Zachary purchased a new car for $27,995. The value of the car linearly depreciated to 9,300 over 10 years. Write a liner equation to represent the value y of Zachary’s car(in dollars) after x years since it’s purchase

well, do a payments table of values, just like before for each mont hmm let's see

1st month.......................3500 + p(1)

2nd month....................3500 + p(2)

3rd month.....................3500 + p(3)

4th month.....................3500 + p(4)

5th month.....................3500 + p(5)

36th month..................3500 + p(36)

[tex]\bf \stackrel{\textit{total value}}{17900}=\stackrel{\textit{down payment}}{3500}+\stackrel{\stackrel{\textit{payments for}}{\textit{36 months}}}{36p} \\\\\\ 14400=36p\implies \cfrac{14400}{36}=p\implies 400=p[/tex]

Answer: Option a:

[tex](f * g) (x) = 2x[/tex]

Step-by-step explanation:

The expression [tex](f * g) (x)[/tex] refers to the multiplication of two functions f and g.

In this case we know that the functions are:

[tex]f (x) = x\\\\g (x) = 2[/tex]

Then you must multiply the two functions we get.

[tex](f * g) (x) = f (x) * g (x)\\\\(f * g) (x) = 2 * x\\\\(f * g) (x) = 2x[/tex]

The correct answer is option a.

Answer: -0.52

Step-by-step explanation:

From the given scatter plot, it can be seen that there is a moderate negative correlation between the variables as variable X increases variable Y decreases.

i.e. the value of correlation coefficient must be negative.

Also, the value of weak correlation coefficient r, lies between the absolute value of 0.40 to 0.59.

From all the given options -0.52  is the value which is contained in interval  0.40 to 0.59 .

Therefore, the best estimate of the correlation coefficient for the variables in the scatter plot = -0.52

Answer:

25 gallons

Step-by-step explanation:

Given:

total no. of gallons= 50

Percentage of sulfuric acid= 50%

Number of gallons of sulfuric acid= total no. of gallons x Percentage of sulfuric acid

Putting values in above equation:

Number of gallons of sulfuric acid= 50 x 50/100

                                                        = 50 x 1/2

                                                        = 25 !

To find the number of gallons of sulfuric acid in a 50-gallon solution with a 50% concentration, multiply the volume of the solution by the concentration.

To find the number of gallons of sulfuric acid in a 50-gallon solution with a 50% concentration, you can use a simple calculation. The percent concentration represents the fraction of sulfuric acid in the solution, so you can calculate the amount of sulfuric acid by multiplying the volume of the solution by the concentration:

Volume of sulfuric acid = Volume of solution * Percent concentration

Volume of sulfuric acid = 50 gallons * 0.50 = 25 gallons

Therefore, there are 25 gallons of sulfuric acid in the 50-gallon solution.

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y < -1/2 x + 2

I will try the first-two points. You can then finish.

Let x = 2 and y = 3.

3 < (-1/2)(2) + 2

3 < -1 + 2

3 < 1

False statement. Choice A is not the answer.

Let x = 2 and y = 1

1 < (-1/2)(2) + 2

1 < -1 + 2

1 < 1

False statement. Choice B is not the answer.

Do the same thing with the remaining points. One of the points will make the given inequality a true statement.

The point that is a solution to the linear inequality y < -1/2 x + 2 is (b) (2,1)

The inequality is given as:

y < 1/2x + 2

Next, we test the options

A. (2, 3)

3 < 1/2 * 2 + 2

3 < 3 ---- false

B. (2, 1)

1 < 1/2 * 2 + 2

1 < 3 ---- true

Hence, the point that is a solution to the linear inequality y < -1/2 x + 2 is (b) (2,1)

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Answer:

look at the calculator.

ANSWER

EXPLANATION

We want to graph the inequality:

[tex]3y - 5x \: < \: - 6[/tex]

To this inequality, we must first of all graph the corresponding linear equation:

[tex]3y - 5x = - 6[/tex]

When x=0, we have

[tex]3y - 5(0) = - 6[/tex]

[tex]3y = - 6[/tex]

y=-2

We plot the point (0,-2)

When y=0,

[tex]3(0) - 5x = - 6[/tex]

[tex]x = \frac{6}{5} [/tex]

[tex]( \frac{6}{5} ,0)[/tex]

We plot the points and draw a dashed straight line through them.

We test for (0,0).

[tex]3(0)- 5(0)\: < \: - 6[/tex]

[tex]0 < \: - 6[/tex]

This is false hence we shade the lower half plane. See attachment.

Hello There!

First, let me just explain briefly what is an independent variable and a dependent variable.

