An lift holds no more than 1200 pounds if you are rolling a cart that weighs 760 pounds how much more can the elevator hold?

Answer:

Step-by-step explanation:

12xy(3y - 4x)

the GCF is 12xy

The simple interest he earns in 2,560 on 17 months at a rate of

12% is 436.22

Calculating the interest on a loan using simple interest is quick and simple. Simple interest is calculated by dividing the principal by the daily interest rate and the number of days between payments.

Although some mortgages employ this calculation method, this type of interest typically applies to auto loans or short-term loans.

On a loan with simple interest, the first portion of every payment is applied to the interest for that month, and the remaining amount is applied to the principal. Interest is never accrued because each month's interest is paid in full. Compound interest, on the other hand, adds some of the monthly interest back onto the loan; you pay new interest on top of previous interest each month.

We have given the simple interest 12% per month for 17 months

Simple interest formula  SI = P × R × T, where P = Principal, R = Rate of Interest, and T = Time period.

SI = 2,560 × 12% × 1.42

SI =  436.224

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The transformation affects the range of values, and the class intervals remain the same.

The class intervals 10- <20, 20- <30, etc. are used to construct a histogram of the original data.

Similarly, the intervals 1.1- <1.2, 1.2- <1.3, etc. are used to construct a histogram of the transformed data. The effect of the transformation is that it changes the shape of the histogram.

Specifically, the histogram of the transformed data will generally be more condensed, or squashed together, than the original data.

This is because the transformation affects the range of values, and the class intervals remain the same.

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Answer:

sorry im in like 6th grade math so i don't really know either sry

Step-by-step explanation:

⇒\

In the given scenario, the line of best fit would indicate the relation between the distance covered in feet and the distance covered in meters in long jump. Question: Connections could make the record 28 feet or \(8.5344\) meters. Beamon's jump obliterated that by jumping over the 28-foot range to over 29 feet!

Your question here, what would the line of best fit? Long Jump: Long jump is a track and field event where the athlete runs down a runway and jumps as far as possible into a sandpit from a wooden takeoff board. The athlete's performance is measured from the edge of the takeoff board to the closest mark in the sand made by any part of their body.

The Line of Best Fit: The line of best fit is a straight line drawn through the center of a group of data points plotted on a scatter plot. The line of best fit is used to show the relationship between two sets of data, such as distance covered in feet and meters in long jump. The best fit line in this case would be a straight line passing through the scatter plot of the points representing the distance covered in feet and meters during a long jump.

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We will not be able to figure out the price of one can of each type of canned food in the same manner of operating on two equations.

This is because the equation are identical.

Let the dog food be represented by d.

Let the cat food be represented by c.

Since Carlos buys 4 cans of dog food and 6 cans of cat food for $12.00. This will be:

4d + 6c = 12

This cane b reduced to lowest term as 2d + 3c = 6

Then the next week, he purchased 2 cans of dog food and 3 cans of cat food for $6.00. This will be:

2d + 3c = 6

Since the equations are the same, we can't calculate the price.

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Answer:

The total area of the shaded region is 16 square units

Step-by-step explanation:

Main Steps:

Step 1. Find length of Square edge & Equilateral triangle leg

Step 2. Find the length from top to bottom of the full diamond

Step 3. Find the Area of the full diamond

Step 4. Find the Area that isn't shaded

Step 5. Find the Area that is shaded

Step 1. Find length of Square edge & Equilateral triangle edge

Since the Square has an area of 16 square units, using the formula for area of a square, the edge length must be 4 units

\(A_{square}=edge^2\)

\((16~\text{units}^2)=edge^2\)

\(4~\text{units}=edge\) of square

Since one edge of the equilateral triangle shares one edge of the square, they are the same length.  Thus, the equilateral triangle also has edge length of 4 units.

Step 2. Find the length from top to bottom of the full diamond

Equilateral triangles have a height that is exactly \(\dfrac{\sqrt{3}}{2}\) the length of their base.  So the height of the equilateral triangle is \(\dfrac{4\sqrt{3}}{2}\), or more simply \(2\sqrt{3}~\text{units}\).

The full diamond, from top to bottom, is the height of two of those equilateral triangles, plus the height of the central square:

\(2\sqrt{3}~\text{units} + 4~\text{units} + 2\sqrt{3}~\text{units}\)

Combining like terms, the length of the Diamond diagonal from top to bottom is \((4 + 4\sqrt{3})~\text{units}\).

