Solve for x. Show each step of the solution.

4.5(8 −)+ 37 = 103 − 2.5(3 + 24)



PLEASE HELP!!!!!

List the hours from 1 to 8

Multiply the hours by how much she is paid per hour ( $12)

X: 1, 2, 3, 4, 5, 6, 7, 8

y: 12, 24, 36, 48, 60, 72, 84, 96

The OLSE for β₁ in the simple regression model is B₁ = (n∑[x₁y₁] - B∑[x₁]) / ∑[x₁²]. It is unbiased, meaning its expected value is equal to the true coefficient β₁.

To find the ordinary least squares estimator (OLSE) for the regression coefficients in the simple regression model, we need to minimize the sum of squared residuals. The OLSE for the coefficient β₁ is obtained by differentiating the sum of squared residuals with respect to β₁ and setting it equal to zero. Let's go through the steps:

Step 1: Model Assumptions

MLR.1: Linearity: The relationship between the response variable (y₁) and the predictor variable (x₁) is linear.

MLR.2: Independence: The observations are independent of each other.

MLR.3: Homoscedasticity: The variance of the errors (ε) is constant for all values of x₁.

MLR.4: No perfect multicollinearity: There is no perfect linear relationship between the predictor variable (x₁) and other predictor variables.

Step 2: Define the sum of squared residuals (SSR)

SSR = ∑[y₁ - (Bo + B₁x₁)]²

Step 3: Minimize SSR

To find the OLSE for β₁, we differentiate SSR with respect to β₁ and set it equal to zero:

∂SSR/∂B₁ = -2∑[y₁ - (Bo + B₁x₁)]x₁ = 0

Step 4: Solve for B₁

Expanding the equation: -2∑[y₁x₁ - Box₁ - B₁x₁²] = 0

Rearranging and dividing by -2: ∑[y₁x₁] - ∑[Box₁] - ∑[B₁x₁²] = 0

Since it is a simple regression model, we have: n∑[x₁y₁] - B∑[x₁] - B₁∑[x₁²] = 0

Simplifying the notation: n∑[x₁y₁] - B∑[x₁] - B₁∑[x₁²] = 0

Step 5: Solve for B₁

Rearranging the equation, we get: B₁∑[x₁²] = n∑[x₁y₁] - B∑[x₁]

Dividing both sides by ∑[x₁²], we obtain: B₁ = (n∑[x₁y₁] - B∑[x₁]) / ∑[x₁²]

Step 6: Show that the OLSE B₁ is unbiased

To demonstrate that B₁ is unbiased, we need to show that its expected value is equal to the true coefficient β₁.

E(B₁) = E((n∑[x₁y₁] - B∑[x₁]) / ∑[x₁²])

Since expectation is a linear operator, we can split it up:

E(B₁) = (nE(∑[x₁y₁]) - BE(∑[x₁])) / E(∑[x₁²])

Now, by the law of iterated expectations:

E(B₁) = (n∑[xE(y₁|x)]) - B∑[xE(x₁)]) / ∑[xE(x₁²)]

Since E(y₁|x) = Bo + B₁x₁, and E(x₁) = x₁, we have:

E(B₁) = (n∑[x(Bo + B₁x₁)] - B∑[x(x₁)]) / ∑[x(x₁²)]

Expanding the sums:

E(B₁) = (nBo∑[x] + nB₁∑[x₁²] - B∑[x(x₁)]) / ∑[x(x₁²)]

Since Bo, B₁, and x₁ are constants, they can be taken out of the sums:

E(B₁) = Bo(n∑[x]) + B₁(n∑[x₁²]) - B(∑[x(x₁)]) / ∑[x(x₁²)]

The terms Bo(n∑[x]) and B₁(n∑[x₁²]) can be written as:

Bo(n∑[x]) = nBo(∑[x]) = n∑[x]Bo

B₁(n∑[x₁²]) = nB₁(∑[x₁²]) = n∑[x₁²]B₁

Substituting back into the equation:

E(B₁) = n∑[x]Bo + n∑[x₁²]B₁ - B(∑[x(x₁)]) / ∑[x(x₁²)]

Now, recall that the true model is given by: y₁ = Bo + B₁x₁ + ε₁

Taking expectations: E(y₁) = E(Bo + B₁x₁ + ε₁)

Since E(ε₁) = 0: E(y₁) = Bo + B₁x₁

Comparing this with the definition of E(B₁), we see that:

E(B₁) = B₁

Therefore, the OLSE B₁ is unbiased, as its expected value is equal to the true coefficient β₁.

