The Ferrells save $150 each month for their next summer vacation. Write an equation that they can use to find y, their savings, after x months

Answer:

I cant even see anything can you reupload your answer, please?

Step-by-step explanation:

Answer:

I think its y=-5x+73

Step-by-step explanation:

The surface area of the triangular prism is of 162 cm².

The surface area of a prism is given by the sum of all the areas of the prism.

This prism is composed by:

For a rectangle, the area is the multiplication of the dimensions, hence:

A1 = 10 x 15 = 150 cm².

For a right triangle, the area is half the multiplication of the sides, hence:

A2 = 0.5 x 6 x 4 = 12 cm².

Hence the surface area is:

A = A1 + A2 = 150 cm² + 12 cm² = 162 cm².

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Answer:

The answer is 38.48

Step-by-step explanation:

Picture with explanation provided below.

Answer:

Step-by-step explanation:

M²N² - MN = MN (MN - 1)

M²N² + MN = MN (MN + 1)

\(\frac{(M^{2}N^{2}-MN)(M^{2}N^{2}-MN)}{MN}= \frac{MN(MN-1) * MN(MN + 1)}{MN}\\\)

                                     = (MN - 1) * MN * (MN + 1)

                                     = (MN - 1)(MN +1) MN             {(a+ b)(a - b) = a² - b² }

                                     = (M²N² - 1²) * MN

                                    = (M²N² - 1)MN

Answer:

x = 106

Step-by-step explanation:

Sum of angles around a point = 360

i.e,

=> 164 + 90 + x = 360

=> 254 + x = 360  

=> x = 360 - 254      

=> x = 106

Answer:

Basic fact:

angles in a point add up to make 360

Step-by-step explanation:

164+90(that is the right angle)+x=360

254+x=360

-254

x=106

Given:

The height h of an object after t seconds is

\(h=-16t^2+48t+210\)

The height of a neighboring 50-foot tall building is modeled by the equation h=50.

The time (t) when the object will be at the same height as the building is found to be t = –2 and t = 5.

To find:

The statement which describes the validity of these solutions.

Solution:

We have,

\(h=-16t^2+48t+210\)

Here, t is the time in seconds.

For t=-2,

\(h=-16(2)^2+48(-2)+210\)

\(h=-64-96+210\)

\(h=50\)

For t=5,

\(h=-16(5)^2+48(5)+210\)

\(h=-400+240+210\)

\(h=50\)

So, the value of h is 50 at t=-2 and t=5.

We know that time is always positive so it cannot be negative value. It means t=-2 is not possible.

The solution t = 5 is the only valid solution to this system since time cannot be negative.

Therefore, the correct option is C.

The response y(t) graphically, we can first plot the individual functions h(t) and x(t) on a graph, and then determine their convolution to obtain y(t). Let's go step by step:

Plotting h(t):

The function h(t) is defined as h(t) = [u(t-1) - u(t-4)].

The unit step function u(t-a) is 0 for t < a and 1 for t ≥ a. Based on this, we can plot h(t) as follows:

For t < 1, h(t) = [0 - 0] = 0

For 1 ≤ t < 4, h(t) = [1 - 0] = 1

For t ≥ 4, h(t) = [1 - 1] = 0

So, h(t) is 0 for t < 1 and t ≥ 4, and it jumps up to 1 between t = 1 and t = 4. Plotting h(t) on a graph will show a step function with a jump from 0 to 1 at t = 1.

Plotting x(t):

The function x(t) is defined as x(t) = t[u(t) - u(t-2)].

For t < 0, both u(t) and u(t-2) are 0, so x(t) = t(0 - 0) = 0.

For 0 ≤ t < 2, u(t) = 1 and u(t-2) = 0, so x(t) = t(1 - 0) = t.

For t ≥ 2, both u(t) and u(t-2) are 1, so x(t) = t(1 - 1) = 0.

So, x(t) is 0 for t < 0 and t ≥ 2, and it increases linearly from 0 to t for 0 ≤ t < 2. Plotting x(t) on a graph will show a line segment starting from the origin and increasing linearly with a slope of 1 until t = 2, after which it remains at 0.

Obtaining y(t):

To obtain y(t), we need to convolve h(t) and x(t). Convolution is an operation that involves integrating the product of two functions over their overlapping ranges.

In this case, the convolution integral can be simplified because h(t) is only non-zero between t = 1 and t = 4, and x(t) is only non-zero between t = 0 and t = 2.

The convolution y(t) = h(t) * x(t) can be written as:

y(t) = ∫[1,4] h(τ) x(t - τ) dτ

For t < 1 or t > 4, y(t) will be 0 because there is no overlap between h(t) and x(t).

For 1 ≤ t < 2, the convolution integral simplifies to:

y(t) = ∫[1,t+1] 1(0) dτ = 0

For 2 ≤ t < 4, the convolution integral simplifies to:

y(t) = ∫[t-2,2] 1(t - τ) dτ = ∫[t-2,2] (t - τ) dτ

Evaluating this integral, we get:

\(y(t) = 2t - t^2 - (t - 2)^2 / 2,\) for 2 ≤ t < 4

For t ≥ 4, y(t) will be 0 again.

Maximum value of y(t):

To find the value of t at which y(t) reaches its maximum value, we need to examine the expression for y(t) within the valid range 2 ≤ t < 4. We can graphically determine the maximum by plotting y(t) within this range and identifying the peak.

Plotting y(t) within the range 2 ≤ t < 4 will give you a curve that reaches a maximum at a certain value of t. By visually inspecting the graph, you can determine the specific value of t at which y(t) reaches its maximum.

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Answer:

As we know each burger costs $5

There are 4 burgers

When you do 4×5 you will get 20

Now subtract that 20 from the total cost

24.50-20=4.5

$4.5 is how much it costs for 3 fries

If you're wanting to calculate the number for one thing of fries then divide that 4.5 by 3

4.5/3=1.5

For one thing of fries it will cost $1.5

I hope this helps :)

Answer:

Ais 66 and B is 40% C is 60%

Step-by-step explanation:

I know A is correct but not b or c hope this helps

Answer:

-1 or 1.

Step-by-step explanation:i hope thats what your looking for.

Theprobability of the employee arriving between 8:30 a.m. and 8:35 a.m. is 0.5 or 1/2.

The probability that the employee will arrive between 8:30 a.m. and 8:35 a.m. has to be determined. The given data is that the particular employee arrives at work sometime between 8:00 a.m. and 8:50 a.m.

Based on past experience the company has determined that the employee is equally likely to arrive at any time between 8:00 a.m. and 8:50 a.m.To find the probability that the employee will arrive between 8:30 a.m. and 8:35 a.m.

Using the above data, the probability that the employee will arrive between 8:00 a.m. and 8:50 a.m. is one. Therefore, the probability that the employee will arrive between 8:00 a.m. and 8:30 a.m. is 0.5, and the probability that the employee will arrive between 8:35 a.m. and 8:50 a.m. is 0.5.

The probability that the employee will arrive between 8:30 a.m. and 8:35 a.m. is also equally likely, so its probability is 0.5.

Therefore, the probability that the employee will arrive between 8:30 a.m. and 8:35 a.m. is 0.5 or 0.5 or 1/2.

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The preliminary estimate of the cost of building a 600-MW fossil-fuel plant for the assembly of the new long-distance aircraft is approximately $700 million.

To estimate the cost of building a 600-MW fossil-fuel plant, we can use the cost capacity exponent factor and the cost index.

First, let's calculate the cost capacity ratio (CCR) for the 600-MW plant compared to the 200-MW plant:

CCR = (600/200)^0.79

Next, we need to adjust the cost of the 200-MW plant for inflation using the cost index. The cost index ratio (CIR) is given by:

CIR = (current cost index / base cost index)

Using the given information, the base cost index is 400 and the current cost index is 1200. Therefore:

CIR = 1200 / 400 = 3

Now, we can estimate the cost of the 600-MW plant:

Cost of 600-MW plant = Cost of 200-MW plant * CCR * CIR

Using the information provided, the cost of the 200-MW plant is $100 million. Plugging in the values, we have:

Cost of 600-MW plant = $100 million * CCR * CIR

Calculating CCR:

CCR = (600/200)^0.79 ≈ 2.3367

Calculating the cost of the 600-MW plant:

Cost of 600-MW plant = $100 million * 2.3367 * 3

Cost of 600-MW plant ≈ $700 million

Your question is incomplete but most probably your full question was

Suppose that an aircraft manufacturer desires to make a preliminary estimate of the cost of building a 600-MW fossil-fuel plant for the assembly of its new long- distance aircraft. It is known that a 200-MW plant cost $100 million 20 years ago when the approximate cost index was 400, and that cost index is now 1,200. The cost capacity exponent factor for a fossil-fuel power plant is 0.79. What is he preliminary estimate of the cost of building a 600-MW fossil-fuel plant for the assembly of the new long-distance aircraft?

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The correct formula for finding the present value of an investment is given by option D) PV = FV x 1/(1 + r)^n.

The present value (PV) of an investment is the current value of future cash flows discounted at a specified rate. The formula for calculating the present value takes into account the future value (FV) of the investment, the interest rate (r), and the number of periods (n).

Option D) PV = FV x 1/(1 + r)^n represents the correct formula for finding the present value. It incorporates the concept of discounting future cash flows by dividing the future value by (1 + r)^n. This adjustment accounts for the time value of money, where the value of money decreases over time.

In contrast, options A), B), and C) do not accurately represent the present value formula and may lead to incorrect calculations.

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Answer:

The first one is correct.

Step-by-step explanation:

The number of shelves depend on the number of trophies there are.

Answer:

t = independent

s = dependent

For the number of trophies her son has will be the number of shelves she will build for the trophy case.

Hope this helps :)

Answer:

37.699 or 12pi

Step-by-step explanation:

Answer:

12π

Step-by-step explanation:

To determine the probability that either Y or Z will win in the game, we need to consider the possible outcomes.

Let's analyze the possible scenarios:

Scenario 1: Y wins

In this scenario, X does not roll an even number, and Y rolls an even number before Z. The probability of Y winning in this scenario can be calculated as the probability of X not rolling an even number multiplied by the probability of Y rolling an even number before Z. Since the die has 3 even numbers (2, 4, 6) and 3 odd numbers (1, 3, 5), the probability of X not rolling an even number is 3/6 = 1/2, and the probability of Y rolling an even number before Z is 1/2.

Scenario 2: Z wins

In this scenario, both X and Y do not roll an even number, and Z rolls an even number. The probability of Z winning in this scenario can be calculated as the probability of X not rolling an even number multiplied by the probability of Y not rolling an even number multiplied by the probability of Z rolling an even number. The probability of X not rolling an even number is 1/2, the probability of Y not rolling an even number is also 1/2, and the probability of Z rolling an even number is 3/6 = 1/2.

Since the two scenarios are mutually exclusive (either Y wins or Z wins), we can calculate the probability that either Y or Z will win by summing the probabilities of the two scenarios:

Probability(Y or Z wins) = Probability(Y wins) + Probability(Z wins)

= (1/2) * (1/2) + (1/2) * (1/2) * (1/2)

= 1/4 + 1/8

= 3/8

Therefore, the probability that either Y or Z will win in the game is 3/8.

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Answer:

x = 61°

Step-by-step explanation:

since the triangle is isosceles the two angles opposite 58° are equal so:

x = (180° - 58°)/2 = 61°

Answer: 264

Step-by-step explanation:

Answer:

The stack of blocks is 25.96 inches tall

Step-by-step explanation:

The Volume of a Cube

Given a cube-shaped figure of side length L, the volume is calculated by:

\(V=L^3\)

If the volume is known, then the side length can be found by solving for L:

\(L=\sqrt[3]{L}\)

We are given three cube-shaped blocks with known volumes. We'll find the individual side lengths and add them up to find the height that results when they stack up vertically.

Block 1, volume 375 cube inches:

\(L_1=\sqrt[3]{375}=7.21\ inch\)

Block 2, volume 648 cube inches:

\(L_2=\sqrt[3]{648}=8.65\ inch\)

Block 3, volume 1029 cube inches:

\(L_3=\sqrt[3]{1029}=10.10\ inch\)

Total height=7.21 inch+8.65 inch+10.10 inch=25.96 inch

The stack of blocks is 25.96 inches tall

Answer:

The midpoint is (4,4)

Step-by-step explanation:

AB is a vertical line. This means the x value must be 4. The y value is halfway between 0 and 8, which is 4. Therefore, the midpoint is (4,4).

Answer:

The midpoint is (4,4)

Step-by-step explanation:

Use the midpoint formula to find the midpoint of the line segment.

Below is a picture of how it is graphed.

Answer:

there are 144 students in total

Answer: (x = 3, y = 9)

Step-by-step explanation:

We can set up a system of equations to represent the given information. Let x be the number of bags of popcorn, and y be the number of candies. Then we have:

9x + 4.5y = 81 (the total cost is $81)

y = x + 6 (she bought 6 more candies than bags of popcorn)

To graphically solve this system of equations, we can plot both equations on the same graph and look for the point of intersection.

