find the distance between the given parallel planes. 3x − 2y z = 12, 6x − 4y 2z = 3

The values for the mean and standard deviation for the original sample are Moriginal = 0.625 and Soriginal = 0.9661, respectively.

Compute the mean and standard deviation for the new sample.

The mean of the original sample Soriginal is 0.625.

Moriginal = 0.625.

For the given sample of n = 8 scores: 0, 1, 1/2, 0, 3, 1/2,0,1.

We have to simplify the arithmetic by first multiplying each score by 2 to obtain a new sample of 0, 2, 1, 0, 6, 1, 0, and 2. Then, we will compute the mean and standard deviation for the new sample.

The calculations are:

\($\overline{x}_{\text{new}}=\frac{\sum x_{\text{new}}}{n}=\frac{0+2+1+0+6+1+0+2}{8}=1.25$$\)

This implies that the mean of the new sample is 1.25.Mnew = 1.25

Now, let us calculate the standard deviation.

To do so, we have to calculate the variance of the data. The variance is the average of the squared deviation from the mean.

That is,

\($\sigma_{\text{new}}^2=\frac{\sum(x_{\text{new}}-\overline{x}_{\text{new}})^2}{n-1}\)

\(=\frac{(0-1.25)^2+(2-1.25)^2+(1-1.25)^2+(0-1.25)^2+(6-1.25)^2+(1-1.25)^2+(0-1.25)^2+(2-1.25)^2}{8-1}\\=3.7321\)

This implies that the variance of the new sample is 3.7321.

Now, we calculate the standard deviation as:

\($\sigma_{\text{new}}=\sqrt{3.7321}=1.9322$\)

Thus, the standard deviation of the new sample is 1.9322.

Snew = 1.9322

We will use the formula for calculating the standard deviation of a new sample from an old sample, as follows:

\($\sigma_{\text{old}}=\frac{\sigma_{\text{new}}}{2}=\frac{1.9322}{2}=0.9661$$\)

So, the standard deviation of the original sample is 0.9661.

Soriginal = 0.9661

To find the mean of the original sample, we will use the following formula:

\($\overline{x}_{\text{old}}=\frac{\overline{x}_{\text{new}}}{2}=\frac{1.25}{2}=0.625$$\)

Therefore, the mean of the original sample is 0.625.

Moriginal = 0.625

Thus, the values for the mean and standard deviation for the original sample are Moriginal = 0.625 and Soriginal = 0.9661, respectively.

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Answer:

13.3 seconds

Step-by-step explanation:

Answer:

12+0.2x=−25−0.7x

Step-by-step explanation:

Answer:

x:b116.67

Step-by-step explanation:

120/100

140×100/120

Answer:

this is the answer (-3,-6)

Answer: \(y=\dfrac12 x\) .

Step-by-step explanation:

We know that \(a f (x)\)  compresses f(x) vertically such that

If we vertically compress the linear parent function, F(x) = x, by multiplying by \(\dfrac12\).

Then, the equation of the new function is \(y=\dfrac12 F(x)=\dfrac12 x\) .

i.e. \(y=\dfrac12 x\) .

If the bag contains a total of n blocks and m of them are blue, we would expect to have selected a blue block approximately (m/n) * 12 times out of the 12 draws, assuming the selection process is random and the probabilities remain constant.

Let's assume that the bag contains a total of n blocks, and m of them are blue blocks. The probability of selecting a blue block on each draw, P(blue), would be m/n.

Since we are replacing the block after each selection, the total number of blocks in the bag remains the same throughout the process. Therefore, the probability of selecting a blue block on each draw remains constant at m/n.

To find the expected number of times we would select a blue block, we can multiply the probability of selecting a blue block on each draw (m/n) by the total number of draws (12):

Expected number of blue blocks = (m/n) * 12

The reasoning behind this is that in each individual draw, the probability of selecting a blue block is m/n. By performing 12 independent draws, we can expect to encounter this probability m/n a total of 12 times on average.

Therefore, if the bag contains n blocks with m blue blocks, we would expect to have selected a blue block approximately (m/n) * 12 times out of the 12 draws.

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The Original price of the meal was $12.16.

Discount Percent is defined as the discount given on the product per hundred .

For Example . if there is 10% discount on a price of $100.

The final amount will be $90.

Final amount paid by Fiona = $8.25

percentage discount = 10%

Let the original amount be x.

According to the question ;

x - 10% of x = 8.25

\(x-\frac{10}{100} *x=8.25\\ \\ \frac{100x-10x}{100} =8.25\\ \\ \frac{90x}{100} =8.25\\ \\ x=\frac{8.25*100}{90}\\ \\ x=\frac{825}{90} \\ \\ x=9.16\)

Since Fiona also had a discount coupon of  $3.

The original amount will be $9.16+$3=$12.16.

Therefore , The original price of the meal was $12.16.

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The location of J' after transformation is (3, 7).

In mathematics, a transformation is a process or operation that changes the position, orientation, size, or shape of a geometric object or a set of objects. Transformations are often used in geometry to study and analyze the properties of shapes and figures, as well as to solve problems related to their construction, symmetry, and congruence.

Given: Silas transformed point J(-3, -7) using the rule (x, y) → (-x, -y).

The rule (x, y) → (-x, -y) reflects a point over both the x-axis and the y-axis. This is a type of transformation known as a "point reflection" or "central symmetry" where the point is reflected across a point located at the origin (0,0).

When Silas applies this rule to point J(-3, -7), the x-coordinate changes from -3 to 3, and the y-coordinate changes from -7 to 7.

Therefore, the location of J' is (3, 7).

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Answer:

5/4

Step-by-step explanation:

Slope is y1-y2/x1-x2 so if you plug in the coordinates you get 4-(-1)/4-0 which you would get 5/4

Answer:   47.5% of 1600= 760 males   which means 840 are females

Step-by-step explanation:

Answer:

53.5 percent.

Step-by-step explanation:

100-47.5=53.5 percent.

Do not copy mines or I will report you.

The true proportion of US teens who believe anxiety and depression are major problems for their peers is between 0.65 and 0.75.

The standard error from a bootstrap distribution is calculated by taking the standard deviation of the sample proportions divided by the square root of the sample size.

Standard Error = SD(p)/√n

In this case, the sample size is 920 and the sample proportion is 644/920 = 0.7.

Therefore, the standard error is:

Standard Error = SD(p)/√n = 0.7/√920 = 0.023.

Using the standard error, we can calculate the 95% confidence interval for the proportion of US teens who believe anxiety and depression are major problems for their peers. The formula for the confidence interval is:

\(CI = [p ± (Z*SE)]\)

where Z is the z-score associated with a 95% confidence interval, which is 1.96, and SE is the standard error.

Therefore, the 95% confidence interval for the proportion of US teens who believe anxiety and depression are major problems for their peers is:

\(CI = [p ± (Z*SE)] = [0.7 ± (1.96*0.023)] = [0.65, 0.75].\)

This means that we are 95% confident that the true proportion of US teens who believe anxiety and depression are major problems for their peers is between 0.65 and 0.75.

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Answer:

-5x+20

Step-by-step explanation:

Distribute the -5: -5(x) and -5(-4)

-5x+20

Since you cannot combine like terms, this is your final answer

Answer:

-5 × 4x = -20x

Step by Step Explanation:

Start with parenthesis

x - 4 = 4x

Multiply

-5 × 4x = -20x

Answer:

554923

Step-by-step explanation:

111 * 5000 + 85 - 6/2 * 54

555000 + 85 - 3 * 54

555000 + 85 - 162

554923

Answer:

No, because it does not have a constant rate of change

Step-by-step explanation:

look at the changes of the y values when going from one x value to the next.

x always changes by 1.

but y changes by +7, +5, +6.

the change rate is the ratio y/x.

as we can see, this changes in each interval.

so, the change rate is not constant.

but this is the deciding property of a linear function. as the name says, a linear function is a straight line. it has the same incline (= changes rate) everywhere on the line. otherwise it is not a straight line.

The solution set for the given graph is (2,1). The solution has been obtained using linear equations.

What is a linear equation?

It is a linear equation that has the greatest degree of one. In a linear equation with an exponent greater than one, this indicates that there are no variables. A straight line is produced on the graph by this equation.

We are given two lines on the graph

The points of the red line are (3,0) and (0,3)

So, the equation of the line comes out to be

y=−x+3      ...(1)

The points of the blue line are (3,2) and (-1,-2)

So, the equation of the line comes out to be

y=x−1     ...(2)

To find the solution set, we need to solve the equations

Substituting (1) in (2), we get,

⇒−x+3 = x−1

⇒−2x = -4

⇒x = 2

So, y = 1

Hence, the solution set for the given graph is (2,1).

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Answer:

Step-by-step explanation:

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The angle θ is maximized when c = 2 (halfway between two points).

The maximum angle at which a conveyor can be inclined while still delivering a predetermined amount of bulk material in a given amount of time. As the maximum angle is approached, the rate of bulk material handling is usually reduced.

Given that, in the figure, find the value of c in the interval [0, 4] on the x-axis that maximizes angle θ.

Express θ as a function of c, Let α be the angle to the left of θ and let β be the angle to the right, then,

tanα = 2/c

and tanβ = 2/(4-c)

At this point, we suppose that it might be easier to use cotangent in order to keep c inn numerator,

cotα = c/2

cotβ = (4-c)/2

We have, α+β+θ = π, so,

θ = π-α-β

= π-cot⁻¹c/2-cot⁻¹(4-c)/2

Differentiate, set equal to 0 and solve

dθ/dc = 1/1+(c/2)².1/2+1/1+(4-c/2)²(1/2)

Put dθ/dc = 0

1/1+(c/2)².1/2+1/1+(4-c/2)²(1/2) = 0

1/1+(c/2)²-1/1+(4-c/2)² = 0

1/1+(c/2)² = 1/1+(4-c/2)²

(4-c/2)² = (c/2)²

(c/2) = (4-c/2)

4-c = c

2c = 4

c = 2

Hence, The angle θ is maximized when c = 2 (halfway between two points).