Note: In the above derivation, I assumed that the error term ε₁ follows the properties of MLR.1 through MLR.4, namely, it has a mean of zero, constant variance, and is normally distributed. These assumptions are necessary for the unbiasedness property of the OLSE.

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the probability of receiving 8 calls in a 13-minute interval.

To compute the probability of receiving 8 calls in a 13-minute interval, we can use the Poisson distribution. Given that calls arrive at a rate of 45 per hour, we need to adjust this rate to match the 13-minute interval.

First, we convert the rate to calls per minute by dividing 45 by 60 (since there are 60 minutes in an hour). This gives us a rate of 0.75 calls per minute.

Next, we use the formula for the Poisson distribution to calculate the probability. The formula is P(x; λ) = (e^(-λ) * λ^x) / x!, where x is the number of events (calls in this case) and λ is the average rate of events per interval.

Substituting the values into the formula, we have P(8; 0.75 * 13). Evaluating this expression will give us the probability of receiving 8 calls in a 13-minute interval.

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Based on the given information, the terminal side of angle 0 lies in quadrant III.

To determine the quadrant in which the terminal side of angle 0 lies based on the given information, we can analyze the signs of the trigonometric functions:

(a) Since sine < 0 and cotangent < 0, we can determine the quadrant as follows:

Sine < 0 implies that the y-coordinate (vertical component) of the point on the unit circle corresponding to angle 0 is negative.

Cotangent < 0 implies that the x-coordinate (horizontal component) of the point on the unit circle corresponding to angle 0 is negative.

In quadrant III, both the x and y-coordinates are negative. Therefore, quadrant III is the correct answer in this case.

(b) The information provided in this option is incorrect. "esce" is not a recognized trigonometric function, and "cos > 0" does not provide enough information to determine the quadrant.

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8 feet from the end of the wall is the nearest edge of the picture.

The process of converting phrases into equations and then solving those equations is known as solving algebraic word problems.

We will only need to use one variable and fundamental arithmetic operations to create the equations we require. In a real-world situation, the variable often stands for an unknowable quantity.

We can model and resolve word problems on the test that have two overlapping groups using Venn diagrams.

Let's say that the distance from the picture to the wall is x.

Since that distance will be on both sides of the picture (it's in the exact middle), we can say that:

x+3+x=19

=> 2x+3 = 19

=>2x=16

=>x= 8

Thus, 8 feet from the end of the wall is the nearest edge of the picture.

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The equation of the line that passes through the points (7, 450) and (14, 401) is y + 7x = 499

The equation of a line  can be represented as follows:

y - y₁ = m(x - x₁)

where

Therefore, (7, 450)(14, 401)

m = 401 - 450 / 14 - 7 = -49 / 7 = -7

Therefore, using (7, 450)

y - 450 = -7(x - 7)

y - 450 = -7x + 49

y + 7x = 49 + 450

y + 7x = 499

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Answer:

0.4 (decimal)

4/9 (fraction)

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

Probability a red marshmallow is picked = number of red marshmallows in the bag / sum of marshmallows in the bag

sum of marshmallows in the bag = 12 + 16 + 8 = 36

Probability a red marshmallow is picked = 16/36

To transform to the simplest form. divide both the numerator and the denominator by 4

= 4/9

to convert to decimal, divide 4 by 9 = 0.4444

0.4 to the nearest tenth

the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero

Answer:

18x+50

Step-by-step explanation:

josh deposited 50 dollars that would be your + 50. josh then deposits 18 dollars a week so that would be your 18x.

