A certain association provided data on the cost of the most popular home remodeling projects. Sample data on the cost in thousands of dollars for two types of remodeling projects are as follows.
Kitchen Master Bedroom
25.2 18.0 16.4 22.9 21.8 26.4 20.9 24.8 18.7 26.9 22.0 17.8 19.7 24.6 15.9 21.0 21.8 22.6
(a) Develop a point estimate of the difference in thousands of dollars) between the population mean remodeling costs for the two types of projects. (Use Kitchen - Master Bedroom.) thousand (b) Develop a 90% confidence interval for the difference in thousands of dollars) between the two population means. (Use Kitchen - Master Bedroom. Round your answers to one decimal place.)

The length of the hypotenuse with legs 8 units and 6 units is 10 units and with leg 8 units and 15 units is 17 units. We calculate the length of a leg of the right triangle by using formula    [tex]h ^ {2} = p ^ {2} + b ^{2}[/tex]

If one of the angles in a triangle is 90 degrees, the triangle is said to have a right angle. The term "right angle" refers to angles in right triangles that are 90 degrees. The side opposite in a 90° angle is the hypotenuse. The hypotenuse is always the longest side. The sum of the other two inner angles is 90 degrees.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

length of legs = 8 units and 6 units

hypotenuse = [tex]\sqrt {8 ^ {2}+6 ^ {2}}[/tex] = 10 units

length of legs = 8 units and 15 units

hypotenuse = [tex]\sqrt {8 ^ {2}+15 ^ {2}}[/tex] = 17 units

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The required amount for phone and computer sales is $1100 and $600 respectively.

Given that,
Houa works at an electronics store as a salesperson. Houa earns a 9% commission on the total dollar amount of all phone sales she makes and earns a 6% commission on all computer sales. Houa made a total of $1700 in sales and earned $135 in commission.

What are simultaneous linear equations?

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

here,
Let the number of phone sales be x and the number of computer sales be y,
According to the question,
0.09x+0.06y=135, - - - - - (1}
x+y=1700 - - - - - - - (2)
Solving equation 1 and 2
Gives, x = $1100 and $600

Thus, the required amount for phone and computer sales is $1100 and $600 respectively.

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Answer:

The correct answer is (1, -3).

Step-by-step explanation:

To solve this question, we should use substitution. This means we can substitute the value given for y (as indicated by the second equation) into the first equation. This is shown below:

4x + y = 1

4x + (x - 4) = 1

We simplify the left side of the equation and then solve for x.

5x - 4 = 1

5x = 5

x = 1

We must also solve for y. To do this, we can plug in x = 1 into either of the given equations.

y = x - 4

y = 1 - 4

y = -3

Therefore, x = 1 and y = -3. The question asks us to express the answer as an ordered pair (x,y), so the answer is (1, -3).

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The difference between the numbers 4.7 and 2.3 is 2.4

what is number line ?

The visual representation of numbers on a straight line is called a number line. On an endless line that extends on both sides, either horizontally or vertically, this line is used to compare numbers that are spaced at equal intervals. The numbers on a horizontal number line grow as we approach towards the right side and drop as we move towards the left.

Between 4 and 5 , there are 10 divisions. Each division shows the value 0.1.

So, 4.7 is marked as shown in the figure.

To find the difference 4.7 - 2.3 , reverse the direction by 2.3 units from 4.7, will give us 2.4..

So, the difference between 4.7 and 2.3 is 2.4

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The real zeros in the given equation y = (x-12)³ - 7 will be x =  13.912.

For the real solutions, we know that a real zero is a real number which makes the value of the function zero. By the question, let

y = 0  ..........(1)

Put values of 'y' in equation (1), and we get.

(x-12)³ - 7 = 0         .........(2)
Adding '7' on both sides of equation (2), we get

(x-12)³ = 7
Taking the cube root on sides, the resulting equation will be:

[tex]\sqrt[3]{(x-12)^{3} }[/tex]  =  [tex]\sqrt[3]{7}[/tex]
x - 12 = 1.912
By adding '12' on both sides.
x =  13.912

So the only real zeros for the given equation will be 13.912. Other solutions are imaginary zeros.

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The subtended arc is 2.14 times as long as the circle's radius.

What is radius of circle?

A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary usage, it also refers to the length of those line segments. The word "radius" is derived from Latin and means "ray" as well as "the spoke of a chariot wheel."

Given:

A circle with a radius 7 cm long is centered at an angle's vertex, and the angle's rays subtend an arc length of 15 cm along the circle.  

The radius of the circle is 7 and length of the subtend are is 15 cm. The required value is given by:

Subtended arc / Radius = 15 / 7 = 2.14

Therefore, option (e) is the correct answer.

Hence, the subtended arc is 2.14 times as long as the circle's radius.

