Starting at the same point, Tom and Juanita go biking in opposite directions. If Tom rides at a speed of 18 mph, and Juanita rides at a speed of 18 mph, how far apart will they be in 2 hours?
A.
54 miles
B.
82 miles
C.
36 miles
D.
72 miles

The area of the given trapezoidal site is 250,000 sq. ft.

The area of the trapezoidal with the dimensions of both bases and the height is given by the formula,

Area = 1/2 × height × (base1 + base2)

Units: square units

The given trapezoidal site has a base of 150 feet, i.e., base1 = 150 ft; a height of 2000 ft, i.e., height = 2000 ft and a parallel base of 100 feet, i.e., base2 = 100 ft.

Then, the area of the trapezoidal is

= 1/2 × 2000 × (150 + 100)

= 1/2 × 2000 × 250

= 250,000 sq. ft

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Answer: x= 3.5

Step-by-step explanation: 4(3x) = 12x

4(-8)= -32

12x - 32 = 10

+32 = +32

12x = 42

x = 3.5

Answer:

x=3.5

Step-by-step explanation:

Start off by using distributive property ---> 12x-32=10, then add 32 on both sides---> 12x=42, then divide 12 on both sides--->x=3.5 and that is the final answer!

I hope this helps, and have a great day!

Answer:

42:30

Step-by-step explanation:

10 x 3 = 30

14 x 3 = 42

Answer:

Up 1 and over 3

Step-by-step explanation:

Answer:

-0.75

Step-by-step explanation:

Answer:

-0.75

Step-by-step explanation:

Answer:

24.25

Step-by-step explanation:

25 x .97=24.5 ;)

Yes

Step-by-step explanation:

its a direct-variation function

the answer to 130x1000 is

130,000

The expression to simplify is

We will simplify by combining like terms.

• There are FIVE x's and TWENTY-SIX more x's. We add.

5x + 26x = 31 x

• There is 1 constant, NEGATIVE THIRTEEN. No combining required so leave it as is.

•

• There is 1 term with y, which is SEVEN y. No combining required, so we leave it as is.

The final expression is

After considering the given data we conclude that the distance between stone and ground level \(h(t) = -4.9t^2 + 900\), time taken for the stone to reach the ground 18.22 seconds,the velocity with which it strikes the ground 178.76 m/s, if thrown with a down ward speed of 3m/s then the duration needed is 18.47 seconds.

A stone is dropped from the upper observation deck of a tower, 900 m above the ground. We can use the kinematic equations of motion to answer the following questions:
a) The distance of the stone above ground level at time t can be found using the equation:
\(h(t) = -1/2gt^2 + v_0t + h_0\)
where g is the acceleration due to gravity (9.8 m/s²), v0 is the initial velocity (0 m/s), h0 is the initial height (900 m), and t is the time elapsed. Plugging in the values, we get:
\(h(t) = -4.9t^2 + 900\)
b) To find how long it takes for the stone to reach the ground, we need to find the time when h(t) = 0:
\(-4.9t^2 + 900 = 0\)
Solving for t, we get:
\(t = \sqrt(900/4.9) = 18.22 seconds\)
Therefore, it takes the stone 18.22 seconds to reach the ground.
c) To find the velocity with which the stone strikes the ground, we can use the equation:
\(v(t) = -gt + v_0\)
where v(t) is the velocity at time t. Plugging in the values, we get:
\(v(t) = -9.8(18.22) + 0 = -178.76 m/s\)
Therefore, the stone strikes the ground with a velocity of 178.76 m/s.
d) If the stone is thrown downward with a speed of 3 m/s, we can use the same equation \(v(t) = -9.8(18.22) + 0 = -178.76 m/s\) to find how long it takes to reach the ground. This time, \(v_0\) is -3 m/s (since it is thrown downward) and \(h_0\) is still 900 m. Plugging in the values, we get:
\(-4.9t^2 - 3t + 900 = 0\)
Solving for t, we get:
t = 18.47 seconds
Therefore, it takes the stone 18.47 seconds to reach the ground when thrown downward with a speed of 3 m/s.
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The expected value of a gamble can be calculated by multiplying the probability of winning by the amount you could win and subtracting the probability of losing multiplied by the amount you could lose.

In this case, we are given that if a red card is drawn from a standard 52-card deck, you win $1200, and if a black card is drawn, you lose $1200.

First, let's determine the probability of drawing a red card from a standard 52-card deck. In a standard deck, there are 26 red cards (13 hearts and 13 diamonds) and 26 black cards (13 spades and 13 clubs). So the probability of drawing a red card is 26/52, which simplifies to 1/2 or 0.5.

Next, let's calculate the probability of losing, which is the probability of drawing a black card. Similarly, the probability of drawing a black card is also 26/52 or 1/2.

Now, we can calculate the expected value using the formula:
Expected value = (probability of winning * amount won) - (probability of losing * amount lost)

Expected value = (0.5 * $1200) - (0.5 * $1200)
Expected value = $600 - $600
Expected value = $0

Therefore, the expected value of the gamble is $0. This means that, on average, you neither win nor lose money in the long run by playing this gamble.

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Thee factory is able to provide 94.38 boxes per hour to the warehouse.

Rate = (2000 - 1245) / 8 = 94.38 boxes per hour

Therefore, the factory is able to provide 94.38 boxes per hour to the warehouse.

Boxes added in 40 hours = rate * time = 94.38 * 40 = 3,775.2

Therefore, the inventory at the end of a 40-hour work week would be:

1245 + 3775.2 = 5020.2 boxes

rate = (50000 - 1245) / time

Simplifying this equation, we get:

time = (50000 - 1245) / rate = 511.64 hours (rounded to two decimal places).

Therefore, it will take approximately 511.64 hours to fill the warehouse to its 50,000 box capacity,

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Moe's present age = 32

Zach's present age = 24

Let Moe's present age be represented by m

Let Zach's present age be represented by z

Moe is 8 years older than Zach now

m = z + 8..........(1)

Twenty years ago, Moe's age would be m - 20

Twenty years ago, Zach's age would be z - 20

Twenty years ago, Moe's age was three times that of Zach

m - 20 = 3(z - 20)

m - 20 = 3z - 60

m = 3z - 60 + 20

m = 3z - 40..........(2)

Let equations (1) and (2) be equal to each other:

z + 8 = 3z - 40

3z - z = 8 + 40

2z = 48

z = 48 / 2

z = 24

Substitute the value of z into equation (1)

m = z + 8

m = 24 + 8

m = 32

Moe's present age = 32

Zach's present age = 24

Answer:

E is the answer

Step-by-step explanation:

hope it is helpful

The function s(h) represents the salary for h number of hours is; s(h) = 17h + 34, found using the equation for weekly salary.

To write the given relationship in function notation, we can use the function s(h) to represent the salary for h number of hours.

The equation y = 17x + 34 represents the total weekly salary, where x is the number of hours worked. To express this equation in terms of the function s(h), we need to substitute x with h, as h represents the number of hours.

So, the function s(h) can be represented as:

s(h) = 17h + 34

In this function, s(h) represents the salary for h number of hours. The coefficient 17 represents the hourly rate, and the constant term 34 represents the flat fee paid each week.

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Answer:

Therefore, the approximate monthly payment is $548.85

Step-by-step explanation:

The amount of student loans Erica currently has = $34,006.00

The duration over which Erica is to pay back the loan = 7 years

The annual interest rate for the loan = 9.1%

Therefore, we have the geometric sequence formula is given as follows;

\(A_n = P( 1 + r)^n - M \times \left [ \dfrac{(1 + r)^n-1}{r} \right ]\)

Where;

M = The monthly payment

P = The initial loan balance = $34,006.00

r = The annual interest rate = 9.1%

n = The number of monthly payment = 7 × 12 = 84

Aₙ = The amount remaining= 0 at the end of the given time for payment

Substituting the values into the above formula, , we get;

\(0 = 34006 \times \left ( 1 + \dfrac{0.091}{12} \right )^{84} - M \times \left [ \dfrac{\left (1 + \dfrac{0.091}{12} \right )^{84}-1}{\dfrac{0.091}{12} } \right ]\)

\(M = \dfrac{34006 \times \left ( 1 + \dfrac{0.091}{12} \right )^{84} }{\left [ \dfrac{\left (1 + \dfrac{0.091}{12} \right )^{84}-1}{\dfrac{0.091}{12} } \right ]} \approx 548.85\)

Therefore, the approximate monthly payment = $548.85

Answer:

30centimeters

Step-by-step explanation:

1.25x

12*2=24months in 2 years

1.25(24)=30cen

Answer:

a strand of hair will grow 30cm in two years

Step-by-step explanation:

I hope this helps!

The modal height of the boys is 140 cm.

Modal height is defined as the most common height or the number that appears most frequently in a set of data.

The height of some boys were measured in cm as follows: 120, 140, 124, 140, 216.

The most frequently occurring height is 140 cm, which means that the modal height is 140 cm.

We can observe that 140 cm appears twice, which is more than any other height in the data set.

Therefore, it is the modal height. Modal height is the most common height or the height that appears most frequently in a data set.

The height of some boys were measured in cm as follows: 120, 140, 124, 140, 216.

The height that appears most often is 140 cm, indicating that the modal height is 140 cm.

We can see that 140 cm appears twice, which is more than any other height in the data set.

Therefore, the most frequently occurring height is 140 cm.

To put it another way, modal height is a term used in statistics to describe the most frequent height, score, or value in a data set. It is the value that appears most frequently in the dataset

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It  takes for the account to reach $200 is 4 years.

Compound Interest is the interest calculated on the cumulative amount, rather than being calculated on the principal amount only quantity.

Given that aldonia deposits $150 into an account that pays 7.3% annual interest compounded quarterly.

\(A = P(1 +\frac{r}{n})^n^t\)

where:

A = the total account balance after t years

P = the initial deposit $150

r = the annual interest rate =0.073

n = the number of compounding periods per year, which is 4 (quarterly) in this case

t = the number of years the money is in the account

Now let us substitute the values

\(A = 150(1 + \frac{0.073}{4} )^4^t\) is the equation to represent Caldonia's account balance after t years.

Now let us determine the number of  years it will take for the account to reach $200.

\(200 = 150(1 + \frac{0.073}{4} )^4^t\)

200=150(1+0.01825)^4t

\(1.333=1.018^4^t\)

Take log on both sides

log1.333=4tlog(1.018)

0.1248=4t 0.0077

0.1248=0.0309t

Divide both sides by 0.0309

t=4.038

Hence, it takes 4 years to reach account balance of $200

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Answer:

The correct answer is:

b. 6

Step-by-step explanation:

We are given the graph of an exponential function.

We have to find the average rate of change for this exponential function from x = 2 to x = 4.

First of all, let us plot the point on the graph on the points x = 2 and x = 4.

Please refer to the attached diagram.

We can easily find that the value of y at x = 2 is 4.

the value of y at x = 4 is 16.

\(\therefore\) the coordinates are (2, 4) and (4, 16).

Let the points be A(2, 4) and B(4, 16)

Now, let us find the average rate of change for exponential function i.e. change in value of y divided by change in value of x from x = 2 to x = 4:

Formula:

\(\text{Average rate of change = } \dfrac{\text{Change in y coordinate}}{\text{Change in x coordinate}}\)

\(\Rightarrow \dfrac{16-4}{4-2}\\\Rightarrow \dfrac{12}{2}\\\Rightarrow 6\)

So, correct answer is option b. 6

Answer:

Vertex: (-3, -5)

Axis of Symmetry: x = -3

Step-by-step explanation:

Heres the sketch:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

The function f(x) = \(x^2 e^{(-x^2)}\) has a maximum value at x = 0, which is a relative maximum point.

To find the relative maximum of the function f(x) =\(x^2 e^{(-x^2)}\), we can take its first derivative, set it to zero, and solve for x.

f(x) = \(x^2 e^{(-x^2)}\)

f'(x) = \(2x e^{(-x^2)} - 2x^3 e^{(-x^2)}\)

Setting f'(x) = 0, we get:

\(2x e^{(-x^2)} - 2x^3 e^{(-x^2)} = 0\)

\(2x e^{(-x^2)} (1 - x^2) = 0\)

This equation is true when either \(2x e^{(-x^2)} = 0\) or \(1 - x^2 = 0\).

Solving \(2x e^{(-x^2)} = 0\), we get x = 0.

Solving \(1 - x^2 = 0\), we get x = 1 or x = -1.

Now, we need to determine whether these values of x correspond to relative maximum, minimum, or inflection points.

To do this, we can use the second derivative test. The second derivative of f(x) is:

f''(x) = \(2e^{(-x^2)} - 4xe^{(-x^2)} - 4x^2e^{(-x^2)}\)

At x = 0, f''(0) = 2, which is positive. This means that f(x) has a relative minimum at x = 0.

At x = 1, f''(1) = \(-6e^{(-1)}\), which is negative. This means that f(x) has a relative maximum at x = 1.

At x = -1, f''(-1) = \(-6e^{(-1)}\), which is negative. This means that f(x) has a relative maximum at x = -1.

Therefore, the answer is (D) -1 and 1 only, as these are the only values of x at which f(x) has a relative maximum.

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Answer:

So we have shown that (AB)^-1 = B^-1 A^-1.

Step-by-step explanation:

Okay, let's solve this step-by-step:

1) We are given the matrices:

A = [[1, 2], [-3, 4]]

B = [[4, 3], [-2, 1]]

2) To find (AB)^-1, we first need to find AB. Matrix multiplication gives:

AB = [[1*4 + 2*-2, 1*3 + 2*1], [-3*4 + 4*-2, -3*3 + 4*1]]

= [[4, 7], [-12, 1]]

3) Next, we need to find the inverses of A and B:

A^-1 = [[4, -2], [-3, 1]] / (4*4 - 4*(-3)) = [[4, -2], [-3, 1]] / 16 = [[ 0.25, -0.125], [-0.1875, 0.0625]]

B^-1 = [[1, -2], [3, -1]] / (1*1 - 1*(3)) = [[1, -2], [3, -1]] / -2 = [[-0.5, 1], [-1.5, 0.5]]

4) Finally, we can multiply the inverses:

(AB)^-1 = A^-1 * B^-1

= [[ 0.25, -0.125], [-0.1875, 0.0625]] * [[-0.5, 1], [-1.5, 0.5]]

= [[0.125, -0.25], [0.28125, -0.03125]]

Therefore, (AB)^-1 = [[0.125, -0.25], [0.28125, -0.03125]]

So we have shown that (AB)^-1 = B^-1 A^-1.

The statement 'when finding a minimum in a linear programming problem, it is possible to find more than one minimum value' is True.

In this question, we have been given a statement - 'when finding a minimum in a linear programming problem, it is possible to find more than one minimum value.'

We need to state whether it is true or false.

We know that, the minimum value of the objective function Z = ax + by in a linear programming problem can also occur at more than one corner points of the feasible region.

Therefore, when finding a minimum in a linear programming problem, it is possible to find more than one minimum value.

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Answer:

x = 8

Step-by-step explanation:

The perimeter (P) is calculated as

P = 2(l + b) ← l is length and b is breadth

Here l = 12 and b = x , P = 40, then

2(12 + x) = 40 ( divide both sides by 2 )

12 + x = 20 ( subtract 12 from both sides )

x = 8

Answer:

In the pic

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below :)

Answer:

See Explanation Section

Step-by-step explanation:

Given

A base 5 numbering system: Envision

Some of the rules are as follows:

3 digit examples

1

Base 5: 100

Base 10: 25 (See calculation below)

\(1 * 5^2 + 0 * 5^1 + 0 * 5^0 = 1 * 25 + 0 + 0 = 25\)

Base 2: 11001 (See calculation below)

\(25 / 2 = 12\ R\ 1\)

\(12 / 2 = 6\ R\ 0\)

\(6 / 2 = 3\ R\ 0\)

\(3 / 2 = 1\ R\ 1\)

\(1 / 2 = 0\ R\ 1\)

Writing the remainder from bottom: 11001

Using the same steps as used in (1) above

2.

Base 5: 211

Base 10: 56

Base 2: 111000

3.

Base 5: 441

Base 10: 121

Base 2: 1111001

4.

Base 5: 230

Base 10: 65

Base 2: 1000001

5.

Base 5: 342

Base 10: 97

Base 2: 1100001

6.

Base 5: 141

Base 10: 46

Base 2: 101110

Answer:

The total number of winners is 17.

Step-by-step explanation:

Let's assume that the number of winners is "x". Then the number of participants who did not win is "45 - x".

The amount of money awarded to the winners is 1000x rupees.

The amount of money awarded to the participants who did not win is 200(45 - x) rupees.

According to the question, the total amount of prize money distributed is 22600 rupees. So we can write:

\(\sf\implies 1000x + 200(45 - x) = 22600 \)

Simplifying this equation:

\(\sf\implies 1000x + 9000 - 200x = 22600 \)

\(\sf\implies 800x = 13600 \)

\(\sf\implies x = 17 \)

Therefore, the total number of winners is 17.

Hope it helps!

Answer:

how much money did he make an hour ?? you cant calculate hours if you dont know his rate

Step-by-step explanation:

total made / hourly rate = hours worked and then you can determine if he gets a lawn mower

The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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