Consider the following hypothesis test:H0: 20Ha: < 20A sample of 60 provided a sample mean of 19.6. The population standard deviation is 1.6.A sample of 60 provided a sample mean of 19.6. The population standard deviation is 1.6.a. Compute the value of the test statistic (to 2 decimals). If your answer is negative, use minus "-" sign.b. What is the p-value (to 3 decimals)?d. Using = .05, what is the critical value for the test statistic (to 3 decimals)? If your answer is negative, use minus "-" sign. _______What is the rejection rule using the critical value?Reject H0 if z ____ _____
Answers
Answer:
a: z = -1.936
b: 0.0265
d: z < -1.645
Reject H0 if z < -1.645
Step-by-step explanation:
We are given:
H0: µ = 20
HA: µ < 20
n = 60, sample mean: 19.6, σ = 1.6
Since the alternate hypothesis has a < sign in it, it is a left tailed test. The < or > sign in the alternate hypothesis points towards the rejection region.
For a: We need to calculate the test statistic for our situation. This is done with a z-score formula for samples.
For b: we need to use the z-score table to look up the p-value for the score we calculate in part a. The p-value is 0.0265. This means that there is only about a 2.65% chance that the sample values were a result of random chance.
For d: Since the significance level is 0.05, and this is a one tailed test, we have a critical value of z < - 1.645. This means that if the z-score we calculate in part a is less than -1.645, we will reject the null hypothesis
See attached photo for all the calculations!
The test statistic is approximately -4.84 with a p-value close to 0. The critical value is approximately -1.645. The rejection rule is to reject H0 if z < -1.645.
Explanation:a. To compute the test statistic, we can use the formula: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Given x = 19.6, μ = 20, σ = 1.6, and n = 60, we can calculate the test statistic as follows:
z = (19.6 - 20) / (1.6 / √60) = -1 / 0.2062 ≈ -4.84
b. The p-value can be determined by looking up the test statistic in the standard normal distribution table. However, in this case, the test statistic is already given as -4.84. The p-value associated with this test statistic is extremely small (close to 0), indicating strong evidence against the null hypothesis.
d. For a significance level α = 0.05, the critical value can be obtained by finding the z-score that corresponds to a cumulative probability of 1 - α = 0.95. Looking up this value in the standard normal distribution table, we find that the critical value is approximately -1.645.
The rejection rule using the critical value is: Reject H0 if z < -1.645.
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Related Questions
If a van traveled 210 miles in 3 hours, how far could the van travel in 5 hours
Answers
Answer:
350
Step-by-step explanation:
Name the different forms of linear equations you learned. If (1, 2) and
(3, 4) lie on the same line, give the slope-intercept equation of the line.
2
Explain how to find the inverse of f(x) = (x-1)/4
2
What is average rate of change? How do you calculate it? What can you tell about the average rate of change for linear functions? Compare the slopes of horizontal and vertical lines.
3/4
Compare the processes of graphing linear equations and inequalities with examples of your own.
3/4
Create a real-life scenario in which you show how you interpret key features of functions and graphs such as slope and y-intercept?
Module 2
1
What is the definition of “i”? What do we use it for? Demonstrate with an example of your own.
2
Why are radicals simplified before adding and subtracting? Explain your reasoning by adding sqrt8 and sqrt32. Compare the process to multiplying and dividing.
2
Give an example of an expression with a rational exponent and explain how to convert it into radical form.
3/4
A good practice in mathematics is to always check your work. Explain why it is very important to do so when you are solving equations that involve radical expressions?
Where in real life do you work with radical expressions and functions? Give an example of your own.
Module 3
Webbs DOK
Discussion Prompt
1
How many different ways can you solve a quadratic equation? List them.
2
Create a trinomial that can be factored and write it in standard form.
2
Factor x^2 – 7x + 10, 4x^2 – 81 and p(x)=3x^3-12x
3/4
What key features of a quadratic graph can be identified and how are the graphs affected when constants or coefficients are added to the parent quadratic equations? Compare the translations to the graph of linear function. Create examples of your own to explain the differences and similarities.
