Use algebra tiles to model the expression and combine like terms. Complete the statements.

x + x + x + x + 4 – 1

Combine the x tiles to get
.
Combine the integer tiles to get
.
The equivalent expression is
.
You can use
to verify the expressions are equivalent.

Therefore, the given statement that the t-distribution has more area in the tails than the standard normal distribution

SO ITS TRUE

Answer: true

Step-by-step explanation:

Answer:

The value of x is 7 if the equation can be reduced to (x + 9)³ = 4096 after applying the properties of the integer exponent option (C) 7 is correct.

What is an integer exponent?

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that:

The equation is:

After solving:

(x + 9)³ = 4096

x + 9 = ∛4096

x + 9 = 16

x = 7

Thus, the value of x is 7 if the equation can be reduced to (x + 9)³ = 4096 after applying the properties of the integer exponent option (C) 7 is correct.

The answer is that 56 cm is equal to 22.05 inches.

Centimeters (cm) and inches (in) are units of length used to measure distances or lengths. Centimeters are part of the metric system, which is widely used around the world, while inches are part of the imperial system, which is still used in some countries, including the United States.

To convert centimeters to inches, you can use the conversion factor of 1 inch being equal to 2.54 centimeters. To convert 56 centimeters to inches, you would divide 56 by 2.54:

56 cm / 2.54 cm/in = 22.05 in

It's important to be precise when converting between different units of measurement, especially in science and engineering, where small inaccuracies can result in significant errors in calculations and results.

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We can proved that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

Let's denote the vertices of the parallelogram as A, B, C, and D, with O as the midpoint of AC and BD.

First, we can see that triangles ABO and CDO are congruent by the Side-Side-Side (SSS) postulate, since they share side BD, and both have sides AB and CO of equal length due to O being the midpoint of BD. Therefore, angles AOB and COD are congruent, and we can denote their measure as θ.

Using the Law of Cosines in triangles ABO and CDO, we can express the squares of the diagonals AC and BD in terms of the sides of the parallelogram:

AC² = AB² + BC² - 2(AB)(BC)cosθ

BD² = AB² + BC² + 2(AB)(BC)cosθ

Adding these two equations together, we get:

AC² + BD² = 2(AB² + BC²)

which is the desired result. Therefore, we have shown that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

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bh, where b is the base and h is the height of the parallelogram.

In the case of the circle, the base of the parallelogram is the circumference of the circle, which is equal to 2πr, where r is the radius of the circle. The height of the parallelogram is the distance from the center of the circle to the edge of the circle, which is also the radius r. Therefore, we have:

b = 2πr

h = r

Substituting these values into the formula for the area of a parallelogram, we get:

Area = bh = (2πr)(r) = 2πr^2

So the formula for the area of a circle is derived from the formula for the area of a parallelogram by using the circumference of the circle as the base and the radius of the circle as the height.

Mean of rt = 0.02,

Variance of rt = 0.02,

Lag-1 Autocorrelation (ρ1) = -0.01,

Lag-2 Autocorrelation (ρ2) = Unknown,

1-step ahead forecast = -0.005,

2-step ahead forecast = 0.02,

The standard deviation of forecast errors = √0.02.

We have,

To find the mean and variance of the return series, we can substitute the given model into the equation and calculate:

Mean of rt:

E(rt) = E(0.02 + 0.5rt-2 + et)

= 0.02 + 0.5E(rt-2) + E(et)

= 0.02 + 0.5 * 0 + 0

= 0.02

The variance of rt:

Var(rt) = Var(0.02 + 0.5rt-2 + et)

= Var(et) (since the term 0.5rt-2 does not contribute to the variance)

= 0.02

The mean of the return series rt is 0.02, and the variance is 0.02.

To compute the lag-1 and lag-2 autocorrelations of rt, we need to determine the correlation between rt and rt-1, and between rt and rt-2:

Lag-1 Autocorrelation:

ρ(1) = Cov(rt, rt-1) / (σ(rt) * σ(rt-1))

Lag-2 Autocorrelation:

ρ(2) = Cov(rt, rt-2) / (σ(rt) * σ(rt-2))

Since we are given r100 = -0.01 and r99 = 0.02, we can substitute these values into the equations:

Lag-1 Autocorrelation:

ρ(1) = Cov(rt, rt-1) / (σ(rt) * σ(rt-1))

= Cov(r100, r99) / (σ(r100) * σ(r99))

= Cov(-0.01, 0.02) / (σ(r100) * σ(r99))

Lag-2 Autocorrelation:

ρ(2) = Cov(rt, rt-2) / (σ(rt) * σ(rt-2))

= Cov(r100, r98) / (σ(r100) * σ(r98))

To compute the 1- and 2-step-ahead forecasts of the return series at

t = 100, we use the given model:

1-step ahead forecast:

E(rt+1 | r100, r99) = E(0.02 + 0.5rt-1 + et+1 | r100, r99)

= 0.02 + 0.5r100

2-step ahead forecast:

E(rt+2 | r100, r99) = E(0.02 + 0.5rt | r100, r99)

= 0.02 + 0.5E(rt | r100, r99)

= 0.02 + 0.5(0.02 + 0.5r100)

The associated standard deviation of the forecast errors can be calculated as the square root of the variance of the return series, which is given as 0.02.

Thus,

Mean of rt = 0.02,

Variance of rt = 0.02,

Lag-1 Autocorrelation (ρ1) = -0.01,

Lag-2 Autocorrelation (ρ2) = Unknown,

1-step ahead forecast = -0.005,

2-step ahead forecast = 0.02,

The standard deviation of forecast errors = √0.02.

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Answer:

3/7

Step-by-step explanation:

Simply we write 3 in numerator and 7 in the denominator as a result 3 divided by 7 can be written as (3/7) in fraction form.

Answer:

a. The company's profit function P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26

b. The number of cars that must be sold in each market are 60 in America, also 60 in Europe and 80 in Asia.

Step-by-step explanation:

Note: This question is not complete and it has some errors in the figures used. The correct complete question is therefore provided before answering the question as follows:

An automobile manufacturer sells cars in America, Europe, and Asia, charging a different price in each of the three markets. The price function for cars sold in America is p = 27 − 0.2x  (for 0 ≤ x ≤ 135), the price function for cars sold in Europe is q = 15 − 0.1y  (for 0 ≤ y ≤ 150), and the price function for cars sold in Asia is r = 19 − 0.1z (for 0 ≤ z ≤ 190), all in thousands of dollars, where x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively. The company's cost function is C = 26 + 3(x + y + z) thousand dollars.

(a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.]

P(x, y, z) =

(b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and Pz equal to zero and solve. Assuming that the maximum exists, it must occur at this point.]

The explanation to the answers is now given as follows:

(a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.]

p = price function for cars sold in America = p = 27 − 0.2x (for 0 ≤ x ≤ 135)

q = price function for cars sold in Europe = 15 − 0.1y (for 0 ≤ y ≤ 150)

r = price function for cars sold in Asia = 19 − 0.1z (for 0 ≤ z ≤ 190)

C = company's cost function = 26 + 3(x + y + z) = 26 + 3x + 3y + 3z

P(x, y, z) = profit function

x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively

Therefore, we have:

TR = Total revenue = px + qy + rz …………………………….. (1)

Substituting the relevant values into equation (1), we have:

TR = (27 − 0.2x)x + (15 − 0.1y)y + (19 − 0.1z)z

TR = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2

Also,

P(x, y, z) = TR – C ……………………………………… (2)

Substituting the relevant values into equation (2), we have:

P(x, y, z) = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2 – (26 + 3x + 3y + 3z)

P(x, y, z) = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2 – 26 – 3x – 3y – 3z

P(x, y, z) = 27x – 3x +15y – 3y +19z – 3z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26

P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26 ……………….. (3)

Therefore, the company's profit function P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26.

(b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and Pz equal to zero and solve. Assuming that the maximum exists, it must occur at this point.]

As indicated in the question, the number cars that should be sold in each market to maximize profit can be calculated by deriving the three partials Px, Py, and Pz from the profit function P(x, y, z), i.e. equation (3) in part a above, and set equal to zero and then solve as follows:

In America

From equation (3), we have:

Px = 24 – 0.4x = 0

Therefore, we have:

24 – 0.4x = 0

24 = 0.4x

x = 24 / 0.4

x = 60

In Europe

From equation (3), we have:

Py = 12 – 0.2y = 0

Therefore, we have:

12 – 0.2y = 0

12 = 0.2y

y = 12 / 0.2

y = 60

In Asia

From equation (3), we have:

Pz = 16 - 0.2z = 0

Therefore, we have:

16 - 0.2z = 0

16 = 0.2z

z = 16 / 0.2

z = 80

Based on the above calculations, the number of cars that must be sold in each market are 60 in America, also 60 in Europe and 80 in Asia.