An independent variable is the variable that changes during an experiment to see if it has an effect on another variable.

A dependent variable is what is being measured in the experiment. It’s also known as outcome or effect.

In this case, the dependent variable is the number of liters of water your drink because that’s what your measuring.

The independent variable is the number of times you drink all the water in your bottle because that changes during the experiment.

Answer:

OPTION A

Step-by-step explanation:

The exponential growth functions has the following form:

[tex]y=a(b)^x[/tex]

Where "a" is the principal coefficient and  "b" is the base greater than 1.

To know which of the functions shown has exponential growth, identify which one has a base greater than 1.

[tex]\frac{4}{3}=1.33>1[/tex]

Therefore, the exponential growth function is the function shown in the option A.

The answer is:

The correct answer is:

A) [tex]y=(\frac{4}{3})^{x}[/tex]

To identify which of the given functions is an exponential growth function, we need to remember the form of the exponenial growth or decay functions.

We can define the exponential growth or decay function by the following way:

[tex]P(x)=y=StartValue*(rate)^{x}[/tex]

Where,

P(x) or y, is the function

Start value is the starting amount or value

Rate, is the growth or decay rate

x, is the variable (time)

Now, we can identify if the function is a exponential growth or decay function by the following way:

If [tex]rate>1[/tex] the function is an exponential growth function.

If [tex]rate<1[/tex] the function is an exponential decay function.

Now, we are given the function first function, A)

[tex]y=(\frac{4}{3})^{x}[/tex]

Where,

[tex]rate=\frac{4}{3}=1.33[/tex]

and we have that:

[tex]rate>1\\1.33>1[/tex]

So, the function is an exponential growth function.

Hence, the correct answer is:

A) [tex]y=(\frac{4}{3})^{x}[/tex]

Have a nice day!

Answer:

-20

Step-by-step explanation:

-Follow PEMDAS.

-2 negatives equal a positive.

-6 + 54/(-9) - 5 - 3

-6 + (-6) - 5 - 3

-12 - 5 - 3

-20

-20

Use PEMDAS

-6- -54/(-9) -5+-3

-6+54/(-9) -5+-3

-6+-6-5-3

-12-5-3

-17-3

-20

Answer:

d

Step-by-step explanation:

Answer:

(x + 2)² + (y - 5)² = 7²

Step-by-step explanation:

Incomplete question.  I believe you meant, "write the equation of the circle with center at (-2, 5) and radius 7.

That would be:

(x + 2)² + (y - 5)² = 7²

The equation of the circle with center (-2,5) and radius 7 is (x+2)² + (y-5)² = 49.

The question is asking for the equation of a circle with center at (-2,5) and radius 7. The general equation for a circle is (x-h)² + (y-k)² = r², with (h,k) as the center and r as the radius. In this case, h = -2, k = 5, and r = 7, so substituting these into the equation gives us the solution:

(x-(-2))² + (y-5)² = 7², which simplifies to (x+2)² + (y-5)² = 49.

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Answer:

 94.18                            

Step-by-step explanation:

Given in the question a semi circle and a right angle triangle

Step 1

Find the diameter of the semi circle

To find the diameter we will use pythagorus theorem

here,

hypotenuse will be diameter of semicircle

height = 9

base = 4

Plug values in the formula above

diameter = √(9²+4²)

diameter = √97

Step 2

Find radius

Step 3

Area

π(√97/2)²

= 76.18

Step 4

Total surface area = area of circle + area of right angle triangle

                               = 76.18 + 1/2(9)(4)

                               = 94.18

The volume of a cylinder is given by

[tex]V = A_bh[/tex]

Where [tex]A_b[/tex] is the base area and h is the height.

So, if we call [tex]V_1,\ V_2[/tex] the volumes with the original and the doubled area, we have

[tex]V_1 = A_bh,\quad V_2 = A_b(2h)[/tex]

Since the height was doubled. We deduce that

[tex]\dfrac{V_2}{V_1}=\dfrac{2A_bh}{A_bh}=2[/tex]

So, if the height is doubled, the volume will double as well.

Answer:

x = 56.7°

Step-by-step explanation:

Sin (x) = Oppo. / Hypo.

Sin (x) = 66/79

Sin (x) = 0.8354

     x = 56.7°

Answer:

x ≈ 56.7

Step-by-step explanation:

In the right triangle with hypotenuse 79 use the sine ratio to find x

sinx° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{66}{79}[/tex], hence

x = [tex]sin^{-1}[/tex] ([tex]\frac{66}{79}[/tex] ) ≈ 56.7

Answer: More bees were observed on both trees from 12:00 p.m. to 6:00 p.m. than from 6:00 p.m. to 9:00 p.m.

Step-by-step explanation:

12:00 p.m. to 6:00 p.m: 135 bees

6:00 p.m to 9:00 p.m: 28 bees

Answer:

V =91.125 in ^3

Step-by-step explanation:

The volume of a cube is given by

V = s^3  where s is the side length

V= 4.5 ^ 3

V =91.125 in ^3

Given : Length of side of a cube = 4.5 inches.

We know that,

Volume of cube = (side)³ cu. units

= (4.5)³ inches³

= 91.125 inches³

Hence,

Volume of a cube = 91.125 inches³

It is important to do the same thing to both sides of an equation because in the end, both sides will be equivalent, or equal, therefor making the problem true. If you didn't do the same thing on both sides of an equation, one side would be incorrect and not equal to the other side. Hope this helps! Please mark brainliest. Thank you v much! :)

It's necessary to do the same thing to both sides of an equation to maintain balance and allow valid operations. This basic principle is crucial for solving and simplifying equations in mathematics.

In mathematics, it is necessary to do the same thing to both sides of an equation to perform valid operations. An equation represents a balance; what is done to one side must also be done to the other to maintain this balance. For instance, if you add, subtract, multiply, or divide a value from/to one side of an equation, you have to do the same to the other side. This principle is essential for solving and simplifying equations. For example, in the equation 5x + 3 = 18, to solve for x, you would subtract 3 from both sides, establishing the new equation 5x = 15, maintaining the balance.

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Check the picture below.

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=&area~of\\ &its~base\\ h=&height\\ \cline{1-2} B=&\stackrel{8.4\times 8.4}{70.56}\\ h\approx& 8.6 \end{cases}\implies V=\cfrac{1}{3}(70.56)(8.6) \\\\\\ V=202.272\implies \stackrel{\textit{rounded up}}{V=202.3}[/tex]

Answer:

2

Step-by-step explanation:

512^(1/9)

Write 512 as power of 2:

(2^9)^(1/9)

Multiply the exponents:

2^(9 × 1/9)

2^1

2

Answer:

2

Step-by-step explanation:

Answer:

√(A/4π) = r

Step-by-step explanation:

A = 4πr²

r² = A/4π

r = √(A/4π)

Answer:

r = [tex]\sqrt{\frac{A}{4\pi } }[/tex]

Step-by-step explanation:

Given

A = 4πr² ( isolate r² by dividing both sides by 4π )

r² = [tex]\frac{A}{4\pi }[/tex]

Take the square root of both sides

r = [tex]\sqrt{\frac{A}{4\pi } }[/tex]

The answer is:

The average speed for the total trip is 753.19 mph.

To calculate the average speed for the total trip, we need to calculate the time of travel for both distances according to their speeds.

So, calculating we have:

- First distance and speed: 3334 miles at 760 mph

Let's use the following formula:

[tex]distance=speed*time\\\\time=\frac{distance}{speed}[/tex]

Then, substituting we have:

[tex]time=\frac{3334miles}{760mph=4.39hours}[/tex]

Therefore, we have that the first distance was covered in 4.39 hours.

- Second distance and speed: 2244.7 miles at 740mph

Let's use the following formula:

[tex]distance=speed*time\\\\time=\frac{distance}{speed}[/tex]

Then, substituting we have:

[tex]time=\frac{2244.7miles}{740mph=3.03hours}[/tex]

Therefore, we have that the second distance was covered in 3.03 hours.

Now, calculating the average speed, we have:

[tex]AverageSpeed=\frac{distance_{1}+distance_{2}}{t_{1}+t_{2}}[/tex]

Substuting we have:

[tex]AverageSpeed=\frac{3344miles+2244.7miles}{4.39hours+3.03hours}[/tex]

[tex]AverageSpeed=\frac{5588.7miles}{7.42hours}=753.19mph[/tex]

Hence, we have that the average speed for the total trip is 753.19 mph.

Have a nice day!

Answer:

x = -2 and y = 2

Step-by-step explanation:

We have the following system of linear equations;

y=x+4

y=-2x-2

To solve the above system, we shall be equating the right hand sides of the two equations since we have y's on the left hand side of both equations;

x + 4 = -2x - 2

add 2x on both sides of the equation;

x + 4 + 2x = -2x - 2 + 2x

3x + 4 = -2

subtract 4 on both sides of the equation;

3x + 4 - 4 = -2 - 4

3x = -6

x = -2

We can use the first equation y=x+4 to determine the value of y;

y = -2 + 4

y = 2

The solution to the system of linear equations is thus;

x = -2 and y = 2

+5 is the additive inverse of (-5)

it is so as. -5 +5 =0

Hope it helps...

