 weeks = 16*9 = 144 miles
Kira runs a total of 144 miles in 9 weeks.
Keywords: addition, multiplication
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There are 81 pencils in a box. Abigail removes 5 pencils, Barry removes 2 pencils, Cathy removes 6 pencils and David adds 5 pencils to the box. How many pencils are left in the box?
Answer:
73 pencils
Step-by-step explanation:
There are 81 pencils in a box.
Abigail removes 5 pencils, thus we have 81-5 = 76 left
Barry removes 2 pencils, it becomes 76-2 = 74
Cathy removes 6 pencils, now it is 74-6= 68
and David adds 5 pencils to the box,
Now we have 68+5=73 pencils left in the box.
List K consists of seven numbers. Is the average (arithmetic mean) of the seven numbers negative?
1) Four of the seven numbers in list K are negative.
2) The sum of the seven numbers in list K is negative.
Answer:
Yes, the average (arithmetic mean) of the seven numbers would be negative.
Step-by-step explanation:
We have been given that list K consists of seven numbers. We have been given two cases about list K. We are asked to determine whether the average (arithmetic mean) of the seven numbers negative.
1st case: Four of the seven numbers in list K are negative.
For 1st case, if the sum of 3 positive numbers is greater than sum of four negative numbers, then the average would be positive.
2nd case: The sum of the seven numbers in list K is negative.
We know that average of a data set is sum of all data points of data set divided by number of data points.
Since we have been given that sum of the seven numbers in list K is negative, so a negative number divided by any positive number (in this case 7) would be negative.
Therefore, the average (arithmetic mean) of the seven numbers would be negative.
Can someone please explain how to do this?? I got the wrong answer and I don't know how to do this question
Find the area of the triangle with a = 19, b = 14, c = 19. Round to the nearest tenth.
thank you
Answer:
[tex]\displaystyle 133\:square\:units[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{1}{2}hb = A, \frac{1}{2}bh = A, or\: \frac{hb}{2} = A[/tex]
For the two legs, no matter what you do, you can either take half of 19 [9½] and multiply it by 14, take half of 14 [7] and multiply it by 19, or you could multiply both 14 and 19 [266] then take of that.
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Which of the following statements shows the distributive property?
5 + (4 – 2) = 20 – 10
5(4 – 2) = 20 – 10
5 + (4 – 2) = 9 + 3
5(4 – 2) = 9 – 7
Answer:
[tex]\displaystyle 5(4 - 2) = 20 - 10[/tex]
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The distributive property is demonstrated in the equation 5(4 - 2) = 20 - 10, where multiplication outside the parentheses is distributed to each term within the parentheses.
The distributive property in mathematics is an algebraic property used to multiply a single term and two or more terms inside a set of parentheses. The correct statement that shows the distributive property among the given options is: 5(4 - 2) = 20 - 10.
Applying the distributive property, we would multiply the 5 by each term inside the parentheses: 5 * 4 = 20 and 5 * (-2) = -10. Hence, we have 5 * 4 - 5 * 2 = 20 - 10, which is a correct demonstration of this property.
To better understand, let me explain it step-by-step:
Multiply the term outside the parenthesis (5) by each of the terms inside the parenthesis (4 and -2).
Perform the multiplication: 5 * 4 = 20 and 5 * (-2) = -10
Combine the results to show that 5(4 - 2) is indeed equal to 20 - 10.
The dot plot represents a sampling of ACT scores:
(picture below)
Which box plot represents the dot plot data?:
(choices in second picture below)
Answer:
Option D.
Step-by-step explanation:
Form the given line plot, first we need to find the data set. So, our data set is
24, 26, 26, 26, 27, 27, 27, 28, 28, 28, 28, 28, 30, 30, 30, 32, 32, 32, 35
Divide the data in two equal parts.
(24, 26, 26, 26, 27, 27, 27, 28, 28), 28, (28, 28, 30, 30, 30, 32, 32, 32, 35)
Divide each of the parenthesis in two equal parts.
(24, 26, 26, 26), 27, (27, 27, 28, 28), 28, (28, 28, 30, 30), 30, (32, 32, 32, 35)
Now, we get
Minimum value = 24
First quartile = 27
Median = 28
Third quartile = 30
Maximum value = 35
It means the box lies between 27 and 30. The line inside the box at 28. Left point of the line isi 24 and right point of the line 35.
This description represented by the box plot in option D.
Hence, the correct option is D.
A 150-pound person burns 5.1 calories per minute when walking at a speed of 4 miles per hour. While walking, this person eats a snack that has 60 calories. This snack subtracts from the calories burned while walking. How long must the person walk at this speed to burn at least 150 calories? Use pencil and paper. Describe what values the person could change so that the amount of time spent walking would be less.
Answer:
He needs to walk 41 mins or 2,76 miles to burn 150 calories.
If he increases the speed of walking or eats snack with less calories, he will spend less time for walking.
Step-by-step explanation:
The person is burning
[tex]5,1*60=306[/tex]
calories per hour.
He needs to burn 150 calories plus 60 calories that comes from the snack. In total 210 calories to burn.