The similar angles and size are \(\mathbf{\hat {BC} \simeq \hat {YZ}, \overline {BC}, \overline{YZ}}\)

The word congruent originate and means "similar" or "the same", so when we talk about congruent angles we are talking about angles that are similar in size and have equal measures or shapes that are similar in structures.

In the given diagram, we are to study the shapes and determine the similar size and angles. So, from what we can deduce, we see that:

Therefore, we can conclude that the similar angles and size are \(\mathbf{\hat {BC} \simeq \hat {YZ}, \overline {BC}, \overline{YZ}}\)

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Here, we want to calculate the measure of angle D

Firstly, we can calculate the measure of angle A

Since BE and AD are perpendicular, it follws that triangle ABE is a right angled triangle

Thus,

52 + A = 90

A = 90-52

A = 38

Now, from the question, we are told that EBD and CBD are congruent, meaning that they are equal

We can deduce from the diagarm that;

The reason for this is that they are all on a straight line and the measure of angles on a straight line is 180

Thus, since we have the two angles equal, then;

The measure of angle B in triangle ABD would be 64 + 52 = 116.

Since we have two angles out of triangle ABD, we can get the measure of the third angle which is angle D (Sum of angles in a triangle = 180)

Mathematically, that would be;

Answer:

Step-by-step explanation:

Step: 1: Convert mixed fraction to improepr fraction.

Step: 2 : Find the LCM of 4 , 5 = 20

Step 3: Find equivalent fractions with denominator as 20

Step 4: Now subtract.

\(3\dfrac{1}{4}-1\dfrac{3}{5}=\dfrac{13}{4}-\dfrac{8}{5}\)

             \(\sf = \dfrac{13*5}{4*5}-\dfrac{8*4}{5*4}\\\\\\ = \dfrac{65}{20}-\dfrac{32}{20}\\\\\\ = \dfrac{65-32}{20}\\\\\\ = \dfrac{33}{20}\\\\ \\ = 1 \dfrac{13}{20}\)

Answer:

\(450000 \leqslant 15000 + 4t\)

Answer:

9.99m

Step-by-step explanation:

d≈9.99m

C Circumference

31.4m

Using the formulas

C=2πr

d=2r

Solving ford

d=C

π=31.4

π≈9.99493m

Answer:

4.8 × 10-5

Step-by-step explanation:

Answer:

The correct equation in slope-intercept form is:

y= 6x+14

Step-by-step explanation:

Given the equation

y-2=6(x+2)

y-2 = 6x+12

Adding 2 to both sides

y-2+2=6x+12+2

y= 6x+14

Thus, the correct equation in slope-intercept form is:

y= 6x+14

1) WHAT WAS YOUR MISTAKE

In the 2nd step, you had added 4 to the right-hand side of the equation instead of 2. The reason is that both sides should have been added by 2. But, you mistakenly added 4 to the right-hand side of the equation instead of 2.

2) SUGGESTION TO AVOID MISTAKE

You must make sure not to disturb the balance of two sides of the equation, meaning whatever the operation (add/subtract, multiply or divide) you do, you make sure to do the same operation on both sides of the equation.

Marcus is using a plant food to fertilize his garden his garden is a rectangle Marcus uses 1 cup of plant food for every square yard of his garden.

To solve it, we need to first find the area of Marcus's garden in square yards, and then multiply it by 1 cup of plant food per square yard. Finally, we need to convert the total cups to ounces using the given conversion rate.

Let the length of Marcus's garden is l yards and the width is w yards. Then the area of his garden in square yards is

A = lw.

If Marcus uses 1 cup of plant food per square yard, then he will use A cups of plant food in total.

To convert cups to ounces, we can use the given conversion rate of 4 cups per 28 ounces.

1 cup = 28/4 ounces

Therefore, the total weight of plant food Marcus uses in ounces is

Total weight = A * (28/4) ounces

By substituting A = lw, we get

Total weight = lw * (28/4) ounces

Total weight = 7lw ounces

Hence, the total weight of plant food Marcus uses to fertilize his garden is 7 times the product of the length and width of his garden, measured in yards.

