Answer:75/8
Step-by-step explanation:
weight gain=81/4-87/8
weight gain=(2x81-1x87)/8
Weight gain=(162-87)/8
weight gain =75/8
A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 16% are pennies and 32% are dimes. There are 5 more nickels than pennies. How much money does the bag contain?
Answer:8pennies,16dimes,13nickels,13quarters
Step-by-step explanation:
total number of coin=50
16% are pennies
16% of 50
16/100 x 50=(16x50)/100=800/100=8
Pennies=8
32% are dimes
32% of 50
32/100 x 50=(32x50)/100=1600/100=16
Dimes = 16
5 more nickels than pennies
Pennies=8
nickels=8+5=13
nickels=13
8+16+13=37
50-37=13
13 quarters
pennies=8,dimes=16,nickels=13,quarters=13
the measure of two complementary angles are 7x + 17 and 3x - 20. find the measures of the angles.
The required measure of the complementary angles is 82.1° and 7.9°.
Given that,
The measure of two complementary angles is 7x + 17 and 3x - 20. To find the measures of the angles.
The angle can be defined as the one line inclined over another line.
Here,
the sum of the two complementary angles is equal to 90°. Implying
7x + 17 + 3x - 20 = 90
10x -3 = 90
10x = 93
x = 93 / 10
x = 9.3
Now,
The measure of angles
7x + 17 = 7 * 9.3 + 17
= 82.1°
3x - 20 = 3 * 9.3 - 20
= 7.9°
Thus, the required measure of the complementary angles is 82.1° and 7.9°.
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What is the range of the data represented in the dot plot below?
Answer:
3
Step-by-step explanation:
Range is the difference between
Which is the unit rate if 4 tuna cans are sold for $6
Answer:
$1.50 per can
Step-by-step explanation:
6/4 = 1.5
to check your answer, do 1.50*4, and you get $6
hope this helps :)
Answer:
The unit rate is $1.50 per can.
Step-by-step explanation:
Price: $6
Number of Cans Purchased at This Price: 4
$6/4 cans=$1.50 per can
Refer to the random sample of customer order totals with an average of $78.25 and a population standard deviation of $22.50. a. Calculate percent 90 confidence interval estimate of the mean, given a sample size of 40 orders. b. Calculate 9 0 percent confidence interval for the mean, given the sample size of 75 orders. c. Explain the difference. d. Calculate the minimum sample size needed to identify a %90 confidence interval for the mean, assuming a $5.00 margin of error.
Answer:
a) [tex] 78.25- 1.64 \frac{22.50}{\sqrt{40}}= 72.416[/tex]
[tex] 78.25+ 1.64 \frac{22.50}{\sqrt{40}}= 84.084[/tex]
b) [tex] 78.25- 1.64 \frac{22.50}{\sqrt{75}}= 73.989[/tex]
[tex] 78.25+ 1.64 \frac{22.50}{\sqrt{75}}= 82.511[/tex]
c) For this case when we increase the sample size the margin of error would be lower and then the interval would be narrower
d) [tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
Solving for n we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
And replacing the info we have:
[tex]n=(\frac{1.640(22.50)}{5})^2 =54.46 \approx 55[/tex]
Step-by-step explanation:
Part a
For this case we have the following data given
[tex]\bar X = 78.25[/tex] represent the sample mean for the customer order totals
[tex]\sigma =22.50[/tex] represent the population deviation
[tex] n= 40[/tex] represent the sample size selected
The confidence level is 90% or 0.90 and the significance level would be [tex]\alpha=0.1[/tex] and [tex]\alpha/2 = 0.05[/tex] and the critical value from the normal standard distirbution would be given by:
[tex] z_{\alpha/2}=1.64[/tex]
And the confidence interval is given by:
[tex] \bar X -z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]
And replacing we got:
[tex] 78.25- 1.64 \frac{22.50}{\sqrt{40}}= 72.416[/tex]
[tex] 78.25+ 1.64 \frac{22.50}{\sqrt{40}}= 84.084[/tex]
Part b
The sample size is now n = 75, but the same confidence so the new interval would be:
[tex] 78.25- 1.64 \frac{22.50}{\sqrt{75}}= 73.989[/tex]
[tex] 78.25+ 1.64 \frac{22.50}{\sqrt{75}}= 82.511[/tex]
Part c
For this case when we increase the sample size the margin of error would be lower and then the interval would be narrower
Part d
The margin of error is given by:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
