The mayor of a town has proposed a plan for the construction of a new community. A political study took a sample of 1300 voters in the town and found that 45% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 42%. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
The value of the test statistic is t = 2.19.
Step-by-step explanation:
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]
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the expected mean, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
Sample of 1300 voters:
This means that [tex]n = 1300[/tex]
Found that 45% of the residents favored construction.
This means that [tex]X = 0.45[/tex]
A political strategist wants to test the claim that the percentage of residents who favor construction is more than 42%.
This means that [tex]\mu = 0.42[/tex], and by the Central Limit Theorem:
[tex]\frac{\sigma}{\sqrt{n}} = s = \sqrt{\frac{0.42*0.58}{1300}} = 0.0137[/tex]
So, the test statistic is:
[tex]t = \frac{X - \mu}{s}[/tex]
[tex]t = \frac{0.45 - 0.42}{0.0137}[/tex]
[tex]t = 2.19[/tex]
The value of the test statistic is t = 2.19.
Geometry Two column prove
Answer:
(see below)
Step-by-step explanation:
First, you know that the first statement given is Given.
Now that you have that, you want to concentrate on your goal, and that goal is to prove that ΔGHI is an isosceles. To do this, you need to prove that the two base angles or two adjacent sides are congruent.
To do this, you can prove ΔGHJ ≅ ΔIHJ first, then use CPCTC.
Because HJ is the perpendicular bisector of GI, GJ ≅ IJ. this will be under Definition of Perpendicular Bisectors because it's a line which cuts a line segment into two equal parts at 90°.
This also means that ∠GJI and ∠IJH are right angles under Definition of Perpendicular Bisectors. Do not combine the two statements.
To clarify everything, ∠GJI ≅ ∠IJH because "all right angles are congruent."
It's also clear that these two triangles share a side, so HJ ≅ HJ. This is the Reflexive Property of Congruence, stating that for any real number a, a ≅ a.
Now you can prove these two triangles congruent by the SAS Postulate.
Using CPCTC, corresponding parts of congruent triangles are congruent, GH ≅ HI.
Your last statement should be ΔGHI is an isosceles because of Definition of Isosceles Triangle. You also want to state the statement exactly as given as the question.
Your proof should look something like IMAGE.A.
Paul will select a random sample of students to create a 95 percent confidence interval to estimate the proportion of students at his college who have a tattoo. Of the following, which is the smallest sample size that will result in a margin of error of no more than 5 percentage points?
Answer:
385
Step-by-step explanation:
Given that:
Margin of Error (MOE) = 5% = 0.05
Zcritical, 95% = Z(1-α/2) = Z0.025 = 1.96
MOE = Zcritical * (√p(1-p))/n)
p is taken as 0.5 when not stated ;
5 = 1.96 * sqrt[(0.5 * 0.5) / n]
5 = 1.96 * sqrt(0.25/n)
Square both sides
(0.05/ 1.96)² = 0.25/n
0.0006507 = 0.25/n
0.0006507 * n = 0.25
n = 0.25 / 0.0006507
n = 384.20162
Sample size = 385
Kelly bought 3 pounds of chicken for 6.99 per pound 20 pounds of dog food 1.95 Per pound prices include the sales tax Kelly gave the cashier $60 how much change should Kelly receive
Answer: 3 cents
Step-by-step explanation: multiply the price per pound by the amount of pounds purchased for both items and add them together. Then take the amount paid and subtract the total from what was paid to get the change.
Suppose that there were 226977 visitors to your website over a period of a week, and of those 56330 clicked on the button to get more information about your product. If you wanted to model the probability distribution of the number of visitors who clicked the button, you would typically estimate the mean of the distribution to be equal to the observed number of visitors who clicked, that is the sample mean: 56330.
Required:
Under this setup, what is the variance of this distribution?
Answer:
The variance of this distribution is 42353.2
Step-by-step explanation:
For each visitor, there are only two possible outcomes. Either they clicked on the button, or they did not. Visitors are independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The variance of the binomial distribution is:
[tex]V(X) = np(1-p)[/tex]
In this question:
226977 visitors, so [tex]n = 226977[/tex]
56330 clicked, so [tex]p = \frac{56330}{226977} = 0.2482[/tex]
Then
[tex]V(X) = 226977*0.2482*(1 - 0.2482) = 42353.2[/tex]
The variance of this distribution is 42353.2
help please i have the answer on picture
Answer:
4/24
Step-by-step explanation:
[tex]\frac{1}{6} = \frac{1*4}{6*4}=\frac{4}{24}[/tex]
Tori earned $62.86 as a bonus from her job. She decided to buy as many CDs as possible since they were on sale for $8.80 each. Estimate how many CDs Tori can buy.