3/4
A ball is kicked into the air and follows the path described by
h(t)= -4.9t^2+6t+0.6, where t is the time in seconds and h is the height in meters above the ground. Find the maximum height of the ball. What value would you have to change in the equation if the maximum height of the ball is more than 2.4 meters?
Answers
The solution to this exercise has been attached below. The problem has been solved in this way:
________________
1. Different forms of linear equations. Point slope-intercept equation of the line that passes through two points.2. Inverse Function. 3. Average Rate of Change.4. Comparison of linear equations and inequalities5. Real-life problems6. Imaginary Number7. Radicals8. Rational exponent and radical form9. Radical expressions10. Quadratic equation11. Trinomial12. Factoring expressions13. Quadratic and linear graph14. A problem of heightAnswer:
Everything he said was correct!
Step-by-step explanation:
I hope this helps!
- sincerelynini
The probability assigned to each experimental outcome must be
Answers
Answer:
Between 0 and 1
Step-by-step explanation:
The probability for each outcome in experimental probability must be a value between 0 and 1. A probability of 0 means the event did not happen; the probability of 1 means it is certain. We cannot have probabilities smaller than 0 or greater than 1.
All of the probabilities in an experiment must sum to 1 whole.
The probability assigned to each experimental outcome must be greater than 0 or less than 1 or lies in between 0 and 1.
The probability of extremely certain event is 1 and the probability of extremely uncertain event is 0. The sum of all the probabilities in an experiment is always equals to 1.
Hence the probability assigned to each experimental outcome must be greater than 0 or less than 1 or lies in between 0 and 1.
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Use the x-intercept method to find all real solutions of the equation.
x^3-7x^2+4x+12=0
Answers
Answer:
the answer is c for apex
Step-by-step explanation:
Answer:
a. [tex]x=-1,2,\:or\:6[/tex]
Step-by-step explanation:
The given equation is
[tex]x^3-7x^2+4x+12=0[/tex]
To find all real solutions using the x-intercept method, we to graph the corresponding function using a graphing tool.
The corresponding function is;
[tex]f(x)=x^3-7x^2+4x+12[/tex]
The real solutions to [tex]x^3-7x^2+4x+12=0[/tex], are the x-intercepts of the graph of the corresponding function.
From the graph the x-intercepts are
(-1,0),(2,0) and (6,0).
Therefore the real solutions are
[tex]x=-1,2,\:or\:6[/tex]
Let t : the set of real numbers2 → the set of real numbers2 be the linear transformation satisfying t(v1) = (4, 3), t(v2) = (−1, 1), where v1 = (1, 1) and v2 = (1, −1). find t(x1, x2) for an arbitrary vector (x1, x2) in the set of real numbers2. t(x1, x2) = correct: your answer is correct. what is t(8, −2)?
Answers
First let's see if (8, -2) can be written as a linear combination of (1, 1) and (1, -1): we want to find [tex]c_1,c_2[/tex] such that
[tex]c_1(1,1)+c_2(1,-1)=(8,-2)\implies\begin{cases}c_1+c_2=8\\c_1-c_2=-2\end{cases}[/tex]
Easily done; we find [tex]c_1=3[/tex] and [tex]c_2=5[/tex].
Since [tex]T[/tex] is linear, we have
[tex]T(8,-2)=T(3(1,1)+5(1,-1))=3T(1,1)+5T(1,-1)=3(4,3)+5(-1,1)[/tex]
[tex]T(8,-2)=(7,14)[/tex]
t(x₁, x) = (1.5x₁ + 2.5x₂, 2 x₁ + x₂). And, t(8, -2) = (7, 14)
To find the linear transformation t applied to an arbitrary vector (x₁, x₂), we begin by expressing (x₁, x₂) as a linear combination of v₁ and v₂. Given t(v₁) = (4,3) and t(v₂) = (-1,1), we can use these results to construct the transformation.