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Answer:

Write in Standard Form

1. The standard form of a linear equation is

Ax + By = Cx-y=-1

2. x = 16

Ig?

I'm not sure.

The balance of Carlos account after this period, using simple interest, is of:

$2,339,488.08.

This is a simple interest problem, hence the balance of the account can be obtained using an exponential function, defined as follows:

[tex]B(n) = B(0)(1 + r)^n[/tex]

In which the parameters of the exponential function are defined as follows:

In the context of this problem, the values of these parameters are given as follows:

B(0) = 1500000, r = 0.025, n = 18, as one and a half year = 18 months.

Then the balance of Carlos account is obtained as follows:

B(18) = 1500000(1.025)^18 = $2,339,488.08

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ANSWER

c

It is c because i did the work and  i know.

The shape of the sampling distribution of the mean for samples of size 45 will be normal.

This is because the sampling distribution of the mean approaches normality as the sample size increases. The center of the sampling distribution will be 67 inches, which is the mean height of the population. The spread of the sampling distribution will be determined by the standard deviation of the population and the sample size. Specifically, the standard deviation of the sampling distribution will be equal to the standard deviation of the population divided by the square root of the sample size. In this case, the standard deviation of the sampling distribution will be 3.8 inches / sqrt(45) = 0.55 inches.

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There would be a 68% chance that the average blood pressure would be between 193 to 197.

The subset chosen from the larger set to make assumptions is known as a random sample. A range of values is a confidence interval.

We know that,

                       E   =   z ( α / 2 )  ×  σ / √n          →  1

As per the given question,

For 68% confidence,

                                z ( α / 2 )   =   0.9944

Substitute the values in 1,

E   =   z ( α / 2 )  ×  σ / √n

     =   0.9944  ×  20 / √100

     =   0.9944  ×  20 / 10

     =   0.9944  ×  2

E    =   1.9888   ≅   1.99

Let us consider,

⇒   x  -  E     <     μ     <     x  +  E

⇒   195  -  1.99     <     μ     <     195  +  1.99

⇒   193.01     <     μ     <     196.99

⇒   193     <     μ     <     197          ( ∵  193.01 ≅ 193 and 196.99 ≅ 197 )

⇒   μ   =   ( 193 , 197 )

Therefore, A 68% chance that the average blood pressure lies between 193 to 197. Hence Option b is correct.

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The complete question is

Blood pressure in a population of very at risk people has an expected value of 195 and a standard deviation of 20. Suppose you take a random sample of 100 of these people. There would be a 68% chance that the average blood pressure would be between Select one:

a.) 155 to 235

b.) 193 to 197

c.) 175 to 215

d.) 191 to 199

e.) 200 to 230

The values of x in the triangles are (a) 15 and (b) 4

From the question, we have the following parameters that can be used in our computation:

Triangle 1 and Triangle 2

Solving triangle 1

In this triangle, we can see that the side lengths of the triangles are congruent

This means that the triangles is an equilateral triangle

The individual angles in an equilateral triangle are 60 degrees

So, we have the following representation

4x = 60

Divide both sides of the equation by 4

x = 15

So, the value of x is 15

Solving triangle 2

In this triangle, we can see that the length KM of the triangle divides the length JL into congruent parts

This means that the JM and LM are congruent

So, we have the following representation

x + 1 = 5

Subtract from both sides of the equation by 1

x = 4

So, the value of x is 4

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On solving the provided question, we got to know that - recursive function to model the geometric sequence is 0.25

In order to create a sequence of terms, a recursive function either repeats itself or uses a previous term to compute a new term. An arithmetic-geometric series with terms that differ from each other frequently is used to explain this function.

Given, geometric sequence

24, 6, 1.5

First term of this sequence = 6

a1 = 6

Recursive formula geometric sequence

[tex]a_{n} = a_{(n-1)}r[/tex]

[tex]Here r = common. ratio .of .successive. and previous term\\From .the given .sequence\\[/tex]

r = a2/a1

r = 6/24

r = 0.25

[tex]Recursive formula of the given sequence will be,[/tex]

[tex]a_{n} = a_{(n-1)}(0.25)[/tex]

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The required slope-intercept form of the equation of the line is y = x/4 + 3.

To determine the equation of the line in slope-intercept form passing through the points (4, 4) and (0, 3).

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

here,

m = (y₂ - y₁) /  (x₂ - x₁)

Substitute the points,
m = [3 - 4] / [0 - 4]
m = 1 / 4

Standard equation of the line
y - y₁ = m (x - x₁)

Substitute one point and m in the above equaiton
y - 3 = 1/4 [x - 0]
y = x/4 + 3

Thus, the required slope-intercept form of the equation of the line is y = x/4 + 3.

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$9483.774 money should be deposited in the account.