Answer:
approximately 7 CDs for her bonus
Answer:
Toris can buy about 7 CDs
Step-by-step explanation:
63 Divided by 9 = 7
What is the domain of the function y= Vx?
-00
O 0
O 0x<00
O 1
The domain of the function is 0 ≤ x ≤ ∞.
Option 3 is correct
What is Domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.
As per the given data:
The function is y = √x
Square root is not defined to for negative values. For negative values, the answer of square root is a complex number which is not in real domain.
So any such values, for which the expression is not defined, are not in the domain. So the domain of the square root of x will be all real numbers greater than or equal to 0.
Hence, the domain of the function is 0 ≤ x ≤ ∞
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[tex] \sqrt{361} [/tex]
Answer:
19
Step-by-step explanation:
Answer:
19
Step by step explanation:
Find the area of the figures below, composed of a rectangle and a semicircle. The radius of the circle is shown. Round to the nearest tenth place
Answer:
50.3 square units
Step-by-step explanation:
area of rectangle: 11 x twice the radius
radius = 2
A(rect): = 11(4) = 44 sq units
A (semi-circle) = (π·r²) / 2
A = 4π / 2 = 2π = 6.28 sq units
44.0 + 6.28 = 50.28
You move right 1 unit. You end at (2, -1). Where did you start?
Answer:
(1, -1)
Step-by-step explanation:
If you end up at (2, -1), after moving 1 unit to the right, that implies that you started at (1, -1). Note that 1 + 1 = 2.
Answer:
(1,-1)
Step-by-step explanation:
Because as it said go across 1 to the right , just go back 1 to the left so you are at were you started
someone help please !
9514 1404 393
Answer:
no, the triangles are not similar
Step-by-step explanation:
The given ratios tell you corresponding side ratios are ...
ED : DC : EC = 8 : 10 : 12 = 4 : 5 : 6
AB : BC : AC = 12 : 15 : 21 = 4 : 5 : 7
Corresponding sides do not have the same ratios. The given information can be used to prove the triangles are NOT similar.
A veterinarian uses a specific formula to calculate the dosage of an antibiotic given to dogs with bacterial infections. For each 10 pounds of a dog's weight, she treats the dog with 50 mg of antibiotic per dose. Which of the following graphs describes the relationship between a dog's weight and the antibiotic dosage used to treat it?
Answer:
The first graph.
Step-by-step explanation:
Just took the test, got it right. Every increase of ten pounds is an increase in 50 mg of treatment, and it should start at 0.
The best option is first graph. The graph clearly shows the relationship between a dog's weight and the antibiotic dosage used to treat the dog.
What is graph?A graph is "diagrammatic or pictorial representation of the collection of data in organized manner."
According to the question,
A veterinarian uses a specific formula to calculate the dosage of an antibiotic given to dogs with bacterial infections. For each 10 pounds of a dog's weight, she treats the dog with 50mg of antibiotic per dose.
The horizontal line in the graph represents the dog's weight in (l b) and the vertical line in the graph represents the amount of dosage is used for treatment for bacterial infection of the dog.
Every increase of ten pounds is an increase in 50 mg dosage of treatment, and it should start at 0 in the graph.
Hence, the best option is first graph. The graph clearly shows the relationship between a dog's weight and the antibiotic dosage used to treat the dog.
Learn more about graph here
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Find the surface area of the rectangular prism.
4 mi
5 mi
4 mi
Answer:
112
Step-by-step explanation:
A = 2 (wl+hl+hw)
A = 2 (4 x 5 + 4 x 5 + 4 x 4)
A = 2 (20 + 20 + 16)
A = 2 x 56
A = 112
Write the phrase as an expression.
28 divided by 7
An expression is
Just to let you guys know the answer is not 28/2 because someone already got it wrong.