Let's express any given vector (x₁, x₂):
v₂ = (1, -1)
An arbitrary vector (x₁, x₂) can be written as a linear combination of v₁ and v₂:
(x₁, x₂) = a * v₁ + b * v₂
Hence,
x₁ = a + b
[tex]b = \frac{(x_1, x_2)}{2}[/tex]
We apply the transformation t:
t(x₁, x₂) = a * t(v₁) + b * t(v₂) = [tex](\frac{((x_1 + x_2) * (4, 3)}{ 2} + \frac{((x_1 - x_2) * (-1, 1) }{ 2})[/tex]
Expanding, Combining terms we get:
t(x₁, x) = (1.5x₁ + 2.5x₂, 2 x₁ + x₂)
To find t(8, -2):
t(8, -2) = (1.5 * 8 + 2.5 * (-2), 2 * 8 + (-2))
This gives:
t(8, -2) = (12 - 5, 16 - 2) = (7, 14)
Lines p and q are perpendicullllar if the slope of line p is 2 what is the slope of line q
Answers
q= -1/2
perpendicular slopes are those that are opposite sign and reciprocal of the original given slope
The sum of 5/11 and 4/11 is
equal to 1
less than 1
greater than 1
Answers
There are 45 members on the board of directors for a certain non-profit institution. if they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible?
Answers
Answer:
1,221,759.
Step-by-step explanation:
This is the number of combinations of 5 from 45.
This = 45! / 40! 5!
= 1,221,759.
Answer:
1,221,759
Step-by-step explanation:
List these solids in order from the one with least volume to the one with the greatest volume. A. A cube with edge 5 cm B. A cylinder with radius 4 cm and height 4 cm C. A square pyramid with base edges 6 cm and height 6 cm D. A cone with radius 4 cm and height 9 cm E. A rectangular prism with a 5 cm-by-5 cm base and height 6 cm
Answers
Answer:
The list in order from the one with least volume to the one with the greatest volume is
case C) A square pyramid with base edges 6 cm and height 6 cm
case A) A cube with edge 5 cm
case E) A rectangular prism with a 5 cm-by-5 cm base and height 6 cm
case D) A cone with radius 4 cm and height 9 cm
case B) A cylinder with radius 4 cm and height 4 cm
Step-by-step explanation:
To solve this problem calculate the volume of each solid
case A) A cube with edge 5 cm
The volume of a cube is equal to
[tex]V=b^{3}[/tex]
where
b is the length side of the cube
substitute the value
[tex]V=5^{3}=125\ cm^{3}[/tex]
case B) A cylinder with radius 4 cm and height 4 cm
The volume of a cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
substitute the value
[tex]V=(3.14)(4)^{2} (4)=200.96\ cm^{3}[/tex]
case C) A square pyramid with base edges 6 cm and height 6 cm
The volume of a pyramid is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base
h is the height of the pyramid
Find the area of the base B
[tex]B=6^{2}=36\ cm^{2}[/tex] ----> is a square
substitute the values
[tex]V=\frac{1}{3}(36)(6)=72\ cm^{3}[/tex]
case D) A cone with radius 4 cm and height 9 cm
The volume of a cone is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base
h is the height of the cone
Find the area of the base B
[tex]B=\pi r^{2}=(3.14)(4^{2})=50.24\ cm^{2}[/tex] ----> is a circle
substitute the values
[tex]V=\frac{1}{3}(50.24)(9)=150.72\ cm^{3}[/tex]
case E) A rectangular prism with a 5 cm-by-5 cm base and height 6 cm
The volume of a rectangular prism is equal to
[tex]V=LWH[/tex]
substitute the values
[tex]V=(5)(5)(6)=150\ cm^{3}[/tex]
therefore
The list in order from the one with least volume to the one with the greatest volume is
case C) A square pyramid with base edges 6 cm and height 6 cm
case A) A cube with edge 5 cm
case E) A rectangular prism with a 5 cm-by-5 cm base and height 6 cm
case D) A cone with radius 4 cm and height 9 cm
case B) A cylinder with radius 4 cm and height 4 cm
Which is 2logx - 6 log(x-9) written as a single logarithm.