9514 1404 393

Answer:

  175.2 square feet

Step-by-step explanation:

The lateral area is the total area of the side faces. It excludes the area of the top and bottom "bases" of the prism.

It can be found by adding the areas of the four rectangles. The two you can't see have the same areas as the two you can see.

Since the height of each rectangle is 4 feet. the total area will be the product of that and the perimeter of the prism.

  LA = Ph . . . . perimeter times height

  LA = 2(L+W)h . . . . the perimeter is twice the sum of length and width

  LA = 2(12.3 ft + 9.6 ft)(4 ft) = 2(21.9 ft)(4 ft) = 175.2 ft²

The lateral area of the prism is 175.2 ft².

__

The attachment shows scribbling on two of the faces that contribute to the lateral area. As stated above, the other two faces are the same size as these.

Answer: Depending on you mean I have answers for them so I hope one of them is for what your looking for.

Answer:

Step-by-step explanation:

Use the speed formula:

\(s = \frac{d}{t}\)

The runner travelled 1 yard in 6  minutes.

\(s = \frac{1\:yard}{6\:minutes}\\s = 0.166...7\)

Hope this helps!

Answer:

\(C(t)= \frac{1}{2} kg (2/3) ^ t\)

Step-by-step explanation:

Original Question:

Explanation:

Therefore, the indicated z-score is 2.45.

To find the indicated z-score, we need to use a standard normal distribution table. From the graph, we can see that the area to the right of the z-score is 0.9850.
Looking at the standard normal distribution table, we find the closest value to 0.9850 in the body of the table is 2.45. This means that the z-score that corresponds to an area of 0.9850 is 2.45.
It's important to note that the standard deviation of the standard normal distribution is always 1. This is because the standard normal distribution is a normalized version of any normal distribution, where we divide the difference between the observed value and the mean by the standard deviation.

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(a) There is no extreme value of A subject to the given constraint,

(b) For x = 0, y + z² ≤ 16.

y is between -4 and 4. In this case, f(y,z) = y² and the maximum value is 16.

For x = ±y, z = 4 - y².

y is between -2 and 2. In this case, f(y,z) = 2y² - y⁴ and the maximum value is 2.

When dividing by a variable, one should always keep in mind that the variable cannot be equal to zero. In other words, if the value of the variable is zero, the function or expression will not be defined or will give an undefined result. The reason is that division by zero is not defined in the set of real numbers.

Therefore, one should exclude the value of zero from the domain of the function or expression.

In part (a) of the given question, we are asked to find the global maximum and minimum of A(x,y,z) = 12 + 3x + y² - 2y subject to the constraint x + y + z = 2.

Let's find the partial derivatives of A with respect to x, y, and z.

∂A/∂x = 3

∂A/∂y = 2y - 2 = 2(y - 1)

∂A/∂z = 0

Now, we have to solve the system of equations consisting of the partial derivatives and the constraint equation.

\(3 = \lambda_1 + \lambda_2,\\2y - 2 = \lambda_1 + \lambda_2,\\\lambda_1x + \lambda_2x = 0,\\\lambda_1y + \lambda_2y - 1 = 0,\\\lambda_1z + \lambda_2z = 1.\)

Substituting the values of the partial derivatives, we get:

\(\lambda_1 + \lambda_2 = 3,\\\lambda_1 + \lambda_2 = -2,\\\lambda_1(3) + \lambda_2(0) = 0,\\\lambda_1(y - 1) + \lambda_2(y - 1) = 0,\\\lambda_1(0) + \lambda_2(1) = 1.\)

The second and third equations are contradictory. So, under the given constraint, A has no extreme value.

In part (b), we are asked to find the global maximum and minimum of A(x,y,z) = x² + y² on the closed bounded domain x² + y + z² ≤ 16.

Let's use the method of Lagrange multipliers to solve the problem. We have to find the critical points of the function f(x,y,z) = x² + y² subject to the constraint x² + y + z² = 16.

We have to solve the system of equations consisting of the partial derivatives of f, the partial derivatives of the constraint function, and the equation of the constraint function.

