The dollar value v (t) of a certain car model that is t years old is given by the following exponential function.
v (t)=24,500 (0.88)
Find the initial value of the car and the value after 12 years.
Round your answers to the nearest dollar as necessary.

Answer:

-54.625 or -54 5/8

Step-by-step explanation:

4\(\frac{3}{4}\) (-11.5) = -54.625 or -54 5-8

Answer:

162.3 in^2

Step-by-step explanation:

C=2πr=2·π·25.83≈162.29468in

Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

The correct option is D: G(x) = -5x².

The equation of G(x) will be -5x² after vertically stretching and flipping.

A function change called a stretch or compression makes a graph bigger or narrower without moving it horizontally or vertically.

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The complete question is -

The graph of F(x) can be stretched vertically and flipped over the x-axis to produce the graph of G(x). If F(x) = x², which of the following could be the equation of G(x)?

A: G(x) = -1/5x²

B: G(x) = 5x²

C: G(x) = 1/5x²

D: G(x) = -5x²

The volume of the cone is: A. 213 ft³.

Given:

radius and height of both the cylinder and the cone are equal.

Volume of Cylinder = 639 ft³

Therefore:

πr²h = ⅓πr²h

This means that volume of cone would be ⅓ of the volume of the cylinder.

Volume of cone = ⅓(639) = 213 ft³

Therefore, the volume of the cone is: A. 213 ft³.

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\(f(x)=-\cfrac{1}{2}x^2 + 5x\hspace{13em}g(x)=x^2+2 \\\\[-0.35em] ~\dotfill\\\\ g(-2)=(-2)^2+2\implies g(-2)=4+2\implies g(-2)=6 \\\\[-0.35em] ~\dotfill\\\\ f(~~g(-2)~~)\implies f(6)\implies f(6)=-\cfrac{1}{2}(6)^2+5(6) \\\\\\ f(6)=-\cfrac{36}{2}+30\implies f(6)=-18+30\implies \stackrel{f(~~g(-2)~~)}{f(6)}=12\)

answer: the x≤-12

Hope that help

Answer:

42.25

Step-by-step explanation:

169/4=42.25

I got 4 because of the sides and the 169 from the total square feet. Hope this answer helps!

Answer:

$6.69

Step-by-step explanation:

Since we know the total cost of 5 pairs of gloves, all we have to do to find the unit price is divide the total cost by how many gloves were are being sold:

33.45 / 5 = 6.69

Therefore, one pair of gloves costs $6.69

Hope this helps :)

Answer:

x=-2

Step-by-step explanation:

if we find sum of same variables ,

3x-2x+y-y=-8+6

x=-2

Answer:

-902.7

I hope this helps

Answer:

I believe the answer is -243

Step-by-step explanation:

Answer:A) 8 miles

Step-by-step explanation:

8 miles

All of the actions listed would have the effect of changing the direction (sign) of the Pearson r value. However, only options (a) and (b) would change the size of the Pearson r value.

a. Adding or subtracting a constant value to each X and Y score would change the location of the data points but not the shape or scatter of the data. This would affect both the means and the standard deviations of X and Y, which are used to compute Pearson r, and thus would change the size of the r value.

b. Same as (a), subtracting a constant value from each X and Y score would also change the size of the r value.

c. Multiplying each X and Y score by a negative constant value would reverse the direction of either X or Y axis, effectively flipping the scatterplot horizontally or vertically. This would only change the sign (positive or negative) of the r value, but not the size.

d. Dividing each X and Y score by a positive constant value would scale the scatterplot along the X and Y axes, effectively changing the units of measurement. This would not change the shape or scatter of the data, and the correlation coefficient would be unchanged.

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Answer:

a

Step-by-step explanation:

The correct answer is not provided in the given options. The sun would not be visible at noon on December 21 in a city at 60°N latitude.

The angle of the sun above the horizon at noon on December 21 depends on the latitude of your city. Since you mentioned that you live at 60°N, we can determine the angle using some knowledge about the tilt of the Earth and the seasons.

On December 21, the winter solstice, the Northern Hemisphere is tilted away from the sun. This means that the angle of the sun above the horizon at noon is lower than on other days of the year.

To calculate the angle, we need to subtract the latitude of your city (60°N) from the tilt of the Earth (23.5°).

So, the angle of the sun above the horizon at noon on December 21 in your city would be:
23.5° - 60° = -36.5°

The negative sign indicates that the sun is below the horizon at noon on December 21. Therefore, the correct answer is not provided in the given options. The sun would not be visible at noon on December 21 in a city at 60°N latitude.

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Answer:

options C and D is the answer

A region in the first quadrant defined by the x-axis, the graph of x=y2+2, and the line x=4 is called R then the area of R be \($-\frac{2 \sqrt{2}}{3}+2 \sqrt{2}$$\)

A parabola is a U-shaped plane curve in which every point is situated at an equal distance from both the focus, a fixed point, and the directrix, a fixed line. A parabola is a U-shaped curve that represents the graph of a quadratic function.

Students are able to fill in the gap between the mathematics they learn in class and the things they see in real life by drawing a comparison between the equation of a parabola and a shape found in the real world (the parabaloid). They can conceive difficult ideas that they might otherwise find repugnant by doing this.

Sketch the graph of \($x=y^2+2$\) by sketching the sideways parabola \($x=y^2$\) then adding 2 to the x coordinates (translate 2 to the right).

Add the x axis and the vertical line x = 4.

The area can be found by either

\($\int_2^4 \sqrt{x-2} d x$$\) or \($\int_0^{\sqrt{2}}\left(4-\left(y^2+2\right)\right) d x$$\)

\($=\int_0^{\sqrt{2}}-x^2+2 d x$$\)

Apply the Sum Rule: \($\int f(x) \pm g(x) d x=\int f(x) d x \pm \int g(x) d x$\)

\($=-\int_0^{\sqrt{2}} x^2 d x+\int_0^{\sqrt{2}} 2 d x$$\)

simplifying the equation, we get

\($\int_0^{\sqrt{2}} x^2 d x=\frac{2 \sqrt{2}}{3}$$\)

\($\int_0^{\sqrt{2}} 2 d x=2 \sqrt{2}$$\)

\($=-\frac{2 \sqrt{2}}{3}+2 \sqrt{2}$$\)

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a) The set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

To find the set of values of k for which the line and curve meet at two distinct points, we need to solve the equation:

x^2 - kx + 2 = 3kx - 2k

Rearranging, we get:

x^2 - (3k + k)x + 2k + 2 = 0

For the line and curve to meet at two distinct points, this equation must have two distinct real roots. This means that the discriminant of the quadratic equation must be greater than zero:

(3k + k)^2 - 4(2k + 2) > 0

Simplifying, we get:

5k^2 - 8k - 8 > 0

Using the quadratic formula, we can find the roots of this inequality:

\(k < (-(-8) - \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = -2/5\\ or\\ k > (-(-8)) + \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = 2\)

Therefore, the set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

b) To find the two values of k for which the line is a tangent to the curve, we need to find the values of k for which the line is parallel to the tangent to the curve at the point of intersection. For m to be the slope of the tangent at the point of intersection, we need to have:

2x - 4 = m

3k = m

Substituting the first equation into the second, we get:

3k = 2x - 4

Solving for x, we get:

x = (3/2)k + (2/3)

Substituting this value of x into the equation of the curve, we get:

y = ((3/2)k + (2/3))^2 - k((3/2)k + (2/3)) + 2

Simplifying, we get:

y = (9/4)k^2 + (8/9) - (5/3)k

For this equation to have a double root, the discriminant must be zero:

(-5/3)^2 - 4(9/4)(8/9) = 0

Simplifying, we get:

25/9 - 8/3 = 0

Therefore, the constant term is 8/3. Solving for k, we get:

(9/4)k^2 - (5/3)k + 8/3 = 0

Using the quadratic formula, we get:

\(k = (-(-5/3) ± \sqrt{((-5/3)^2 - 4(9/4)(8/3)))} / (2(9/4)) = -1/3 \\or \\k= 4/3\)

Therefore, the two values of k for which the line is a tangent to the curve are k = -1/3 and k = 4/3. To show that the two tangents meet on the x-axis, we can find the x-coordinate of the point of intersection:

For k = -1/3, the x-coordinate is x = (3/2)(-1/3) + (2/3) = 1

For k = 4/3, the x-coordinate is x = (3/2)(4/3) + (2/3) = 3

Therefore, the two tangents meet on the x-axis at x = 2.

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The surface area of the cylinder, given the diameter, can be found to be 18. 84 inch .

The surface area of a cylinder can be found by the formula :

= 2 π r ² + 2 π h

The radius can be found to be:

= Diameter / 2

= 2 / 2

= 1 inch

The value of π is 3. 14.

