(a) Null Hypothesis (H0): μ ≤ 100 ppb (The average level of BPA in the tomato soup is less than or equal to 100 ppb)
Alternative Hypothesis (H1): μ > 100 ppb (The average level of BPA in the tomato soup is greater than 100 ppb)
(b) A Type I Error would occur if the agency finds evidence that the average level of BPA is greater than 100 ppb (rejects H0) when, in fact, the true average level is less than or equal to 100 ppb.
(c) A Type II Error would occur if the agency fails to find evidence that the average level of BPA is greater than 100 ppb (fails to reject H0) when, in fact, the true average level is greater
(a) Null Hypothesis (H₀): The average level of BPA in the company's tomato soup is less than or equal to 100 ppb.
Mathematically: μ ≤ 100 ppb
Alternative Hypothesis (H₁):
The average level of BPA in the company's tomato soup is greater than 100 ppb.
Mathematically: μ > 100 ppb
(b) A Type I error occurs when we reject the null hypothesis when it is actually true. In this context, a Type I error would mean that the consumer protection agency concludes that the average BPA level is greater than 100 ppb and recalls the soup and sues the company, when in reality, the average BPA level is less than or equal to 100 ppb. This would result in unnecessary product recall and legal action against the company.
(c) A Type II error occurs when we fail to reject the null hypothesis when it is actually false. In this context, a Type II error would mean that the consumer protection agency concludes that the average BPA level is less than or equal to 100 ppb and does not recall the soup or sue the company, when in reality, the average BPA level is greater than 100 ppb. This would allow unsafe products to remain on the market, potentially harming consumers.
which expressions are equivalent to the one below? Check all that apply 10^x
The statement equivalent to 10^x is A,C and F.
We have to find the expression equivalent to 10^x.
What is the meaning of the equivalent statement?Equivalent Statements are statements that are written differently but hold the same logical equivalence.
[tex]A.(50/5)^x\\=10^x[/tex]
This is equivalent to the 10^x.
[tex]10 \times 10^x-1\\=10 \times 10^x\times 10^-1\\=10^x[/tex]
This is equivalent to the 10^x.
[tex]50^x / 5^x\\=10^x[/tex]
This is equivalent to the 10^x.
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The expression 10^x represents a form of exponential notation, which includes any expression that has 10 as the base in the format a x 10^x. This is often used in scientific notation to conveniently write very small or large numbers. Such an expression could also be manipulated using rules of exponential arithmetic.
Explanation:The expression 10^x is equivalent to any expression with exponential notation where 10 is the base. This includes expressions like 1.23 x 10^x or 3.6 x 10^-x, where the 'x' in the exponent can be replaced by any number. This introduces the concept of scientific notation, which allows very large and small numbers to be written compactly. For example, 1,230,000,000 can be written 1.23 x 10^9, and 0.00000000036 can be written 3.6 x 10^-10. Exponential Arithmetic further explains how these notations can simplify arithmetic operations. It explains that to multiply two numbers written in exponential form, one should multiply the numbers in the front and add the exponents.
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A crate is 2 feet in length, 5 feet in height, and has a volume of 40 cubic feet. What is the width of the crate?
Answer: 4 feet
Step-by-step explanation:
The formula for volume is length x width x height
Answer:
The answer to your question is 4 ft
Step-by-step explanation:
Data
length = 2 ft
height = 5 ft
Volume = 40 ft³
width = ?
Process
A crate is a rectangular prism, so to calculate the volume we use
Volume of a rectangular prism = height x length x width
-Solve for width
width = Volume / height x length
-Substitution
width = 40 / (5 x 2)
-Simplification
width = 40/10
-Result
width = 4 ft
For a large supermarket chain in a particular state, a women's group claimed that female employees were passed over for management training in favor of their male colleagues. The company denied this claim, saying it picked the employees from the eligible pool at random to receive this training. Statewide, the large pool of more than 1000 eligible employees who can be tapped for management training is 30% female and 70% male. Since this program began, 39 of the 50 employees chosen for management training were male and 11 were female. Complete parts a through d. LOADING... Click the icon to view the results of using technology. a. The company claims that it selected employees for training according to their proportion in the pool of eligible employees. Define a parameter of interest and state this claim as a hypothesis. Explain why this hypothesis is a no-effect hypothesis. Define a parameter of interest. Choose the correct answer below.