Note, that due to symmetry of construction, this is also the length of the diamond's diagonal from left to right.

Step 3. Find the Area of the full diamond

One fact from geometry is that the area of a rhombus (all side lengths congruent), is given by the following formula:

\(A_{\text{rhombus}}=\frac{1}{2}d_{1}d_{2}\), where d1 and d2 are the lengths of the two diagonals.

The "diamond" that was constructed, has all sides congruent (all sides the same length), so it is a rhombus (with matching diagonal lengths that we just calculated in Step 2)

Thus, the Area of the rhombus is:

\(A_{\text{rhombus}}=\frac{1}{2}((4 + 4\sqrt{3})~\text{units})((4 + 4\sqrt{3})~\text{units})\)

Using FOIL,

\(A_{\text{rhombus}}=\frac{1}{2}(4^2 + 4*4\sqrt{3}+4*4\sqrt{3}+ (4\sqrt{3})^2)~\text{units}^2\)

\(A_{\text{rhombus}}=\frac{1}{2}(16 + 32\sqrt{3}+ (16*3))~\text{units}^2\)

\(A_{\text{rhombus}}=\frac{1}{2}(64 + 32\sqrt{3})~\text{units}^2\)

Distributing...

\(A_{\text{rhombus}}=(32 + 16\sqrt{3})~\text{units}^2\)

Step 4. Find the Area that isn't shaded

The area that isn't shaded is the area of the square, plus 4 equilateral triangles.

\(A_{\text{not shaded}}=4~A_{\text{equilateral triangle}}+A_{\text{square}}\)

Recall that the area of a triangle is 1/2 * b * h

\(A_{\text{equilateral triangle}}=\frac{1}{2}(4)(2\sqrt{3})~\text{units}^2\)

\(A_{\text{equilateral triangle}}=4\sqrt{3}~\text{units}^2\)

\(A_{\text{not shaded}}=4~A_{\text{equilateral triangle}}+A_{\text{square}}\)

\(A_{\text{not shaded}}=4~(4\sqrt{3}~\text{units}^2)+(16~\text{units}^2)\)

\(A_{\text{not shaded}}=(16\sqrt{3}~\text{units}^2)+(16~\text{units}^2)\)

\(A_{\text{not shaded}}=(16+16\sqrt{3})~\text{units}^2\)

Step 5. Find the Area that is shaded

Lastly, the area that is shaded is the area of the full diamond/rhombus, minus the area that is not shaded:

\(A_{\text{shaded}}=A_{\text{Rhombus}}-A_{\text{not shaded}}\)

\(A_{\text{shaded}}=((32+16\sqrt{3})~\text{units}^2)-((16+16\sqrt{3})~\text{units}^2)\)

Combining like terms and simplifying...

\(A_{\text{shaded}}=16~\text{units}^2\)

Answer:

a

Step-by-step explanation:

(3/4) to the power of 2 means to multiply it by itself and so, 3/4 times itself is 9/16

Answer:

Step-by-step explanation:

Hello

\(\large\displaystyle\text{$\begin{gathered} \sf Apply \ the \ third \ exponent \ rule-: \bigg(\dfrac{x}{y}\bigg)^m=\dfrac{x^m}{y^m} \end{gathered}$}}\)

Solve-:

\(\large\displaystyle\text{$\begin{gathered} \sf \bigg(\dfrac{x}{y}\bigg)^2= \dfrac{3^2} {4^2} =\boxed{\sf{\frac{9}{16}}} \end{gathered}$ }}\)

\(\pmb{\tt{done \ !!}}\)

\(\orange\hspace{300pt}\above2\)

Answer: i think its c

Step-by-step explanation:

Euler's method will be more accurate if the solution to the differential equation is a lower order polynomial. As the order of the polynomial increases, the accuracy of Euler's method decreases.

Euler's method is a numerical approximation technique used to estimate the solution to a differential equation. It is not exact and introduces some error due to its approximation nature.

The accuracy of Euler's method depends on the order of the polynomial that represents the solution.

In general, Euler's method is more accurate for lower order polynomials. This means that if the solution to the differential equation is a lower order polynomial, the approximation obtained using Euler's method will be more accurate.

To understand this, let's consider an example. Suppose we have a first-order polynomial as the solution to the differential equation.

In this case, Euler's method will provide a reasonably accurate approximation. However, as the order of the polynomial increases, the accuracy of Euler's method decreases.

It's important to note that higher order polynomials have more complex behavior, and Euler's method cannot capture all the intricacies of the solution.

In such cases, other numerical approximation methods, like the Runge-Kutta method, may be more suitable.

In summary, Euler's method will be more accurate if the solution to the differential equation is a lower order polynomial. As the order of the polynomial increases, the accuracy of Euler's method decreases.

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The probability of the total being equal to 8 is 1/9 or 11.11%.

To calculate this probability, we must first calculate all the possible combinations of two six-sided dice that add up to 8. Since both the dice are showing an even number, the possible combinations are (2, 6), (4, 4), and (6, 2). the total number of possible combinations for two six-sided dice is 36 (6 x 6). Therefore, the probability of the total being equal to 8 is 3/36 or 1/9 or 11.11%.

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The measure of angles JKL, KJM and KRL are -51°, 105° and 51° respectively and the length of diagonal JL is 81 units.

An isosceles trapezoid is a four-sided polygon with two opposite sides parallel and two other sides of equal length.

In Quadrilateral JKLM,

KR = 42 and JR = 39,

R being the midpoint of diagonal.

Also, angle KMJ = 27° and KML = 78°.

The measure of angle JKL is equal to the difference of given angles KMJ and KML.

Therefore,

Angle JKL = KML-KMJ

       = 78°- 27°

       = 51°

The measure of angle KJM is equal to the sum of given angles KMJ and KML.

Therefore,

Angle KJM = KMJ + KML

       = 27° + 78°

       = 105°

The measure of angle KRL is equal to the difference of given angles KML and KMJ.

Therefore,

Angle KRL = KML - KMJ

       = 78° - 27°

       = 51°

The length of Diagonal JL is equal to the sum of lengths of given sides KR and JR.

Therefore,

Length of JL = KR + JR

        = 42 + 39

        = 81

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Mia can create a scale drawing of a football field using a scale of 1:1,000. The scale drawing will provide a Visual representation of the field, allowing for easier analysis and planning.

To create a scale drawing of a football field using a scale of 1:1,000, Mia can follow these steps:

1. Determine the dimensions: The football field's dimensions are given as 120 yards by 53 1/3 yards. Convert the fractional measurement to a decimal for simplicity. In this case, 1/3 yard is approximately 0.333 yards.

2. Decide on the units: Since the scale is 1:1,000, Mia needs to determine the unit of measurement she will use in her scale drawing. For consistency, she can choose to use feet as the unit.

3. Calculate the scaled dimensions: To create the scale drawing, Mia needs to scale down the dimensions of the football field. Since the scale is 1:1,000, she can divide the actual dimensions by 1,000 to obtain the scaled dimensions. The scaled dimensions would be 120 yards / 1,000 = 0.12 yards (or 0.36 feet) for the length and 53.333 yards / 1,000 = 0.053333 yards (or 0.16 feet) for the width.

4. Draw the scaled football field: Using a ruler and a grid paper, Mia can draw a rectangle with dimensions of 0.12 feet by 0.053333 feet (or inches, depending on the size of the grid paper). She can label the sides of the rectangle with the corresponding measurements in feet.

5. Add additional markings: Mia can add other markings to the scale drawing, such as the goal posts, yard markers, and any other important features of the football field. She can refer to the actual measurements and proportions of these elements to ensure accuracy.

By following these steps, Mia can create a scale drawing of a football field using a scale of 1:1,000. The scale drawing will provide a visual representation of the field, allowing for easier analysis and planning.

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The linear programming model would include equation for profit will be Z = 0.85X + 0.9Y and production constraints are 0.3X <= Y <= 0.6X; demand constraints are X <= (5000 + 3A) and Y <= (4000 + 5B); and cost constraint are 0.6X + 0.85Y + A + B <= 16,000.

Optimal values of X, Y, A, and B that maximize profit (Z) can be determined by using Excel Solver.

The linear programming model for the given problem is shown below:

Let X be the number of jars of applesauce produced. Y be the number of bottles of apple juice produced.

The objective function will be to maximize profit, which can be calculated by the following equation:

Profit = revenue - cost

Revenue can be calculated by multiplying the number of units produced by their respective selling prices. Cost can be calculated by multiplying the number of units produced by their respective production costs. The equation for profit will be:

Z = 1.45X + 1.75Y - (0.6X + 0.85Y)

Z = 0.85X + 0.9Y

The marketing manager estimates that the demand for applesauce is a maximum of 5,000 jars, plus an additional 3 jars for each $1 spent on advertising. The maximum demand for apple juice is estimated to be 4,000 bottles, plus an additional 5 bottles for every $1 spent on promoting apple juice. The maximum amount of money that can be spent on production and advertising is $16,000.

