In a survey of 2500 registered voters, 1900 of them said that they plan to vote in the next presidential election. Let p denote the proportion of all registered voters who plan to vote. Find the 95% confidence interval for p.

1. Number of athletes did not own any of the three items = 259 - 228

= 31.

2. Number of athletes own a convertible and a TV but not a store = 44 - 9

= 35.

3. Number of athletes own a convertible or a TV = 110 + 91 - 44

= 157.

4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

5. Number of athletes owned at least one type of item = 259 - 31

= 228

6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71

= 118.

The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.

Total number of athletes surveyed = 259

Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228

Number of athletes who did not own any of the three items = 259 - 228 = 31.

The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.

Number of athletes who own a convertible and a TV = 44

Number of athletes who own all three items = 9

Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35

The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.

Number of athletes who own a convertible or a TV = 110 + 91 - 44

= 157.

The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.

Number of athletes own a convertible only = 110 - 15 - 9 = 86

Number of athletes own a TV only = 91 - 44 - 9 = 38

Number of athletes own a store only = 120 - 15 - 43 - 9 = 53

Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

The number of athletes who owned at least one type of item can use the result from part (1).

Number of athletes who owned at least one type of item = 259 - 31

= 228

The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.

Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159

Number of athletes own a TV or a store not a convertible = 13 + 34 +71

= 118.

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Answer:

11.3 cm

Step-by-step explanation:

The diagonal of the cylinder can be calculated using Pythagorean Theorem as follows:

Height of the cylinder = 8 cm

Diameter = 8 cm

Diagonal = hypotenuse = x

Thus:

8² + 8² = x²

64 + 64 = x²

128 = x²

x = √128

x = 11.3 cm

The range of the function f(x)= IxI+5 is x+5 for x>=0 and -x+5 for x<0.

Given that the function is f(x)=IxI+5.

We are required to find the range of the function.

Function is relationship between two or more variables expressed in equal to form. In a function each value of x must have a corresponding value of y. The value of x is known as domain of the function and the value of y is known as codomain of the function. Range of a function is a limit of values in which the values of function lies.

Function is f(x)= IxI+5

We know that IxI=x for x>=0 and -x<0.

We have to just put the value of IxI in f(x) to get the range of function.

f(x)=x+5 for x>=0 and -x+5 for x<0.

Hence the range of the function f(x)= IxI+5 is x+5 for x>=0 and -x+5 for x<0.

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Answer: 160

Step-by-step explanation:

40/\(\frac{1}{4}\) is the same as 40× 4 which makes it 160

Jorge's percent of markup based on the selling price is 34.78%.

The Percent markup based on Selling Price is calculating using the formula

Percent Markup = ( Markup/Selling Price )*100

In the given question

The Selling Price of chair = $230

Markup = $80

Substituting the values of Selling price and Markup in the Percent markup formula,

We get ,

Percent Markup = (80/230) * 100

=0.3478

=34.78

Therefore , the percent markup based on the selling price is 34.78%.

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a) Range is 24 , b) MAD is 8.88 , c) Variance is 126.60 , d) Standard deviation is 11.25.

a. The range is the difference between the largest and smallest values in the data set. The largest value is 50 and the smallest value is 26, so the range is:

50 - 26 = 24

b. MAD stands for Mean Absolute Deviation, which is the average of the absolute differences between each value in the data set and the mean of the data set. To calculate the MAD, first we need to find the mean:

Mean = (40 + 48 + 26 + 50 + 38 + 46) / 6 = 39.67

Next, we find the absolute difference between each value and the mean, and then take the average of those absolute differences:

|40 - 39.67| = 0.67

|48 - 39.67| = 8.33

|26 - 39.67| = 13.67

|50 - 39.67| = 10.33

|38 - 39.67| = 1.67

|46 - 39.67| = 6.33

Average of absolute differences = (0.67 + 8.33 + 13.67 + 10.33 + 1.67 + 6.33) / 6 = 6.89

So the MAD is 6.89.

c. The sample variance measures how spread out the data is by calculating the average of the squared differences between each value in the data set and the mean of the data set. To calculate the sample variance, first we need to find the mean (which we already calculated in part b):

