Answer:
a) Since np >= 5 and n(1-p) >= 5, the approximation is justified
b) 0.7
c) 0.0725
d) 0.5098 = 50.98% probability that a sample proportion, p,would differ from p = 0.70 by as much as 0.05
Step-by-step explanation:
We use the normal distribution and the central limit theorem to solve this question.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question, we have that:
[tex]p = 0.7, n = 40[/tex]
a. Show that this sample size is large enough to justify using the normal approximation to thesampling distribution of p.
We need that: np >= 5, n(1-p) >= 5. So
np = 40*0.7 = 28 > 5
n(1-p) = 40*0.3 = 12 > 5
Since both conditions are satisfied, the approximation is justified.
b. What is the mean of the sampling distribution of p if the real estate agents are correct?
This is [tex]\mu = p = 0.7[/tex]
c. What is the standard deviation of the sampling distribution of p if the real estate agents are correct?
This is [tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.7*0.3}{40}} = 0.0725[/tex]
d. If the real estate agents are correct, what is the probability that a sample proportion, p,would differ from p = 0.70 by as much as 0.05?
This is the pvalue of Z when X = 0.7 + 0.05 = 0.75 subtracted by the pvalue of Z when X = 0.7 - 0.05 = 0.65. So
X = 0.75
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.75 - 0.7}{0.0725}[/tex]
[tex]Z = 0.69[/tex]
[tex]Z = 0.69[/tex] has a pvalue of 0.7549
X = 0.65
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.65 - 0.7}{0.0725}[/tex]
[tex]Z = -0.69[/tex]
[tex]Z = -0.69[/tex] has a pvalue of 0.2451
0.7549 - 0.2451 = 0.5098
0.5098 = 50.98% probability that a sample proportion, p,would differ from p = 0.70 by as much as 0.05
Dewayne is thinking of a number n, and he wants his sister to guess the number. His first clue is that seven less than five times his number is between thirteen and eighteen. Write a compound inequality that shows the range of numbers that Dewayne might be thinking of.
Answer:4<n<5
Step-by-step explanation: 13<5n-7<18
20<5n<25
4<n<5
Inequalities help us to compare two unequal expressions.The compound inequality that shows the range of numbers that Dewayne might be thinking of is 8<(5n-7)<13.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The given clue by Dewayne can be written in the form of inequality as shown below. Therefore, we can write,
Five times the number → 5nSeven less than five times a number → 5n-7Seven less than five times his number is between thirteen and eighteen → 8 < (5n - 7) <13.Hence, the compound inequality that shows the range of numbers that Dewayne might be thinking of is 8<(5n-7)<13.
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4) Terry missed the sale on a $210 jacket. When he went to purchases it,
he jacket increased to a cost of $262.50 By what percent did the jacket
ncrease in price?
Answer:
The jacket increase by 25% in price.
Step-by-step explanation:
Given that:
Sale price of jacket = $210
New cost of jacket = $262.50
Change = New cost - Sale price
Change = 262.50 - 210 = $52.50
Percent increase = [tex]\frac{Change}{Sale\ price}*100[/tex]
Percent increase = [tex]\frac{52.50}{210}*100[/tex]
Percent increase = 0.25 * 100
Percent increase = 25%
Hence,
The jacket increase by 25% in price.
Find two consecutive whole numbers that 54 lies between.
The two consecutive whole numbers that 54 lies between are 27 and 28, since 54 is greater than 27 and less than 28.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
To find two consecutive whole numbers that 54 lies between, we can start by dividing 54 by 2 and rounding down to the nearest whole number since we want two consecutive numbers that are less than and greater than 54:
54 ÷ 2 = 27
So the two consecutive whole numbers that 54 lies between are 27 and 28, since 54 is greater than 27 and less than 28.
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15.
Using the grid below. indicate what four points
could be the vertices of a square..
Need help quick first person gets that brain award
Triangle A'B'C' is a dilation of AABC. What is AB?
