Keisha has 27 cars available to rent.
Let c be the number of cars she would have left after renting r of them.
Write an equation relating c to R. Then use this equation to find the number of
cars she would have left after renting 22 of them.

Answer:

- $308.50

Step-by-step explanation:

Given that :

Total change in savings account due to car loan payment = - $3702

Amount paid as car loan paynmet monthly is the same ;

Number of months in a year = 12

Change in saving account per month die to car loan payment :

Total change in account over a year / number of months on a year

= - $3702 / 12

= - $308.50

A monthly change of - $308.50 in savings account.

Answer:

A

Step-by-step explanation:

Answer:

0.05

Step-by-step explanation:

Hi! Ok, let's get started!

5 to the power of -2 is like dividing 5 by 10 to the second power.

That becomes 5 / 100 = 0.05

Hope that helps! :)

-Aphrodite

Answer:

8

Step-by-step explanation:

13 - 5 = 8

Answer:8x=10y

Step-by-step explanation:

A proportional relationship between the number of stickers Xander buys, x, and the total cost, y is 8x=10y.

Given that, Xander pays $8 for 10 skateboard stickers.

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 know as the "constant of proportionality".

Given, the number of stickers Xander buys, x, and the total cost, y.

Now, 8x=10y

⇒ x/y = 10/8

Therefore, a proportional relationship between the number of stickers Xander buys, x, and the total cost, y is 8x=10y.

To learn more about the proportional relationship visit:

https://brainly.com/question/12917806.

#SPJ5

Answer:

-82

Step-by-step explanation:

Answer:

C) 50

Step-by-step explanation:

One leg is 30, the other is 40, and the hypotenuse is 50

Please brainliest!

X+Y+Z=180°(sum of angles of a triangle)

33°+Y+118°=180°

Y=180°-33°-118°

Y=29°

Answer:

0.15

Step-by-step explanation:

3/20= 0.15

15/100= 0.15

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

carnival game:

spinner: 1 to 8

Step 02:

simple probability:

p = favorable outcomes / total outcomes

1. probability of an event:

a. p (odds):

p (odds) = 4 / 8 = 1 / 2

b. p (evens):

p (evens) = 4 / 8 = 1 / 2

c. p (3):

p (3) = 1 / 8

d. p (4 or 6):

p (4 or 6) = 2 / 8 = 1 / 4

e. p (7'):

p (7') = 7 / 8

f. p (1):

p (1) = 1 / 8

That is the full solution.

Equations of the asymptotes,

y = ± (√(3673/16) / √(3673/25))(x + 5) + 1

To determine the coordinates of the center, foci, vertices, and equations of the asymptotes of the given conic section, we need to rewrite the equation in a standard form.

Let's start by completing the square for both the x and y terms.

25x^2 – 16y^2 + 250x + 32y + 109 = 0

Rearranging the terms:

25x^2 + 250x – 16y^2 + 32y = -109

Completing the square for the x terms:

25(x^2 + 10x) – 16y^2 + 32y = -109

To complete the square for the x terms, we take half of the coefficient of x (which is 10), square it (which gives 100), and add it inside the parentheses.

However, since we added 25 * 100 inside the parentheses, we need to subtract 25 * 100 outside the parentheses to keep the equation balanced:

25(x^2 + 10x + 25) – 16y^2 + 32y = -109 - 25 * 100

Simplifying:

25(x + 5)^2 – 16y^2 + 32y = -109 - 2500

25(x + 5)^2 – 16(y^2 - 2y) = -3609

Now, let's complete the square for the y terms:

25(x + 5)^2 – 16(y^2 - 2y + 1) = -3609 - 16 * 1

25(x + 5)^2 – 16(y - 1)^2 = -3673

Next, let's divide both sides of the equation by -3673 to make the right side equal to 1:

25(x + 5)^2 / -3673 – 16(y - 1)^2 / -3673 = 1

Now the equation is in standard form: (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1

Comparing this to our equation, we can see that h = -5, k = 1, a^2 = -3673/25, and b^2 = -3673/16.

The center of the conic section is given by (h, k), so the center is (-5, 1).

To find the vertices, we can use the values of a to determine the distance from the center along the x-axis.

Since a^2 = -3673/25, we can take the square root to find

a. However, since the value is negative, we take the absolute value to get a positive value for a. So, a = √(3673/25) ≈ 8.56.

The vertices are located at a distance of a units from the center along the x-axis, so the vertices are (-5 + 8.56, 1) ≈ (3.56, 1) and (-5 - 8.56, 1) ≈ (-13.56, 1).

To find the foci, we can use the values of c, where c^2 = a^2 + b^2.

Since a^2 = -3673/25 and b^2 = -3673/16, we can find c.

c^2 = a^2 + b^2

c^2 = -3673/25 + (-3673/16)

c^2 ≈ 285.46

Taking the square root, we find c ≈ √285.46 ≈ 16.89.

The foci are located at a distance of c units from the center along the x-axis, so the foci are (-5 + 16.89, 1) ≈ (11.89, 1) and (-5 - 16.89, 1) ≈ (-21.89, 1).

To find the equations of the asymptotes, we can use the formula y = ±(b/a)(x - h) + k.

Plugging in the values, we get:

y = ± (√(3673/16) / √(3673/25))(x + 5) + 1

Simplifying:

y = ± (√(3673/16) / √(3673/25))(x + 5) + 1

Now, we can graph the results to show the conic section.

Learn more about hyperbola from this link:

https://brainly.com/question/30995659

#SPJ11

Answer: B

Hope this helps :)

Answer:

\(n=35\)

Step-by-step explanation:

From the question we are told that:

Standard Deviation \(\sigma=4min\)

Let

\(CI=95\%\)

Since

Significance level \(\alpha\)

\(\alpha =1-CI\)

\(\alpha =1-0.95\)

Therefore

\(Z_{\alpha/2}=Z_{0.025\)

\(Z_{\alpha/2}}=1.96\)

Generally the equation for Sample size is mathematically given by

\(n = (Z_{\alpha/2}* \frac{\sigma}{E})^2\)

\(n= \frac{1.96 * 3}{1}^2\)

\(n=35\)

The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

Know more about equation for the hyperbola here:

https://brainly.com/question/30995659

#SPJ11

Answer:

8a-36 is the answer.

Step-by-step explanation:

=a+3a-4(9-a)

=a+3a-36+4a

=4a+4a-36

=8a-36

Hope it will help ^_^

Answer:

8a - 36

Step-by-step explanation:

a + 3a - 4(9-a)

4a - 4(9-a)

4a- 36 - 4a

8a - 36

The length of a leg of an isosceles right triangle can be found using the concept of Pythagoras' theorem by the formula sqrt (hypotenuse ^ 2 / 2) = x.

Since, two sides of an isosceles triangle are equal, let us consider the two equal sides as 'x' and let the hypotenuse of the triangle be 'h'.

Being a right triangle, by Pythagoras' theorem,

h ^ 2 = x ^ 2 + x ^ 2

h ^ 2 = 2x ^ 2

Hence, we can find the length of a leg of an isosceles triangle by:

sqrt (h ^ 2 / 2) = x

To know more about isosceles triangle:

https://brainly.com/question/13020541

#SPJ4

Answer: circumference

Step-by-step explanation:

Answer:

circumference

Step-by-step explanation:

N/A

Answer:

30%

Step-by-step explanation:

3/10=30/100 and 30/100 is the same as 30%

because %'s mean out of 100 so 30% means 30 out of 100 which can be simplified to 3 out of 10 or 3/10 (so its all equal)

Answer:

3%

Step-by-step explanation:

Answer: 8.4 miles

Step-by-step explanation:

d = rt

Solve for her rate

21 = 5r

r = 21/5

r = 4.2

Solve for if the time is 2 hours and rate (solved previously) is 4.2

d = 4.2*2

d = 8.4

The distance traveled by Rebecca in 2 hours is given by d = 8.4 miles and the speed is S = 4.2 miles / hour

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the total distance ran by Rebecca be D = 21 miles

The time taken by her to travel 21 miles T = 5 hours

So , the speed of Rebecca S = D / T

On simplifying , we get

S = 21/5

S = 4.2 miles per hour

Therefore , the speed of Rebecca is 4.2 miles / hour

Now , let the time taken be T₂ = 2 hours

So , the distance traveled in 2 hours , D = ST₂

D = 4.2 x 2

D = 8.4 miles

Hence , the distance traveled is 8.4 miles

To learn more about speed click :

https://brainly.com/question/19930939

#SPJ2

If the intercept of a multiple linear regression is not statistically significant but the slopes are, it means that the relationship between the independent variables and the dependent variable starts from zero, and the slopes represent the change in the dependent variable for each unit change in the independent variables.

In multiple linear regression, the intercept represents the value of the dependent variable when all independent variables are zero. If the intercept is not statistically significant, it means that the relationship between the independent variables and the dependent variable does not start from a non-zero value. Instead, it starts from zero.

On the other hand, if the slopes are statistically significant, it means that there is a significant relationship between the independent variables and the dependent variable, and each unit change in the independent variables leads to a significant change in the dependent variable. The slopes represent the magnitude and direction of this change. Therefore, although the intercept is not significant, the slopes provide meaningful information about the relationship between the variables.

Learn more about independent variables here:

https://brainly.com/question/33270051

#SPJ11

Tom can paint the room alone in 12 hours.

Let's assume that the work required to paint the room is equivalent to 1 unit of work. If John can paint the room alone in 6 hours, his work rate per hour is 1/6.

Similarly, if John and Tom together can paint the room in 4 hours, their combined work rate per hour is 1/4. Let x be Tom's work rate per hour.

Then, we can set up the following equation:1/6 + x = 1/4

To solve for x, we can simplify the equation as follows:

Multiplying both sides by 12 (the LCM of 6 and 4) yields:2 + 12x = 3Solving for x gives:12x = 1x = 1/12Therefore, Tom's work rate per hour is 1/12, which means he can paint the room alone in 12 hours.

Summary:Tom can paint the room alone in 12 hours

Learn more about equation click here:

https://brainly.com/question/2972832

#SPJ11

Answer:

16.75

Step-by-step explanation:

I'm not sure of the answer but i hope its right!

The values of the t statistic that are statistically significant at the α=0.005 level are t < -2.977 or t > 2.977.

To determine the values of the t statistic that are statistically significant at the α=0.005 level, we need to find the critical values of the t-distribution with 14 degrees of freedom (df = n - 1 = 15 - 1 = 14).

Using a t-table or a calculator, we can find that the critical values for a two-tailed test with α=0.005 are -2.977 and 2.977. This means that any t statistic less than -2.977 or greater than 2.977 would be considered statistically significant at the α=0.005 level.

In other words, if the calculated t statistic falls within the range of -2.977 to 2.977, we would fail to reject the null hypothesis (H0: μ=10) and conclude that there is not enough evidence to suggest that the population mean is different from 10. However, if the calculated t statistic falls outside of this range, we would reject the null hypothesis and conclude that there is evidence to suggest that the population mean is different from 10.

So, the values of the t statistic that are statistically significant at the α=0.005 level are t < -2.977 or t > 2.977.

To learn more about the values of the t statistic that are statistically significant, click here: https://brainly.com/question/16244531

#SPJ11

The considerations include drawing a free-body diagram, leveling the rotating platform, and ensuring the string is parallel to the platform to maintain uniform circular motion.

1) A free-body diagram for the rotating mass in this experiment would include the following forces:

2) It is necessary to level the rotating platform to ensure uniform circular motion. If the base is not level, the motion of the revolving mass would be affected in several ways.

Firstly, it would introduce an additional horizontal component of the weight, leading to an unbalanced force and causing the mass to move horizontally.

Secondly, it would result in an uneven tension in the string, leading to an uneven centripetal force and causing the mass to deviate from a circular path.

3) It is important that the string attached to the revolving mass be parallel to the platform to maintain a constant radius throughout the circular motion.

If the string is not parallel to the platform, it would introduce an angular component to the tension force, which would change the direction of the net force acting on the mass and cause it to move in a curved or elliptical path rather than a perfect circle.

Learn more about considerations

brainly.com/question/30759148

#SPJ11

To find the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3, we first need to compute the derivative of the function.

f(x) = ln(4sec(x))
f'(x) = (1/sec(x)) * (4sec(x)) * tan(x) = 4tan(x)
Next, we use the arc length formula:
L = ∫ [a,b] √[1 + (f'(x))^2] dx
Substituting in the values, we get:
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
We can simplify this by using the identity 1 + tan^2(x) = sec^2(x):
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
 = ∫ [0,π/3] √[1 + 16tan^2(x)] dx
 = ∫ [0,π/3] √[sec^2(x) + 16] dx
 = ∫ [0,π/3] √[(1 + 15cos^2(x))] dx
 = ∫ [0,π/3] √15cos^2(x) + 1 dx
Using the substitution u = cos(x), we get:
L = ∫ [0,1] √(15u^2 + 1) du
This can be solved using trigonometric substitution, but the details are beyond the scope of this answer. The final result is:
L = 4/3 * √(15) * sinh^(-1)(√15/4) - √15/2
Therefore, the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3 is approximately 3.195 units.

To know more about derivative visit:

https://brainly.com/question/29144258

#SPJ11

the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

Learn more about volume here:

https://brainly.com/question/13338592

#SPJ11

Answer:

{5, 6, 7}

Step-by-step explanation:

When we have a given relation, the domain is the set of inputs, and the range as the set of the outputs.

so for a function f(x), and a domain {a. b. c}

The range is:

{f(a), f(b), f(c)}

In this case, we have:

f(x) = x + 6

and the domain is {-1, 0, 1}

Then the range is:

{ f(-1), f(0), f(1) }

{-1 + 6, 0 + 6, 1 + 6}

{5, 6, 7}

The correct option is the third one.

The smallest integer is 1 and solution is (₋1)

Given, the inequality is 2x ₋ 8 ≥ ₋11

The mathematical expressions with inequalities are those with unequal sides on both sides. Unlike equations, we compare two values when we work with inequality. A statement that two things are not equal is what is meant by the word "inequality." It's possible for one of the items to be more than, smaller than, equal to, or equal to the other things.

now add 8 on both sides.

2x ₋ 8 ₊ 8 ≥ ₋11 ₊ 8

2x ≥ ₋3

dividing both sides by 2.

2x/2 ≥ ₋3/2

⇒ x ≥ ₋3/2

₋3/2 is not an integer.

hence the smallest integer value of x is 1, and solution is (₋1)

Hence we get the integer value as 1.

Learn more about Inequality equations here:

brainly.com/question/24372553

#SPJ9