2x = λ(2x),

2y = λ(1),

2z = λ(2z).

Substituting the value of λ from the second equation into the first equation, we get: x = 0 or x = ±y.

Substituting the values of x and λ from the first and second equations into the third equation, we get:

z = 4 - y² or z = 0.

Since the constraint is x² + y + z² ≤ 16, we have to consider the following cases:

Case 1: x = 0, y + z² ≤ 16.

So, y is between -4 and 4. The maximum value of f(y,z)=y² is 16 in this case.

Case 2: x = ±y, z = 4 - y².

So, y is between -2 and 2. The maximum value of f(y,z) = 2y² - y⁴ is 2 in this case.

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Answer:

2/3 feet

Step-by-step explanation:

Available length = 11/12 feet

Piece cut out = 1/4 feet

How much paper is left to make the banner?

Paper remaining = available length - piece cut out

= 11/12 - 1/4

= 11-3 /12

= 8/12

= 2/3 feet

Paper left to make the banner = 2/3 feet

Answer:

$558.60

Step-by-step explanation:

First you would take 399 and multiply that by 0.40. Then you would take that answer and add it to 399.

Answer:

D. y=0.3(x+0.8)^2 -10

Step-by-step explanation:

When looking at the y-intercepts (the number at the very end of the equation) of the equations -10 is the one farthest away from the y-axis

7 ≤ p

8 ≤ p

8 < p

9 < p

Answer:

Step-by-step explanation:

Given the following :

Number of signatures required = at least 1000 ( ≥ 1000)

Number of signatures already obtained = 380

Given that a petition page holds 80 signatures

How many more pages does Devin need

Number of signatures left = ≥ 1000 - 380 = ≥ 620 more signatures

Let the number of pages required = p

With 380 signatures,

380 / 80 = 5 pages (20 more signatures to complete the 5 th page)

Number of signatures left = 620

(620 - 20) = 600

= 600/ 80

= 7.5 pages to the nearest whole number = 8 pages

The most appropriate option is 8 less than or equal to the number of pages needed .

8 ≤ p

Answer:

8 ≤ p

Step-by-step explanation:

Answer: The answer is B: Changed

Step-by-step explanation:

Given the following functions:

To compose then, is basically use the inside function as the argument.

If we call '3x-1' as 'u'

We know the following

And this is our answer.

Answer:

ZD = 10

Step-by-step explanation:

In a parallelogram

Let us solve the question

∵ ABCD is a parallelogram

∵ AC and DB are its diagonals

→ By using the 5th property above

∴ AC and BD bisect each other

∵ AC ∩ BD at point Z

→ That means Z is the midpoint of them

∴ Z is the midpoint of BD

→ That means Z divides BD into 2 equal parts BZ and ZD

∴ BZ = ZD

∵ BZ = 10

∴ ZD = 10

Answer: 0.33

Step-by-step explanation:

You get 0.33 repeating

Answer:

1/3

Step-by-step explanation:

0.5 divided by 1.5 can also be written as 1/2 divided by 3/2.

So lets rewrite it like this:

(1/2)/(3/2)

From here there are two ways we can solve this. One is to multiply by the reciprocal:

(1/2) × (2/3)= 2/6

which simplifies to 1/3 as your final answer.

The other method is to "oreja"

you multiply the top most number and the bottom most number together and then the two middle ones like so:

(1/2)/(3/2) -> (1×2)/(2×3)

which is 2/6 once again and simplifies to 1/3 the final answer.

Answer:

She can make 5 trips.

Step-by-step explanation:

Answer:

4.8%

Step-by-step explanation:

Answer:4.8

Step-by-step explanation:

Trust

To find the intensity of the sound with the top up and with the top down, we need additional information such as the specific decibel level or the change in decibel level caused by the top being up or down. Please provide the decibel level or the change in decibel level.


The formula for loudness in decibels (dB) is given by loudness = 10 log(I/I₀), where I is the intensity and I₀ is the reference intensity of 10⁻¹² W/m².

To determine the intensity of the sound with the top up or down, we need the decibel level or the change in decibel level caused by the top position. Without that information, we cannot calculate the exact intensity values.

However, we do have some reference points for loudness. The human threshold for pain is typically considered to be 120 dB, and instant perforation of the eardrum occurs at 160 dB. These thresholds can help us understand the range of intensities associated with different decibel levels.