B'
B
6
A4
10
C
A
15
С
o
A. 4
o
B. 5
C. 9
o
D. 16
Answer:
C. 9
Step-by-step explanation:
Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)
Suppose you obtain a 30-years fixed-rate mortgage for$100000 at a rate of 3%.
Answer:
yes
Step-by-step explanation:
$2.79 markdown 35% what is the answer?
Answer:
about 1.81
Step-by-step explanation:
Answer:
1.81?
Step-by-step explanation:
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YOU MUST SHOW YOUR WORK OR I WILL NOT GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
In the morning, Jasmine biked to her grandma's house in 45 minutes. When she was biking back home in the evening it was foggy and she went 4 mph slower. The trip back took her 1 hour and 10 minutes. How far from her house does her grandmother live?
Answer:
8.4 milesStep-by-step explanation:
Let the speed in the morning be s, then in the evening it is s - 4
The distance is equal both directions:
45 min *s = 1 hr 10 min *(s - 4)Time in hours:
45*1/60*s = (1 + 10*1/60)(s - 4)3/4s = 7/6s - 7/6*4Multiply all terms by 12 to clear fraction:
9s = 14s - 565s = 56s = 56/5s= 11.2 mphThe distance is:
3/4*11.2 = 0.75*11.2 = 8.4 milesAnswer:
the answer is 8.4
Step-by-step explanation:
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A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there is 50 mg/L of the material present and after 2 hours it is observed that the material has lost 10 percent of its original concentration, find (a) an expression for the concentration of the material remaining at any time.
Answer:
[tex]Q(t) = 50e^{-0.0527t}[/tex]
Step-by-step explanation:
A certain radioactive material is known to decay at a rate proportional to the amount present.
This means that the situation can be described by the following differential equation:
[tex]\frac{dQ}{dt} = -rQ[/tex]
In which r is the decay rate.
Solving the differential equation by separation of variables, we have that:
[tex]\frac{dQ}{Q} = -r dt[/tex]
Integrating both sides:
[tex]\ln{Q} = -rt + K[/tex]
In which K is the integrative constant.
Applying the exponential to both sides, to remove the ln, we get:
[tex]Q(t) = Ke^{-rt}[/tex]
In which K is the initial amount present.
Initially there is 50 mg/L
This means that [tex]K = 50[/tex].
After 2 hours it is observed that the material has lost 10 percent of its original concentration
This means that [tex]Q(2) = 0.9K[/tex]. So
[tex]0.9K = Ke^{-2r}[/tex]
[tex]e^{-2r} = 0.9[/tex]
[tex]\ln{e^{-2r}} = \ln{0.9}[/tex]
[tex]-2r = \ln{0.9}[/tex]
[tex]r = -\frac{\ln{0.9}}{2}[/tex]
[tex]r = 0.0527[/tex]
So
[tex]Q(t) = Ke^{-rt}[/tex]
[tex]Q(t) = 50e^{-0.0527t}[/tex]
In Omak the sales tax is 8.4%. What is the total cost including tax Aakel spent on a $48 purchase?
Answer:
$52.03
Step-by-step explanation:
1. Approach
To solve this problem, first one needs to calculate the sales tax, then one must add that to the amount spent on the purchase. To calculate sales tax, one must convert the percent to decimal form, this can be done by dividing the percent by 100. Then one will multiply the decimal by the amount spent.
2. Find the tax
As states above; to calculate sales tax, one must convert the percent to decimal form, this can be done by dividing the percent by 100. Then one will multiply the decimal by the amount spent.
a. convert percent to decimal
8.4 / 100 = 0.084
b. multiply the decimal by the amount spent
48 * 0.084 = 4.032
The amount spent on sales tax is, $4.032
3. Find the total amount spent
Now all one has to do is add the amount spent in tax by the amount spent on the purchase.
48 + 4.032 = 52.032
Since money is only spent rounded to the second decimal point, one has to round the number;
52.03
An bakery chef wants to construct a pie graph to represent types of pies sold in November. He sold 700 pies, 350 of which were pumpkin ples The pumpkin ples represent how many degrees in the circle?