Answer:
Step-by-step explanation:
Hello!
Tha claim is those female employees have less probability of being selected for management training than the males employees of a supermarket chain.
The company denies this claim and assures that the employees are picked at random from an eligible pool, i.e. that there is no gender bias in the manager selection
If you consider the variables:
X₁: Number of female employees selected for management training
X₂: Number of male employees selected for management training
The parameter of interest would be
p₁: population proportion of female employees selected for management training
p₂: population proportion of male employees selected for management training
If the company claims that there is no gender bias in the management selection is true, then the proportion of female employees selected for management training and the proportion of male employees selected for management training should be the same, symbolically: p₁ = p₂
If the company's claim is incorrect, then these proportions should be different: p₁ ≠ p₂
I hope this helps!
Secants P N and L N intersect at point N outside of the circle. Secant P N intersects the circle at point Q and secant L N intersects the circle at point M. The length of P N is 32, the length of Q N is x, the length of L M is 22, and the length of M N is 14. In the diagram, the length of the external portion of the secant segment PN is . The length of the entire secant segment LN is . The value of x is .
Answer:
In the diagram, the length of the external portion of the secant segment PN is x. The length of the entire segment LN is 36. The value of x is 17.75.
Step-by-step explanation:
I just did it on Edge.
NEED HELP ASAP!! FILL IN THE BLANKS!! I'LL MARK YOU BRAINLIEST IF YOU ANSWER RIGHT!!!
Answer:
(x+8)^2 = 127
Step-by-step explanation:
Lily paid $19.16 for a 1 kg Apple basket this amount includes the tax of 3% what was the cost of the Apple before tax
Answer:
0.57 or 0.6
Step-by-step explanation:
I need help please?!!
Answer:
No, the expression is not linear because the highest power of x is 2.
Answer:
No it isn't it is Quadratic
Which type of number is 0.46?
A Whole
B Natural
c Terminating and rational
D Terminating and irrational
Answer:
terminating and rational
Step-by-step explanation:
Answer:
C: Terminating and Rational
Step-by-step explanation:
A whole number is a number with no decimal places so the answer is not A.
A natural number is a whole number which is equal to or greater than 0, and since 0.46 is not a whole number, the answer is not B either.
A terminating number is a number which does not go on forever, like 3.86. A rational number is a number which can be expressed as a fraction, and 0.46 can be expressed as 46/100. Thus 0.46 is both terminating and rational, making C the answer.
Gabriel finds some wooden boards in the backyard with lengths of 5 feet, 2.5 feet and 4 feet. He decides he wants to make a triangular garden in the yard and uses the triangle inequality rule to see if it will work.
PLEASE ANSWER IMMEDIATELY Which sums prove that the boards will create a triangular outline for the garden? Select all that apply.
5 + 2.5 > 4
5 + 2.5 < 4
4 + 2.5 > 5
4 + 2.5 < 5
4 + 5 > 2.5
first one to answer will get brainliest
Answer:
Third one
4 + 2.5 > 5
Step-by-step explanation:
To form a triangle, the longest side should be less than the sum of the two shorter sides (triangular inequality)
Longest side < sum of the shorter ones
Longest side: 5
Shorter ones: 2.5 & 4
5 < 2.5 + 4
This is the same as:
4 + 2.5 > 5
Answer:
1 3 5
Step-by-step explanation:
Suppose we have a collection of the heights of all students at your college. Each of the 250 people taking statistics randomly takes a sample of 40 of these heights and constructs a 95% confidence interval for mean height of all students at the college. Which of the following statements about the confidence intervals is most accurate?
A. About 95% of the heights of all students at the college will be contained in these interval
B. About 95% of the time, a student’s sample mean height will be contained in his or her interval.
C. About 95% of the intervals will contain the population mean height.
D. About 95% of the intervals will be identical.
Answer:
Correct option: (C)
Step-by-step explanation:
The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.
Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.
Or, if n such (1 - α)% confidence intervals are constructed then (1 - α)% of these interval will consist of the true parameter value.
It is provided that each of the 250 people taking statistics randomly takes a sample of 40 of these heights and constructs a 95% confidence interval for mean height of all students at the college.
So there sill be n = 250, 95% confidence intervals for mean height of all students at the college.
Then 95% of these 250 confidence intervals for mean will consist of the true mean height of the college students.
Thus, the correct option is (C).
A movie theater is keeping data on the number of tickets sold and the price of a single ticket. Which scatterplot is
correctly labeled?
Answer: 3rd option
Step-by-step explanation:
Answer:the third option is the answer
Step-by-step explanation:I just took the assignment on edge
PLEASE HELP I WILL GIVE YOU BRAINLIEST
Your friend earns $10.50 per hour.This is 125% of her hourly wage last year. How much did your friend earn per hour last year?
Let your friend's hourly wage last year be $x.
125% of x = 10.50
[tex]\frac{125}{100}[/tex] x = 10.5
[tex]\frac{5}{4}[/tex] x = 10.5
5x = 42
x = $8.40
Your friend's hourly wage last year was $8.40.
I hope this helps! If you have any doubts, feel free to ask.
Answer:
it is $8.40
Step-by-step explanation:
sorry my answer got deleted :(
R=1/6 the problem is 3r2
Step-by-step explanation:
Putting the value of r
3 ( 1/6) 2
So 3 × (1/6) = 0.5 × 2 = 1
The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 38 feet and the height of the arch over the center of the roadway is 12 feet. Two trucks plan to use this road. They are both 8 feet wide. Truck 1 has an overall height of 11 feet and Truck 2 has an overall height of 12 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge.
Answer:
Only truck 1 can pass under the bridge.
Step-by-step explanation:
So, first of all, we must do a drawing of what the situation looks like (see attached picture).
Next, we can take the general equation of an ellipse that is centered at the origin, which is the following:
[tex] \frac{x^2}{a^2}+\frac{y^2}{b^2}[/tex]
where:
a= wider side of the ellipse
b= shorter side of the ellipse
in this case:
[tex] a=\frac{38}{2}=19ft[/tex]
and
b=12ft
so we can go ahead and plug this data into the ellipse formula:
[tex] \frac{x^2}{(19)^2}+\frac{y^2}{(12)^2}[/tex]
and we can simplify the equation, so we get:
[tex] \frac{x^2}{361}+\frac{y^2}{144}[/tex]
So, we need to know if either truk will pass under the bridge, so we will match the center of the bridge with the center of each truck and see if the height of the bridge is enough for either to pass.
in order to do this let's solve the equation for y:
[tex] \frac{y^{2}}{144}=1-\frac{x^{2}}{361}[/tex]
[tex] y^{2}=144(1-\frac{x^{2}}{361})[/tex]
we can add everything inside parenthesis so we get:
[tex] y^{2}=144(\frac{361-x^{2}}{361})[/tex]
and take the square root on both sides, so we get:
[tex] y=\sqrt{144(\frac{361-x^{2}}{361})}[/tex]
and we can simplify this so we get:
[tex] y=\frac{12}{19}\sqrt{361-x^{2}}[/tex]
and now we can evaluate this equation for x=4 (half the width of the trucks) so:
[tex] y=\frac{12}{19}\sqrt{361-(8)^{2}}[/tex]
y=11.73ft
this means that for the trucks to pass under the bridge they must have a maximum height of 11.73ft, therefore only truck 1 is able to pass under the bridge since truck 2 is too high.
Truck 1 and Truck 2 can both pass under the bridge.
Explanation:To determine which truck can pass under the bridge, we need to compare the height of the truck to the height of the arch over the center of the roadway. The height of the arch is given as 12 feet. Truck 1 has an overall height of 11 feet, so it can pass under the bridge. Truck 2 has an overall height of 12 feet, which is equal to the height of the arch, so it can also pass under the bridge.