Let the amount to be invested be P=$x so that the amount accumulated is A = $12000. We have t=3 years. The rate of interest is r=0.04 per year.     n  = 2 as interest will be compounded twice a year.

Interest, in its most simple form, is calculated as a percent of the principal.

Interest is the amount of money a lender or financial institution receives for lending out money. Interest can also refer to the amount of ownership a stockholder has in a company, usually expressed as a percentage.

Now,

                         [tex]x (1 + \frac{0.04}{2} )^{2 * 3}[/tex] [tex]= 12000[/tex]

                                 [tex]x(1.04)^{6}[/tex] [tex]= 12000[/tex]

                                           [tex]x = \frac{12000}{(1.04)^{6} }[/tex]

                                              ≈ 9483.774

                   ∴ Amount invested  ≈  $9483.774.

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The graph of the system of equations -2x - y = -2 and 13x - y = -2 is attached and the solution is

(0, 2)

Graphs are plotted using the input values in the x coordinates and the output in the y coordinate

assuming an input of -4 0 4 we calculate the output for the graphs as

-2x - y = -2

y = -2x + 2

For x = -4, y = -2 * -4 + 2 = 10

For x = 0, y = -2 * 0 + 2 = 2

For x = 4, y = -2 * 4 + 2 = -6

table of values

x     y

-4   10

0     2

4     -6

13x - y = -2 rearranging gives y = 13x + 2

y = 13x + 2

For x = -4, y = 13 * -4 + 2 = -50

For x = 0, y = 13 * 0 + 2 = 2

For x = 4, y = 13 * 4 + 2 = 54

table of values

x     y

-4   -50

0     2

4     54

The point of intersection of the two line is the solution and this is (0, 2)

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Answer:

Step-by-step explanation:

A rectangle measures 75 cm by 15 cm.Find the length of the perimeter?

P = (75 + 15) x 2

P = 90 x 2

P = 180 cm

Total $234.95 is the cost of 5 band shirts and 5 pair of pants.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given, Molly bought 4 band shirts and 3 pair of pants for $159.99.

And Christian bought 3 band shirts and 2 pair of pants for $113.00.

Let x be the band shirts and y be the pair of pants.

So, according to the question;

4x + 3y = 159.99         equation 1

3x + 2y = 113                equation 2

Now, we have the system of the equations.

In order to solve the system of equations:

Multiply 4 to the equation 2 and multiply 3 to the equation 2.

12x + 9y = 479.97

12x + 8y = 452

Subtracting the transformed equation 2 to transformed equation 1.

y = 27.97

Then 12x = 479.97 - 251.73

 12x = 228.24

x = 228.24 / 12

x = 19.02.

To find the amount of 5 band shirts and 5 pair of pants:

5x + 5y

= 5 (19.02) + 5(27.97)

= 95.1 + 139.85

= 234.95

Therefore, 5 band shirts and 5 pair of pants cost $234.95.

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The value of the stock yield will be;

⇒ 3.1%

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

McDonald’s Corp (MCD) stock is selling for $90.24 per share.

And, They offer a dividend of $2.80 per share.

Now,

Since, McDonald’s Corp (MCD) stock is selling for $90.24 per share.

And, They offer a dividend of $2.80 per share.

Hence, The value of the stock yield is;

⇒ 2.80/90.24  ×  100

⇒ 0.0310 × 100

⇒ 3.1%

Thus, The value of the stock yield will be;

⇒ 3.1%

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Answer:

6

Step-by-step explanation:

3 is 3/5 of 5 therefore 6 would be 3/5 of 10 and the triangles are similar so

Part a: Roy sweeps out 2.15/0.7 radians.

Part b: When Roy stops skiing, he is cos(3.071)(0.7) km to the center of the ski trial

Part c: When Roy stops skiing he is sin(3.071)(0.7) km above the centre of the ski trail

The radius of the ski trail= 0.7 km

Roy starts 3 o'clock position and travels 2.15 km in the counter-clockwise direction.

Let O be the centre of ski trial, A be the starting point(3-o'clock position) and consider he is now at point B.

Now, using the formula for arc length.

Arc length=(Radius)(angle at center)

2.15=(0.7)θ

θ=2.15/0.7

Roy sweep out 2.15/0.7 radians.

Part b:

When Roy stops skiing how many km is Roy to the right of the ski trial

In part, a figure draws the vertical line from point B on the horizontal line. Get the right-angle triangle

Here to find the length OP. In right angle triangle cos θ=Adjacent side/hypotenuse,

As in part, a central angle is 2.15/0.7=3.071.

Therefore,

cos(3.071)=OP/0.7

OP=cos(3.071)(0.7)  

cos(3.071)(0.7) km.  

Part c:

When Roy stops skiing how many km is Roy above the centre of the ski trial

From figure part of part b, we have to calculate side BP.