If you provide the decibel level or the change in decibel level caused by the top being up or down, we can use the formula to calculate the corresponding intensity.

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The corresponding parts are:

The statement is given as:

△ABC was transformed using two rigid transformations.

The rigid transformations imply that:

The images of the triangle after the transformation would be equal

So, the corresponding parts are:

The results are true because rigid transformations do not change the side lengths and the angle measures of a shape

To do this, we simply make use any of the following congruent theorems:

The classmate's claim is that

Only two pairs of corresponding parts are enough to prove the congruent triangle

The above is true because of the following congruent theorems:

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Since t-value  is less than the critical value, at α = 0.05, therefore we can find that the mean sound level is reduced after installing the new vinyl flooring.

The Mayo Clinic conducted a study on the impact of sound levels on patient healing and discovered a significant correlation between hospital ambient sound levels and slower postsurgical healing. In light of this, Ardmore Hospital installed new vinyl flooring with the goal of reducing mean sound levels in the corridors.

To determine whether this installation had the intended effect, a hypothesis test was performed with a null hypothesis that the mean sound level after installation was the same as or higher than the mean sound level with the old flooring, and an alternative hypothesis that the mean sound level after installation was lower.

A one-tailed t-test was used with a significance level of α = 0.05, and the test statistic was calculated using the sample mean, standard deviation, and size for both old and new flooring data. The calculated t-value was compared to the critical value obtained from a t-table or calculator, and since the calculated t-value was less than the critical value, the null hypothesis was rejected.

Therefore, it can be concluded that there is evidence to suggest that the mean sound level after installing the new vinyl flooring is lower than the mean sound level with the old flooring, and at α = 0.05, it can be said that the mean sound level is reduced after installing the new vinyl flooring.

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Answer:

Step-by-step explanation:

15 rolls................................? %

48 rolls................................100%

(15*100)/48=31.25% used

round to the nearest tenth is 31.30%

Answer: 2.5

Step-by-step explanation:

To convert ounces to pounds you divided by 16

40 divided by 16 is 2.5

Answer:

2.5 lbs

Step-by-step explanation:

We need a conversion factor that converts ounces into pounds.

It is accepted that 16 ounces (oz) = 1 pound (lb).  Make this a conversion factor:

   Conversion factor =   (1 lb)/(16 oz)

We want to convert oz into pounds.  If the 40 oz is multiplied by (1 lb/16 oz) the oz will cancel, leaving justs lbs:

   (40 oz)*((1 lb)/(16 oz)) = (40/16) lbs

40 oz is equal to 2.5 lbs

Answer:

4(x+4)

Step-by-step explanation:

Find to GCF of 4x+16.

Now factor out the GCF by dividing each term in the expression by 4.

4x divided by the GCF is x, and 16 divided by the GCF is 4.

The equivalent expression is 4(x+4).

In order to maximize the profit \(50\) pints of chocolate concussion should produce.

" Linear programming is defined as it represents the extreme value of the given linear function with given subject to constraints."

According to the question,

\('x'\) represents the number of chocolate concussion

\('y'\) represents the number of Vanilla Brain  Freeze

\('z'\) represents the maximize cost

As per the given condition of linear programming,

Maximize Cost   \(z =5x + 7y\)

Subject to constraint

\(6x + 9y \leq 360\\\\8x + 5y \leq 400\\\\x\geq 0, y\geq 0\)

For

\(6x + 9y \leq 360\)

\(x= 0 \implies y=40\\\\y=0 \implies x=60\)

And

For

\(8x + 5y \leq 400\\\\x=0 \implies y=80\\\\y=0 \implies x= 50\)

Cost for each value of given linear programming we have,

\((x, y) = (0,40) \\\\\implies z = 5(0) + 7(40)\\\\ \implies z = $280\)

\((x, y) = (60,0) \\\\\implies z = 5(60) + 7(0)\\\\ \implies z = $300\)

\((x, y) = (0,80) \\\\\implies z = 5(0) + 7(80)\\\\ \implies z = $560\)

\((x, y) = (50,0) \\\\\implies z = 5(50) + 7(0)\\\\ \implies z = $250\)

To maximize the profit \(50\) pints of chocolate concussion.

Hence, Option (C) is the correct answer.

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