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2/-3 ÷(−1 2/7) ……...
Answer:0.518518519
Step-by-step explanation:
In 2011, a U.S. Census report determined that 71% of college students work. A researcher thinks this percentage has changed since then. A survey of 110 college students reported that 91 of them work. Is there evidence to support the reasearcher's claim at the 1% significance level? A normal probability plot indicates that the population is normally distributed.
a) Determine the null and alternative hypotheses.
H0: p =
Ha:P Select an answer (Put in the correct symbol and value)
b) Determine the test statistic. Round to two decimals.
c) Find the p-value. Round to 4 decimals.
P-value =
Answer:
(a) Null Hypothesis, [tex]H_0[/tex] : p = 71%
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 71%
(b) The test statistics is 3.25.
(c) The p-value is 0.0006.
Step-by-step explanation:
We are given that a U.S. Census report determined that 71% of college students work. A researcher thinks this percentage has changed since then.
A survey of 110 college students reported that 91 of them work.
Let p = proportion of college students who work
(a) Null Hypothesis, [tex]H_0[/tex] : p = 71% {means that % of college students who work is same as 71% since 2011}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 71% {means that % of college students who work is different from 71% since 2011}
The test statistics that will be used here is One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of college students who reported they work = [tex]\frac{91}{110}[/tex] = 82.73%
n = sample of students = 110
(b) So, test statistics = [tex]\frac{\frac{91}{110}-0.71}{\sqrt{\frac{\frac{91}{110}(1-\frac{91}{110})}{110} } }[/tex]
= 3.25
The test statistics is 3.25.
(c) P-value of the test statistics is given by the following formula;
P-value = P(Z > 3.25) = 1 - P(Z [tex]\leq[/tex] 3.25)
= 1 - 0.99942 = 0.0006
So, the p-value is 0.0006.
The null and alternative hypotheses is [tex]\rm H_0:[/tex] p = 71% and [tex]\rm H_a[/tex] : p [tex]\neq[/tex] 71%, the value test statistics is 3.25, and the p-value is 0.0006.and this can be determined by using the given data.
Given :
In 2011, a U.S. Census report determined that 71% of college students work.A survey of 110 college students reported that 91 of them work.a) The hypothesis is given by:
Null hypothesis -- [tex]\rm H_0:[/tex] p = 71%
Alternate Hypothesis -- [tex]\rm H_a[/tex] : p [tex]\neq[/tex] 71%
b) The statistics test is given by:
[tex]\rm TS = \dfrac{\hat{p}-p}{\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}} }[/tex]
[tex]\rm TS = \dfrac{\dfrac{91}{110}-0.71}{\sqrt{\dfrac{\dfrac{91}{110}(1-\dfrac{91}{110})}{110}} }[/tex]
Simplify the above expression.
TS = 3.25
c) The p-value is given by:
P-value = P(Z>3.25) = 1 - P(Z [tex]\leq[/tex] 3.25)
= 1 - 0.99942
= 0.0006
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Which of the following illustrates the product rule for logarithmic equations?
1.log2 (4x) = log2(4) / log2(x)
2.log2 (4x) = log2(4)x log2(x)
3.log2 (4x) = log2(4)-log2 (x)
4.log2 (4x) = log2(4)+log2 (x)
Answer:log2 (4x) = log2(4)+log2 (x) it is D
Step-by-step explanation:
The manufacturer of a machine to package soap powder claimed that her machine could load cartons at a given weight with a range of no more than 0.4 ounce. The mean and variance of a sample of eight 3-pound boxes were found to equal 3.5 and 0.015, respectively. Test the hypothesis that the variance of the population of weight measurements is σ2 = 0.01 against the alternative that σ2 > 0.01.
Answer:
Please see the attached file for the complete answer.
Step-by-step explanation:
Please use mean = 3.5 instead of 3.1 and varience = 0.015 instead of 0.018 in the solution.
