The total cost of owning a home for 6 years is $120,000. The
rent for a comparable home is $1500 per month. If you had invested the
down payment for the home, you could have earned $10,000 in interest.
After 6 years, how much more, in dollars, is the cost of owning compared
to the cost of renting?

No, there is significant difference in the use of e readers by different age groups.

Given sample 1 ( 29 years old) [tex]n_{1}[/tex]=628, [tex]p_{1}[/tex]=7%, sample 2( 30 years old)[tex]n_{2}[/tex]=2309, [tex]p_{2}[/tex]=0.11.

We have to first form hypothesis one null hypothesis and other alternate hypothesis.

[tex]H_{0}:[/tex]π1-π2=0

[tex]H_{1}:[/tex]π1-π2≠0

α=0.05

Difference between proportions [tex]p_{1}-p_{2} =-0.04[/tex]

[tex]p_{d}=0.07-0.11=-0.04[/tex]

The pooled proportion needed to calculate standard error is:

[tex]p=(X_{1} -X_{2} )/(n_{1} +n_{2} )[/tex]

=(44+254)/(628+2309)

=0.10146

The estimated standard error of difference between means is computed using the formula:

[tex]S_{p_{1} -p_{2} }=\sqrt{p(1-p)/m_{1}+p(1-p)/n_{2} }[/tex]

=[tex]\sqrt{0.101*0.899/628+0.101*0.899/2309}[/tex]

=[tex]\sqrt{0.000143+0.00003}[/tex]

=[tex]\sqrt{0.000173}[/tex]

=0.01315

Z= Pd-(π1-π2)/[tex]S_{p_{1} -p_{2} }[/tex]

=-0.04-0/0.013

=-3.0769

This test is a two tailed test so the p value for this test is calculated as (using z table)

p value:2 P(Z<-3.0769)

=2*0.002092

=0.004189

P value< significance level of 5%.

Hence there is enough evidence to show the claim that there is a significant difference in the use of e readers by different age groups.

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Question is incomplete as it also includes:

Significance level of 5%.

Answer:

[tex]4\sqrt2[/tex]

Step-by-step explanation:

[tex]2\sqrt{2} +\sqrt{8}=2\sqrt{2}+2\sqrt{2}=4\sqrt{2}[/tex]

Step-by-step explanation:

i sent the solution in the photo pls check it

Answer:

[tex]sin\theta=\dfrac{1}{2}[/tex]

=============

Use identity [tex]sin^2\theta+cos^2\theta=1[/tex] :

the answer is

X=5

y=3

hope you like it

The percentage depreciation is 27 % .

What is percentage ?

Given ,

         from 4500 to 3285 is depreciation value of a motor bike.

So,

         =      [tex]\frac{( 4500 - 3285 )} {4500} * 100[/tex]

         =       [tex]\frac{1215}{4500} * 100\\[/tex]

           = [tex]\frac{121500}{4500}[/tex]

          = 27 %

Therefore, The percentage depreciation is 27 % .

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The solution to the system of equations is x = -1 and y = 4

The system of equations is given as:

5x + 2y = 3

2x + 3y = 10

Multiply the first equation by 2 and the second by 5.

10x + 4y = 6

10x + 15y= 50

Subtract the above equations

10x - 10x + 4y - 15y = 6 - 50

This gives

-11y = -44

Divide by -11

y = 4

Substitute y = 4 in 5x + 2y = 3

5x + 2 * 4 = 3

This gives

5x + 8 = 3

Subtract 8 from both sides

5x = -5

Divide by 5

x = -1

Hence, the solution to the system of equations is x = -1 and y = 4

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Using the together rate, it is found that it will take 18 hours for Erick to build the garden box himself.

The together rate is given by the sum of each separate rate.

In this problem, the rates are given as follows:

Hence:

[tex]\frac{1}{x} + \frac{2}{x} = \frac{1}{6}[/tex]

[tex]\frac{3}{x} = \frac{1}{6}[/tex]

x = 18.

Hence, it will take 18 hours for Erick to build the garden box himself.

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The fraction of 5 seconds in 1 minute or part of 5 seconds in 1 minute is 1/12.

The fraction of 5 seconds in 1 minute or part of 5 seconds in 1 minute is calculated as follows;

1 minute = 60 secs

Fraction = 5 / 60

Fraction = 1/12

Thus, the fraction of 5 seconds in 1 minute or part of 5 seconds in 1 minute is 1/12.

The complete question is below:

What is part of 1 minute is 5 seconds?

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Step-by-step explanation:

the circumference of a circle is

2×pi×r

with r being the radius, which is always half of the diameter.

r = 1.8 / 2 = 0.9 cm

circumference :

2×pi×0.9 = 1.8×pi = 1.8 × 3.142 = 5.6556 cm ≈ 5.7 cm

Answer:

5.7cm

Step-by-step explanation:

circumference = π · d

(2πr)

{note: "d" is diameter; "r" is radius; "π" is pi}

we know our diameter (d) to be 1.8

let's plug this into our cicumference formula! :

π · d = circumference

(3.142) · (1.8)

3.142 · 1.8 = 5.6556

let's round our answer to 1 decimal place,

remember, if the next digit is ≥5 we round up; < 5 we keep the same

so, our answer is 5.7 cm

hope this helps!! have a lovely day :)

If the function is translated 4 units down, the resulting function will be

y = x - 4 while the vertical stretch by 3units will be y = 3(x-4)

Transformation of function is a way of changing the position of a line or curve on an xy place.

Given the equation of a line as shown;

y = x (This will serve as the parent function)

If the function is translated 4 units down, the resulting function will be

y = x - 4. If the resulting function is stretched by a factor of 3, the final function will be y = 3(x - 4)

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Answer:

[tex]\frac{1}{16}, \frac{1}{4}, \frac{3}{16}[/tex]

Step-by-step explanation:

Recall a probability: [tex]P=\frac{F}{T}[/tex] , where F is a number of favorable outcomes and T is a number of total outcomes.

The probability to get tail is [tex]\frac{1}{2}[/tex] as well as probability to get head.

The probability to choose number 7 of 8 numbers at total is equal to [tex]\frac{1}{8}[/tex].

Therefore, the probability to get number 7 and a tail is:

[tex]\frac{1}{8}\cdot \frac{1}{2}=\frac{1}{16}[/tex]

Prime numbers from 1 to 8 are: 2, 3, 5 and 7, so there are 4 numbers of 8 numbers in total, so the probability to get a prime number is  [tex]\frac{4}{8}=\frac{1}{2}[/tex].

The second probability is equal to [tex]\frac{1}{2}\cdot \frac{1}{2}=\frac{1}{4}[/tex].

The numbers greater than 5 are: 6,7,8, so there are 3 numbers of 8 in total, so the probability to get a number greater than 5 is [tex]\frac{3}{8}[/tex].

The third probability is equal to:  [tex]\frac{3}{8}\cdot \frac{1}{2}=\frac{3}{16}[/tex].

The probability that a person wins the game is 32.1%

Based on the information given, the following can be depicted. It should be noted that there are 6 sides as well as 4 cards.

Therefore, the numbers on the dice i.e from 1 - 6 will be represented 4 times each. This gives a total of (4 × 6) = 24. There are also 4 cards. The total in sample space will now be:

= 24 + 4 = 28

The frequency table will be such that 28 or more has a relative frequency of 9. Therefore, the probability that a person wins the game will be:

= 9/28 = 32.1%

When you win 25% of the time, this illustrates that the number of products picked will be:

= 25% × 28

= 7 products.

The probability of participants achieving a winning score of 36 or higher in four consecutive attempts will be:

= 1/6⁴

= 1/1296

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Answer:

Option D

Step-by-step explanation:

Looking at the graph each jump is 2 units on the x-axis and y-axis :

We are looking for a quadratic with x values of 3 and 6 when y=0  

Solving the last quadratic gives us :

(x-3)(x-6)=0

x = 3 , x = 6

Our answer will be Option D

Hope this helped and have a good day  

Answer:

D: [tex]y=x^{2} -9x+18\\[/tex]

Step-by-step explanation:

x intercept of the curve is 3 and 6

meaning that when y=0, x is either 3 or 6

mathematically stated:

0 = (x - 3)  (x - 6)

0=x(x-6)-3(x-6)

[tex]0=x^{2} -6x-3x+18\\therefore \ y=x^{2} -9x+18\\[/tex]

Limit of x approaches two from the left of f of x: 3. Limit of x approaches two from the right of f of x: - 1 (negative 1)

If limits exist, we can take limits of the function, where x tends to -∞ or ∞, and that limiting value will be the value the function will approach.

In order to find the limit as x approaches two from the left of f of x:

Lim x→2- f(x) = ?

According to the graph, when x approaches two from the left (x<2), the function approaches 3:

Lim x→2- f(x) = 3

IN order to find the limit as x approaches two from the right of f of x:

Lim x→2+ f(x) = ?

According to the graph, when x approaches two from the right (x>3), the function approaches -1:

Lim x→2+ f(x) = - 1

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The equation representing the cost in The Free Press is 12 + 5d.

The equation representing the cost in The Free Press will be:

= 12 + (5 × d)

= 12 + 5d

The equation representing the cost in The Banner will be:

= 8 × d

= 8d

The table of value for Free Press will be:

1st day = 12

2nd day = 17

3rd day = 22

4th day = 27

5th day = 32

The table of value for the Banner will be:

1st day = 8

2nd day = 16

3rd day = 24

4th day = 32

5th day = 40

The newspaper that will be used to run the advertisement for the first day is Free Press since it's cheaper.

The newspaper that will be used to run the advertisement for twelve days will be:

Free press = 12 + 5d

= 12 + 5(12)

= 12 + 60 = 72

The banner = 8d = 8 × 12 = 96

Therefore, for 12 days, Free Press is cheaper.

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Answer:

(x + 4)(x - 2) = x · x

(option L)

Step-by-step explanation:

we know that area = length × width

So, can write out the lengths and widths that we know:

(note: I will use the square as the reference point, because we can simply say "x" for both of its side lengths--you'll see why this is easier later)

Rug A:

length = x

width = x

Rug B:

length: x + 4

(4 feet greater than rug A length)

width: x - 2

(2 feet less than rug A width)

we can now set these areas to be equal to each other:

(rug A) = (rug B)

(length · width of A) = (length · width of B)

(x · x) = [ (x + 4)(x - 2) ]

So, the equation:

(x + 4)(x - 2) = x · x

can be used to find x (the length in feet) of rug A

hope this helps!! have a lovely day :)

The length of a in the triangle to the nearest tenth is 8.1 units.

The side a of the triangle can be found using cosine formula.

Therefore,

a²= b² + c² - 2bc cos A

a² = 10² + 12² - 2 × 10 × 12 cos 42°

a² = 100 + 144 - 240cos 42

a² = 244 - 178.354758115

a = √65.6453

a = 8.10217871933

a = 8.1

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The equation of the line passing through the point (3, 0) and parallel to the y axis is x = 3.

An equation is an expression that shows the relationship between two or more variables and numbers.

The graph passes through the point (3, 0) and parallel to the y axis, the equation of this line is x = 3.

The equation of the line passing through the point (3, 0) and parallel to the y axis is x = 3.

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Answer: What you picked

Step-by-step explanation:

I can't see the dropdown menus, but those answers make sense.

Answer:

The bottom part of the chest is best modeled by rectangular prism because each face is a rectangle The top part of the chest is best modeled by part of a cylinder because some faces are curved

The maximum height of the projectile fired from the ground with an upward speed of 245 m/s is 3001.25 m

An equation is an expression that shows the relationship between two or more variables and numbers.

The maximum height (H) of a projectile is given as:

H = u²/2g

Where u is the initial speed = 145 m/s, g is the acceleration due to gravity = 10 m/s²

H = 245²/ 2(10) = 3001.25 m

The maximum height of the projectile fired from the ground with an upward speed of 245 m/s is 3001.25 m

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The value of m and n that shows that point p(m,5-n) when reflected on line y=0 is m = 3, n = 3.

Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.

The rule for the reflection over the line y = 0 (x axis) is (x, y) ⇒ (x, -y)

If the point p(m,5-n) is reflected on line y=0, this would give (m, -(5 - n)) = p'(2m-3,2n-8). Hence:

2m - 3 = m

m = 3

Also:

-(5 - n) = 2n - 8

-5 + n = 2n - 8

n = 3

The value of m and n that shows that point p(m,5-n) when reflected on line y=0 is m = 3, n = 3.

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An equivalent situation, in which the binomial distribution could be used, is given by:

Flip a fair coin four times, with heads representing teenagers who prefer watching a movie at a theater and tails representing those who do not.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the parameters are:

p = 0.5, n = 4;

The other situation that would represent a binomial distribution with the same parameters is given by:

Flip a fair coin four times, with heads representing teenagers who prefer watching a movie at a theater and tails representing those who do not.

The other situations have different values of p, hence they are not equivalent.

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Answer:

Options (1), (5), and (6)

Step-by-step explanation:

See attached image

Three pairs of measurements which are possible side lengths for the triangle are,

1.  AB = 4, BC = 4√3

5 AB = 7, AC = 14.

6. AB = 11, BC = 11√3

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Now, We get;

The sides of this triangles has lengths in the ratio x : √3x : 2x

where 2x is the hypotenuse.

Now, When C = 30,  the side AB is the small leg (=x).

When B = 90, the hypotenuse is AC ( =2x).

When A =  60, the larger leg is BC (=√3x).

1.  AB = 4, BC = 4√3 :- Are possible legs.

5 AB = 7, AC = 14. :-  AB = small leg, AC = hypotenuse.

6. AB = 11, BC = 11√3:-   AB = small, BC = larger leg.

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Answer:

y = -1.5x

How to build equation?

Given points: (0, 0), (2, -3)

Find slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope \ (m) = \dfrac{-3-0}{2-0} = -1.5[/tex]

Then find equation:

[tex]y-y_1 = m(x - x_1)[/tex]

[tex]y - 0 = -1.5(x -0)[/tex]

[tex]y = -1.5x[/tex]

Answer:

y = (-3/2)x

Step-by-step explanation:

I am going to answer this question in slope-intercept form, which is y = mx + b (m is the slope, b is the y-intercept). The question already gives us the y-intercept, or the point at which the graph crosses the y-axis. It is (0, 0). Now, all we have to do is find the slope, which we can do using the following formula:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

In this formula, (x1, y1) and (x2, y2) are two points that are given to us [the first point is (0,0) and the second point is (2,-3). We can solve for the slope by plugging in:

[tex]m=\frac{-3-0}{2-0}=\frac{-3}{2}[/tex]

Now that we have m and b, we can plug into slope-intercept form to get our equation: y = (-3/2)x + 0 or y = (-3/2)x

Answer: a

Step-by-step explanation:

[tex]\left(\frac{f}{g} \right)(x)=\frac{f(x)}{g(x)}=\frac{\sqrt{x^{2}-1}}{\sqrt{x-1}}}=\sqrt{\frac{x^{2}-1}{x-1}}=\sqrt{\frac{(x-1)(x+1)}{x-1}}=\boxed{\sqrt{x+1}}[/tex]

Step-by-step explanation:

It is given that Joe paid 14.00 for a board game this is 70% of the original price what is the original price.

Let the original price of board game be

X.

x * 70/100 = 14

x * 7/10 = 14

Multiply both sides by 10.

7x = 140

Divide both sides by 7.

x = 20

Answer:

c because have great day

Now, ORQ is a straight angle and RS its bisector.

It means:

So, ∠ORS and ∠QRS are supplementary.

We also have ray RP, that divides the angles ORQ and QRS.

It gives us one more pair of supplementary angles:

Since ∠QRS is right angle, its parts are forming a pair of complementary angles:

A team of 3 boys and 3 girls be selected from 5 boys and 4 girls in 40 ways

The selections are given as:

3 boys from 5 boys

3 girls from 4 girls

Each selection is calculated using:

[tex]^nC_r = \frac{n!}{(n- r)!r!}[/tex]

So, we have:

[tex]Ways = ^5C_3 * ^4C_3[/tex]

Apply the combination formula

[tex]Ways = \frac{5!}{2!3!} * \frac{4!}{1!3!}[/tex]

Expand

[tex]Ways = \frac{5 * 4 * 3!}{2 * 3!} * \frac{4 * 3!}{1 * 3!}[/tex]

Simplify

Ways = 5 * 2 * 4

Evaluate

Ways =40

Hence, the number of ways is 40

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