Mean = 39.67

Next, we find the squared difference between each value and the mean, and then take the average of those squared differences:

\((40 - 39.67)^2 = 0.1089\)

\((48 - 39.67)^2 = 75.0089\)

\((26 - 39.67)^2 = 187.4889\)

\((50 - 39.67)^2 = 108.0089\)

\((38 - 39.67)^2 = 2.7889\)

\((46 - 39.67)^2 = 39.3489\)

Average of squared differences = (0.1089 + 75.0089 + 187.4889 + 108.0089 + 2.7889 + 39.3489) / 6 = 66.2567

So the sample variance is 66.26.

d. The sample standard deviation is the square root of the sample variance. So the sample standard deviation is:

\(\sqrt{(66.26)} = 8.13\)  (rounded to 2 decimal places)

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4. x= 40

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you .

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Answer:

the answer is 48/100 im pretty sure .

Step-by-step explanation:

Answer:

12/25

Step-by-step explanation:

first you take your decimal and because it is a decmial the decimal is in a fraction, 48/100 don't pay attention to any 0's behind any other number.

once you have 48/100 divide the numerator(the top of the fraction) and the denominator(the bottom of the fraction) and divide it by 4

Answer: infinitely many

Answer:

a) 360 mice

b) 364 mice

Step-by-step explanation:

Assume :

A = number of infected mice , B = number of non-infected mice

P( infected mice overcoming infection ) = 70% = 0.7

P ( Infected mice not overcoming infection ) = 1 - 0.7 = 0.3

P( mice becoming infected ) = 40% = 0.4

P ( mice not becoming infected ) = 1 - 0.4 = 0.6

Number of infected mice = 400

Number of non-infected mice = 1000 - 400 = 600

step 1 ; express the probabilities in matrix form

\(P = \left[\begin{array}{ccc}0.3&0.4&\\0.7&0.6&\\\end{array}\right]\)

\(X = \left[\begin{array}{ccc}400\\600\\\end{array}\right]\)

step 2 : multiply the matrix above to determine the number of mice that will be infected

a) For next week

PX = \(\left[\begin{array}{ccc}360\\640\\\end{array}\right]\)

i.e. 360 mice will get infected next week

next 2 week = P ( PX )

= \(\left[\begin{array}{ccc}0.3&0.4&\\0.7&0.6&\\\end{array}\right]\)  * \(\left[\begin{array}{ccc}360\\640\\\end{array}\right]\)  = \(\left[\begin{array}{ccc}364\\636\\\end{array}\right]\)

b) In 3 weeks time

P ( P(PX) = \(\left[\begin{array}{ccc}0.3&0.4&\\0.7&0.6&\\\end{array}\right]\)  * \(\left[\begin{array}{ccc}364\\636\\\end{array}\right]\)  

               = \(\left[\begin{array}{ccc}363.6\\636.4\\\end{array}\right]\)

i.e.  364 mice will get infected in 3 weeks time

Answer:

Kate's age now is 30 years old and Jan's age now is 10 years old.

Step-by-step explanation:

Kate age now is 3x

Jan age now is x

3x-6=6*(x-6)

3x-6=6x-36

-3x    -3x

-6=3x-36

+36      +36

30=3x

10=x

x=10

3x=30

Kate's age now is 30 years old and Jan's age now is 10 years old.

A quadratic function has a extreme point which is called vertex.

This point correspond to the maximum or the minimum value of the function depending on the sign of the quadratic coefficient.

In physics many representations of movement of objects are represented with quadratic equations, like a projectile trajectory. In those cases, the vertex may represents the maximum height.

When representing the mechanical energy of a particule with a quadratic function, the verex can represent the equilibrium point as it corresponds to a minimum.

In business, it depends on what variable we are representing with that function. Whatever the function represents, the vertex will represent a maximum or a minimum for that variable.

