To determine the minimum sample size needed to estimate the population proportion, and the minimum sample size needed, assuming no prior information is available, is approximately 6636.
Explanation:To determine the minimum sample size needed to estimate the population proportion, we can use this formula: [tex]n = (Z^2 * p * (1-p)) / E^2.[/tex]
Where:
n is the minimum sample sizeZ is the z-value corresponding to the desired confidence level (in this case, 99% confidence corresponds to Z = 2.58)p is the estimated proportion (0.5 is typically used when there is no preliminary estimate available)E is the margin of error (0.02 in this case)By plugging in the values into the formula, we get:
[tex]n = (2.58^2 * 0.5 * (1-0.5)) / 0.02^2[/tex]
= 6635.44
Similarly, a prior study found that 38% of the respondents think the president can control the price of gasoline, which is 9448.7 The sample size needed when using the prior estimate (9449) is larger than when assuming no prior information (6636). This is because having a prior estimate reduces the uncertainty, which allows for a smaller sample size to achieve the same level of confidence and margin of error.
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Final answer:
The minimum sample size needed for estimating the population proportion depends on the desired confidence level, margin of error, and estimated proportion. The formula used is n = (Z^2 * p * (1-p)) / E^2, and without prior estimate, p is taken as 0.5, whereas using a prior study, the actual estimate from the study is used.
Explanation:
To calculate the minimum sample size needed to estimate the population proportion with certain confidence and precision, we use the following formula for sample size calculation:
n = (Z^2 * p * (1-p)) / E^2
Where:
n is the sample size
Z is the Z-score corresponding to the desired confidence level
p is the estimated proportion of the population (p-hat)
E is the margin of error
(a) Without preliminary estimate: Assuming that no prior information is available, we use p = 0.5 for the most conservative sample size estimate. For a 99% confidence level, the Z-score is approximately 2.576. With a margin of error E of 0.02, the formula becomes:
n = (2.576^2 * 0.5 * (1-0.5)) / 0.02^2
(b) Using a prior study: If a prior study found p = 0.38, the calculation uses this value. The formula with Z = 2.576 and E = 0.02 becomes:
n = (2.576^2 * 0.38 * (1-0.38)) / 0.02^2
(c) Comparing results: Using p = 0.5 in (a) will result in a larger sample size than using p = 0.38 in (b) because the variance (p * (1-p)) is maximized when p = 0.5.
Use the grouping method to factor the polynomial below completely.
x3-5x2+3x-15
Answer:
x^3 - 3x^2 + 5x - 15
x^2(x-3) +5(x-3)
(x^2 + 5)(x - 3) <==Answer
Step-by-step explanation:
PLEASE HELP WILL GIVE 1ST RIGHT ANSWER AS BRAINIEST The radius of a circle is x+6 and its diameter is 3x+5. What is the circumference of the circle, in terms of pi? (Do not include the variable x in your answer.)
Answer:
The circumference of the circle = 26π unit.
Step-by-step explanation:
Given:
Radius of the circle, r = "x+6"
Diameter of the circle, d = "3(x)+5"
We have to find the circumference of the circle in terms of pi.
Formula to be used:
Circumference of a circle = 2πr or πd
As we know that:
Radius = Half of diameter
So,
⇒ [tex]radius=\frac{diameter}{2}[/tex]
⇒ [tex]x+6=\frac{3x+5}{2}[/tex]
⇒ [tex]2\times (x+6)=\frac{3x+5}{2}\times 2[/tex]
⇒ [tex]2x+12=3x+5[/tex]
⇒ [tex]12-5=3x-2x[/tex] ...Arranging variables and constants.
⇒ [tex]7=x[/tex]
Plugging x = 7 we will find the radius and the diameter.
⇒ Radius = "x+6" = "7+6" = 13
⇒ Diameter = "3(x)+5" = 3(7)+5 =26
Lets find the circumference of the circle.
⇒ Circumference = [tex]2\pi r= 2\pi (13) = 26 \pi[/tex] Or
⇒ Circumference = [tex]\pi d=\pi (26)=26\pi[/tex]
The circumference of the circle = 26π unit.
can someone write this in standard form? 1/7(14x+7)-5
Answer:
No because it is mathematically incorrect.