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The solution to the system of differential equations is:

To solve the system of differential equations:

Start by finding the general solutions for each equation separately.

For the equation x' = 3x - 15y:

We can rewrite it as dx/dt = 3x - 15y.

This is a first-order linear homogeneous differential equation.

The general solution for x(t) can be found using the integrating factor method or by solving the characteristic equation.

Using the integrating factor method, we multiply the equation by the integrating factor e^(∫3 dt) = e^(3t) to make it integrable:

e^(3t)dx/dt - 3e^(3t)x = -15e^(3t)y.

Now, we integrate both sides with respect to t:

∫e^(3t)dx - 3∫e^(3t)x dt = -15∫e^(3t)y dt.

This simplifies to:

e^(3t)x = -15∫e^(3t)y dt + C1,

where C1 is the constant of integration.

Simplifying further:

x = -15e^(-3t)y + C1e^(-3t).

For the equation y' = 0x - 2y:

This is a separable first-order linear differential equation.

We can separate the variables and integrate both sides:

dy/y = -2dt.

Integrating both sides:

∫dy/y = -2∫dt,

ln|y| = -2t + C2,

where C2 is the constant of integration.

Taking the exponential of both sides:

|y| = e^(-2t + C2) = e^(-2t)e^(C2).

Since C2 is an arbitrary constant, we can combine it with e^(-2t) and write it as another arbitrary constant C3:

|y| = C3e^(-2t).

Considering the absolute value, we can have two cases:

Case 1: y = C3e^(-2t),

Case 2: y = -C3e^(-2t).

Now, we can use the initial conditions x(0) = 3 and y(0) = 2 to determine the specific values of the constants.

For x(0) = 3:

3 = -15e^0(2) + C1e^0,

3 = -30 + C1,

C1 = 33.

For y(0) = 2:

2 = C3e^0,

C3 = 2.

Plugging in the specific values of the constants, we obtain the particular solutions.

For x(t):

x = -15e^(-3t)y + C1e^(-3t),

x = -15e^(-3t)(2) + 33e^(-3t),

x = -30e^(-3t) + 33e^(-3t),

x = 3e^(-3t).

For y(t):

y = C3e^(-2t),

y = 2e^(-2t).

Therefore, the solution to the system of differential equations is:

x(t) = 3e^(-3t),

y(t) = 2e^(-2t).

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The graph of the system of inequalities can be seen below, there we can see that one possible solution is x = 10, y = 5.

Let's define the variables:

x = number of mangos she buys.

y = number of peaches she buys.

We know that she wants to buy no less than 13 fruits, then:

x + y ≥ 13

And she wants to spend $15 at most, then:

x*0.75 + y*1.25 ≤ 15

Then the system of inequalities is:

x + y ≥ 13

x*0.75 + y*1.25 ≤ 15

And the graph can be seen below:

There we can see that one possible solution is x = 10, y = 5.

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Answer:

6(c+5)

Step-by-step explanation:

You do distributive property, so then it would be 6c +30.

Hope it helps

To make sure the accessory is proportional from Dan to Marcellus, we need to maintain the same ratio of height between the two figures.

Since Marcellus is two times as tall as Dan, we can use the ratio stated above to determine the appropriate size of the accessory.

For example, let's say we want to give Dan and Marcellus a hat. We would need to make sure that the size of the hat for Marcellus is twice the size of the hat for Dan, to maintain the same ratio of height between the two figures.

To know that it is proportional, we can use a ruler or measuring tape to measure the height of Dan and Marcellus in the image, and then measure the size of the accessory for each figure.

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Cube rolled = 50 times

1 or 2 came up = 19 times

In percentage, that is >>>

So, 1 or 2 occured 38% of the times where it should occur around 20% of the times.

Looking at the answer choice, third option (C) is right.