A test contains twenty true false questions. A student either knows the answer to a question, or guesses at random if he does not know the answer. On any question, the student knows the answer with probability .7. What is the probability that he gets exactly 2 of the twenty questions wrong, if his performance on different questions is independent
Answer:
2.78% probability that he gets exactly 2 of the twenty questions wrong
Step-by-step explanation:
For each question, there are only two possible outcomes. Either he knows the answer, or he does not. The probability of him knowing the answer for a question is independent of other questions. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
On any question, the student knows the answer with probability .7.
This means that [tex]p = 0.7[/tex]
What is the probability that he gets exactly 2 of the twenty questions wrong, if his performance on different questions is independent
2 of 20 wrong, 20-2 = 18 correctly. So this is P(X = 18).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 18) = C_{20,18}.(0.7)^{18}.(0.3)^{2} = 0.0278[/tex]
2.78% probability that he gets exactly 2 of the twenty questions wrong
Raj has a full deck of 52 cards. Sydney chooses the queen of clubs and holds onto it. Then Yolanda chooses a card. What is the total number of possible outcomes for Yolanda’s card?
The total number of possible outcomes for Yolanda’s card is 51.
What is Probability?A branch of mathematics concerned with the analysis of random phenomena, or occurrence of things.
Given that, Raj has a full deck of 52 cards. Sydney chooses the queen of clubs and holds onto it. Then Yolanda chooses a card.
Since, there is only 1 queen of clubs in a deck of cards, so, after choosing 1 card from deck there will be remaining only 51 cards.
Therefore, there will be 51 cards remaining for Yolanda to choose.
Hence, The total number of possible outcomes for Yolanda’s card is 51.
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Solve equation by using the quadratic formula.
8x^2+5x=3
Help plzzz
Answer:
x=−1, 3/8
Step-by-step explanation:
Answer:
x= 3/8 or x=-1
Step-by-step explanation:
Step 1: Subtract 3 from both sides.
8x2+5x−3=3−3
8x2+5x−3=0
Step 2: Factor the left side of the equation.
(8x−3)(x+1)=0
Step 3: Set factors equal to 0.
8x−3=0 or x+1=0
x=3/8 or x=-1
1 of 6
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Peter rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total of 11.
Answer:
1/18
Step-by-step explanation:
Total 11: (5,6) (6,5)
2/36
1/18
You are offered the following gamble based on coin flips. If the first heads occurs on the first flip, you get $2. If the first heads occurs on the second flip, you get $4, and so on, so that if the first heads is on the Nth flip, you get $2N. The game continues until there is a heads. Which of the following best represents the expected value of this gamble in dollars? e 0 π [infinity] When offered, most people say they would pay only less than $10 to play this game.
Answer:
infinity
Step-by-step explanation:
a) the expected value of this gamble in dollars is Infinity
i.e
expected value = [tex]\frac{1}{2}*2 + \frac{1}{4}*4 + \frac{1}{8}*8 + \frac{1}{16}*16 + ... + \to \infty (infinty) \\[/tex]
= [tex]1+1+1+1+1 + ... = \infty[/tex]
b)
When offered, most people say they would pay only less than $10 to play this game.
What are two reasons why people are willing to pay so much less than the expected value?
These people are ready to pay less than $10 to play this game due to the fact that people usually overlook the unlikely event when making decisions. In a bid to that logic, they gamble in order to double their amount of money and the probability that heads may never come is ignored by these people and they may hope for a likely event i.e a head every time they play the game.
Also, the expected value is so humongous that if and only if that the first head appears after a long series of tails which is very less certain to occur, because mostly people would think that on an average the length of a series of tails ( or heads) is somewhat near 10 or so, but definitely infinity.
"The CEO of a large electric utility claims that 80% of all his customers are very satisfied with the service they receive. To test this claim, the local newspaper surveyed 100 customers, using simple random sampling. Among the sampled customers, 73% say they are very satisfied. Were these surveyed customers less likely to be satisfied than all the CEO’s customers ( \alpha =0.05)?"
Answer:
The claim made by the CEO was correct.
Step-by-step explanation:
The CEO of a large electric utility claims that 80% of all his customers are very satisfied with the service they receive.