The expression simplifies to [tex]\( 2x - 4 \)[/tex] in standard form after distributing and combining like terms.
Let's break it down step by step:
1. Start with the given expression: [tex]\( \frac{1}{7}(14x+7) - 5 \)[/tex]
2. Distribute [tex]\( \frac{1}{7} \)[/tex] across the parentheses:
[tex]\[ \frac{1}{7} \cdot 14x + \frac{1}{7} \cdot 7 \][/tex]
3. Simplify each term after distributing:
[tex]\[ \frac{1}{7} \cdot 14x = 2x \][/tex]
[tex]\[ \frac{1}{7} \cdot 7 = 1 \][/tex]
4. Now, rewrite the expression with the distributed terms:
[tex]\[ 2x + 1 - 5 \][/tex]
5. Combine like terms (1 and -5):
[tex]\[ 2x + (1 - 5) \][/tex]
6. Simplify the terms inside the parentheses:
[tex]\[ 2x + (-4) \][/tex]
7. Simplify further:
[tex]\[ 2x - 4 \][/tex]
So, the expression [tex]\( \frac{1}{7}(14x+7) - 5 \)[/tex] in standard form simplifies to [tex]\( 2x - 4 \).[/tex]
Kelly wants to buy 3 boxes of cereal.She wants to use the coupon that says buy one get on half off. If each box of cereal costs 4.75 how much will she pay in total
Answer:
$11.88
Step-by-step explanation:
Given that Kelly would get one box of cereal half off if she buys one, then we must take that into account.
Box 1: $4.75
Box 2: $4.75 ÷ 2 = $2.38
Box 3: $4.75
Now we simply add the totals:
4.75 + 2.38 + 4.75 = $11.88
how many decimals are in a product
Answer: 2 decimal digits
Step-by-step explanation:
When multiplying decimals, placement of the decimal point is very important. Since there is one decimal digit in each factor, there must be two decimal digits in the product. This is because tenths x tenths = hundredths
Hope this helps and good luck! :)
Answer:
Depends on the question
For example 2x1.3=2.6
or 2.3x 5.2343= 12.03889
To answer your question It could range between 0-2
Step-by-step explanation:
A circle with diameter of StartFraction 7 over 2 EndFraction centimeters. The radius is cm. The circumference in terms of π is π cm. Using 3.14 for π, the approximate circumference of the circle is cm.
Answer:
1 is 7/4
2 is 7/2
3 is 11.0
Step-by-step explanation:
they all the right answer thank me later
Answer:
the guy above is right on edge 2021
Step-by-step explanation:
i got the question right because of them
Can someone help find these angles??
Incredibly, Enzo wins 555 tickets from every game, and Beatriz wins 111111 tickets from every game. When they stopped playing games, Enzo and Beatriz had won the same number of total tickets. What is the minimum number of games that Enzo could have played
Answer:
55 games.
Step-by-step explanation:
We have been given that Enzo wins 5 tickets from every game, and Beatriz wins 11 tickets from every game. When they stopped playing games, Enzo and Beatriz had won the same number of total tickets. We are asked to find the minimum number of games that Enzo could have played.
To solve our given problem, we need to find least common multiple of 1 and 55.
We know that least common multiple of two numbers is smallest umber, which is divisible by both numbers.
We know that 5 and 11 are prime numbers, so there LCM would be product of both numbers.
[tex]5\times 11=55[/tex]
Therefore, Enzo could have played 55 games at least.
When do you not use the completing the square method
Answer:
You can use it in different ways
Step-by-step explanation:
sometimes it may be in correct as it is not a 100 percent way to get and answer
You do not use the completing the square method when the quadratic coefficient is not a perfect square, when the middle coefficient is odd, or when dealing with complex numbers. The quadratic formula is often more efficient under these circumstances.
The completing the square method is typically not used in certain circumstances in solving quadratic equations. For example, it is not the best approach when the quadratic coefficient (the 'a' term when the quadratic is in the form ax^2+bx+c=0) is not a perfect square and cannot be easily made into one. Additionally, this method is often avoided if the middle coefficient (the 'b' term) is odd, making it cumbersome to deal with fractional or decimal numbers when completing the square.