This means the surface area would be:

= (2 x 3. 14 x 1 x 1) + (2 x 3. 14 x 1 x 2 )

= 6. 28 + 12. 56

= 18. 84 inch

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Answer:

The given expression can be simplified using the rule for multiplying powers with the same base by adding their exponents.

(9^-3)(9^12) can be written as (1/9^3)(9^12)

Now, using the rule of adding exponents, (1/9^3)(9^12) can be simplified as 9^(12-3) = 9^9.

Therefore, the expression (9^-3)(9^12) simplified as 9^9.

Step-by-step explanation:

Answer:

  a) 56.25 mph

  b) $1.59/lb

Step-by-step explanation:

The units of the "unit rate" tell you the math operation you need to perform.

Miles per hour (mi/h) is found by dividing miles by hours.

  (450 mi)/(8 h) = (450/8) mi/h = 56.25 mi/h

Dollars per pound ($/pound) is found by dividing dollars by pounds.

  ($7.95)/(5 pounds) = (7.95/5) $/pound = 1.59 $/pound

__

Additional comment

In the context of unit rates, "per" means "divided by."

What makes a rate a "unit rate" is the "1 unit" in the denominator. For miles per hour, the denominator is 1 hour. For dollars per pound, the denominator is 1 pound.

The area of the surface is (2/3)π.

We can solve this problem using a double integral. First, we need to find the limits of integration for x and y. From the equation x + y + z = 1, we get:

z = 1 - x - y

Substituting this into the equation x² + 7y² ≤ 1, we get:

x² + 7y² ≤ 1 - z² + 2xz + 2yz

Since we want to find the area of the surface, we need to integrate over x and y for each value of z that satisfies this inequality. The limits of integration for x and y are given by the ellipse x² + 7y² ≤ 1 - z² + 2xz + 2yz, so we can write:

∫∫[x² + 7y² ≤ 1 - z² + 2xz + 2yz] dA

where dA is the area element.

To evaluate this integral, we can change to elliptical coordinates u and v, defined by:

x = √(1 - z²) cos u

y = 1/√7 √(1 - z²) sin u

z = v

The limits of integration for u and v are:

0 ≤ u ≤ 2π

-1 ≤ v ≤ 1

The Jacobian for this transformation is:

J = √(1 - z²)/√7

So the integral becomes:

∫∫[u,v] (x² + 7y² )J du dv

Substituting in the values for x, y, z, and J, we get:

∫∫[u,v] [(1 - z²) cos² u + 7/7 (1 - z²) sin² u] √(1 - z²)/√7 du dv

Simplifying, we get:

∫∫[u,v] [(1 - z²) (cos² u + sin² u)] (1/√7) dz du dv

= ∫∫[u,v] [(1 - z²)/√7] dz du dv

= (2/3)π

Therefore, the area of the surface defined by x + y + z = 1, x² + 7y² ≤ 1 is (2/3)π.

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Answer: \(14.9^{\circ}\)

Step-by-step explanation:

Given

Applied force is 9 lb to hold of 35 lb crate on a hill

Suppose the hill makes an angle of \(\theta\) with horizontal

There will be two component of weights i.e. along and perpendicular to the hill

Only the component along the hill pulls the crate backwards

So,

\(\Rightarrow 35\sin \theta=9\\\\\Rightarrow \sin\theta =\dfrac{9}{35}\\\\\Rightarrow \theta =14.89^{\circ}\approx 14.9^{\circ}\)

The required value of x is 7.

In the given statement is:

m/HGS = 3x + 5,

m/SGF=21x +3, and m/HGF = 176º.

and, to find the value of 'x'

The two angles, ∠HGS & ∠SGF, when combined, will result in ∠HGF

m ∠HGS = 3x + 5

m ∠SGF = 21x + 3

m ∠HGF = 176°

Set the equation:

m ∠SGF + m ∠HGS = m ∠HGF

Plug in the corresponding terms to the corresponding variables:

21x + 3 + 3x + 5 = 176°

24x + 8 = 176°

24x = 176° - 8

24x = 168°

x = 168°/24

x = 7

Hence, The required value of x is 7.

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Answer:

Step-by-step explanation:

What is the measure of ACF:

90-35=55 degrees

What is the measure of BCE

55 degrees

BCE is opposite of ACF

What is the measure of ACE

ACE = (DCF+ 90)

ACE = (35+90)

ACE = 125 degrees