Answer:
[tex]180^{\circ}[/tex]
Step-by-step explanation:
Given that,
Total pies that sold = 700
Pumpkin pies = 350
We need to represent the degrees in the circle. It can be calculated as follows :
[tex]x=\dfrac{350}{700}\times 360\\\\x=180^{\circ}[/tex]
So, the pumpkin pies are represented by [tex]180^{\circ}[/tex].
Solve the system of equations.
= y = 7x + 43 y = 2x + 13
a. (-6, 1)
b. (6, -1)
c. (6, 1)
d. No solution
No solution Please select the best answer from the choices provided
A class of 32 students earned
grades of A, B, C, or Don a test.
One-fourth of the students earned
an A Half of the remaining students
earned a B. Two students earned a
D. What fraction of the students
earned a C?
Answer:
5/16 Got a C
Step-by-step explanation:
A = 1/4 x 32
B = (32 - A)/2
D = 2
A = 8
B = (32 - 8)/2
B = 24/2
B = 12
D = 2
8 + 12 + 2 = 22
22/32 did not get a C
32/32 - 22/32 = 10/32
10/32 - > 5/16
Sheronda uses 1 cups of sugar in every batch of homemade muffins
she makes. One day, while making muffins for her son's bake sale, she
used 19 cups of sugar in all. How many batches of muffins did she make?
Answer:
19 batches of homemade muffins
Step-by-step explanation:
1 cup per 1 batch
You will get an amount of batches equal to the amount of cups of sugar, so if there are 19 cups there would be 1 batch of homemade muffins for each of the cups.
Answer:
19 batches of muffins
Step-by-step explanation:
She uses 1 cup for 1 batch which means
1 cup = 1 batches
So if you multiply 19 by 1 you should get 19 which means
19 cups = 19 batches
Need help right now!!! Due soon!
Answer:
Step-by-step explanation:
HAHAHAHAHA! NOT IN THE MOOD!
Need help don’t know what to do I’m confused
Express the sum of 1.202 x 10^3 and 3.45 x 10^2 in scientific notation.
Answer:
4.1469 x 10^5
Step-by-step explanation:
multiply the coefficients and add the exponents
1.202 x 3.45 = 4.1469
10³ x 10² = 10^5
Write the equation of an exponential function that has an initial
value of 150 and a growth rate of 4%, which occurs every 8
years.
Answer:
Step-by-step explanation:
A box has length 5 feet, width 6 feet, and height 3 inches. Find the volume of the box in cubic feet and in cubic inches.
Answer:
90 inches
Step-by-step explanation:
The formula for volume is LxWxH so you just gotta do 5x6x3
which is 90.
tue/false
The Place valueof Thedigit 5 in 26,59,360 in Ten Thousand
Answer: True.
Step-by-step explanation:
Here we have the number:
26,59,360
To find the place value of the 5, we first need to count the number of decimals at the right of the 5 (until we reach the decimal point)
For this case, at the left of the 5 we have 4 decimals (9, 3, 6 and 0)
Then the place value of the 5 in that number will be 10^4
this is equal to:
10^4 = (10)*(10)*(10)*(10) = 10,000
This means that the place value of the 5 is then thousand.
Then the statement is true.
Mr. Kazadi said that in his 2nd-period class, 23 out of 25 students passed the test. What percent of the students passed the test?
%
[tex]\text{Hello there!}[/tex]
To find a percentage, you will need to divide both numbers by each other. In this case, it would look similar to this:
[tex]\text{23 / 25 = ???}[/tex]
Once you divide the two numbers, you should end up with a result of [tex]0.92[/tex]
Now, we are going to move the decimal two spaces to the right to end up with the result:
[tex]\text{092.}[/tex]
Now, we are going to remove the [tex]0[/tex] as it is no longer required. Next, add a percentage symbol to the last number, and remove the decimal from the number.