Instead, it might be more efficient to use the quadratic formula, which can handle any type of quadratic equation. The quadratic formula, x equals minus 'b', plus-or-minus the square root of 'b' squared minus four 'a' 'c', all over two 'a', provides a direct solution without the need for making any initial transformations to the equation. This formula is also preferred when the equation has coefficients that do not lend themselves to simple arithmetic or when the equation is not easily factorable.
In contrast, the completing the square method is best when dealing with integrals in calculus or when you need the equation in vertex form for analyzing the properties of a parabola. In such scenarios, completing the square provides additional insight into the problem at hand.
A cube has side length
a. The side lengths are decreased to 30% of their original size. Write an expression in simplest form for the volume of the new cube in terms of
a.
Answer:
.027(a^3)
Step-by-step explanation:
The volume of a cube is s^3, where s is the sidelength
We plug in .3a for s, because the sidelength has been reduced to 30% of a.
We get (.3a)^3 = .027(a^3)
Answer:
.027(a^3)
Step-by-step explanation:
Scott is making a snack mix using almonds and raisins. For every 2 cups of almonds in the snack mix, there are 3 cups of raisins. Ariel is making a snack mix that has 3 cups of almonds for every 5 cups of sunflower seeds. If Scott and Ariel each use 6 cups of almonds to make a batch of snack mix, who will make a larger batch?
Answer:
Ariel will make a bigger batch.
Step-by-step explanation:
Scott- Every 2 cups Almonds = 3 cups raisins
so 6 cups almonds = 9 cups raisins
6+9= 15
Scott's batch- 15 cups
Ariel- Every 3 cups Almonds = 5 cups sunflower seeds
so 6 cups almonds = 10 cups sunflower seeds
6+10= 16
Ariel's batch- 16 cups
16 > 15 so Ariel's is bigger.
Ariel makes the larger batch of snack mix
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Equation for Scott :
Number of cups of Almonds = 2 cups
Number of cups of Raisins for 2 cups of almonds = 3 cups
Number of cups of almonds = 6 cups
Number of cups of raisins for 6 cups of almonds = 3 x 3
= 9 cups
So , total number of cups by Scott =
Number of cups of almonds + Number of cups of raisins for 6 cups of almonds
Total number of cups by Scott = 6 + 9 cups
The batch of snack mix by Scott has 15 cups
Equation for Ariel :
Number of cups of Almonds = 3 cups
Number of cups of sunflower seeds for 3 cups of almonds = 5 cups
Number of cups of almonds = 6 cups
Number of cups of raisins for 6 cups of almonds = 5 x 2
= 10 cups
So , total number of cups by Ariel =
Number of cups of almonds + Number of cups of sunflower seeds for 6 cups of almonds
Total number of cups by Ariel = 6 + 10 cups
The batch of snack mix by Ariel has 16 cups
Therefore , the batch mix of snack by Ariel is more than the batch mix of snack by Scott
Hence , Ariel makes the larger batch
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which one is greater 0.74 or 0.084
Answer:.74 is the higher number
Step-by-step explanation: i'm bad at explaining things but i hope this helps
The number 0.74 is larger than 0.084. This can be determined by comparing the numbers from left to right.
Explanation:The question asks for the larger number between 0.74 and 0.084. When comparing decimal numbers, look at each digit from left to right. In our case, the first number has 7 in the tenths place, while the second number has 0. Therefore, 0.74 is greater than 0.084. As a general rule in mathematics, larger numbers often have more digits to the left of the decimal point or larger digits in the most leftward position for numbers to the right of the decimal point.
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Tickets for a play were $2 for each child and $4 for each adult. At one showing of the play, one adult brought 4 children and the remaining adults brought 2 children each. The total ticket sales from the children and adults are $60. How many CHILDREN attended the play
Answer:
16 children attended the play
Step-by-step explanation:
Since one adult brought four children. The cost of their tickets should be:
($4×1) + ($2×1)
= 4+8
= $12
Since the remaining adults brought 2 children each, it means that each of the remaining adults will pay the cost of three tickets (1 for themselves and 2 for their children) which is:
($4×1) + ($2×2) = $4 + $4 = $8.
Since total cost of tickets for adults and children = $60, we will subtract $12 from $60 in order to know the cost of the tickets for the remaining adults and their children.
$60 - $12 = $48
Each of the remaining adults paid $8 as ticket cost for themselves and their kids. If the adults that brought only 2 kids paid a combined $48, then the number of adults that brought 2 kids each
= $48/$8
= 6 adults.
If each of these 6 adults brought 2 kids each, then the number of children that they brought = 2 × 6 = 12
We now add this to the four children of the first adult
12 + 4 = 16
Therefore the number of children that attended the play = 16
The problem is solved by setting up and solving equations, determining that 16 children attended the play.
Explanation:The subject of this problem is setting up and solving equations. The given information can be translated into equations. Four children and one adult make up one group. For this group, the total cost is $4 (for the adult) + $2 * 4 (for the children) = $12. For the remaining adults and children, we know each adult brought 2 children and the cost would be $4 (for the adult) + $2 * 2 (for the children) = $8 per group. We know the total cost was $60. So, subtract the $12 from the first group, which leaves $48. As we know each of the remaining groups cost $8, we divide $48 by $8 to find that there were 6 more groups. Each of these groups consists of 1 adult and 2 children, so there were 6 * 2 = 12 children in these groups. Added to the original 4 children, that makes 16 children in total.
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In the figure below, the two adjacent polygons are regular. What is the measure of ∠ABC?
Answer:
= 150°
Step-by-step explanation:
Since the polygons are regular, certain mathematical assumptions would help us here.
A square is a quadrilateral with all it's 4 sides equal and all it's angles equal.
Sum of angles of a regular quadrilateral = 360.
Therefore, a single angle = 360/4
= 90°.
The Triangle is adjacent to the side of the square. We will thus assume it's an Equilateral triangle.
For an equilateral triangle, all it's 3 angles = 180.
A single angle = 180/3
= 60°.
With this,
Angle ABC = 90° + 60=
= 150°
N n N n N n N n N n n N N Suppose that you were to draw a random sample of one letter from the set of letters above. Two possible events are A = the chosen letter is upper-case and B = the chosen letter is underlined. Find P(A or B). Round your answer to three (3) decimal places.
Answer:
10/13 = 76.92%
Step-by-step explanation:
The question is missing some information because the underline is missing.
If we make table based on if the letter upper case (A) or lower case(a), and if the letter underlined(B) vs not underlined(b) the data will be:
A a
B 4 3 7
b 3 3 6
total 7 6
There are total of 13 letter there. The calculation will be:
P(A or B) = P(A) + P (B) - P(A and B) = (7 + 7 -4) / 13= 10/13 = 76.92%
When the temperature stays the same, the volume of gas is inversely proportional to the pressure of the gas. If a balloon is filled with 228 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 38 cubic inches.
Answer:
84 pounds per square inch
Step-by-step explanation:
Extracting the key information from the question:
*** Volume of a gas is inversely proportional to pressure of the gas.
*** A balloon is filled with 228 cubic inches of a gas at a pressure of 14 pounds per square inch.
*** Volume is then decreased to 38 cubic inches. we are required to find the new pressure of the gas.
Since volume is inversely proportional to pressure, then:
V = k × (1/p)
V = k/p
V = volume, p= pressure, k = mathematical constant
Since, V = 228 cubic inches, P = 14 pounds per square inches, k = ?
Substituting appropriately, we have:
228/1 = k/14
cross multiply
K = 228 × 14 = 3192
Using the same formula, we can calculate the new pressure of the gas since we know our mathematical constant and the volume it was decreased to.
V = k/p
Here, volume = 38, k = 3192
We now have:
38/1 = 3192/p
Cross multiply
38 × p = 3192
p = 3192/38
p = 84 pounds per square inch.
The new pressure of the gas after decrement of the volume= 84 pounds per square inch
When the temperature stays the same, the new pressure of the gas if the volume is decreased is 84 pounds per square inch.
Given the following data:
Pressure A = 14 pounds per square inchVolume A = 228 cubic inchesVolume B = 38 cubic inchesTo find the new pressure of the gas if the volume is decreased:
Translating the word problem into a mathematical expression, we have;
[tex]V \alpha \frac{1}{P} \\\\V = \frac{k}{P}[/tex]
Where:
P is the pressure.V is the volume.First of all, we would determine the constant of proportionality.
[tex]k = VP\\\\k = 228 \times 14[/tex]
k = 3,192
To find the new pressure:
[tex]P = \frac{k}{V} \\\\P = \frac{3192}{38}[/tex]
New pressure, P = 84 pounds per square inch
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which of the following could be the ratio of the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse ?
Answer:
Step-by-step explanation:
Please share the answer choices next time.
The simplest diagram of a 30-60-90 triangle indicates leg lengths of 1 and √3 and hypotenuse 2. Thus, the desired ratio is √3/2. This is the sine of 60° and also the cosine of 30°
Answer: 3\3 :6 , \3:2 and 3 :2/3
Step-by-step explanation:
The Drama Club is showing a video of their recent play. The first showing begins at 3:45 p.m. The second showing is scheduled at 6:25 p.m. with a 1 2 −hour break between the showings. How long is the video in hours and minutes? The video is hours and minutes. Complete the explanation of how you can use a number line to find the answer. You can work backward from the start time of the second showing at : . You count back 1 2 hour, which is minutes, for the break between showings to : . The second showing started 20 minutes late. Will the second showing be over by 8:45 p.m.? Complete the explanation why your answer is reasonable. The second showing started at : p.m. The movie lasts hours minutes, so it ends at :55 p.m. So, the second showing be over by 8:45 p.m.
Answer:
a) The movie is 2 hours and 10 minutes long.
b) Check Explanation
c) The second showing starts at 6:45 p.m. The movie lasts 2 hours and 10 minutes, so it ends at 8:55 p.m. So, the second showing will not be over by 8:45 p.m.
Step-by-step explanation:
The first showing starts at 3:45 pm, the second showing starts at 6:25 pm and there's a break of (1/2) hour between the showings,
To now find how long the video was.
The length of the film.is the difference between the times 6:25 pm and 3:45 pm while also removing the (1/2) hour break time too.
The time between 3:45 pm and 6:25 pm is 2 hours, 40 minutes. Now removing the (1/2) hour break from this time, we are left with 2 hours, 10 minutes.
Hence, the movie is 2 hours and 10 minutes long.
b) To use the number line, we would convert the times into hours, that way, it works.
The time 3:45 is 3.75 on the number line, the time, 6:25 is 6.4167 on the number line. And the (1/2) hour break is a length of 0.5 on the number line.
Working backwards from 6.4167, we go back a length of 0.5 and land on 5.9167.
We can then calculate the length of time between 3.75 and 5.9167
5.9167 - 3.75 = 2.16667 hours
Which directly translates to 2 hours and 10 minutes as obtained in (a)
c) The second showing started 20 minutes late. Will the second showing be over by 8:45 p.m.? Complete the explanation why your answer is reasonable.
The second showing is known to initially start at 6:25 pm, but now, there's a delay of 20 minutes, which pushes the start time to 6:45 pm and the movie lasts for 2 hours and 10 minutes as calculated in (a).
So, 2 hours and 10 minutes from 6:45 pm gives 8:55 pm. So, the second showing will end by 8:55 pm if it starts 20 minutes late.
And the second showing will not be over by 8:45 pm.
Hope this Helps!!!
I need to know these three
Answer:
x = 3.5
perimeter of each figure = 54
Step-by-step explanation:
Perimeter of square: 4(3x + 3) 12x + 12
Perimeter of equilateral triangle: 3(5x + 0.5) = 15x + 1.5
Solve for x: 12x + 12 = 15x + 1.5
Grouping like terms results in 10.5 = 3x, which leads to x = 3.5.
Each polygon has a perimeter of 12x + 12, which here is 12(3.5) + 12 = 54
x = 3.5
perimeter of each figure = 54
Why do cats bang their head against humans?!!..
Im sorry but why are you putting this on here?
Answers:
They probably bump their heads against humans because they want someone to pet them or they like humans.
Explanation:hope I get brainliest!:D
You decide to take a guitar lessons. Each half-hour lesson costs $20. How much will you budget to pay for a half-hour lesson each week for 26 weeks?
Answer:
520
Step-by-step explanation:
If you pay for a half an hour lesson that is 20 dollars.
So if you do that for a total of 26 weeks you would multiply 20 dollars by 26 weeks.
20*26=520
Therefore she spends 520 dollars for half hour lessons that cost 20 for 26 weeks
A gemstone is cut in the shape of a triangular pyramid.The area of the base of the pyramid is 42 square millimeters.the height of the pyramid is 4 millimeters.what is the volume of the gemstone.
Answer:
The volume of this pyramid is 56 millimeters³
Step-by-step explanation:
The volume for a triangular pyramid is given by the following formula:
volume = (1/3)*(base area)*h
In order to solve this problem we must take the given data for the pyramid and apply it to the formula above. We have:
volume = (1/3)*42*4
volume = 14*4
volume = 56 millimeters³
The volume of this pyramid is 56 millimeters³
7.5 liters of a certain solution contain 37 grams of salt. What is the density of salt in the solution? Round your answer, if necessary, to the nearest tenth.
Answer:
The density of salt solution is [tex]4.94\times 10^{-3}\ g/cm^3[/tex].
Step-by-step explanation:
Given that,
Volume of certain solution, V = 7.5 litres
Mass of salt in solution, m = 37 grams
We know that, [tex]1\ L=1000\ cm^3[/tex]
We need to find the density of salt in the solution. The density of salt is given by mass per unit volume. The formula can be written as:
[tex]d=\dfrac{m}{V}\\\\d=\dfrac{37\ g}{7.5\times 10^3\ cm^3}\\\\d=4.94\times 10^{-3}\ g/cm^3[/tex]
So, the density of salt solution is [tex]4.94\times 10^{-3}\ g/cm^3[/tex].
Answer:4.9
Step-by-step explanation:
Identify the zeros of the polynomial function N(x)=1/2 (x-1)(x+3).
a:x+-3
b:x=-1
c:x=1
d:x=3
Answer:
a:x=-3
c:x=1
Step-by-step explanation:
The zeros of a function are the values of x for which the value of the function f(x) becomes zero.
In this problem, we have the following function:
[tex]f(x)=\frac{1}{2}(x-1)(x+3)[/tex]
Here we want to find the zeros of the function, i.e. the values of x for which
[tex]f(x)=0[/tex]
In order to make f(x) equal to zero, either one of the factors [tex](x-1)[/tex] or [tex](x+3)[/tex] must be equal to zero.
Therefore, the two zeros can be found by requiring that:
1)
[tex]x-1=0\\\rightarrow x=+1[/tex]
2)
[tex]x+3=0\\\rightarrow x=-3[/tex]
So the correct options are
a:x=-3
c:x=1
4. If the complement of ∠1 is 80° and m∠2 = 80°, what is m∠3?
Two complementary angles equal 90.
If angle 1’s complementary angle is 80, then angle 1 is 10 (90-80=10)
The three angles of a triangle need to equal 180.
Angle 3 = 180 - angle 1 - angle 2
Angle 3 = 180 - 10 - 80 = 90
Angle 3 = 90 degrees
Solve for p.
16 – 3p = 2/3p+5
Answer:
p=3
Step-by-step explanation:
16-3p=2/3p+5
16=3 2/3p+5
11=3 2/3p
3=p
Answer:
p = -33/7
Step-by-step explanation:
We first re-organize the equation.
3p - 2/3p = 5 - 16
9-2/3p = -11
7p/3 = -11
Then we cross multiply-
7p = -33
p = -33/7
What is 2+2
I need help right nowwwwww
Answer:
4
Step-by-step explanation:
Answer:
21
(4)
Step-by-step explanation:
Suppose that $9500 is invested at 5.8%, compounded quarterly. Find the amount of money in the account after 8 years. Round your answer to the nearest dollar, and input it into the following box. Only NUMBERS are allowed in the input field.
Answer:
The amount of money in the account after 8 years is $15,059
Step-by-step explanation:
The formula for compound interest, including principal sum, is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where
A is the future value of the investment/loan, including interestP is the principal investment amountr is the annual interest rate (decimal)n is the number of times that interest is compounded per unit tt is the time the money is invested or borrowed for∵ $9500 is invested at 5.8%, compounded quarterly
∴ P = 9500
∴ r = 5.8% = [tex]\frac{5.8}{100}[/tex] = 0.058
∴ n = 4 ⇒ compounded quarterly
∵ The amount of money will be in the account for 8 years
∴ t = 8
Substitute all of these value in the formula above
∵ [tex]A=9500(1+\frac{0.058}{4})^{4(8)}[/tex]
∴ [tex]A=9500(1.0145})^{32}[/tex]
∴ A = 15058.7613 dollars
- Round it to the nearest dollar
∴ A = 15059 dollars
The amount of money in the account after 8 years is $15,059
The two figures are proportional find the value of x
Answer:
c
Step-by-step explanation:because ive done this assignment and got 100
The value of x from the given figures is 30 inches. Therefore, option C is the correct answer.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
Given that, the two figures are proportional.
Here, 36/12 =x/10
x/10 =3
x=30 inches
Therefore, option C is the correct answer.
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A company is criticized because only 20 of 47 executives at a local branch are women. The company explains that although this proportion is lower than it might wish, it's not a surprising value given that only 45% of all its employees are women. The company has more than 500 executives worldwide. Test an appropriate hypothesis and state the conclusion.
Answer:
There is insufficient evidence to support the claim that it's not a surprising value given that only 45% of all its employees are women
Step-by-step explanation:
-Given that [tex]p_o=0.45, n=47, x=20[/tex]
-We state our hypothesis as:
[tex]H_o:p=0.45\\\\H_a:p\neq 0.45[/tex]
#We apply the one-proportion z-test to test the claim about the one population proportion.
-The sample proportion is calculated as:
[tex]\hat p=\frac{x}{n}\\\\=\frac{20}{47}\approx0.4255[/tex]
#We determine the value of the test statistic as:
[tex]z=\frac{\hat p-p_o}{\sqrt{\frac{p_o(1-p_o}{n}}}\\\\=\frac{0.4255-0.45}{\sqrt{(0.45\times 0.55)/47}}\\\\=-0.3376[/tex]
#We determine the p-value using the normal probability table:
[tex]P=P(Z<-0.3376 \ or \ Z>0.3376)\\\\=2P(Z<-0.3376)\\\\=2\times 0.32636 \\\\=0.6527[/tex]
[tex]P>0.05[/tex] =>Fail to reject [tex]H_o[/tex]
There is insufficient evidence to support the claim that it's not a surprising value given that only 45% of all its employees are women
To test the claim that female representation among executives is in line with company-wide figures, we perform a hypothesis test. While the observed female proportion in the local branch is below the stated company-wide figure, further analysis using test statistics and p-value comparison with a level of significance (for instance, 0.05) is necessary to decide if this difference is statistically significant.
Explanation:The subject of this question is a hypothesis test related to population proportions. To test the hypothesis that the percentage of female executives in the local branch is not significantly below the overall percentage within the company, we establish the null hypothesis: H0: The proportion of female executives is equal to or greater than 45%, and the alternative hypothesis: H1: The proportion of female executives is less than 45%. Using the given figures, we can calculate the observed proportion of female executives in the local branch as 20/47 = 0.4255 or roughly 42.55%, which is less than 45%. Given the borderline nature of the result, we would typically proceed by calculating the test statistic and looking up the corresponding p-value. If the p-value is less than our level of significance (say α = 0.05), we would reject the null hypothesis, indicating that the imbalance is statistically significant. If not, we fail to reject the null hypothesis, implying that there isn't enough evidence to prove a significant disproportion. Ultimately, the final conclusion needs the actual p-value.
Learn more about the Hypothesis Test here:https://brainly.com/question/34171008
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