Step-by-step explanation:

To calculate the required monthly payment to accumulate $32,000 in 10 years at an APR of 7.9% compounded monthly for an annuity, we can use the formula for the present value of an annuity due:

PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)

where:

- PV is the present value of the annuity due ($32,000)

- PMT is the monthly payment we want to find

- r is the annual interest rate (7.9%)

- n is the number of times interest is compounded per year (12 for monthly compounding)

- t is the number of years (10)

PMT = PV / ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n) = **$292.07**

Therefore, the required monthly payment to accumulate $32,000 in 10 years at an APR of 7.9% compounded monthly for an annuity is **$292.07**.

Answer:

The new expression is:  12 x^2 - 12 x+ 30

Step-by-step explanation:

if C = x^2 + 7

and

D = 3 x^2 - 4 x + 3

Then, 3 C + 3 D can be obtained via:

3 ( x^2 + 7 ) + 3 ( 3 x^2 - 4 x + 3 )  = 3 x^2 + 21 + 9 x^2 - 12 x + 9 =

= 12 x^2 - 12 x+ 30

Answer:

x=0.4

Step-by-step explanation:

isolate the variable by dividing each side by factors that don't contain the variable

Answer:

Local minimum at x = 0.

Step-by-step explanation:

Local minimums occur when g'(x) = 0 and g"(x) > 0.

Local maximums occur when g'(x) = 0 and g"(x) < 0.

Set g'(x) equal to 0 and solve:

0 = 2x (x − 1)² (x + 1)²

x = 0, 1, or -1

Evaluate g"(x) at each point:

g"(0) = 2

g"(1) = 0

g"(-1) = 0

There is a local minimum at x = 0.

Answer:

Local minimums occur when g'(x) = 0 and g"(x) > 0.

Local maximums occur when g'(x) = 0 and g"(x) < 0.

Set g'(x) equal to 0 and solve:

0 = 2x (x − 1)² (x + 1)²

x = 0, 1, or -1

Evaluate g"(x) at each point:

g"(0) = 2

g"(1) = 0

g"(-1) = 0

There is a local minimum at x = 0.

Answer:

P = 16

Step-by-step explanation:

Given

5W = 2P + 3R ← substitute W = 4 and R = - 4 into the equation

5(4) = 2P + 3(- 4), that is

20 = 2P - 12 ( add 12 to both sides )

32 = 2P ( divide both sides by 2 )

16 = P

Answer:15

Step-by-step explanation:

The sum of the geometric sequence in this problem is given as follows:

5.77.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number, which is called the common ratio q.

The first term, the common ratio and the number of terms for this problem are given as follows:

\(a_1 = 10, q = -\frac{2}{3}, k = 8\)

The formula for the sum of the first n terms is given as follows:

\(S_n = a_1\frac{1 - r^n}{1 - r}\)

Hence the sum for this problem is given as follows:

\(S_8 = 10 \times \frac{1 - \left(-\frac{2}{3}\right)^8}{1 + \frac{2}{3}}\)

\(S_8 = 5.77\)

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Answer:

1.41

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

36% of 15120 =

36% * 15120 = 36/100 * 15120 = 36 *

false 36% of 15120 is 544.32

g(x) = -2√x + 8 is the function that has the same range as f(x) = -2√(x - 3) + 8. Both functions have the range of y ≤ 8

The function that has the same range as f(x) = -2√(x - 3) + 8 is g(x) = -2√x + 8. Both functions have the range of y ≤ 8.There are a few steps involved in determining which function has the same range as f(x) = -2√(x - 3) + 8. The range of a function refers to all the possible output values that the function can produce.Let's begin by examining the original function:f(x) = -2√(x - 3) + 8The square root symbol (√) implies that x-3 must be greater than or equal to 0. If x-3 is negative, then the function would produce an imaginary result.

Let's solve for x when f(x) = 0:0 = -2√(x - 3) + 8-8 = -2√(x - 3)4 = √(x - 3)16 = x - 3x = 19This tells us that the x-value that produces an output of 0 is x = 19. To determine the range, we need to find the maximum and minimum output values. We can use a graphing calculator or sketch a graph to determine the shape of the function and the range.The shape of the function suggests that the range is y ≤ 8, which means that the maximum value of the function is 8. This tells us that any function with the same maximum output value of 8 will have the same range as f(x).