A one-proportion z-test can be used to determine whether the claim made by the CEO of a large electric utility is correct or not.
The hypothesis can be defined as:
H₀: The proportion of customers that are very satisfied with the service they receive is 80%, i.e. p = 0.80.
Hₐ: The proportion of customers that are very satisfied with the service they receive is not 80%, i.e. p ≠ 0.80.
The information provided is:
[tex]\hat p[/tex] = 0.73
n = 100
α = 0.05
Compute the test statistic as follows:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.73-0.80}{\sqrt{\frac{0.80(1-0.80)}{100}}}=-1.75[/tex]
The test statistic value is -1.75.
The decision rule is:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
Compute the p-value of the two-tailed test as follows:
[tex]p-value=2\times P(Z<-1.75)\\=2\times [1-P(Z<1.75)]\\=2\times [1-0.95994]\\=0.08012 \\\approx 0.08[/tex]
*Use a z-table for the probability.
The p-value of the two-tailed test is 0.08.
p-value = 0.08 > α = 0.05
The null hypothesis was failed to be rejected at 5% level of significance.
Thus, it can be concluded that the claim made by the CEO was correct. The proportion of customers that are very satisfied with the service they receive is 80%.
60x-24=__(__)
35pts!!!!!
Answer:
Step-by-step explanation:
Answer:
12(5x−2)
Step-by-step explanation:
i think this is the answer plz tell me if im wrong
Which on of the following expression can be used to find the area of the polygon? Select all that apply
Answer:
Choices A, C, D, and E are the right choices.
Step-by-step explanation:
Area of the given figure = [tex]174 \:ft^2[/tex]
Option A = 174
Option B = 150
Option C = 174
Option D = 174
Option E = 174
Where are the negative rational numbers placed on a vertical number line?
Answer:
on the top the negative rational numbers are placed
Answer:
On a horizontal number line, the positive rational numbers are placed To the right of, To the left of, above or below zero, and the negative rational numbers are placed To the right of, To the left of, above or below zero.
A bookstore had 45 copies of a magazine. Yesterday, it sold 23 of them. Today, it sold 15 of what remained. How many copies does the bookstore have left?
Answer:
45 original books then 23 is sold = 22
next day 15 is sold so
23-15=7
7 books remain
Step-by-step explanation:
45-23-15=7
The following 5 questions are based on this information. An economist reports that 47% (p¯=0.47p¯=0.47) of a random sample of 1200 middle-income American households actively participate in the stock market. The goal is to construct a 95% confidence interval of the proportion (pp) of all middle-income Americans who actively participate in the stock market. The standard error (SE) of p¯p¯ is Select one:
a. 0.47
b. 0.047
c. 0.021
d. 0.014
Answer:
Option D) 0.014
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 1200
Sample proportion =
[tex]\hat{p} = 0.47[/tex]
We have to make a 95% confidence interval.
Formula for standard error:
[tex]S.E = \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
Putting the values, we get:
[tex]S.E = \sqrt{\dfrac{0.47(1-0.47)}{1200}} = 0.014[/tex]
Thus, the correct answer is
Option D) 0.014
Find the quotient of 4/7 and 3/5
Give your answer as a fraction in its simplest form.
The quotient of [tex]\frac{4}{7} $ and $ \frac{3}{5}[/tex] is [tex]\frac{20}{21}[/tex]
Recall:
The quotient of two quantities or values is the result you get by dividing one with the other.
Therefore, the quotient of [tex]\frac{4}{7} $ and $ \frac{3}{5}[/tex] is solved as shown below:
[tex]\frac{4}{7} \div \frac{3}{5} \\[/tex]
Change the division sign to multiplication sign and turn the second fraction upside down
[tex]\frac{4}{7} \times \frac{5}{3} \\[/tex]
Multiply both fractions together
[tex]= \frac{4 \times 5}{7 \times 3}\\= \frac{20}{21}[/tex]
Therefore the quotient of [tex]\frac{4}{7} $ and $ \frac{3}{5}[/tex] is [tex]\frac{20}{21}[/tex]
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