Now, you should end up with something like this:
[tex]92\%[/tex]
[tex]\fbox{So your final answer is going to be 92\%}[/tex]
[tex]\rule{299}{1.5}[/tex]
Dover City Printers needs to ship 419 graduation programs to a university. The printing company can fit 24 programs in each box. How many programs will be in the partially filled box?
Answer:
There will be 11 graduation programs in partially filled box.
Step-by-step explanation:
It is given that:
Number of graduation programs need to be shipped = 419
Number of programs in each box = 24
Number of boxes = [tex]\frac{419}{24}[/tex]
Number of boxes = [tex]17\frac{11}{24}[/tex]
Here,
17 is the number of full boxes and 11 is the remainder.
Therefore,
There will be 11 graduation programs in partially filled box.
Answer:
11
Step-by-step explanation:
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it takes 20 minutes to walk to school .it takes Andre 80% as long to walk to school.how long does it take Andrea to walk to school
Answer:
16min
Step-by-step explanation:
80%*20min=4/5*20min=16min
Answer:
16 minutes
Step-by-step explanation:
If it takes 20 minutes and it takes Andre 80% as long, then you multiply 20 by %80
oints
What is the value of 10y + 2 3x + 2) if x = -2 and y = 3?
Step-by-step explanation:
When x = -2 and y = 3,
10y + 2(3x + 2)
= 10(3) + 2[3(-2) + 2]
= 30 + 2(-4)
= 30 - 8
= 22.
Answer:
I think its help you
Step-by-step explanation:
10y+23x+2
10×3+23×-2+2
30+23
53
Subtract (2xy-2y) from the sum of (10x-2y) and (-3y)
-8x-3y
-8x+3y
8x-3y
8x+3y
Answer:
I think its C
Step-by-step explanation:
Step-by-step explanation:
8x-3y
Evaluate: ab – bc if a = 4, b = 3, and c = 2
ab - bc =
Answer:
6
Step-by-step explanation:
To evaluate the expression if a = 4, b = 3, and c = 2, substitute those values for the variables and solve. So, substitute 4 for a, 3 for b, and 2 for c, then simplify by the correct order of operations, PEMDAS:
[tex]ab - bc \\(4)(3)-(3)(2)\\= 12 - 6 \\= 6[/tex]
Therefore, the answer is 6.
Which congruence best expresses the relationship showing that the triangles below are
congruent?
76°
76°
F SSS
GSSA
H SAS
3
ASA
The relationship of congruency that describes that the given triangles are congruent is SAS.
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
Given, are two triangles with an included angle of 76° and the corresponding sides are congruent to each other.
∴ The relationship that shows that the triangles below are congruent are
side angle side or SAS.
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The surface area, S, of a right rectangular prism with lengih I, width w, and height h, can be found using the formula S = 2[/w + wh + hl). What is the surface area, in square inches, of a prism with a length of 12 inches, a width of 9 inches, and a height of 2 inches?
PLEASE HELP! I'LL GIVE BRAINLIEST!
Write an equation for the line (y = mx + b)
Write a sentence explaining a real-life situation that this line could represent. (Make sure you use the word ascending in your sentence.)
How many meals would be packed in 20 hours?
Given :
A graph of Total Meals Packed vs Time( in hours ).
To Find :
How many meals would be packed in 20 hours.
Solution :
First we will find the equation of line.
Now, the line passes through ( 0, 0 ) and ( 4, 500 ).
So, equation of line passing through ( 0, 0 ) and ( 4, 500 ) is :
[tex]y - 0 = \dfrac{500-0}{4-0}( x - 0 )\\\\y = 125x[/tex]
Now, putting the value of x = 20 hours in above equation, we get :
y = 125 × 20 meals
y = 2500 meals
Therefore, number of meals packed in 20 hours is 2500 meals.
Subtract 1/2h -1 from 3/4 h -4
A.1/4h+3
B.-1/4+5
C.1/4h+5
D.-1/4h+5
Help plzzzz
Answer:
It would be option A.
Step-by-step explanation:
1/4h + 3