A local club charges an initial membership fee of $75 as well as a monthly cost. Jeshua paid a total of $285 for 6 months at the gym. What does Jeshua pay each month at the local club? *

The area and perimeter of the parallelogram are: 56 square units and 30 units respectively

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The parameters that will help us do the math are

base = 7

height = 8

Area = 8*7 = 56 square units

perimeter 2b + 2h

perimeter = 2*7 + 2*8

= 14 +16

P = 30 units

Therefore, the perimeter of the parallelogram and area are 30 units and 56 square units

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The expression {P(x) + Q(x)} − {R(x) + S(x)} is a zero polynomial.

From the question, we have the following polynomial that can be used in our computation:

P(x) = 2x² (x + 3) − (7x − 10)

Q(x) = 8(x − 1) (x² + x + 1) − 3x² + 4

R(x) = (2x + 1)² - (2x² + 7)

S(x) = 2(5x³+6) + x(x - 11)

Add the expressions P(x) and Q(x)

So, we have

P(x)  + Q(x) = 2x² (x + 3) − (7x − 10) + 8(x − 1) (x² + x + 1) − 3x² + 4

Evaluate

P(x)  + Q(x) = 10x³ + 3x² - 7x + 6

Add the expressions R(x) and S(x)

So, we have

R(x) + S(x) = (2x + 1)² - (2x² + 7) + 2(5x³+6) + x(x - 11)

R(x) + S(x) = 10x³ + 3x² - 7x + 6

So, we have

P(x) + Q(x)} − {R(x) + S(x)} = 10x³ + 3x² - 7x + 6 - (10x³ + 3x² - 7x + 6)

Evaluate

P(x) + Q(x)} − {R(x) + S(x)} = 0

Hence, the expression {P(x) + Q(x)} − {R(x) + S(x)} is a zero polynomial.

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Answer:

0.0001 = 0.01% probability of the Celtics winning eight straight championships.

Step-by-step explanation:

For each year, there are only two possible outcomes. Either the Celtics are the champions, or they are not. Each year is independent of other years. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

What would be the probability of the Celtics winning eight straight championships?

Each year, we have that \(p = 0.32\)

Eight straight championships: \(P(X = 8)\) when n = 8. So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 8) = C_{8,8}.(0.32)^{8}.(0.68)^{0} = 0.0001\)

0.0001 = 0.01% probability of the Celtics winning eight straight championships.

Answer:

Less than 90⁰

Step-by-step explaination:

If p is an acute angle then, p can be equal to any measurement less than 90⁰

It can be upto 89⁰

Answer:

0 < angle < 90

Step-by-step explanation:

Acute angles are between 0 and up to 90 degrees

Right angles are 90 degrees

Obtuse angles are greater than 90 degrees and less than 180 degrees

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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Answer: 0

Step-by-step explanation:

1/2(2x+5)=3/4(x+1)+5/2

distribute 1/2 to 2x and 5

distribute 3/4 to x and 1

1/4x+5/2=5/2

subtract 5/2 to 5/2

1/4=0

multiply 1/4 by the reciprocal

4/1*1/4=0*4/1

Answer= 0

The firm’s economic value added (EVA), that is, how much value did management add to stockholders’ wealth during 2018 is $0.42 million

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

Net operating profit = (22 million - 19 million)*(1 - 0.36)

                                = $1.92  million

EVA = net operating profit after taxes - invested capital*WACC

       = 1.92 million - 15 million*0.10

       = $0.42 million

Therefore, The firm’s economic value added (EVA), that is, how much value did management add to stockholders’ wealth during 2018 is $0.42 million.

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The size of the land that Muya's son and daughter received is \(1\frac{11}{12}\) hectares.

We can see that, Muya started with a \(6\frac{2}{3}\) hectares piece of land, which we can write as an improper fraction i.e.:

\(6\frac{2}{3}\) = (6 × 3 + 2) / 3 = \(\frac{20}{3}\) hectares

The Muya donated \(\frac{7}{8}\) hectares to a school and \(1 \frac{1}{2}\) hectares to a children's home. The total amount of land he donated is:

\(= \frac{7}{8}+ \frac{11}{2} \\\\= \frac{7}{8} + \frac{3}{2} \\\\= \frac{14}{8} + \frac{12}{8} \\\\= \frac{26}{8} \\\\= \frac{13}{4} hectares\)

The size of the land left is:

\(\frac{20}{3} - \frac{13}{4} = (\frac{80}{12}) - (\frac{39}{12}) = \frac{41}{12} hectares\)

Muya's son and daughter share this remaining land equally, so each of them gets:

\((\frac{41}{12}) / 2 = \frac{20.5}{12} = 1 \frac{11}{12} hectares\)

Therefore, the size of the land that Muya's son and daughter received is 1 11/12 hectares.

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Answer: 14

Step-by-step explanation:

Answer:

I'm pretty sure it should be 14 :)

The value of x which I suppose is the angle M is calculated to be 32°

In a right-angled triangle KLM, it is a known fact that the sum of the three angles in any triangle is 180°.

Since angle L is a right angle and has a measure of 90°, we can find angle M by subtracting the sum of angles K and L from 180°.

Thus,

angle M = 180° - angle K - angle L

= 180° - 58° - 90°

= 32°

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The baby whale would be 35 years old.

\(7*10^3\) in standard notation is 7000

To find the whales age, you must divide 7000 by 200, which is 35.

Using the formula for the future value

in which p is the annual salary for the first year, i the raise per year and t the time in years.

We calculate only 4 years with the increment because in the first year there is not a raise.

Replace in the formula

then calculate this for the other years and add all the future values together.

add all together

The range of f(x) = |x - 3| + 2 is calculated to be y ≥ 2

In geometry range refers to all the possible values of the y coordinate

using the equation f(x) = |x - 3| + 2 and plotting the values shows that the range of f(x) = |x - 3| + 2 is [2, ∞),

this means that it includes all values greater than or equal to 2, but not 2 itself.

This can be visualized on a number line as all values to the right of 2, extending towards positive infinity.

The plot is attached

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Answer:

9000

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x + 1)/2 = -3

x + 1 = -6

x = -7

(y + 1)/2 = -1

y + 1 = -1

y = -2

(-7, -2)

Answer:

Hard bop energetic and emotional style of music developed in response to cool jazz and featured fast tempos, loud dynamics, and blues and gospel influences.

Step-by-step explanation:

Answer:

Your answer is every number is divided by 4

Step-by-step explanation:

so for the 4th term it would be 3/4, then divide that by 4, and then divide that by 4, and so on and so forth.

Answer: 400

Step-by-step explanation:

Area required by each couple = 72 inch by 72 inch

= 6 feet by 6 feet   [ 1 feet = 12 inches and \(72\text{ inches}=\dfrac{72}{12}\text{ feet}=6 \text{ feet}\)]

= 36 square feet

Area in each studio = 30 ft by 30 ft = 900 square feet

Then, Area of 8 studios in Houstan = 8 x (900 feet) = 7200feet

Total couple the dance company can accommodate in the city of Houston for all of it's locations = \(\dfrac{7200}{36}=200\)

Total people = 2 x (Total couples)= 2 x 200=400

Hence, a reasonable estimate for the total number of people the dance company can accommodate in the city of Houston for all of it's locations = 400

The equation of the circle is (x + 4)² + (y - 1)² = 81

Given is an equation of a circle we need to convert it in standard form,

x² + y² + 8x - 2y = 64,

To convert the equation of a circle to standard form, you need to complete the square for both the x and y variables.

The standard form of a circle equation is:

(x - h)² + (y - k)² = r²

where (h, k) represents the center of the circle, and r represents the radius.

Let's convert the given equation to standard form step by step:

x² + y² + 8x - 2y = 64

Rearrange the equation to group the x-terms and y-terms:

x² + 8x + y² - 2y = 64

Now, complete the square for the x-terms.

Take half of the coefficient of x (which is 8 in this case), square it, and add it to both sides of the equation:

x² + 8x + 16 + y² - 2y = 64 + 16

Simplify:

(x + 4)² + y² - 2y = 80

Complete the square for the y-terms.

Take half of the coefficient of y (which is -2 in this case), square it, and add it to both sides of the equation:

(x + 4)² + y² - 2y + 1 = 80 + 1

Simplify:

(x + 4)² + (y - 1)² = 81

Now, the equation is in standard form, with the center at (-4, 1) and a radius of √81 = 9.

Hence the equation of the circle is (x + 4)² + (y - 1)² = 81

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Answer:

(0,3)

(-1,1)

Step-by-step explanation:

Hello!

Since both equations are equal to y, we can set the right-hand side of the equations equal to each other.

X can either be 0 or -1. Remember, a solution to a system is not complete without a y-value. Plug in 0 and -1 for x in the first equation, and find the corresponding y-values.

\(y = 2(0) + 3\\y = 3\)

And

\(y = 2(-1) + 3\\y = -2 + 3\\y = 1\)

So the solutions to the system are (0,3) and (-1,1)

Answer:

The p-value of the test is of 0.2776 > 0.01, which means that the we accept the null hypothesis, that is, the manager's claim that this is only a sample fluctuation and production is not really out of control.