Therefore, we can write the constraints as follows:

Production constraints:

0.3X <= Y <= 0.6X

Demand constraints:

X <= (5000 + 3A)

Y <= (4000 + 5B)

Cost constraint:

0.6X + 0.85Y + A + B <= 16,000

Where A and B are the amounts spent on advertising for applesauce and apple juice, respectively.

To solve the model by using the computer, we can use any software that solves linear programming problems.

One such software is Microsoft Excel Solver. We can set up the problem in Excel as follows:

Cell C9: 0.85X + 0.9Y

Cell C12: 0.6X + 0.85Y + A + B

Cell C13: $16,000

Cell C15: 0.3X

Cell C16: XCell C17: 0.6X

Cell C18: 5000 + 3A (for applesauce)

Cell C19: Y

Cell C20: 4000 + 5B (for apple juice)

Cell C21: A

Cell C22: B

We then use Excel Solver to find the optimal values of X, Y, A, and B that maximize profit (Z).

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So, 174 children, 100 students, and 87 adults attended the movie theater.Let's denote the number of children as x, the number of students as y, and the number of adults as z. We can use the given information to form the following equations:

1) x + y + z = 361 (Total seating capacity)
2) z = 0.5x (Half as many adults as children)
3) 5x + 7y + 12z = 2614 (Total ticket sales)
Now, substitute equation (2) into equation (3):
5x + 7y + 12(0.5x) = 2614
5x + 7y + 6x = 2614
11x + 7y = 2614
Next, substitute equation (2) into equation (1):
x + y + 0.5x = 361
1.5x + y = 361
Now we can solve these two linear equations:
11x + 7y = 2614
1.5x + y = 361
Multiply the second equation by 7 to match the y-coefficients:
10.5x + 7y = 2527
Subtract the new equation from the first equation:
0.5x = 87
x = 174
Now, find y:
1.5(174) + y = 361
261 + y = 361
y = 100
Finally, find z:
z = 0.5x = 0.5(174) = 87

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There are 174 children, 100 students, and 87 adults in attendance.

Let's use the following variables to represent the number of attendees for each category:
C = number of children
S = number of students
A = number of adults
We are given the following information:
The theater's seating capacity is 361.
\(C + S + A = 361\)
There are half as many adults as there are children.
\(A = 0.5C\)
The total ticket sales amount to $2614.
\(5C + 7S + 12A = 2614\)
Now, we will solve the system of equations.
First, let's rewrite equation (2) to express C in terms of A:
\(C = 2A\)
Next, substitute this expression for C in equation (1):
\(2A + S + A = 361\)
\(3A + S = 361\)
Now, substitute the expression for C in terms of A into equation (3):
\(5(2A) + 7S + 12A = 2614\)
\(10A + 7S + 12A = 2614\)
\(22A + 7S = 2614\)

We already have an expression for S from equation (1):
\(S = 361 - 3A\)
Now, substitute this expression for S in the last equation:
\(22A + 7(361 - 3A) = 2614\)
\(22A + 2527 - 21A = 2614\)
\(A = 2614 - 2527\)
\(A = 87\)
Now that we have the number of adults \((A = 87)\), we can find the number of children (C) and students (S) using the expressions we derived earlier:
\(C = 2A = 2(87) = 174\)
\(S = 361 - 3A = 361 - 3(87) = 361 - 261 = 100\)

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Answer:

Juanita and Esperanza run 400 meters and 8400 meters respectively and Evelyn make 4.125 laps.

Step-by-step explanation:

The complete question is: A telesecundaria school has a race track that measures one kilometer .

Three students ran the following distances Juanita: 1 laps, Esperanza  21 laps and Evelyn: 1650 m. How many meters did Juanita and Esperanza run?  And how many laps did Evelyn make?

As we know that 1 meter = 0.0025 laps

So, the number of laps Evelyn make = 1650 \(\times\) 0.0025

                                                             = 4.125 laps

Also, 1 lap = \(\frac{1}{0.0025}\) meters

        1 lap = 400 meters

So, the meters that Juanita run = 1 \(\times\) 400 = 400 meters

Similarly, the meters that Esperanza run = 21 \(\times\) 400

                                                                   = 8400 meters

Hence, Juanita and Esperanza run 400 meters and 8400 meters respectively and Evelyn make 4.125 laps.