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Answer:

Step-by-step explanation:

The first two questions are answered here

Use the equation for exterior angle

Exterior angle  = sum of non-adjacent interior angles

Answer:

x = 26° degrees the work bellow is correct i double checked it :)

Step-by-step explanation:

Answer:

The price of the shirt is $24.63.

Step-by-step explanation:

Let's assume the price of the shirt is x. Then the price of the wallet will be x - 15. We know that the total cost before tax is 34.26, so we can set up the equation:

x + (x - 15) = 34.26

Simplifying, we get:

2x - 15 = 34.26

Adding 15 on both sides:

2x = 49.26

Dividing by 2:

x = 24.63

Therefore, the price of the shirt is $24.63.

Answer:

x = 2, -1

Step-by-step explanation:

Move all terms to the left side and set equal to zero Then set each factor equal to zero

If this is the graph of f(x) = b^x-h + k, then the two statements that are true include:

4.The range of the function is (-∞, k).

8.The domain of the function is (-∞, h).

All of the statements that apply to this graph include the following:

1. h < 0

4. k > 0

In Mathematics, the x-intercept can be defined as the point at which the graph of an exponential function crosses the x-coordinate and the value of "y" is equal to zero (0).

This ultimately implies that, the x-intercept of the exponential function shown in the graph above is given by x < 0 or h < 0.

In Mathematics, a horizontal asymptote simply refers to a horizontal line (y = b) where the graph of a function approaches the line as the input values approach negative infinity (-∞) to positive infinity (∞). Therefore, the horizontal asymptote is given by y > 0 or h > 0.

Based on the graph, we can logically deduce that f(x) decreases as the x-value increases, therefore, we have: 0 < b < 1.

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The money Jena will have after buying a set of markers in algebra expression is y = 15 - x.

Arithmetic operations like subtraction, addition, division, multiplication, and exponentiation are used to combine variables and integers to produce any algebraic expression. A variable, a number, or a variable and number with an exponent as a product can all be used as the phrase.

Cost is the amount of money spent by a business to produce or create goods or services.

The cost of one set of markers is x dollars.

Now Jen has a total of $15.

Then, the amount of money "y" Jena will have after buying one set of markers will be:

y = 15 - x

Hence, the algebraic expression after buying one set of markers is y = 15 - x.

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The image coordinates of NMO after the translation is option d: N′(−5, −6), M′(−2, −5), and O′(−3, −7).

To get the image coordinates of the preimage translated -2 units to the left, we simply subtract -2  from the y-coordinates of each vertex:

N' = (Nx - (-2), Ny) = (−5 , 2- (-2)) = (−5, 4)

M' = (Mx - (-2), My) = (−2 , 1 - (-2)) = (−2, 3)

O' = (Ox - (-2), Oy) = (−3 , 3- (-2)) = (−3, 5)

Therefore, based on the above, the image coordinates of NMO after the translation are N′(−5, 4), M′(-2,3 ), O′(−3, 5)

So the reflected vertices are:

The distance from N to the line y = -2 is 4, and -6 - (-2) = -4, so one need to move down 4 units to have  a y-coordinate of -6.

The distance from M to the line y = -2 is 3, and -5 - (-2) = -3, so  one need to move down 3 units to have a y-coordinate of -5.

The distance from O to the line y = -2 is 5, and -7 - (-2) = -5, so  one need to move down 5 units to have  a y-coordinate of -7.

So it will be: N′ (−5, −6), M′(−2, −5), O′(−3, −7)

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Answer:

---------------------

Given triangle MNO with vertices:

It is reflected in line y = - 2.

This reflection doesn't affect the x-coordinates of the vertices and the y-coordinates change.

Since y = - 2 is the line of symmetry,  it also represents midpoints of the segments formed by corresponding endpoints of image and preimage.

Using midpoint equation, find the y-coordinates.

So the coordinates of the image are:

This is matching the option D.

See attached for visual representation of the problem.

Answer:

3. -3,0,|3|, (-3)^2

Step-by-step explanation:

Answer:

answer would be option 3

Step-by-step explanation:

help this helps