In right angle triangle sin(θ)=Opposite side/hypotenuse

Therefore,

sin(3.071)=BP/0.7

BP=sin(3.071)/(0.7)

sin(3.071)(0.7) km.

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Answer:

9

Step-by-step explanation:

2|-9| - |-2|

=2+9-2 the negative number becomes positve when it come out of absolute value

=11-2

=9

The slope of the line parallel to the given lines are as follow:

a. Slope of the line parallel to 2x + y =  -7 is -2.

b. Slope of the line parallel to y = (- 1 + 2x) 3 is 6.

c. Slope of the parallel lines are always equal.

d. Equation parallel to the given line y = 3x -5 are y = 3x + c , c may have any real value.

As given in the question,

Slope of two or more parallel lines are always same.

Equation in the form y = mx + c ,

here 'm' is the slope.

a.  Slope of the line parallel to 2x + y =  -7

y = -2x -7

Slope of the line is -2.

Slope of the line parallel to the given line is -2.

b.  y = (- 1 + 2x) 3

⇒ y = 6x -3

Slope of the line is 6 .

Slope of the line parallel to the given line is also 6.

c. Slope of the parallel lines are always equal.

d. Equation of the line parallel to the given line y = 3x -5 is given by:

y = 3x + c , here slope remain same only c value get change.

Therefore, slope of the given lines are:

a. Slope of the line parallel to 2x + y =  -7 is -2.

b. Slope of the line parallel to y = (- 1 + 2x) 3 is 6.

c. Slope of the parallel lines are always equal.

d. Equation parallel to the given line y = 3x -5 are y = 3x + c , c may have any real value

The complete question is:

a. What is the slope of a line parallel to the line whose equation is

2x + y =- 7?

b. What is the slope of a line parallel to the line whose equation is

Y = (- 1 + 2x) 3 ?

c.  How do you find the slope of a parallel line?

d. Which is the equation of a line parallel to the line with equation y=3x- 5?

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77532 is the total cost to Russell

percentage, a relative value indicating hundredth parts of any quantity.

Given,

Russell Slater bought 700 shares of Disney stock at $106.50 per share

The amount for 700 shares is 700×106.5

74550

commission of 4% of the purchase price.

We have to convert 4% to decimal value by dividing 4 by 100

0.04

Now multiply 0.04 with 74550 to get the commission

0.04×74550

2982

Now add this commission amount with 74550 to find total cost,

2982+74550

77532

Hence, 77532 is the total cost to Russell

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Answer:

n = 16

Step-by-step explanation:

-1/2 n = -8

(-1/2 * n = -8) * 2  ==> multiply the equation by 2 to remove fractions

-1 * n = -16

-n = -16 ==> simplify

n = 16

Answer: 16

Step-by-step explanation:

-1/2n=-8

Divide by -1/2

n=16

The mean score is 6.48. If we were to give this quiz to more and more students, the mean score for these students would approach 6.48.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

To find the mean score, we need to calculate the expected value of the score. The expected value is calculated by multiplying the score by its probability and summing over all possible scores.

The expected value is:

(5 * 0.06) + (6 * 0.18) + (7 * 0.37) + (8 * 0.22) + (9 * 0.11) + (10 * 0.06) = 6.48

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In the picture we can see the graph represents of the function f(x)=-x²+5 that is curve graph.

Given that,

We have to find the graph represents the function f(x)=-x²+5.

We know that,

The quadratic function is f(x)=-x²+5.

This is a vertical parabola open downward

The vertex is a maximum

We know,

A vertical parabola's equation in vertex form is equal to

y= a(x-h)²+k

where

a is a coefficient

(h,k) is the vertex

Here

a=-1

(h,k)=(0,5) is vertex

The y-intercept is the point (0,5) is value of y when the value of x is equal to zero (is the same point that the vertex)

The x-intercepts are the points is values of x when the value of y is equal to zero  

Therefore, In the picture we can see the graph represents of the function f(x)=-x²+5.

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Solving the expression 35.1 = 12.9 + 10.2x gives x to be 2 3/17

A group of numbers or variables coupled with the operations +, -,, or form an expression.

Algebraic expressions with variables, numbers, and mathematical operators, as opposed to arithmetic expressions that simply contain numbers and mathematical operators.

The given algebraic expression is 35.1 = 12.9 + 10.2x

solving for x

35.1 - 12.9 = 10.2x

10.2x = 22.2

x = 22.2/ 10.2

x = 2 3/17 as a mixed number in simplest form

the value of x is 2 3/17

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Answer:

A.

Step-by-step explanation:

Multiply the x like terms than multiply the other like terms

Answer:

A

Step-by-step explanation:

2p - 5p < 8 + 4

- 3p < 12

-3/-3 p > 12/-3

p  > -4

-2, - 3