[tex]210/306=0,69[/tex]
He needs to walk 0,69 hours (aprrox. 41 mins) to burn 210 calories
[tex]0,69*4=2,76[/tex]
In total he need to walk 2,76 miles to burn 210 calories.
Final answer:
A 150-pound person must walk approximately 17.65 minutes at 4 mph to burn at least 150 calories, after accounting for a 60-calorie snack. To decrease walking time, they can increase activity intensity or choose lower-calorie snacks.
Explanation:
To calculate the time required for a 150-pound person to burn at least 150 calories at a rate of 5.1 calories per minute while walking at 4 miles per hour, we must account for the 60-calorie snack they consumed. We first subtract the 60 calories from the 150-calorie goal, which leaves 90 calories to be burned through exercise. Dividing 90 calories by the 5.1 calories burned per minute gives us the time needed in minutes.
Calculation:
Total calories to burn = 150 - 60 (from snack) = 90 calories
Calories burned per minute = 5.1
Time (in minutes) = Total calories to burn ÷ Calories burned per minute = 90 ÷ 5.1 = 17.65 minutes
So, the person must walk approximately 17.65 minutes to burn at least 150 calories, minus the calories from the snack. To reduce the time spent walking, the person could increase their walking speed, engage in a more vigorous exercise, or consume a lower-calorie snack.
What is the average rate of change of the function
f(x)=480(0.3)x from x = 1 to x = 5?
Enter your answer, as a decimal, in the box.
Do not round your answer.
Answer:
Average rate of change [tex]=-35.7084[/tex]
Step-by-step explanation:
Given function is [tex]f(x)=480(0.3)^x[/tex] and we need to find average rate of change of the function from [tex]x=1\ to\ x=5[/tex].
Average rate of change [tex]=\frac{f(b)-f(a)}{b-a}[/tex]
So,
[tex]here\ b=5\ and\ a=1\\f(5)=480(0.3)^5\\=480\times0.00243=1.1664\\and\\f(1)=480(0.3)^1\\=480\times0.3=144[/tex]
Average rate of change
[tex]=\frac{f(b)-f(a)}{b-a}\\\\=\frac{f(5)-f(1)}{5-1}\\\\=\frac{1.1664-144}{5-1}\\\\=\frac{-142.8336}{4}= -35.7084[/tex]
Hence, average rate of change of the function [tex]f(x)=480(0.3)^x[/tex] over the intervel [tex]x=1\ to\ x=5[/tex] is [tex]=-35.7084[/tex].
Answer:
-35.8074 is the correct answer
Step-by-step explanation:
Two thirds of a number reduced by 11 is equal to 4 more than the number. Find the number. n= Answer
Answer:
-45
Step-by-step explanation:
2/3x - 11 = x + 4
I created an inequality representing the above statement first. This makes things look less complicated than what the question is asking.2/3x = x + 15
solve for x. I started by adding 11 to both sides.-1/3x = 15
multiply both sides by -3x = -45
Answer:
-45.
Step-by-step explanation:
2/3 x - 11 = x + 4
2/3 x - x = 4 + 11
-1/3x = 15
x = 15 * -3
x = -45.
A boat whose speed in 15km/hr in still water goes 30 km downstream and come back in a total of 4 hours 30 minutes.The speed of the stream(in km/hr) is
Answer: total Distance = 60km
Time = 4.5hrs
Speed = 60/4.5
13⅓km/hr
Step-by-step explanation:
It takes 313131 employees and \$7500$7500dollar sign, 7500 to build a car, and it takes 191919 employees and \$4300$4300dollar sign, 4300 to build a motorcycle. Genghis Motors wants to spend more than \$84000$84000dollar sign, 84000 to build cars and motorbikes using at most 706706706 employees. Let CCC denote the number of cars they build and MMM the number of motorbikes they build. Write an inequality that represents the condition based on the number of employees. Write an inequality that represents the condition based on the number of dollars.
Answer:
a) 31c + 19m ≤ 706
b) 7500c + 4300m > 84000
Step-by-step explanation:
To build a car, we need 31 employees and $7500.
To build a motorcycle, we need 19 employees and $4300.
Let C denote the number of cars they build.
Let M denote the number of motorbikes they build.
Recall that ;
To build a career, we need 31 employees. To build "c" cars, we will need 31*c = 31c employees
To build a motorcycle, we need 19 employees. To build "m" motorcycle, we will need 19*m = 19m
Since the maximum number of employees used to build the car and motorcycle is at most 706, we have
31c + 19m ≤ 706
It takes $7500 to build car. To build "c" cars, we need 7500*c = $7500c
It also takes $4300 to build "m" motorcycles. We need 4300*m = $4300m
Since Genghis motors wont to spend more than $84000 on both cars and motorcycles, we have
7500c + 4300m > 84000
For the condition based on the number of employees, we have
31c + 19m ≤ 706
For the condition based on the number of dollars, we have
7500c + 4300m > 84000
Answer:
31c + 19m ≤ 706 and 7500c + 4300m > 84000
Step-by-step explanation: