A board is 17 5/8 in. long. If it must be divided into seven pieces of equal​ length, how long must each piece​ be?

Answer:

\(y=\frac{1}{2} x-40\)

Step-by-step explanation:

Slope interccept form: y=mx+b

(m= the slope, b= the y-intercept (the y value when x=0))

for every 2 x-values the y-value increases by 1. Slope is written as  \(\frac{rise}{run}\) or  \(\frac{y_{1}-y_{2} }{x_{1}-x_{2}}\) which is the change in the y-values divided by the change in x-values. You can find the slope by plugging in points.

\(\frac{(-42)-(-41)}{(-2)-(-4)} =\frac{1}{2\\}\)     so now you have \(y=\frac{1}{2}x+b\)

b is whatever the value of y is when x=0. According to the table when x=0 then y=-40. The final equation is \(y=\frac{1}{2} x-40\)

Answer:

no it not

Step-by-step explanation:

X = y2 would be a sideways parabola and therefore not a function. ... If a vertical line passes thru two points on the graph of a relation, it is NOT a function

Answer:

Step-by-step explanation:

1. 500

2. 10

3. 25000

Answer:

Step-by-step explanation:

Answer:First, write the expression

✔ p – 5

.

Second,

✔ substitute

7 in for the variable, p.

Third,

✔ simplify

by

✔ subtracting

7 and 5.

The answer is

✔ 2

Step-by-step explanation:

Answer:

Part of the solution region includes a negative number of tomato plants in a row; therefore, not all solutions are viable for the given situation.

Step-by-step explanation:

got right on edmentum/plato

The value of x in the similar triangle is 43.2 units.

Two triangles are said to be similar when they have two corresponding angles congruent and the sides proportional.

The triangle CDE is similar to triangle FGE. Therefore, let's use proportion to find the the side length x as follows:

ΔCDE ~ ΔFGE

Hence,

27 / x = 25 / 40

cross multiply

40 × 27 = 25x

1080 = 25x

divide both sides by 25

Therefore,

x = 1080 / 25

x = 43.2

Therefore,

x = 43.2 units

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Answer:

Larry is wrong

Step-by-step explanation:

Multiplying big numbers will give significantly bigger results then multiplying smaller numbers then adding them. 14 + 12 = 26 & 8 + 12 = 20. 14 x 12 = 68 & 8 x 12 = 96. 96 + 168 is alot less then 26 * 20 so that is why larry is wrong

Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.

To determine whether Alicia's estimate of the surface area of the rectangular prism is reasonable, we first need to check if her calculation of the volume of the rectangular prism is correct.

The formula for calculating the volume of a rectangular prism is:

Volume = length x width x height

Substituting the given values in the formula, we get:

Volume = 11 meters x 5.6 meters x 7.2 meters

Volume = 449.28 cubic meters

As we can see, Alicia's estimate of 334 cubic meters is significantly lower than the actual volume of the rectangular prism, which is 449.28 cubic meters. Therefore, her estimate of the surface area is likely to be incorrect as well.

It is also important to note that the problem statement asks about the estimate of the surface area, not the volume. However, since the formula for calculating the surface area of a rectangular prism also involves the dimensions of length, width, and height, it is highly likely that Alicia's estimate of the surface area would also be incorrect given her miscalculation of the volume.

In conclusion, Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.

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The fraction that satisfies the problem is 20/24.

Equivalent fractions are fractions that have the same value, but different numerators and denominators.

If the fraction is equivalent to 5/6, then the numerator and denominator of the fraction is a multiple of 5 and 6, respectively.

Let x be the factor

fraction = 5x / 6x

If the sum of my numerator and my denominator is 44, then:

5x + 6x = 44

11x = 44

x = 4

fraction = 5x / 6x = 20/24

The final statement says that the sum of the digits in the denominator is 6.

2 + 4 = 6

Hence, the fraction is 20/24.

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We can conclude that the function f(x) has two distinct real number zeros.

To find the number of solutions of a quadratic equation, we need to consider the discriminant of the quadratic function, which is given by the expression b2 - 4ac.

In the case of f(x) = (x2 – 170x +3), we can see that the coefficients a, b, and c are 1, -170, and 3, respectively.

Therefore, the discriminant of the function can be calculated as follows:

b2 - 4ac = (-170)2 - 4(1)(3) = 28996

The value of the discriminant is positive, which means that the function has two distinct real number zeros.

This is because a positive discriminant indicates that the quadratic function intersects the x-axis at two points, which correspond to the two solutions of the equation.

Therefore, we can conclude that the function f(x) has two distinct real number zeros.

Note that we did not need a calculator to calculate the discriminant in this case, since the coefficients of the quadratic function were relatively simple to work with.

However, if the coefficients were more complicated, we could use a calculator to simplify the calculation.

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Answer:

3x^2-9x+3

Step-by-step explanation:

150 because he is not using all of his money and because the marginal utility of his spending for each product differs.

The design adopted for this study is a plan for solving issues that entails first figuring out the worth of one unit, then scaling that value to figure out the needed value. Simple terms, the unit approach is employed to derive a single unit amount from a multiple that also is supplied. For reference, 40 pens would require 400 rupees, which itself is equal to the expense of one pen. This technique might follow a typical procedure. a distinct nation. anything with a distinct character. Its capable of integrating and equivalent are identical in terms of geometry, algebra, algebra, numerical modeling, or algebra of matrices or operators.

given

Utility for every dollar spent on the twenty-first aubergine is 160 utils, and marginal Utility for every dollar spent on the thirty-first kiwi is 190 utils.

Here 160<190

Spending currently is 150

Additionally, the budget is 180 and the intake of eggplant is 20. vegetable cost is $3.

Kiwi intake equals 30; eggplant costs 3

Anaiah's present spending is equal to 3*20 plus 5*30, or 60 plus 90, or 150.

150 because he is not using all of his money and because the marginal utility of his spending for each product differs.

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Answer: \(x\in [53,\infty)\)

Step-by-step explanation:

Given

Ade doubles her number and subtract 5 from it. The result cannot be less than 100

Suppose the number is \(x\)

According to the question

\(\Rightarrow 2x-5\geq100\\\text{Solve the inequality}\\\Rightarrow 2x\geq105\\\Rightarrow x\geq52.5\\\text{for integer number, the range is given by }\\\Rightarrow x\in [53,\infty)\)

Answer:

Step-by-step explanation:

Assume that the number is x. Angle #1: 7x - 5. Angle #2: 7x + 8.

The probability that you will win the trip to Orlando would be = 1

To calculate the probability that you will win the trip to Orlando the formula for probability should be used and this is given below;

Probability = possible outcome/sample space.

The total small space = 7

For first Letter;

Possible outcome = 1

probability = 1/7. This will be done for the total number of letters used to spell Orlando = 1/7+1/7+1/7+1/7+1/7+1/7+1/7 = 7/7 = 1

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Answer:

W

Step-by-step explanation:

I think it's w, hope this helps

The mode is the most appropriate measure of center to represent the data in the graph because it reflects the most common value(s) observed in the dataset. In this case, the mode is 3.

The most appropriate measure of center to represent the data in the given line plot is the mode.

The mode is the value or values that occur most frequently in a dataset. In this case, we can observe the frequencies of the data points on the line plot:

There is one dot above 2, 4, 8, and 9.

There are two dots above 6 and 7.

There are three dots above 3.

Based on this information, the mode(s) of the dataset would be the values that have the highest frequency. In this case, the mode is 3 because it appears most frequently with a frequency of three. The other data points have frequencies of one or two.

The mode is particularly appropriate in this scenario because it represents the most common or frequently occurring value(s) in the dataset. It is useful for identifying the central tendency when the data is discrete and there are distinct peaks or clusters.

While the median and mean are also measures of center, they may not be the most appropriate in this case. The median represents the middle value and is useful when the data is ordered. However, the given line plot does not provide an ordered arrangement of the data points. The mean, on the other hand, can be affected by outliers and extreme values, which may not accurately represent the central tendency of the dataset in this scenario.

Therefore, the mode is the most appropriate measure of center to represent the data in the graph because it reflects the most common value(s) observed in the dataset. In this case, the mode is 3.

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The correlation coefficient ρ is zero, we can conclude that X and Y are uncorrelated.

We know that the correlation coefficient between two random variables X and Y is given by:

ρ = Cov(X, Y) / (σX * σY)

where Cov(X, Y) is the covariance between X and Y, and σX and σY are the standard deviations of X and Y, respectively.

To determine if X and Y are uncorrelated, we need to show that their correlation coefficient ρ is zero.

We can start by finding the expected values of X and Y:

E(X) = E(cos ω) = ∫cos ω f(ω) dω

= ∫cos ω dω / ∫dω (since o is uniformly distributed in the interval [0, 1])

= 0

Similarly,

E(Y) = E(sin ω) = ∫sin ω f(ω) dω

= ∫sin ω dω / ∫dω (since o is uniformly distributed in the interval [0, 1])

= 0

Next, we need to find the covariance between X and Y:

Cov(X, Y) = E(XY) - E(X)E(Y)

We can find E(XY) as follows:

E(XY) = E(cos ω * sin ω)

= ∫cos ω * sin ω f(ω) dω

= ∫(sin 2ω / 2) f(ω) dω (using the identity cos ω * sin ω = sin 2ω / 2)

= 1/4

Therefore,

Cov(X, Y) = E(XY) - E(X)E(Y) = 1/4 - 0 * 0 = 1/4

Finally, we need to find the standard deviations of X and Y:

σX = sqrt(E(X^2) - E(X)^2) = sqrt(E(cos^2 ω) - 0^2) = sqrt(∫cos^2 ω f(ω) dω) = sqrt(1/2) = 1/sqrt(2)

σY = sqrt(E(Y^2) - E(Y)^2) = sqrt(E(sin^2 ω) - 0^2) = sqrt(∫sin^2 ω f(ω) dω) = sqrt(1/2) = 1/sqrt(2)

Putting it all together, we have:

ρ = Cov(X, Y) / (σX * σY)

= (1/4) / (1/sqrt(2) * 1/sqrt(2))

= 0

Since the correlation coefficient ρ is zero, we can conclude that X and Y are uncorrelated.

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Answer:

The answer for this is x=-5

Answer:

x=-5

Step-by-step explanation:

-4x+1=21

move the 1 to the right side and subract it so it will turn into -4x=20

divide -4 to get the x by itself and then you will get x=20/-4 this will now divide and be x=-5

The 3-month simple moving average for May is 132.

To calculate the 3-month simple moving average for May, we need to take the average of the demand values for the three preceding months (February, March, and April).

The demand values for these months are 120, 134, and 142, respectively. To find the moving average, we sum these values and divide by 3 (the number of months):

Moving Average = (120 + 134 + 142) / 3 = 396 / 3 = 132

Therefore, the 3-month simple moving average for May is 132.

The simple moving average is a commonly used method to smooth out fluctuations in data and provide a clearer trend over a specific time period. It helps in identifying the overall direction of demand changes. By calculating the moving average, we can observe that the average demand over the past three months is 132 units. This provides an indication of the demand trend leading up to May. It's important to note that the moving average is a lagging indicator, as it relies on past data to calculate the average.

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The minimum yield value of the key material should be determined based on the yield stress of the shaft, which is 36 kg/m², the dimensions of the key, and the safety factor of 2.

To ensure that the key smoothly transmits the torque of the shaft, it is essential to choose a key material with a minimum yield value that can withstand the applied forces without exceeding the yield stress of the shaft.

The dimensions of the key given are 20x20x120 mm. To calculate the torque transmitted by the key, we need to consider the dimensions and the applied forces. However, the specific values for the applied forces are not provided in the question.

The safety factor of 2 indicates that the material should have a yield strength at least twice the expected yield stress on the key. This ensures a sufficient margin of safety to account for potential variations in the applied forces and other factors.

To determine the minimum yield value of the key material, we would need additional information such as the expected torque or the applied forces. With that information, we could calculate the maximum stress on the key and compare it to the yield stress of the shaft, considering the safety factor.

Please note that without the specific values for the applied forces or torque, we cannot provide a precise answer regarding the minimum yield value of the key material.

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The reason why the following hypotheses are not constructed correctly is because of option B. The hypothesized value is not the same under the null and alternative hypotheses.

In hypothesis testing, the null hypothesis (H0) and the alternative hypothesis (HA) should have the same hypothesized value, but with opposite signs. In this case, the hypothesized value is 10, but the signs are not opposite. The null hypothesis has a less than or equal to sign (≤) and the alternative hypothesis has a greater than or equal to sign (≥). This means that there is overlap between the two hypotheses, which is not correct.

The correct way to construct the hypotheses would be:
H0: μ ≤ 10; HA: μ > 10
or
H0: μ ≥ 10; HA: μ < 10

Option A is incorrect because the alternative hypothesis can have the equality sign if the null hypothesis does not have it. Option C is also incorrect because hypothesis testing is about a population parameter, not a sample statistic.

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Ground-state electron configuration of gas-phase Co²+ is [Ar] 3d⁷. Answer: (E) [Ar] 3d⁷.Explanation: First of all, we need to find the electron configuration of Cobalt (Co).

The electron configuration of Cobalt (Co) is 1s²2s²2p⁶3s²3p⁶4s²3d⁷.Now, we can remove the electrons to get the electron configuration of gas-phase Co²+ .Co: 1s²2s²2p⁶3s²3p⁶4s²3d⁷Co²+: 1s²2s²2p⁶3s²3p⁶3d⁷The full electron configuration of Co²+ will be [Ar] 3d⁷. Therefore, the answer is (E) [Ar] 3d⁷.

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False. The columns of matrix P are not necessarily eigenvectors of matrix A. While the diagonal matrix D contains the eigenvalues of A, the eigenvectors are not explicitly determined by the columns of P.

False. The columns of matrix P are not guaranteed to be eigenvectors of the transpose of matrix A (A.T).

In the given equation, \(a = PDP^(-1),\)

where D is a diagonal matrix and P is an invertible matrix.

The diagonal elements of D represent the eigenvalues of matrix A, while the columns of P correspond to the eigenvectors of A.

When considering the transpose of matrix A (A.T), we have \((A.T) = (PDP^(-1)).T = (P^{(-1)})^T D^T P^T.\)

Taking the transpose of a product involves reversing the order of the matrices and transposing each matrix individually.

Therefore, we have \((A.T) = P^T D^T (P^{(-1)})^T.\)

Since P is an invertible matrix, its transpose \(P^T\) is also invertible. Similarly, the transpose of the inverse of \(P, (P^{(-1)} )^T,\) is also invertible.

However, the key point is that the diagonal matrix\(D^T\) is not guaranteed to have the same eigenvalues as matrix A.

The eigenvalues of A are present in D, but they may not remain on the main diagonal after transposing.

Thus, the columns of matrix P, which correspond to the eigenvectors of A, may not necessarily be the eigenvectors of A.T.

In conclusion, the statement is false.

The columns of matrix P do not have to be eigenvectors of the transpose of matrix A (A.T).

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Answer:

To solve for the trigonometric functions of x, we need to recall the ratios they represent as shown below.

sin x = O/H

cos x = A/H

tan x  = O/A

where O stands for opposite, A for adjacent, and H for hypotenuse. So, for example, the sine of x is equal to the side opposite of angle x over the hypotenuse. The same goes for cosine and tangent. Using the diagram attached, we have the expressions of the trigonometric functions as shown below.

sin x = f/d

cos x = e/d

tan x = f/e

Step-by-step explanation:

The trigonometric ratio's as per given side length of a triangle are as follow,

cosx = f/e , sinx = d/e , and tanx = d/f.

Let us consider triangle name as ABC,

Measure of angle ABC = x degree

Measure of angle BAC = 90 degree

Side length AB = f

Side length AC = d

Side length BC = e

For angle x ,

AC is the opposite side , AB is the adjacent side, and BC is the hypotenuse.

cosx = adjacent side / hypotenuse

       = f / e

sinx = opposite side / hypotenuse

       = d / e

tanx  = opposite side / adjacent side

       = d / f

Therefore, the value of the trigonometric ratio for the given side length of a triangle are cosx = f/e , sinx = d/e , and tanx = d/f.

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The statements that accurately compare the domain and range of the functions are: The domain of all three functions is all real numbers, The range of f(x) and h(x) is all real numbers, but the range of g(x) is all real numbers except 0.

The domain of a function refers to all the possible input values that make the function defined. For the quadratic function f(x) = 3x², there are no values of x that make the function undefined, so the domain of f(x) is all real numbers. To find the range of f(x), we can calculate the vertex of the parabola, which is (0,0). The range of f(x) is all real numbers greater than or equal to zero.

For the quadratic function f(x) = 3x², we can determine the vertex using the formula:

h = -b/2a

In this case, a = 3 and b = 0, so:

h = -0/2(3) = 0/6 = 0

The x-coordinate of the vertex is 0.

To find the y-coordinate, we evaluate the function at the vertex:

f(0) = 3(0)² = 0

So the vertex of the parabola is (0,0).

Since the coefficient of x² is positive, the parabola opens upwards, and the minimum value of the function occurs at the vertex. Therefore, the range of f(x) is all real numbers greater than or equal to zero.

For the rational function g(x) = 1/3x, the function is undefined when the denominator is equal to zero. Thus, we solve for the value(s) of x that make the denominator zero:

3x = 0

Dividing both sides by 3, we get:

x = 0

Therefore, the domain of g(x) is all real numbers except zero. The range of g(x) is all real numbers except zero, since the function cannot equal zero.

For the linear function h(x) = 3x, there are no values of x that make the function undefined. Thus, the domain of h(x) is all real numbers. The range of h(x) is also all real numbers, since the function is a straight line that passes through the origin and extend infinitely in both directions.

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Answer:

He should play for 12 days

Step-by-step explanation:

Answer:

The full price was $176.

Step-by-step explanation:

To solve this problem, solve backwards. Since the total is $100, you subtract $12 from it, which leaves you with $88. You then multiply $88 by 2 (for the half price).