The functions 7 are inverse functions while the functions 8 are not inverse functions

To verify that f and g are inverse functions, we need to show that:

Let's apply these conditions to the given functions:

f(x) = 5x + 2; g(x) = (x−2)/5

f(g(x)) = f((x−2)/5) = 5((x−2)/5) + 2 = x − 2 + 2 = x

g(f(x)) = g(5x + 2) = ((5x + 2) − 2)/5 = 5x/5 = x

Since f(g(x)) = x and g(f(x)) = x, we can conclude that f and g are inverse functions.

f(x) = ½x − 7; g(x) = 2x + 14

f(g(x)) = f(2x + 14) = ½(2x + 14) − 7 = x

g(f(x)) = g(½x − 7) = 2(½x − 7) + 14 = x − 7 + 14 = x + 7

Since f(g(x)) = x and g(f(x)) ≠ x, we can conclude that f and g are not inverse functions.

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The root test is inconclusive for the series Σ 1/n8n.

To determine the convergence or divergence of the series Σ 1/n8n using the root test, we need to calculate the limit as n approaches infinity of the nth root of the absolute value of the nth term. In this case, the nth term is 1/n8n.

Calculating the limit, we have lim n→∞ (n√|1/n8n|).

Simplifying the expression inside the absolute value, we get 1/n^8n = 1/n^(8n) = 1/n^(8n) = 1/(nⁿ⁸) = 1/(n⁸ⁿ).

Taking the nth root of the absolute value, we have

n√|1/n⁸ⁿ| = n√(1/(n⁸ⁿ)).

As n approaches infinity, the expression (1/(n^8n)) approaches zero because the denominator, n⁸ⁿ, grows much faster than the numerator, 1. Therefore, the nth root of the absolute value approaches 1.

Since the limit is equal to 1, the root test is inconclusive. The root test does not provide sufficient information to determine whether the series

Σ 1/n8n is convergent or divergent.

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Answer:

208

Step-by-step explanation:

20 × 0 = 0

40 + 40 = 80

125 + 3 = 128

The given expression \(40+40-20\times 0+3+125\) is reduced to 208 and this can be determined by using the arithmetic operations.

Given :

Expression - \(40+40-20\times 0+3+125\)

The following steps can be used to evaluate the given expression:

Step 1 - Write down the expression.

\(=40+40-20\times 0+3+125\)

Step 2 - First, multiply -20 by 0 in the given expression.

\(=40+40-0+3+125\)

Step 3 - Now, Add 40 and 40 in the above expression.

= 80 + 3 + 125

Step 4 - Add 80 and 3 in the above expression.

= 83 + 125

Step 5 - Add 83 and 125 in the above expression.

= 208

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If demand or annual usage increases by 10 percent, the Economic Order Quantity (EOQ) will increase. The EOQ model is used in inventory management to determine the optimal order quantity that minimizes total inventory costs.

The Economic Order Quantity (EOQ) is a model used in inventory management to determine the optimal order quantity that minimizes total inventory costs. It takes into account factors such as demand, holding costs, and ordering costs. When demand or annual usage increases by 10 percent, it means that more units are being consumed or sold within a given time period.

With an increase in demand, the EOQ will also increase. This is because the EOQ formula takes into consideration the trade-off between holding costs and ordering costs. Holding costs are the costs associated with holding inventory, such as warehousing and insurance, while ordering costs are the costs incurred when placing an order, such as administrative and transportation costs.

When demand increases, more units need to be ordered to meet the higher demand. This results in an increase in ordering costs, as more frequent orders will need to be placed. Consequently, the EOQ will increase to find the new optimal order quantity that balances the increased ordering costs with the holding costs.

In summary, if demand or annual usage increases by 10 percent, the EOQ will increase due to the need to order more frequently to meet the higher demand, resulting in increased ordering costs. This adjustment ensures that the inventory management system remains efficient and cost-effective.

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Answer:

200 crayons

Step-by-step explanation:

Let the total crayons be  'x'

24% of x = blue crayons

24% of x = 48

\(\dfrac{24}{100}*x =48\\\\x=48*\dfrac{100}{24}\\\\x = 2*100\\\\x = 200\)