To graph the first equation, we can rearrange it to slope-intercept form:

4.5y = -9x + 81

y = (-2)x + 18

To graph the second equation, we can rearrange it to slope-intercept form:

y = x + 6

Now we can plot both lines on the same graph:

(May be difficult to see on phone) ->>>>

   y

   |

12 -|              . (3,9)

11 -|          .  

10 -|      .      

9 -|  .          

8 -|              

7 -|              

6 -| .            

5 -|   .          

4 -|     .        

3 -|        .      

2 -|          .    

1 -|              .

0 -|_______________________

    0  1  2  3  4  5  6  7  8  x

The point of intersection is (3,9), which means that Taylor bought 3 bags of popcorn and 9 candies.

Answer:

25x10^-5

Step-by-step explanation:

We are expected to represent the decimal number in scientific notation

the decimal number is 0.00025

Given that the number in decimal is 0.00025 pounds

in scientific notation we will have to count 4 decimal point to the left from the second number which is 2

=2.5x10^-4

or we can still write it as

25x10^-5

either of the above is correct, only take note of the number of places you count and the sign

The solution of the equation x^ay! + 5xy + (4 + x)y = 0, where x > 0, can be represented as a power series of the form y = ΣCnx^n, where C0 = 1 and Cn = 0 for n = 1, 2, 3, ...

To find the solution of the equation x^ay! + 5xy + (4 + x)y = 0, we can represent the solution as a power series expansion of the form y = ΣCnx^n, where Cn is the coefficient of x^n and n ranges from 0 to infinity. Plugging the power series into the equation, we get:

x^a*(ΣCnx^nn!) + 5x*(ΣCnx^n) + (4 + x)(ΣCn*x^n) = 0

We can then collect the terms with the same powers of x:

ΣCnx^(n+a)n! + Σ5Cnx^(n+1) + Σ(4 + x)Cnx^n = 0

For the equation to hold true for all powers of x, each term with the same power of x must be zero. Therefore, we can determine the coefficients Cn for each power of x. For n = 0, the term ΣCnx^a0! simplifies to C0x^a0! = C0*x^a. Since the equation must hold for all x > 0, the coefficient C0 must be non-zero. Therefore, C0 = 1. For n = 1, the term Σ5Cnx^2 simplifies to 5C1x^2 = 0. Therefore, C1 = 0. Similarly, for n = 2, 3, 4, ... , the terms involving Cn will also be zero, as they are multiplied by powers of x. Hence, the solution of the equation x^ay! + 5xy + (4 + x)y = 0 can be represented as y = C0x^a = x^a, where a is a positive real number, and the coefficients Cn are zero for n = 1, 2, 3, ....

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(a) The exact value of sinh(log(6) - log(5)) is 11/60.

To calculate sinh(log(6) - log(5)), we can use the identity: sinh(x) = (\(a^n\) - \(e^-x\))/2

So, substituting x = log(6) - log(5), we get:

sinh(log(6) - log(5)) = (\(e^(log(6)\) - log(5)) - \(e^-(log(6)\) - log(5)))/2

= ((\(e^log(6)\))/(\(e^log(5)\)) - (\(e^-log(6)\))/(\(e^-log(5)\)))/2

= ((6/5) - (5/6))/2

= (36/30 - 25/30)/2

= 11/60

Therefore, sinh(log(6) - log(5)) = 11/60.

(b) The exact value of sin(arccos(76)) is undefined.

To calculate sin(arccos(76)) exactly, we can use the Pythagorean identity \(sin^2\)(x) + \(cos^2\)(x) = 1.

Let's assume arccos(76) = x. Applying the cosine function to both sides, we have cos(arccos(76)) = cos(x).

Since arccos and cosine are inverse functions, cos(arccos(76)) simplifies to 76.

Now, using the Pythagorean identity, we can calculate sin(x):

sin(x) = sqrt(1 - \(cos^2\)(x)) = sqrt(1 - 76^2) = sqrt(1 - 5776) = sqrt(-5775).

The square root of -5775 is an imaginary number, which cannot be expressed exactly without using complex numbers or numerical methods.

Therefore, the exact value of sin(arccos(76)) cannot be determined without using a calculator or numerical methods.

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Answer:

50, 130, 30, 60

Step-by-step explanation:

For the boys row (Simpsons)-20

For the girls row (Simpsons)-70

For the girls row (Lone Ranger)-50

For the total of Sesame Street- 110

Hope this helped!