Answer:
28 divided by 7 is 4
Step-by-step explanation:
example: There 28 cupcakes if there are 7 people how many will each get? Ok so you have 28 groups of 7 and then you'll get your answer which is 4.
The mathematical expression for the phrase 28 divided by 7 is 28 ÷ 7 and the value of the expression is 4.
What is division?It is the basic arithmetic operation, in which you are separating the number into some parts. One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.
Given:
28 divided by 7,
The mathematical expression for the above statement can be written as shown below,
28 ÷ 7
Calculate the value of the expression as shown below,
28 ÷ 7 = 4
Thus, the expression is 28 ÷ 7.
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1a. Alex skateboards at a constant speed from his house to school 4 miles away. It takes him 15 minutes. What fraction represents his constant speed, C?
The following data give the estimated prices of a 6-ounce can or a 7.06-ounce pouch of water-packed tuna for 14 different brands, based on prices paid nationally in supermarkets are reproduced here.
0.99 1.92 1.23 0.85 0.65 0.53 1.41
1.12 0.63 0.67 0.69 0.60 0.60 0.66
a. Find the range.
b. Find the sample variance.
c. Find the sample standard deviation.
Answer:
a) Range = 1.39
b) the sample variance is 0.1597
c) the sample standard deviation is 0.3996
Step-by-step explanation:
Given the data in the question;
a) Find the range.
To determine the range, we simple subtract the smallest value from the largest value. i.e
Range = largest value - smallest value
from data set; our smallest is 0.53 while our largest value is 1.92
so
Range = 1.92 - 0.53 = 1.39
b) Find the sample variance.
To determine our variance, we use the following formula;
∑([tex]X_{i}[/tex] - [tex]x_{bar}[/tex])² / n - 1 = [ ∑[tex]X_{i}[/tex]²/n-1 ] - [ [tex]\frac{n}{n-1}[/tex]([tex]x_{bar}[/tex])²]
where [tex]x_{bar}[/tex] = ∑[tex]X_{i}[/tex]/n
n is sample size = 14 so lets calculate ∑[tex]X_{i}[/tex]
∑[tex]X_{i}[/tex] = 0.99 + 1.92 + 1.23 + 0.85 + 0.65 + 0.53 + 1.41 + 1.12 + 0.63 + 0.67 + 0.69 + 0.60 + 0.60 + 0.66
∑[tex]X_{i}[/tex] = 12.55
∑[tex]X_{i}[/tex]² = 0.99² + 1.92² + 1.23² + 0.85² + 0.65² + 0.53² + 1.41² + 1.12² + 0.63² + 0.67² + 0.69² + 0.60² + 0.60² + 0.66²
∑[tex]X_{i}[/tex]² = 13.3253
so
our [tex]x_{bar}[/tex] = ∑[tex]X_{i}[/tex]/n = 12.55 / 14 = 0.8964
so our Variance will be;
= [ ∑[tex]X_{i}[/tex]²/n-1 ] - [ [tex]\frac{n}{n-1}[/tex]([tex]x_{bar}[/tex])²]
= [ 13.3253 / 14-1 ] - [ [tex]\frac{14}{14-1}[/tex] (0.8964)²]
= 1.025 - 0.8653
= 0.1597
Therefore, the sample variance is 0.1597
c) Find the sample standard deviation.
we know that standard deviation is the square root of variance;
standard deviation = √Variance
standard deviation = √0.1597
standard deviation = 0.3996
Therefore, the sample standard deviation is 0.3996
Solve for the value of x and y if ADCB - NOPM.
I need that please
Answer:
can we see the picture?
If 3/10 = 30/100, then 4/10 = ___/100
Answer:
40/100
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
If 3/10 = 30/100, then 4/10 = 40/100
If ∆HBN~∆LYR, find the value of x.
Answer:
x=6
Step-by-step explanation:
32-21 = 11
28-11 = 17
17-11 = 6
x=6
A school’s math department has money to spend on calculators. It uses the equation y = 1,000 – 80x to determine how much money is left in the account to spend on calculators, where x represents the number of calculators purchased. What is the meaning of the slope of the equation?
A. Each calculator costs $1,000.
B. The account had $1,000 before buying calculators.
C. Each calculator costs $80.
D. The account had $80 before buying calculators.
Answer:
C. Each calculator costs $80.
Step-by-step explanation:
Linear equation:
Has the following format:
[tex]y = mx + b[/tex]
In which m is the slope, and the meaning is how much the output changes when the input changes by 1 unit.