Step-by-step explanation:

A manufacturer considers his production process to be out of control when defects exceed 3%.

At the null hypothesis, we test if the production process is in control, that is, the defective proportion is of 3% or less. So

\(H_0: p \leq 0.03\)

At the alternate hypothesis, we test if the production process is out of control, that is, the defective proportion exceeds 3%. So

\(H_1: p > 0.03\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

0.03 is tested at the null hypothesis

This means that \(\mu = 0.03, \sigma = \sqrt{0.03*0.97}\)

In a random sample of 100 items, the defect rate is 4%.

This means that \(n = 100, X = 0.04\)

Value of the test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{0.04 - 0.03}{\frac{\sqrt{0.03*0.97}}{\sqrt{100}}}\)

\(z = 0.59\)

P-value of the test

The p-value of the test is the probability of finding a sample proportion above 0.04, which is 1 subtracted by the p-value of z = 0.59.

Looking at the z-table, z = 0.59 has a p-value of 0.7224

1 - 0.7224 = 0.2776

The p-value of the test is of 0.2776 > 0.01, which means that the we accept the null hypothesis, that is, the manager's claim that this is only a sample fluctuation and production is not really out of control.

Answer:

You need to use y=mx+b

In this case, m=1.5 so that means that y=1.5x

Now you must find out the y intercept which is "b" in y=mx+b

I think it is the first one (y=1.5x+72)

====================================================

Explanation:

The given slope is m = 1.5

We want the line to go through (x,y) = (6,72). This means x = 6 and y = 72 pair up together.

We'll plug those m, x, and y values into the equation below to solve for b

y = mx+b

72 = 1.5*6+b

72 = 9+b

72-9 = b ... subtract 9 from both sides

63 = b

b = 63 ... y intercept

-------------------

Since m = 1.5 and b = 63, we go from y = mx+b to y = 1.5x+63

Answer:

Z - statistic = 0.25

P-value

P(Z=0.25) =  0.802587

The result is not significant at p<0.01

Step-by-step explanation:

Step(i):-

Given the random sample size 'n'' = 400

A random sample of 400 items where 82 were found to be​ defective

Sample proportion

                     \(p = \frac{x}{n} = \frac{82}{400} = 0.205\)

Given Population proportion

                    P = 0.20

Null Hypothesis : P = 0.20

Alternative Hypothesis : P≠ 0.20

Step(ii):-

Test statistic

          \(Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }\)

         \(Z = \frac{0.205-0.20}{\sqrt{\frac{0.20X0.80}{400} } }= \frac{0.005}{0.02} =0.25\)

Z - statistic = 0.25

Level of significance =0.01

P-value

P(Z=0.25) =  0.802587

Conclusion:-

The result is not significant at p<0.01

Using the general equation for depreciation which is y = A(1 – r)^t, The value of the car in 4 years is $12528.15

The value of the car is solved by using the formula for depreciation which is  y = A(1 – r)t

definition of variables

where

y = current value, = ?

A = original cost, = $24,000

r = rate of depreciation, = 15% and

t = time, in years. = 4 years

substituting the variables

current value, y = A(1 – r)t

current value, y = 24000 * (1 - 0.15)⁴

current value, y = 12528.15

the depreciation is $12528.15

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The larger number is 26 and the smaller number is 13.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let, The two numbers be 'a' and 'b'.

Therefore, a + b = 39 and a = 2b.

So, a + b = 39.

2b + b = 39.

3b = 39.

b = 39/3.

b = 13.

Hence, a = 26.

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This means that the football’s height when it was kicked 41 yards away was -1.762 yards.

A yard is a unit of length measurement in the imperial and US customary systems of measurement. It is equal to 3 feet or 36 inches.

The equation given is a parabolic equation which models the path of the football. It is a quadratic equation in the form of y = ax² + bx + c, where a, b, and c are coefficients that determine the shape of the path. The coefficient a represents the rate of change in the football’s height as it moves away from the punter. In this equation, a is -0.035, which indicates that the football’s height decreases as it moves away from the punter. The coefficient b indicates the rate of change in the football’s height as it moves back toward the punter, and in this equation, b is 1.4, which means that the football’s height increases as it moves back towards the punter. Finally, the coefficient c is 1, which indicates the height of the football when it is kicked.

In this case, the football was kicked 41 yards, so plugging x = 41 into the equation gives us y = -0.035(41²) + 1.4(41) + 1 = -1.762.

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