Solving for n we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
And replacing the info we have:
[tex]n=(\frac{1.640(22.50)}{5})^2 =54.46 \approx 55[/tex]
what is the derivative of 66lnx +135
Answer:
[tex]\displaystyle \frac{dy}{dx} = \frac{66}{x}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = 66 \ln x + 135[/tex]
Step 2: Differentiate
Derivative Property [Addition/Subtraction]: [tex]\displaystyle y' = \frac{d}{dx}[66 \ln x] + \frac{d}{dx}[135][/tex]Derivative Property [Multiplied Constant]: [tex]\displaystyle y' = 66\frac{d}{dx}[\ln x] + \frac{d}{dx}[135][/tex]Logarithmic Differentiation: [tex]\displaystyle y' = \frac{66}{x}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Please answer this correctly
Answer:
n=9 10 11
Step-by-step explanation:
Answer: 10
Step-by-step explanation:
Which graph represents the solution set for the inequality StartFraction one-half EndFraction x is less than or equal to 18.x ≤ 18?
Answer:
the answer is D
Step-by-step explanation:
i guessed until it gave me the answer yw
Answer:
D
Step-by-step explanation:
The radius of a circle is 1 units. What is the diameter of the circle?
Answer:
2 units
Step-by-step explanation:
As the radius is half of the diameter. To work this out you would simply multiply 1 by 2, which gives you 2.
1) Multiply 1 by 2.
[tex]1*2=2[/tex]
A bus travels on an east-west highway connecting two cities A and B that are 100 miles apart. There are 2 services stations along the route. The first service station is located 20 miles from city A, and the second service station is located 30 miles from city B. If the bus breaks down at a random point along the route, find the expected value of the distance of the bus from the nearest service station.
Answer:
51/4
Step-by-step explanation:
To begin with you have to understand what is the distribution of the random variable. If X represents the point where the bus breaks down. That is correct.
X~ Uniform(0,100)
Then the probability mass function is given as follows.
[tex]f(x) = P(X=x) = 1/100 \,\,\,\, \text{if} \,\,\,\, 0 \leq x \leq 100\\f(x) = P(X=x) = 0 \,\,\,\, \text{otherwise}[/tex]
Now, imagine that the D represents the distance from the break down point to the nearest station. Think about this, the first service station is 20 meters away from city A, and the second station is located 70 meters away from city A then the mid point between 20 and 70 is (70+20)/2 = 45 then we can represent D as follows
[tex]D(x) =\left\{ \begin{array}{ll} x & \mbox{if } 0\leq x \leq 20 \\ x-20 & \mbox{if } 20\leq x < 45\\ 70-x & \mbox{if } 45 \leq x \leq 70\\ x-70 & \mbox{if } 70 \leq x \leq 100\\ \end{array}\right.[/tex]
Now, as we said before X represents the random variable where the bus breaks down, then we form a new random variable [tex]Y = D(X)[/tex], [tex]Y[/tex] is a random variable as well, remember that there is a theorem that says that
[tex]E[Y] = E[D(X)] = \int\limits_{-\infty}^{\infty} D(x) f(x) \,\, dx[/tex]
Where [tex]f(x)[/tex] is the probability mass function of X. Using the information of our problem
[tex]E[Y] = \int\limits_{-\infty}^{\infty} D(x)f(x) dx \\= \frac{1}{100} \bigg[ \int\limits_{0}^{20} x dx +\int\limits_{20}^{45} (x-20) dx +\int\limits_{45}^{70} (70-x) dx +\int\limits_{70}^{100} (x-70) dx \bigg]\\= \frac{51}{4} = 12.75[/tex]
Is 5/8 mile larger or less than 1 mile
Answer:
5/8 mile is less than 1 mile
Step-by-step explanation:
in this question, one could assume a mile is 8/8
5/8<8/8
The nutrition label for Oriental Spice Sauce states that one package of sauce has 1100 milligrams of sodium. To determine if the label is accurate, the FDA randomly selects 40 packages of Oriental Spice Sauce and determines the sodium content. The sample has an average of 1088.64 milligrams of sodium per package with a sample standard deviation of 234.12 milligrams. Step 2 of 2 : Using the confidence interval approach, is there evidence that the sodium content is different from what the nutrition label states
Answer:
We conclude that the sodium content is same as what the nutrition label states.
Step-by-step explanation:
We are given that the nutrition label for Oriental Spice Sauce states that one package of sauce has 1100 milligrams of sodium.
The FDA randomly selects 40 packages of Oriental Spice Sauce and determines the sodium content. The sample has an average of 1088.64 milligrams of sodium per package with a sample standard deviation of 234.12 milligrams.
Let [tex]\mu[/tex] = average sodium content.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 1100 milligrams {means that the sodium content is same as what the nutrition label states}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 1100 milligrams {means that the sodium content is different from what the nutrition label states}
The test statistics that would be used here One-sample t test statistics as we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average sodium content = 1088.64 milligrams
s = sample standard deviation = 234.12 milligrams
n = sample of packages of Oriental Spice Sauce = 40
So, test statistics = [tex]\frac{1088.64-1100}{\frac{234.12}{\sqrt{40}}}[/tex] ~ [tex]t_3_9[/tex]
= -0.307
The value of z test statistics is -0.307.
Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 0.05 significance level the t table gives critical values of -2.0225 and 2.0225 at 39 degree of freedom for two-tailed test.
Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the sodium content is same as what the nutrition label states.
To determine if the sodium content of the Oriental Spice Sauce is different from what the label states, a confidence interval approach can be used. A t-test is used to compare the sample mean to the hypothesized population mean. If the p-value is less than the level of significance, the null hypothesis is rejected.
Explanation:To determine if the sodium content of the Oriental Spice Sauce is different from what the nutrition label states, we can use a confidence interval approach.
Step 1: Define the null and alternative hypotheses. Null hypothesis (H0): The sodium content is the same as what the nutrition label states. Alternative hypothesis (Ha): The sodium content is different from what the nutrition label states.
Step 2: Calculate the test statistic and p-value. We can use a t-test to compare the sample mean to the hypothesized population mean (the sodium content stated on the label).
Step 3: Determine the level of significance and compare the p-value to it. If the p-value is less than the level of significance, we reject the null hypothesis and conclude that there is evidence that the sodium content is different from what the nutrition label states.
1
Terry mixed 1/4 of a can of red paint
and 1/3 of a can of blue paint to makepurple. What fraction of purple paint does Terry have now?
Answer:
7/12 of a can
Step-by-step explanation:
Can someone please help me with this question ?
Answer:
1350 square inches
Step-by-step explanation:
The area of the end trapezoid is ...
A = (1/2)(b1 +b2)h = (1/2)(12 +36)(5) = 120 . . . . . square inches
The perimeter of the end trapezoid is ...
P = 13 +12 +13 + 3×12 = 74 . . . . inches
so the total area of the rectangular surfaces (including the bottom) is ...
(74 in)(15 in) = 1110 in²
The total area of the ramp is this rectangular area plus the two trapezoidal ends:
total area = rectangle area + 2×trapezoid area
= 1110 in² +2×120 in²
total area = 1350 square inches
3x+9+4x+x=
In no solution, one solution, infinite solutions
Answer:
It's one infinite solutions
Step-by-step explanation:
Any number can be put in for x beings there is no set answer to the equation. if there was a set number like 3x+9+4x+x=40 for instance, there would be only one solution, but since there's not, it is infinite solutions.
For the same signal emitted by a radio antenna,
Observer A measures its intensity to be 16 times the
intensity measured by Observer B. The distance of
Observer A from the radio antenna is what fraction
of the distance of Observer B from the radio
antenna?