Regards,

Leukonov.

The additive inverse of a number is what you need to add to the given number to equal 0. This would be the opposite of the given number.

The opposite of -5 would be positive 5.

-5 + 5 = 0

The answer is 5

Answer:

c=$1.59-s

Step-by-step explanation:

Let

s ----> the sale price per pack

c ---> cost savings

we know that

The  equation that represent this situation is

c=$1.59-s

Answer:

Step-by-step explanation:

Givens

Formula

V = (a * b)/2  * h

Solution

V = (10 * 11)/2   * 10

V = 110/2  * 10

V = 55 * 10

V = 550

For this case we have that by definition, the volume of the prism shown is given by:

[tex]V = A_ {b} * h[/tex]

Where:

[tex]A_ {b}:[/tex] It is the area of the base

h: It's the height

[tex]A_ {b} = \frac {b * h} {2}[/tex]

Where:

b: It is the base of the triangle

h: It's the height of the triangle

Substituting the values:

[tex]A_ {b} = \frac {10 * 11} {2}\\A_ {b} = 55 \ cm ^ 2[/tex]

Then, the volume is:

[tex]V = 55 * 10\\V = 550 \ cm ^ 3[/tex]

ANswer:

550

Answer:

The error was on the diameter. The tire diameter was supposed to be;

4.6+15+4.6=24.2

The student only includes one sidewall width

Step-by-step explanation:

The question is on circumerence of a tire

Here we apply the formulae for circumference of a circle

C=2 [tex]\pi[/tex]×r or [tex]\pi[/tex] × d where r is the radius of the tire and d is the diameter

Finding d= diameter of rim + sidewall to the right +sidewall to the left

d= 15+4.6+4.6=24.2 inches

r=d/2= 12.1

C=2 ×[tex]\pi[/tex]×r

C=2×3.14×12.1 =75.99 Inches

Answer:

Step-by-step explanation:

45 Mins

Answer:

Required system of equation is

4s+3c=26 and 5s+2c=29.

Step-by-step explanation:

Let cost of 1 sundaes = s

Let cost of 1 cone = c

Then statement "Marcus is treating his family to ice cream he buys 4 Sundaes and 3 cones for the total of $26", gives equation:

4s+3c=26...(i)

And statement "Brian also buy ice cream for his family his total is 29 for purchasing 2 cones and 5 Sundaes " gives equation:

5s+2c=29...(ii)

Hence required system of equation is

4s+3c=26 and 5s+2c=29.

Answer:

4s+3c=26

5s+2c=29.

Step-by-step explanation:

Answer:

The value of P( A and B ) is 0.08.

Step-by-step explanation:

When two events are independent then the probability of both occurring is equal to the product of probabilities of both events individually,

That is, If X and Y are independent events,

Then, P(X∩Y) = P(X) × P(Y),

or P(X and Y) = P(X) × P(Y),

Here, P(A) = 0.40 and P(B) = 0.20,

Hence, P(A∩B) = P(A) × P(B)

= 0.40 × 0.20

= 0.08

The value of [tex]\( P(A \text{ and } B) \)[/tex] is 0.08. So option(a) is correct.

To determine[tex]\( P(A \text{ and } B) \)[/tex] for two independent events ( A ) and ( B ) with given probabilities ( P(A) = 0.40 ) and ( P(B) = 0.20 ), follow these steps:

Step 1: Understand the Concept of Independence

For independent events, the probability of both events occurring together (the intersection of A and B, denoted as [tex]\( P(A \cap B) \))[/tex] is the product of their individual probabilities.

Step 2: Apply the Independent Event Formula

Since (A ) and (B ) are self-contained,

[tex]P(A) \times P(B) = P(A \cap B)[/tex]

Step 3: Substitute the Given Probabilities

Insert the given probabilities [tex]\( P(A) = 0.40 \)[/tex] and [tex]\( P(B) = 0.20 \)[/tex] into the formula:

[tex]\[ P(A \cap B) = 0.40 \times 0.20 \][/tex]

Step 4: Perform the Multiplication

Calculate the product of 0.40 and 0.20:

[tex]\[ P(A \cap B) = 0.40 \times 0.20 = 0.08 \][/tex]

Step 5: Interpret the Result

The probability that both events ( A ) and ( B ) occur is 0.08.

Therefore, the correct answer is (a) 0.08.

Complete Question:

A and B are independent events. P(A)=0.40 and P(B)=0.20 . What is P(A and B) ?

A. 0.08

B. 0.60

C. 0

D. 0.80

b and c is the answer .

Number 7 - Second answer

Number 8 - Third answer