Answer:

\(10g - 8 = 8g \\ \\ 2g = 8 \\ \\ g = 4\)

G is equal to 4.

Without the standard deviation, we cannot calculate the standard error or the 95 percent confidence interval for the mean time required to stabilize emergency condition 4 using display panel B.

To calculate a 95 percent confidence interval for the mean time required to stabilize emergency condition 4 using display panel B, we can use the least squares means estimates provided in the JMP output.

According to the JMP output, the estimate for the mean time required to stabilize emergency condition 4 using display panel B is 10.375000.

To calculate the confidence interval, we need to find the margin of error. The margin of error can be calculated using the formula:

Margin of Error = Critical Value * Standard Error

In this case, we need to find the critical value for a 95 percent confidence interval. Since we have a sample size of 24 (as mentioned in the question), we can use the t-distribution with (24-1) degrees of freedom to find the critical value.

Looking up the critical value in the t-distribution table, with (24-1) degrees of freedom and a confidence level of 95 percent, we find that the critical value is approximately 2.064.

The standard error can be calculated using the formula:

Standard Error = Standard Deviation / √(sample size)

The standard deviation is not provided in the given information. Therefore, we cannot calculate the standard error or the confidence interval without this information.

In summary, without the standard deviation, we cannot calculate the standard error or the 95 percent confidence interval for the mean time required to stabilize emergency condition 4 using display panel B.

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Answer:

750

Step-by-step explanation:

30/40 students dislike it from the sample, so 0.75

1000 x 0.75 = 750

Let's try to understand how we can solve this equation

Given equation,4f+2=6f-12

Now we will take the terms on one side and constants on the other.

=> 2+12=6f-4f

=> 14=2f

=>7=f

So, the value of f would be 7. Remember that while bringing value to another side, the sign of that value changes. If it is a positive sign then it is going to be transformed into a negative one and vice versa.

Answer:

area = 8 × 18 = 144 cm^2

volume 8×18×5 = 720cm^3

Answer:

What we need to do is simply multiply the values in both columns e.g 4 * 3/36 = 12/36

Please check explanation for complete answer

Step-by-step explanation:

Here, we are concerned about filling the empty columns of the table.

What we want to do here is simply straightforward. All we need to do is to

multiply the values of x by the values of P(x) in each of the individual rows.

Also recall, we do not need to reduce the fractions.

So we have;

2. 3 * 2/36 = 6/36

3. 4 * 3/36 = 12/36

4. 5 * 4/36 = 20/36

5. 6 * 5/36 = 30/36

6. 7 * 6/36 = 42/36

7. 8 * 5/36 = 40/36

8. 9 * 4/36 = 36/36

9. 10 * 3/36 = 30/36

10. 11 * 2/36 = 22/36

11. 12 * 1/36 = 12/36

Answer:

2 to the power of 6

Step-by-step explanation:

2 x 2 x 2 x 2 x 2 x 2

Answer:

15

Step-by-step explanation:

sold 1/3 so 2/3 remain

(2/3)x + 15 = 25

Subtract 15 from both sides

(2/3)x = 10

Multiply both sides by 3/2

x = 15

Answer:

That would be ~p through~v.

We have derived the desired expressions: E[Y] = μE[N], Var(Y) = σ²E[N] + μ²Var[N]

To answer your question, let's start by defining the given terms:

N = number of shops visited (positive integer random variable)
Xi = amount of money spent in the i-th shop
Y = X1 + X2 + ... + XN (total amount of money spent)
μ = mean of the Xi's
σ² = variance of the Xi's

We are given that N and all Xi are independent, and we want to show that:

E[Y] = μE[N]
Var(Y) = σ²E[N] + μ²Var[N]

First, let's find E[Y]:

E[Y] = E[X1 + X2 + ... + XN]
By linearity of expectation:
E[Y] = E[X1] + E[X2] + ... + E[XN]

Since all Xi's have the same mean (μ), we can rewrite this as:

E[Y] = Nμ
Since N is a random variable, we take the expectation of N:
E[Y] = μE[N]

Next, let's find Var(Y):

Var(Y) = Var(X1 + X2 + ... + XN)

As N and all Xi are independent, we can say:

Var(Y) = Var(X1) + Var(X2) + ... + Var(XN)

Since all Xi's have the same variance (σ²), we can rewrite this as:

Var(Y) = Nσ²

Now, we need to find the variance of N:

Var(Y) = σ²E[N] + μ²Var[N]

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Answer:

x=8

Step-by-step explanation: