You and your friend walk to school together every day. You meet at the halfway point between your houses first and then walk to school. Each unit in the coordinate plane corresponds to 50 yards. A) What are the coordinates of the midpoint of the line segment joining the two houses? B) What is the distance that the two of you walk together?
Please show the steps

Answer:

6 is the ten thousand number

3 is the thousand number

6 is 20 times larger than 3

Step-by-step explanation:

5 = units

4 = tens

0 = hundred

3 = thousand

6  = ten thousand

7 = 100 thousand

comparison of the value of 6 to 3

 60,000 / 3000 = 20 times

By Cavalieri's Principle, the volume of that slanted cylinder will be the same volume of a non-slanted cylinder with the same altitude.

so we have a cylinder with a radius of 3 and a height of 7 and a cone hitching a ride on it, with a radius of 3 and a height of 3, so let's simply get the volume of each.

\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=7\\ r=3 \end{cases}\implies V=\pi (3)^2(7) \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=3\\ r=3 \end{cases}\implies V=\cfrac{\pi (3)^2(3)}{3} \\\\[-0.35em] ~\dotfill\\\\ \pi (3)^2(7)~~ + ~~\cfrac{\pi (3)^2(3)}{3}\implies 63\pi +9\pi \implies 72\pi ~~ \approx ~~ \text{\LARGE 226.19}~in^3\)

Answer:

15t+12r

Step-by-step explanation:

you have to do like term like -8t and-7t that is like term so the next like term is 3r and -9r

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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Answer:

really

Step-by-step explanation:

really hdnsbsv z

The value of such that the matrix is the augmented matrix of a linear system with The system has an infinite number of solutions if $k=-1$.

To find out the value of $k$ that results in the matrix being the augmented matrix of a linear system with infinitely many solutions, you need to reduce the matrix to row echelon form and check the conditions. If you get a row of all zeroes but the last entry in that row is not zero, then there is no solution. If you get a row of all zeroes including the last entry in that row, then there are infinitely many solutions. Therefore, the value of $k$ that leads to the augmented matrix of a linear system with infinitely many solutions is $k=-1$.

A system of linear equations has an infinite number of solutions if and only if its augmented matrix, after being transformed to row-echelon form, has at least one free variable column.

The matrix in question is given as:

\($$\begin{bmatrix}2 & -2 & 4 \\ -3 & 3 & -6 \\ 1 & -1 & k\end{bmatrix}$$\)

To find the value of $k$, we need to convert it to a row-echelon form.

\($$ \begin{bmatrix}2 & -2 & 4 \\ -3 & 3 & -6 \\ 1 & -1 & k\end{bmatrix} \overset{R2\rightarrow R2+\frac{3}{2}R1}{\longrightarrow} \begin{bmatrix}2 & -2 & 4 \\ 0 & 0 & 0 \\ 1 & -1 & k\end{bmatrix} $$\)

Notice that the second row of the matrix is all zeros, so the system either has no solution or has an infinite number of solutions. Therefore, we need to determine the value of $k$ to figure out which of the two cases apply. Since the third row is independent, we can choose to work with it only.

\($$1a - 1b = c \rightarrow c = a - b$$\)

We can also write it as a linear combination of $a$ and $b$:

\($$\begin{aligned} c &= a - b \\ &= a(1) + b(-1) \end{aligned}$$\)

Therefore, it follows that if $k$ equals -1, we can rewrite the last row as a linear combination of the first two rows.

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Answer:

It is c you are subtracting for the 4 pack of muffins

Answer:

C

Step-by-step explanation:

Assuming that m represents the cost, the correct answer would be C because you are buying 4 packs of muffins and you are subtracting 2 dollars. This is very hard to explain, it's easier to explain with numbers.

Let's assume that each pack of muffins is 2 dollars. Since we are buying 4 packs, we would multiply the number of packs (4) by the amount each pack costs (2). Then since we have a 2 dollar coupon, we subtract two dollars off of the price, so the equation would be 4(2)-2 where 2 represents m.

It wouldn't make sense to add two dollars because we have a coupon, so we're saving money, not adding money.

and it wouldn't make sense for the coupon to be saving more money by how much the cost of the muffin is, otherwise we would get it for free!!

The only logical answer is C because we are saving money and 4m represents the amount of money we are spending on the muffins.

Answer:D

Step-by-step explanation:D

The value of exponent x, if \($\sqrt[\text X]{81} = 3\), is 4, in the given equation.

Exponent is the process of expressing large numbers as powers, according to the definition. Accordingly, the exponent describes the number of times a number has been multiplied by itself. Using 6 as an example, multiply it by itself four times, or 6×6×6×6. 6⁴ can be used to represent this. In this case, the base is 6 and the exponent is 4. You can interpret this as 6 raised to the power of 4.

Exponents are represented by the symbol. The word "carrot" refers to this symbol (). 4 raised to a power of two, for instance, can be expressed as 4^2 or 4². Thus, 4^2 = 4 × 4 = 16. A few exponent-based numerical expressions are represented in the table below.

The value of x, if \($\sqrt[\text X]{81} = 3\)

3 × 3 = 9

9 × 3 = 27

27 × 3 = 81

Thus, The value of x, if \($\sqrt[\text X]{81} = 3\), is 4.

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Answer:

The scale that Pedro used for the drawing is: 17:600.

Step-by-step explanation:

A scale of a drawing is expressed as: Drawing length:actual length.

Since you know that the pool is 119 centimeters long in the drawing and 42 meters long in real life, first you have to find  the cm in 42 meter taking into account that 1 meter is equal to 100 cm:

1 m     →    100 cm

42 m   →          x

x=(42*100)/1

x=4200 cm

Now, the scale would be:

119:4200

Finally, you need to simplify and you can do it by dividing each number by 7:

17:600

According to this, the answer is that the scale that Pedro used for the drawing is: 17:600.

In all cases, we evaluate the function based on the given values or variables provided. The function f(x, y) consists of terms involving squares, linear terms, and a constant. Substituting the appropriate values or variables allows us to compute the corresponding results.

Here's a detailed explanation for each evaluation of the function f(x, y):

(a) To evaluate f(0, 0), we substitute x = 0 and y = 0 into the function:

  f(0, 0) = (0^2) + (0^2) - 0 + 2 = 0 + 0 - 0 + 2 = 2

(b) For f(1, 0), we substitute x = 1 and y = 0:

  f(1, 0) = (1^2) + (0^2) - 1 + 2 = 1 + 0 - 1 + 2 = 2

(c) Evaluating f(0, -1):

  f(0, -1) = (0^2) + (-1^2) - 0 + 2 = 0 + 1 - 0 + 2 = 3

(d) The expression f(a, 2) indicates that 'a' is a variable, so we leave it as it is:

  f(a, 2) = (a^2) + (2^2) - a + 2 = a^2 + 4 - a + 2 = a^2 - a + 6

(e) Similarly, f(y, x) indicates that both 'y' and 'x' are variables:

  f(y, x) = (y^2) + (x^2) - y + 2

(f) Evaluating f(x + h, y + k) involves substituting the expressions (x + h) and (y + k) into the function:

  f(x + h, y + k) = ((x + h)^2) + ((y + k)^2) - (x + h) + 2

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Answer:

Corresponding angles

Step-by-step explanation:

The name of these angels lying in the same position are called corresponding angle.

These angles are equal. When we talk of parallel lines, they are sets of lines that travel in the same direction but never meet. The third line that cuts through the two sets of parallel lines is referred to as the transversal line.

So the positions of these angles on each of the set of the parallel lines are equal in each of the cases and they are equal and are referred to as being corresponding to each other

The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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Answer:

100 beats per minute

Step-by-step explanation:

If it takes 28.8 secs for the piano to play 48 beats, then it would take 60 secs (1 minute) to play x number of beats.

To find the value of x, which is the number of beats the piano makes per minute, let's set the proportion as shown below:

28.8 secs = 48 beats

60 secs = x beats

Cross multiply

28.8*x = 60*48

28.8x = 2,880

Divide both sides by 28.8

x = 2,880/28.8

x = 100

✅Thus, if the Piano plays 48 beats in 28.8 secs, therefore, the tempo of the piano in beats per minute would be 100 BPM

The number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels is 3060.

To calculate the number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels, we can use the concept of stars and bars.

First, we need to ensure that we have at least one of each type of bagel. So, we take one bagel of each type, which leaves us with 14 bagels to buy.

Now, we can use stars and bars to distribute the remaining 14 bagels among the 6 types of bagels. We represent the 14 bagels as stars and the 5 possible locations between the types of bagels as bars.

Using this method, we need to distribute 14 stars among 5 bars, which can be done in

(14+5-1) choose (5-1) = 18 choose 4 = 3060 ways.

Therefore, the number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels is 3060.

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Answer: Margo does 48 activities in 4 weeks.

Step-by-step explanation:

In the calendar,

Red dots represent homework, yellow dots represent work, and green dots represent practice.

On a typical week , she uses 5 red dots, 3 yellow dots, and 4 green dots.

That means , total activity he does in a week = 5+3+4=12

Then, total activities in 4 weeks = 4 x 12 = 48

Hence, Margo does 48 activities in 4 weeks.

Answer:

A. 37

Explanation:

The angles F and G

Answer: If Caleb bought 5/4 of the 12 grams of tea for his mom, we can use the following equation to find out how many grams he got his mom:

5/4 * 12 grams = (5/4) * 12 = 15 grams

So Caleb bought 15 grams of tea for his mom

Step-by-step explanation:

For the given sample space we have the probabilities as follows: 1. P(sum=11) = 6/64 = 3/32 2. P (sum < 6) = 10/64 3. P ( sum is greater than or equal to 7) = 49/64 4.  P(sum is a multiple of 3 or a multiple of 4) = 33/64.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

For the sample space of rolling two 8 sided die we have:

1. P (sum = 11):

The samples that give the sum equal to 11 are:

(3, 8), (4, 7), (5, 6), (6, 5), (7, 4), and (8, 3)

Thus,

P(sum=11) = 6/64 = 3/32

2. P (sum < 6):

(1, 1), (1, 2), (1, 3), (1, 4)

(2, 1), (2, 2), (2, 3)

(3, 1), (3, 2)

(4, 1)

Thus, P (sum < 6) = 10/64

3. P ( sum is greater than or equal to 7):

(1, 6), (1, 7), (1, 8) = 3

(2, 5), (2, 6) (2, 7), (2, 8) = 4

(3, 4), (3, 5) (3, 6) (3, 7) (3, 8) = 5  

(4, 3) (4, 4) (4, 5) (4, 6), (4, 7) (4, 8) = 6

(5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (5, 7) (5, 8) = 7

(6, 1) upto (6, 8) = 8

(7, 1) upto (7, 8) = 8

(8, 1) upto (8, 8) = 8

Total = 3 + 4 + 5 + 6 + 7 + 8 + 8 + 8 = 49

Thus, P ( sum is greater than or equal to 7) = 49/64

4. P (sum is a multiple of 3 or a multiple of 4):

Multiple of 3: 3, 6, 9, 12, ........

(1, 2) (1, 5) (1, 8) (2, 1) (2, 4) (2, 7) (3, 1) (3, 3) (3, 6) (4, 2) (4, 5) (4, 8) (5, 1) (5, 4) (5, 7), (6, 3), (6, 6) (7, 2) (7, 5) (7, 8) (8, 1) (8, 4), (8, 7) = 23

Multiple of 4: 4, 8, 12, 16, .........

(1, 3) (1, 7) (2, 2) (2, 6) (3, 1) (3, 5) (4, 4) (4, 8), (5, 3), (5, 7), (6, 2), (6, 6) (7, 1) (7, 5) (8, 4) (8, 8) = 16

Common terms = 6

Thus, P(sum is a multiple of 3 or a multiple of 4) = 23 + 16 - 6 / 64 = 33/64

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Answer:

A

Step-by-step explanation:

is the function.

Am % sure

After 12 years, 1996 rabbits remained in the park when a state park had 330 rabbits living there.

Given that,

A state park had 330 rabbits living there. With continuous compounding, the population increased at a rate of 15% per year for 12 years.

We have to find after 12 years, how many rabbits remained in the park.

We know that,

The population of rabbit is p=330

The rabbit increasing rate is r=15%

Time is t=12 years

Use the continuously compounded formula to determine the number of rabbits after 12 years.

A= P\(e^{rt}\)

A=330\((2.17828)^{(0.15)(12)}\)

A= 1996.38

A=1996     (approximately)

Therefore, After 12 years, 1996 rabbits remained in the park when a state park had 330 rabbits living there.

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Answer:

The Probability = 0.16

Step-by-step explanation:

Empirical rule formula states that:

68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

Average = 13.1 years

Standard deviation = 1.5 years

x = 14.6 years

= 14.6 -13.1/1.5

= 1

This falls within 1 standard deviations of the mean

68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.

Hence:

100 - 68%/2 = 32/2 = 16%

Converting to probability = 0.16

The probability of a meerkat living longer than 14.6 years is 0.16

Answer:

Use the empirical rule (68 - 95 - 99.7\%)(68−95−99.7%)left parenthesis, 68, minus, 95, minus, 99, point, 7, percent, right parenthesis to estimate the probability of a meerkat living longer than 14.614.614, point, 6 years.

16%

The measure of the fourth interior angle of the quadrilateral is 65°. Hence, the correct answer is (a) 65°.

To calculate the measure of the fourth interior angle of a quadrilateral when the measures of three interior angles are known, we can use the fact that the sum of the interior angles of a quadrilateral is always equal to 360 degrees.

Let's denote the measure of the fourth interior angle as x.

Provided that the measures of the three known interior angles are 120°, 100°, and 75°, we can write the equation:

120° + 100° + 75° + x = 360°

Combining like terms, we have:

295° + x = 360°

To solve for x, we subtract 295° from both sides of the equation:

x = 360° - 295°

Calculating this, we obtain:

x = 65°

Hence, the answer is (a) 65°.

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Answer:

153.061869-2.88950=      150.172819

Step-by-step explanation:

The estimated monthly average daily radiation on a horizontal surface in June in Amman is approximately 7.35 kWh/m(^2)/day.

To estimate the monthly average daily radiation on a horizontal surface H in June in Amman, we can use the following equation:

\([H = S \times H_s \times \frac{\sin(\phi)\sin(\delta)+\cos(\phi)\cos(\delta)\cos(H_a)}{\pi}]\)

where:

S is the solar constant, which is approximately equal to 1367 W/m(^2);

\(H(_s)\) is the average number of sunshine hours per day in Amman in June, which is given as 10 hours;

(\(\phi\)) is the latitude of the location, which for Amman is approximately 31.9 degrees North;

(\(\delta\)) is the solar declination angle, which is a function of the day of the year and can be calculated using various methods such as the one given in the answer to Q1;

\(H(_a)\) is the hour angle, which is the difference between the local solar time and solar noon, and can also be calculated using various methods such as the one given in the answer to Q1.

Substituting the given values, we get:

\([H = 1367 \times 10 \times \frac{\sin(31.9)\sin(\delta)+\cos(31.9)\cos(\delta)\cos(H_a)}{\pi}]\)

Since we are only interested in the monthly average daily radiation, we can assume an average value for the solar declination angle and the hour angle over the month of June. For simplicity, we can assume that the solar declination angle (\(\delta\)) is constant at the value it has on June 21, which is approximately 23.5 degrees North. We can also assume that the hour angle \(H(_a)\) varies linearly from -15 degrees at sunrise to +15 degrees at sunset, with an average value of 0 degrees over the day.

Substituting these values, we get:

\([H = 1367 \times 10 \times \frac{\sin(31.9)\sin(23.5)+\cos(31.9)\cos(23.5)\cos(0)}{\pi}]\)

Simplifying the equation, we get:

\([H \approx 7.35 \text{ kWh/m}^2\text{/day}]\)

Therefore, the estimated monthly average daily radiation on a horizontal surface in June in Amman is approximately 7.35 kWh/m(^2)/day.

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The point that lies on the bisector of angle PQR in the diagram given is: point Y.

An angle bisector is a segment that cuts an angle into two equal parts.

From the image given, point Y lies directly opposite to vertex Q. Point Y divides angle PQR into equal parts.

Therefore, the bisector of angle PQR is: point Y.

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Answer:

81

Step-by-step explanation:

\(2z^2+2z-3\)

Using PEMDAS/BODMAS, we will have to do the exponent first, which is \(z^{2}\).

Substitute the variable z with 6, since z = 6.

\(2(6^{2} )+2(6)-3\)

\(6^{2} =36\).

Thus, we will get

\(2(36)+2(6)-3\)

Solve the multiplication next.

\(72+12-3\)

Finally, add/subtract the numbers:

\(84-3\)

\(81\)

The value of the equation 2z² + 2z - 3 at 'z' equal to 6 is 81.

Substitution in mathematics is when we replace some specific numerical values to variables according to our wants or given in the problem.

Given, A quadratic equation 2z² + 2z - 3.

Now, The value of the equation at z = 6 can be obtained if we replace the variable z with it's numerical value which is,

= 2(6)² + 2(6) - 3.

= 2(36) + 12 - 3.

= 72 + 9.

= 81.

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The population 4 years later is approximately 6,000. To find the population 4 years later, we need to integrate the rate of growth equation dN/dt = 500 + 600√t with respect to t.

The population of the new city 4 years after its incorporation can be found by integrating the rate of the growth equation dN/dt = 500 + 600√t with the initial condition N(0) = 3,000.

This will give us the function N(t) that represents the population at any given time t.

Integrating the equation, we have:

∫dN = ∫(500 + 600√t) dt

N = 500t + 400√t + C

To find the value of the constant C, we use the initial condition N(0) = 3,000. Substituting t = 0 and N = 3,000 into the equation, we can solve for C:

3,000 = 0 + 0 + C

C = 3,000

Now we can write the equation for N(t):

N(t) = 500t + 400√t + 3,000

To find the population 4 years later, we substitute t = 4 into the equation:

N(4) = 500(4) + 400√(4) + 3,000

N(4) = 2,000 + 800 + 3,000

N(4) ≈ 6,000

Therefore, the population of the new city 4 years after its incorporation is approximately 6,000.

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