In this question:
Amount remaining after buying x calculators:
[tex]y = 1000 - 80x[/tex]
So the slope of -80 means that each calculator costs $80, since after buying a calculator, 80 is retired from the amount.
The answer is given by option C.
What percent of 75 is 21?
48 - 2C = 88 solve for C
Answer:
c = -20
Step-by-step explanation:
Isolate the variable, c. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operation, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
First, subtract 48 from both sides of the equation:
-2c + 48 = 88
-2c + 48 (-48) = 88 (-48)
-2c = 88 - 48
-2c = 40
Next, divide -2 from both sides of the equation:
(-2c)/-2 = (40)/-2
c = 40/(-2) = -20
c = -20 is your answer.
~
Using the rational root theorem, identify all the possible rational roots of the equation x^4+25x^3-14x^2-19x+30
Answer: D on Edg
Step-by-step explanation:
Mr. Gary wrote the sequence below on the board.
10,5, 0, -5, -10
Drag and drop an answer choice into each empty box below.
0 5 10
+
Drag and drop items from the box above to accurately complete the
statement below.
Identify the value of aj and complete the recursive rule for Mr. Gary's
sequence.
ai =
an = an-1
Answer:
this could be wrong but for this question i put 10 as the first blank and for the second blank i put - and then for the third i put 5
Step-by-step explanation:
Im not sure on this. I have the same fsq and we haven't learned this yet but this is what I put because the sequence is subtracting 5
Answer:
Step-by-step explanation:
the answers is 75,000,000
Which line , or solid , is the best line of best fit ? What evidence can you provide to prove this is the best line of best fit ?
Combine like terms.
Please help me.
Answer:
15y^2-45
Step-by-step explanation:
5y^2+10y^2-45 = 15y^2-45
a scientist recorded the temperature of the first day of spring for 24 hours starting from Midnight their hours the scientist recorded a low of 44°f and a high of 67°f.
Answer:
so what is the question?
Help with substitution show work please!!!!!!!
Answer: x=4, y=-2
Step-by-step explanation: 4x+y=14, x-2y=8
4x+y-y=14-y
4x/4=14/4-y/4
x=14-y/4-(2y)(4)/4
4(14-9y)/4=(8)(4)
14-9y-14=32-14
-9y/-9=18/-9
y=-2
(14)-(-2)/4
14+2/4
16/4
4
x=4
x=4, y=-2
Answer:
Solution of given system of equations is: x=4, y=-2 or (4,-2)
Step-by-step explanation:
Solve the equation using substitution
4x+y=14
x-2y=8
Substitution method involves placing value of x or y from one equation to other equation.
We have
[tex]4x+y=14--eq(1)\\x-2y=8--eq(2)\\[/tex]
Finding value of x from equation 2
x-2y=8
x=2y+8
Put this value of x in equation 1
[tex]4x+y=14Put\:x=2y+8\\4(2y+8)+y=14\\8y+32+y=14\\9y=14-32\\9y=-18\\y=\frac{-18}{9}\\y=-2[/tex]
We get y=-2
Now, put value of y into equation 2 to find value of x
[tex]x-2y=8\\x-2(-2)=8\\x+4=8\\x=8-4\\x=4[/tex]
We get x = 4
So, solution of given system of equations is: x=4, y=-2 or (4,-2)
Many grocery store chains offer customers a card they can scan when they check out and offer discounts to people who do so. To get the​ card, customers must give​ information, including a mailing address and​ e-mail address. The actual purpose is not to reward loyal customers but to gather data.
Required:
What data do these cards allow stores to​ gather, and why would they want that​ data?
Answer:
1. The data that these cards allow stores to gather are customer data.
2. The stores want the data to enable them understand the customer, their buying goals, customer preferences, and spending patterns. These data enable the stores to stock their stores to meet customers needs. They also use the data to understand the individual customers credit history and buying habits.
Step-by-step explanation:
Customer data are essential assets which businesses use to understand their customers. They obtain the data through firsthand responses from customers, through investigation, or by asking direct questions. Many organizations use loyalty cards to help them gather customer data, such as individual preferences and spending patterns.