Answer: The distance of Observer A from the radio antenna is what fraction of the distance of Observer B from the radio antenna?
It is 1/4.
Step-by-step explanation:
We know that the intensity of electromagnetic waves decreases with the radius squared, this means that we can write a simple relation as:
Intensity(r) = A/r^2
Observer A measures 16 the intensity of observer B.
if Ia is the intensity that observer A measures and Ib is the intensity that observer B measures, we have that:
Ia = 16Ib
A/(ra)^2 = 16*A/(rb)^2
1/(ra)^2 = 16/(rb)^2
rb^2 = 16*ra^2
and we know that 16 = 4*4 = 4^2
rb^2 = (4*ra)^2
then rb = 4*ra
this means that the distance between observer B and the antenna is equal to 4 times the distance between observer A and the antenna.
The fraction is ra = rb/4
The distance of
Observer A from the radio antenna is what fraction of the distance of Observer B from the radio antenna?
It is 1/4.
Observer A measures the intensity of the signal to be 16 times the intensity measured by Observer B. The distance of Observer A from the radio antenna is 4 times the distance of Observer B.
Explanation:Observer A measures the intensity of the signal to be 16 times the intensity measured by Observer B. Let's denote the distance of Observer A from the radio antenna as dA and the distance of Observer B as dB.
We can use the inverse square law to relate the intensity to the distance: Intensity is inversely proportional to the square of the distance.
So, we have:
IntensityA/IntensityB = (dA/dB)^2 = 16
Solving for dA/dB, we find:
dA/dB = sqrt(16) = 4
Therefore, the distance of Observer A from the radio antenna is 4 times the distance of Observer B.
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Mathews usually makes the 100 km journey to visit his family. The trip involves three separate stages:
a) A stage of 20 km that is travelled on small roads at a constant speed of 30 km/h.
b) A stage of 50 km that is travelled on the highway at a constant speed of 100 km/h.
c) A stage of 30 km that is travelled on standard roads at a constant speed of 40 km/h.
1- How long does it normally take Mathews to make this journey?
Last week there were roadworks on a section of the highway, and he was only able to travel at 60 km/h for the length of the roadworks. Matthews's journey last week took 6 minutes longer than usual.
2- What was the length of the section of roadworks?
Answer:
1 . Total time = 1 hr 55 minutes
2 Distance = 121 km
Step-by-step explanation:
Mattew journey
stage a
Distance = 20km
Speed = 30km/h
Time = distance/speed
Time = 20/30
Time = 2/3 h
Time = 40 minutes
Stage b
Distance = 50 I'm
Speed = 100 km/h
Time = distance/speed
Time = 50/100
Time = 0.5 h
Time = 30 minutes
Stage c
Distance = 30 km
Speed = 40 km/h
Time = distance/speed
Time = 30/40
Time = 3/4 h
Time = 45 minutes.
Total time taken =( 40 + 30 + 45 ) minutes
Total time = 115 minutes
Total time = 1 hr 55 minutes
2.
Speed =60 km/h
Time= 6 minutes + x
And x = 1 hr 55 minutes
Time = 1 hr 55 minutes + 6 minutes
Time = 2 hr 1 minute
Time = 2.01666667 hr
Distance covered = speed * time
Distance = 60*2.016667
Distance = 121 km
In this exercise we have to use the knowledge of time and distance, so we have to:
1) Total time = 1 hr 55 minutes
2) Distance = 121 km
To calculate Matthew's journey we have to use the formula of :
[tex]Time= \frac{Distance}{Speed}[/tex]
Are doing the calculations for each Stage, like this:
Stage A, we know that:
Distance: [tex]20\ km[/tex] Speed: [tex]30\ km/h[/tex]
[tex]Time = 20/30\\T = 2/3 h\\Time = 40 \ minutes[/tex]
Stage B, we know that:
Distance: [tex]50\ km[/tex] Speed: [tex]100\ km/h[/tex]
[tex]Time = 50/100\\T = 0.5 h\\Time = 30\ min[/tex]
Stage C, we know that:
Distance: [tex]30 \ km[/tex] Speed: [tex]40 \ km/h[/tex]
[tex]Time = 30/40\\T= 3/4 h\\Time = 45\ min[/tex]
1) So using all the values calculated above, let's calculate the total value of the trip that will take place by:
[tex]Total =( 40 + 30 + 45 ) minutes\\Total = 115 \ minutes\\Total = 1 \ hr \ 55 \ minutes[/tex]
2) For the second part of this question we want to calculate the total distance of travel hours so:
Speed: [tex]60 km/h[/tex] Time: [tex]6 minutes + x[/tex]
[tex]x = 1 \ hr \ 55 minutes\\Time = 1 \ hr\ 55 \ minutes + 6 \ minutes = 2 \ hr \ 1 minute\\Time = 2.01666667\\Distance = speed * time\\Distance = 60*2.016667\\Distance = 121 km[/tex]
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A college entrance exam company determined that a score of 2323 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics. To achieve this goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 150150 students who completed this core set of courses results in a mean math score of 23.423.4 on the college entrance exam with a standard deviation of 3.23.2. Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 2323 on the math portion of the exam? Complete parts a) through d) below.
Answer:
a) The null and alternative hypothesis are:
[tex]H_0: \mu=23\\\\H_a:\mu> 23[/tex]
c) Test statistic t=1.53
P-value=0.064
d) The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that students who complete the core curriculum are ready for college-level mathematics. That is that the true score for the group is not significantly higher than 23.
Step-by-step explanation:
The question is incomplete:
a) State the appropriate null and alternative hypotheses.
c) Use the P-value approach at the 0.05 level of significance to test the hypotheses in part (a). ldentify the test statistic. (Round to two decimal places as needed.) Identfy the P-value. P-value (Round to three decimal places as needed.)
d) Write a conclusion based on the results. Choose the correct answer below. ? the null hypothesis and claim that there ? sufficient evidence to conclude that the population mean is ? than 20.
This is a hypothesis test for the population mean.
The claim is that students who complete the core curriculum are ready for college-level mathematics.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=23\\\\H_a:\mu> 23[/tex]
The significance level is assumed to be 0.05.
The sample has a size n=150.
The sample mean is M=23.4.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3.2.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3.2}{\sqrt{150}}=0.261[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{23.4-23}{0.261}=\dfrac{0.4}{0.261}=1.531[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=150-1=149[/tex]
This test is a right-tailed test, with 149 degrees of freedom and t=1.531, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t>1.531)=0.064[/tex]
As the P-value (0.064) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that students who complete the core curriculum are ready for college-level mathematics.
A researcher is studying the monthly gross incomes of drivers for a ride sharing company. (Gross incomes represent the amount paid to drivers before accounting for the costs associated with driving.) The researcher obtains a list of all the drivers in San Francisco and randomly selects 200 of them to contact. The list of incomes in the sample has an average of $800 per month, with an SD of $1000. (a) Does the histogram of the sample incomes follow the normal curve? Explain why or why not.
Answer:
The histogram of the sample incomes will follow the normal curve.
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
In this case the researches wants to determine the monthly gross incomes of drivers for a ride sharing company.
He selects a sample of n = 200 drivers and ask them their monthly salary.
As the sample selected is quite large, i.e. n = 200 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample mean by the Normal distribution.
Thus, the histogram of the sample incomes will follow the normal curve.
If "f" varies directly with "m," and f=-19 when m=14, what is "f" when m=2?if
Answer:-19/7
Step-by-step explanation:
f varies directly as m
f=k x m
When f=-19,m=14
-19=k x 14
k=-19/14
Relationship is f=-19m/14
When m is 2
f=(-19x2) ➗ 14
f=-38 ➗ 14
f=-19/7
If 3/4 of a number minus 1/2 of the number is 4. What is the number?
Answer:
16
Step-by-step explanation:
Number = x
(3/4 of x) - (1/2 of x) = 4
3x/4 - x/2 = 4
3x - 2x / 4 = 4
x/4 = 4
x = 16
The distribution of durations for which apartments remain empty after the resident moves out for one property management company over the past 101010 years was approximately normal with mean \mu = 85μ=85mu, equals, 85 days and standard deviation \sigma = 29σ=29sigma, equals, 29 days. The property management company intends to update the kitchen appliances in the apartments that were empty for top 10\%10%10, percent of durations. What is the minimum duration for which an apartment remained empty for the company to update the kitchen appliances? Round to the nearest whole number.
Answer:
123 days
Step-by-step explanation:
The minimum duration for which an empty apartment remains to update the kitchen appliances is approximately 120 days.
Explanation:To find the minimum duration for which an apartment remained empty for the company to update the kitchen appliances, we need to find the duration that corresponds to the top 10% of durations. Since we know the distribution is approximately normal with a mean of 85 days and a standard deviation of 29 days, we can use z-scores to find the corresponding duration.
First, we need to find the z-score corresponding to the top 10%. We can use the z-table or a calculator to find that the z-score is approximately 1.28.
Next, we can use the formula z = (x - mean) / standard deviation to solve for x, the minimum duration:
1.28 = (x - 85) / 29.
Solving for x, we get x ≈ 120.12. Rounding to the nearest whole number, the minimum duration for which the apartment remained empty is 120 days.
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40% is NOT equivalent to....?
A. 0.4
B.2/5
C.40/100
D. 0.04
E. None correct
Answer: D
A is correct because when you convert 40% into a decimal the results will be .40 or .4
B is correct because 2/5 as a percent is 40%. It's like having 5 questions on a quiz and you get 2 right and 3 wrong. That means your grade is 40%.
C is correct because 40/100 means the decimal will be .4. 40÷100 will equal .4 which means 40/100 is also 40%.
D is incorrect due to the fact when you convert it to a fraction it'll be 4/25. When converting it to a percent the result will be 16%.
The number 40% in not equivalent to 0.04.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
The number is,
⇒ 40%
Now,
Since, The number is,
⇒ 40%
Hence, It can be written as;
⇒ 40% = 40/100
= 4/10
= 2/5
= 0.4
Thus, The number 40% in not equivalent to 0.04.
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Wendy had 20 apples. If 1/4 of them were red, how many apples were red?
Answer:
5
Step-by-step explanation:
split 20 into 4 and find out how much is one portion the four
Plz mark brainliest
Four golfers are asked to play a round of golf each on two consecutive Saturday afternoons. During the first round, one of two club types is to be used. During the second round, another club type is to be used. The order in which a golfer uses each brand is determined randomly. Scores are recorded. The results are given below.
Golfer Brand 1 Brand 2
1 93 95
2 88 86
3 112 111
4 79 77
To determine if the mean scores differ by brand of club, we would use
a. the one-sample t test.
b. matched pairs t test.
c. two-sample t test.
d. Any of the above are valid. It is at the experimenter's discretion.
Answer:
c) Two sample t-test
Step-by-step explanation:
Given data
Golfer 1 2 3 4
Brand1 (x) 93 88 112 79
Brand 2 (y) 95 86 111 77
Mean of x =
[tex]\frac{93+88+112+79}{4} = 93[/tex]
x⁻ = 93
Mean of y
[tex]\frac{95+86+111+77}{4} = 92.25[/tex]
y ⁻ = 92.25
Given data
Brand1 (x) : 93 88 112 79
Brand 2 (y) : 95 86 111 77
x- x⁻ : 0 -5 19 -14
y -y ⁻ : 2.75 -6.25 18.75 -15.25
(x- x⁻)² : 0 25 361 196
( y -y ⁻ )² : 7.5625 39.0625 351.5625 232.5625
S² = [tex]\frac{sum((x- x^{-} )^{2} +sum (y- y^{-} )^{2} }{n_{1}+n_{2} -2 }[/tex]
[tex]S^{2} = \frac{582+630.75}{4+4-2} = 202.125[/tex]
S = 14.21706
Null hypothesis: H₀: There is no significant difference between the means
Alternative hypothesis: H₁: There is significant difference between the means
Student's t test for difference for means
The test statistic
[tex]t = \frac{x^{-} -y^{-} }{\sqrt{S^{2}(\frac{1}{n_{1} } +\frac{1}{n_{2} } } }[/tex]
[tex]t = \frac{93 -92.25}{\sqrt{202.125(\frac{1}{4 } +\frac{1}{4 } } }[/tex]
on calculation , we get
t = 0.0746
Degrees of freedom ν = n₁ +n₂ -2 = 4+4-2 =6
[tex]t_{\frac{\alpha }{2} } = t_{\frac{0.05}{2} } = t_{0.025} = 2.447[/tex]
The calculated value t = 0.0746 < 2.447 at 0.05 level of significance
null hypothesis is accepted
Conclusion:-
There is no significant difference between the means
Final answer:
The matched pairs t-test is the correct method for analyzing the difference in golfers' scores with two different brands of clubs, as each golfer serves as their control.
Explanation:
The appropriate test to determine if the mean scores differ by brand of club is b. matched pairs t-test. Since the data consists of scores from the same golfers using two different brands of clubs in a controlled setting (meaning, the same golfer's scores are paired with each type of golf club), the analysis compares two related samples. In matched pairs designs, we test the differences by subtracting one measurement from the other. The golfers serve as their controls, eliminating variations between different individuals' performances, which could affect the scores. This is a classic scenario of a paired sample t-test, where each golfer's scores with Brand 1 are paired with their scores with Brand 2, and the difference in scores is analyzed.
what is a way you can use a distributive property for 6x82
Answer:
Well all the distributive property is is just splitting up a number so you can distribute it to other numbers so you could do 2x(3x82)
Step-by-step explanation:
graph the two lines y=2x + 5 and y= x -1 what is the the x-value of the point where they intersect
Answer:
x=-6
Step-by-step explanation:
y=2x + 5
y= x -1
Plug in the equation for y
x-1=2x+5
Combine like terms
-1=x+5
-6=x
Hope this helps! Please mark brainliest :)
Check all the statements that are true: A. If a relation is symmetric, it cannot be anti-symmetric. B. The equality relation on the real numbers is an equivalence relation. C. If RR is a reflexive relation on a set S, then any two RR- related elements of S must also be R2R2 related. D. There are n2n2 relations from a set with n elements to itself. E. If a relation is anti-symmetric, it cannot be symmetric. F. The less than or equal relation on the real numbers fails to be an equivalence relation because it is reflexive and transitive but not symmetric. G. A relation from a set with n elements to itself can have up to n2n2 elements. H. If RR is an equivalence relation, then R2
Answer:
See explaination
Step-by-step explanation:
B. The equality relation on the real numbers is an equivalence relation.
This statement is true
C. If RR is a reflexive relation on a set S, then any two RR- related elements of S must also be R2R2 related.
This statement is true
F. The less than or equal relation on the real numbers fails to be an equivalence relation because it is reflexive and transitive but not symmetric
This statement is true
H. If RR is an equivalence relation, then R2
This statement is true
Find the sum of the first 10 terms if a(n) = n^2 - n +1
Answer: 36
Step-by-step explanation:
explicit
Sequence: 10, 21, 32, 43, 54, ... Find the 75th term.
Answer:
186
Step-by-step explanation:
definition: a_n = a_1 + f × (n-1)
Common difference is 11
The sum of all numbers up through the 17th: 1666
Answer: 824
Step-by-step explanation:
This is problem on progression.
Considering the series/ sequence,
10, 21, 32, 43, 54, ........
To find the 75th term, we first of all find which of the sequence is it, is it, Arithmetic or Geometric sequence .
Now fro this, it is an AP sequence because, when the first term us subtracted from the second term and the common difference added to the second term it produces the third term and so on, . Haven't gotten this, we now apply the formula for finding the number if terms in an AP.
Tn = a + (n - 1 )d, where n = number of terms we are computing for = 75, a = first term = 10, and d = 21 - 10 = 11.
Now substitute for those values in the formula above
T75 = 10 + ( 75 - 1 )11
= 10 + 74 × 11
= 10 + 814
= 824.