Answers
Answer: option c
Step-by-step explanation:
To solve this problem you must keep on mind the properties of logarithms:
[tex]log(b)-log(a)=log(\frac{b}{a})\\\\log(b)+log(a)=log(ba)\\\\a*log(b)=log(b)^a[/tex]
Therefore, knowing the properties, you can write the expression gven in the problem as shown below:
[tex]2logx-6log(x-9)\\logx^2-log(x-9)^6\\\\log\frac{x^2}{(x-9)^6}[/tex]
Answer:
c edge
Step-by-step explanation:
Color-blindness is any abnormality of the color vision system that causes a person to see colors differently than most people, or to have difficulty distinguishing among certain colors (www.visionrx.com).Color-blindness is gender-based, with the majority of sufferers being males.Roughly 8% of white males have some form of colorblindness, while the incidence among white females is only 1%.A random sample of 20 white males and 40 white females was chosen.LetXbe the number of males (out of the 20) who are color-blind.LetYbe the number of females (out of the 40) who are color-blind.LetZbe the total number of color-blind individuals in the sample (males and females together).Which of the following is true about the random variables X, Y, and Z?X is binomial with n = 20 and p = .08.Y is binomial with n = 40 and p = .01.Z is not binomial.All of the above are true.Only (A) and (B) are true.What is the probability that exactly 2 of the 20 males are color-blind? (Note: Some answers are rounded.).08.2711.0143.5422.0159
Answers
Only (A) and (B) are true.
Explanation:Variable distributions:
X: Since we are sampling a specific number (20) of individuals with a known probability of color blindness (8%), X follows a binomial distribution with n = 20 and p = 0.08.
Y: Similarly, Y follows a binomial distribution with n = 40 and p = 0.01.
Z: Z is not a simple binomial because it combines two independent binomial variables (X and Y) with different parameters. Therefore, Z's distribution is not directly binomial.
Probability of 2 color-blind males:
Using the binomial probability formula for X, the probability of exactly 2 color-blind males (out of 20) is:
P(X = 2) = 20C2 * 0.08^2 * (1 - 0.08)^18 ≈ 0.2711
Therefore, only statements (A) and (B) are true:
(A) True: X is binomial with n = 20 and p = 0.08.
(B) True: Y is binomial with n = 40 and p = 0.01.
Statements (C), (D), and the answer choices for the probability of 2 color-blind males are incorrect.
Find the product of x^2+2x-4 and 3x.
a. 3x^3+6x^2+12x
b. 3x^3+6x^2-12x
c. 3x^3+2x-4
d. -3x^3
Answers
[tex] 3x({x}^{2} + 2x - 4)[/tex]
[tex]3x \times {x}^{2} = {3x}^{3} [/tex]
[tex]3x \times 2x = 6 {x}^{2} [/tex]
[tex]3x \times - 4 = - 12x[/tex]
[tex]b. \: 3 {x}^{3} + 6 {x}^{2} - 12x[/tex]
HELP PLEASE!!! NEED FAST ANWER!!
Identify the slope of a line that described by:
down 3 and right 5
m=3/5
m=-3/5
m=5/3
m=-5/3
which one is it???
Answers
Answer: second option.
Step-by-step explanation:
The equation of the line in slope-intercept form is:
[tex]y=mx+b[/tex]
Where m is the slope of the line and b the y-intercept.
We know that we can calculate the slope with:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, keeping the above on mind, you have that:
- If the line moves upward from the left to right, then the slope is positive.
- If the line moves down from the left to right, then the slope is negative.
Then, if the slope described moves 3 units down and 5 units to the right, the it is negative. Therefore:
[tex]m=-\frac{3}{5}[/tex]
Answer:
[tex]-\frac{3}{5}[/tex]
Step-by-step explanation:
We are to identify the slope of a line which is described as:
'down 3 and right 5'
We know that a straight line which is sloping downwards from left to right has a negative slope.
And a straight line which goes upwards from left to right side has a positive slope.
According to the describe slope of a line, it goes 3 units down and 5 units right so it makes a negative slope which is equal to [tex]-\frac{3}{5}[/tex].
Marc is 46 years old. He is 4 years older than 3 times his sons age, find the age of his son.
Answers
Marc's son is 14 years old. We found this by creating the equation 3x + 4 = 46 based on the question, solving for x, and determining that x equals 14.
Explanation:This is a problem that requires an understanding of simultaneous linear equations. Let's denote Marc's son's age as x.
Marc is 4 years older than 3 times his son's age. Therefore, we can write this as: 3x + 4 = 46.
To find the value of x, which represents the son's age, we first subtract 4 from both sides of the equation (3x + 4 - 4 = 46 - 4). Now we have 3x = 42. To get the value of x alone, we will then divide by 3 from both sides of the equation (3x/3 = 42/3). As a result, we'll find out that x equals 14, which means Marc's son is 14 years old.
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what quadrilateral always has 4 congruent angles and opposite sides that are congruent and parallel?
Answers
Answer:
See below.
Step-by-step explanation:
A rectangle has 4 * 90 degree angles and opposite sides are congruent and parallel. A square also fits the bill.
The point (4, -2) lies on a circle and the center of the circle is at the point (4, 1).
What is the equation of this circle?
A. (x - 1)2 + (y - 4)2 = 9
B. (x - 1)2 + (y - 4)2 = 3
C. (x + 4)2 + (y + 1)2 = 9
D. (x - 4)2 + (y - 1)2 = 9
Answers
Answer:
D
Step-by-step explanation:
The equation of the circle is (x-x0)^2 + (y-y0)^2 = r^2, where (x0,y0) is the center of the circle. Radius is the distance from any point to the center. Using distance formula you get r = 3.
The equation of the circle having center at point (4,1) and passing through the point (4,-2) is Option (D) [tex](x - 4)^{2} + (y - 1)^{2} = 9[/tex]
Equation of circle in parametric form -A circle having radius r and having center at (x0,y0) can be represented by the parametric equation as -
[tex](x - x0)^{2} + (y - y0)^{2} = r^{2}[/tex]
Any point say (x1,y1) which lies on the circle, must satisfy the given parametric equation of the circle.
How to frame the equation of circle from the information given in the question ?Given that the point (4,-2) lies on the circle. Also the center of circle is at (4,1). Therefore, calculating the radius of the circle which is the distance from the center to the point lying on the circle.
Using distance formula,
radius = [tex]\sqrt{(4 - 4)^{2} + (-2 - 1)^{2} }[/tex] = [tex]\sqrt{9 }[/tex] = [tex]3[/tex]
Thus forming the equation of circle from the general parametric equation,
⇒ [tex](x - 4)^{2} + (y - 1)^{2} = 3^{2}[/tex]
∴ [tex](x - 4)^{2} + (y - 1)^{2} = 9[/tex]
Therefore the equation of circle is Option (D) [tex](x - 4)^{2} + (y - 1)^{2} = 9[/tex]
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FIND ST OF THIS CIRCLE.
Answers
[tex]\bigtriangleup RSP \cong\bigtriangleup RQT\Rightarrow \frac{RS}{RQ}=\frac{RP}{RT}\Leftrightarrow RS=3 \\ \Rightarrow ST=RT-RS=5[/tex]
Brian and Carlos are sharing a large sub sandwich. Brian ate 2 / 5 of the sandwich, and Carlos ate 1 / 5 of the sandwich. How much of the sandwich is left over?
Answers
if I'm right it would be 2/5. you get your answer by adding 2/5 and 1/5 then subtract 5/5- 3/5 to get 2/5
Randle plans to work 8 hours every two days. At this rate how many hours will he work in 7 days
Answers
Answer:
The answer is 28
Step-by-step explanation:
The total number of work hours in 7 days will be 28 hours.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Randle plans to work 8 hours every two days. The total work hours in 7 days will be calculated as,
Number of hours for 6 days,
N = (6 / 2) x 8
N = 24 hours
Number of hours for 1 day,
N = 8 / 2 = 4 hours
Total hours = 24 + 4 = 28 hours
Therefore, the total number of work hours in 7 days will be 28 hours
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A laptop was originally sold for $975. The laptop is now on sale for $828.75. What is the percent markdown.
Answers
so the difference is 975 - 828.75 = 146.25.
if we take 975 to be the 100%, how much is 146.25 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 975&100\\ 146.25&x \end{array}\implies \cfrac{975}{146.25}=\cfrac{100}{x}\implies 975x=14625 \\\\\\ x=\cfrac{14625}{975}\implies x=15[/tex]
Answer:
146.25
Step-by-step explanation:
When you multiply expressions with the same base, you ______ the exponents. Add multiply
Answers
Answer:
... you add the exponents
Step-by-step explanation:
An exponent is a way of showing repeated multiplication. For example, ...
x^2 means x·x
and
x^3 means x·x·x
If we multiply these two expressions together, we get ...
(x^2)·(x^3) = (x·x)·(x·x·x) = x·x·x·x·x
This is a product in which x appears as a factor 5 times, so we can write it using an exponent as ...
x·x·x·x·x = x^5
___
That is, when we multiply the expressions, we add the numbers of times the factor appears in the product:
2 + 3 = 5
x^2 · x^3 = x^(2+3) = x^5
Answer: Add
Step-by-step explanation: When you multiply expression with the same base you ADD the exponents. The exponent tells you how many times you multiply the base by itself. This means the exponent corresponds to the amount of base replications. If you add the exponents you are adding the replications of the base.
The bus from Karen's house to school runs 26 to 75 minutes of the bus runs on Monday at 7:05am at which time could the bus run next
Answers
I’m pretty sure the answer is 8:25 a.m
Find the area of the trapezoid. leave your answer in simplest radical form.
Answers
Answer:
Area[tex]=70in^2[/tex]
Step-by-step explanation:
The given diagram is a tra-pezoid.
The area of a tra-pezoid is calculated using the formula;
Area[tex]=\frac{1}{2} (Sum\:of\:parallel\:sides)\times height[/tex]
This implies that;
Area[tex]=\frac{1}{2} (8+12)\times 7[/tex]
Area[tex]=\frac{1}{2} (20)\times 7[/tex]
Area[tex]=(10)\times 7[/tex]
Area[tex]=70in^2[/tex]
The last choice is correct.
You are buying shoes online.The selling price is $29.99. Round to the nearest penny if necessary.
Answers
it's 30 dollars because it's the closest whole number
Final answer:
To calculate the total cost of an online purchase, round the sales tax to the nearest penny and add it to the item's price. When combining multiple items, sum their prices and add the rounded sales tax to find the total cost.
Explanation:
When buying shoes or any item online and encountering a selling price that includes cents, you may need to perform rounding if further calculations are required. For example, to round $6.375 to the nearest penny, we would get $6.38 because the third digit after the decimal is 5 or more, thus we increase the second digit by one. From there, we would add the rounded sales tax to the original price of the item to find the total cost.
In a different scenario where you are adding two prices together, like $8.99 and $11.99, you get the subtotal of $20.98 before tax. Then calculate the sales tax by converting the percent to a decimal and multiplying by the subtotal, rounding again to the nearest cent if necessary. Finally, add the sales tax to the subtotal to get the total cost. For instance, if the sales tax was $1.47, adding this to the subtotal of $20.98 would give you a total of $22.45.
The figures below are similar. Compare the larger figure to the smaller. which of the following is the ratio of the areas of the figures?
Answers
Answer:
4:3
Step-by-step explanation:
The ratio is 8:6, which simplifies to 4:3.
Answer:
16:9
Step-by-step explanation:
Angenita drives to work at 50 mph and arrives 1 minute late. she drives to work at 60 mph and arrives 5 minutes early.
Answers
Answer:
2 mpm
Step-by-step explanation
The rectangle shown has a perimeter of 48 cm and the given area. Its length is 6 more than twice its width. Write and solve a system of equations to find the dimensions of the rectangle.
Answers
Answer:
The length of the rectangle is 18 cm
The width of the rectangle is 6 cm
Step-by-step explanation:
Let
x-----> the length of the rectangle
y----> the width of the rectangle
we know that
The perimeter of the rectangle is
[tex]P=2(x+y)[/tex]
we have
[tex]P=48\ cm[/tex]
so
[tex]48=2(x+y)[/tex] ------> equation A
[tex]x=2y+6[/tex] ------> equation B
Substitute equation B in equation A and solve for y
48=2(2y+6+y)
48=2(3y+6)
48=6y+12
6y=48-12
y=36/6=6 cm
Find the value of x
x=2(6)+6=18 cm
The area of the rectangle is
A=xy
A=18*6
A=108 cm^2
Final answer:
To solve for the dimensions of the rectangle, we set up a system of equations based on the given perimeter and the relationship between length and width and solve for both variables.
Explanation:
The student is asked to find the dimensions of a rectangle given the perimeter and a relationship between its length and width. Since the perimeter is 48 cm and the length (L) is 6 cm more than twice the width (W), two equations can be set up: 2L + 2W = 48 and L = 2W + 6. By substituting the second equation into the first, we get 2(2W + 6) + 2W = 48. Simplifying yields 4W + 12 + 2W = 48, which simplifies further to 6W + 12 = 48. Solving for W gives W = 6 cm, and substituting back gives L = 18 cm.
Find the critical numbers of the function. (Enter your answers as a comma-separated list. Use n to denote any arbitrary integer values. If an answer does not exist, enter DNE.) f(θ) = 10 cos(θ) + 5 sin2(θ)
Answers
If
[tex]f(\theta)=10\cos\theta+5\sin^2\theta[/tex]
then the derivative is
[tex]f'(\theta)=-10\sin\theta+10\sin\theta\cos\theta[/tex]
Critical points occur where [tex]f'(\theta)=0[/tex]. This happens for
[tex]-10\sin\theta+10\sin\theta\cos\theta=0[/tex]
[tex]-10\sin\theta(1-\cos\theta)=0[/tex]
[tex]\implies-10\sin\theta=0\text{ or }1-\cos\theta=0[/tex]
In the first case, we find
[tex]-10\sin\theta=0\implies\sin\theta=0\implies\theta=n\pi[/tex]
In the second,
[tex]1-\cos\theta=0\implies\cos\theta=1\implies\theta=2n\pi[/tex]
So all the critical points occur at multiples of [tex]\pi[/tex], or [tex]n\pi[/tex]. (This includes all the even multiples of [tex]\pi[/tex].)
The critical numbers of the function will be at ([tex]\pi, n\pi[/tex])
Given the function
f(θ) = 10 cos(θ) + 5 sin2(θ)
At the turning point, [tex]\frac{df(\theta)}{d\theta} = 0[/tex]
[tex]\frac{df(\theta)}{d\theta} = -10sin \theta + 5(2sin\theta cos\theta)\\\frac{df(\theta)}{d\theta} = -10sin \theta + 10sin\theta cos\theta\\[/tex]
At the turning point,
[tex]-10sin \theta + 10sin \theta cos \theta=0\\-10sin \theta(1-cos\theta) =0\\-10sin\theta = 0 \ and \ 1-cos\theta =0\\sin\theta =0\\\theta=0 + n\pi\\\\For \ 1-cos\theta =0\\cos\theta = 1\\\theta = cos^{-1}1\\\theta = 0 + n\pi[/tex]
Hence critical numbers of the function will be at ([tex]\pi, n\pi[/tex])
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Train a travels in 840 miles in 7.5 hours. Train b travels 1080 miles in 9 hours. Which train was traveling at the fastest speed, and what was that speed?
Answers
Answer:
Train B is traveling faster at a speed of 120 MPH
How to solve:
Train A is 840/7.5 = 112 which is the MPH so its 112 MPH
Train B is 1080/9 = 120 MPH
Final answer:
Train B is the faster train with an average speed of 120 miles per hour, compared to Train A which has an average speed of 112 miles per hour.
Explanation:
The question is asking to compare the average speed of two trains. To find the average speed, we divide the total distance traveled by the time taken. For Train A, it travels 840 miles in 7.5 hours, and for Train B, it travels 1080 miles in 9 hours.
Calculating the average speed of Train A: 840 miles / 7.5 hours = 112 miles per hour.
Calculating the average speed of Train B: 1080 miles / 9 hours = 120 miles per hour.
Therefore, Train B is traveling at the fastest speed with an average of 120 miles per hour.
PLEASE HELP! URENT!
What is the measure of ∠R ?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
m∠R=
°
Answers
Answer:
R = 48.59 degrees
Step-by-step explanation:
We know that
sin theta = opposite / hypotenuse
sin R = 30/40
sin R = 3/4
Taking the inverse sin of each side
sin^-1 (sin R) = sin ^-1(3/4)
R = 48.59037789
To the nearest hundredth
R = 48.59 degrees