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Answer:

See attached

Step-by-step explanation:

The form is filled in and attached

Answer:

8x = 16    x=2

Step-by-step explanation:

Answer: Simplifying

8x = 0

Solving

8x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '8'.

x = 0

Simplifying

x = 0

Step-by-step explanation:

Answer:

X = -9.1

Step-by-step explanation:

Add 9.1 and -2.4 together to get

x + 6.7 = -2.4

subtract 6.7 from both sides to get

x = -9.1

Answer:

A single number that estimates the value of an unknown parameter is called a point estimate.

Step-by-step explanation:

Don't see the point (haha) of elaborating

Step-by-step explanation:

When a graph is reflected about the x-axis, their x-intercept(s) are invariant point(s).

For y = 2x + 3, the x-intercept is -3/2.

Also the slope of the line graph when reflected about the x-axis will change from m to -m.

Therefore the new slope is -2.

We have y = -2x + c.

When x = -3/2, y = 0.

=> (0) = -2(-3/2) + c, c = -3.

Hence the answer is y = -2x - 3. (E)

Answer:

a

Step-by-step explanation:

x² - 3 = 2x ( subtract 2x from both sides )

x² - 2x - 3 = 0 ← in standard form

consider the factors of the constant term (- 3) which sum to give the coefficient of the x- term (- 2)

the factors are - 3 and + 1 , since

- 3 × + 1 = - 3 and - 3 + 1 = - 2 , then

x² - 2x - 3 = (x - 3)(x + 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 3 = 0 ⇒ x = 3

Answer: 1.87 kg of pears

Step-by-step explanation:

7.5 kg of both apples and pears were sold. 3/4 of this 7.5 kg is apples which means the amount of apples sold is:

= 7.5 * 3/4

= 5.63 kg of apples

The amount of pears sold would therefore be:

= Total amount sold - Amount of apples

= 7.5 - 5.63

= 1.87 kg of pears

none of the provided options (a, b, c, d) appear to be accurate or close to the minimum space required.

To determine the minimum space required for a male restroom design with the given plumbing requirements, we need to consider the minimum space required for water closets and lavatories.

The minimum space required for water closets is typically around 30-36 inches per unit, and for lavatories, it is around 24-30 inches per unit.

Since the design requires a minimum of 12 water closets and 13 lavatories, we can estimate the minimum space required as follows:

Minimum space required for water closets = 12 water closets * 30 inches = 360 inches

Minimum space required for lavatories = 13 lavatories * 24 inches = 312 inches

Adding these two values together, we get a total minimum space requirement of 672 inches.

Among the given options, the closest value to 672 inches is option d) 249. However, this value seems significantly lower than the expected minimum space requirement.

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The value of x from the given equation is -10.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Step 1: 2x-6+7-3x=11 (Distributive property)

Step 2: 2x-3x-6+7=11 (Commutative property of addition)

Step 3:-x+1=11 (Write equivalent expression)

Step 4: -x=10 (Addition property of equality)

Step 5: x=-10 (Multiplication property of equality)

Therefore, the value of x is -10.

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The activation energy of the reaction is approximately 126.8 kJ/mol. The calculation was done using the Arrhenius equation and the natural logarithm of the rate constants at the two temperatures.

To calculate the activation energy of a reaction, we can use the Arrhenius equation:

k = A * e⁽⁻ᴱᵃ/ᴿᵀ⁾

where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

We have two rate constants at different temperatures, so we can set up two equations:

k₁ = A * e⁽⁻ᴱᵃ/ᴿᵀ₁⁾

k₂ = A * e⁽⁻ᴱᵃ/ᴿᵀ₂⁾

We want to solve for Ea, so we can take the natural logarithm of both sides of each equation:

ln(k₁) = ln(A) - Ea/RT₁

ln(k₂) = ln(A) - Ea/RT₂

We can subtract the second equation from the first to eliminate ln(A):

ln(k₁) - ln(k₂) = Ea/R * (1/T₂ - 1/T₁)

Now we can solve for Ea:

Ea = -R * (ln(k₁) - ln(k₂)) / (1/T₂ - 1/T₁)

Plugging in the given values, we get:

Ea = -8.314 J/mol/K * (ln(6.20 x 10⁻⁴) - ln(2.39 x 10⁻²)) / (1/760 K - 1/700 K)

Ea ≈ 126.8 kJ/mol

Therefore, the activation energy of the reaction is approximately 126.8 kJ/mol.

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Answer:

0.059 (to 3 dp)

Step-by-step explanation:

\(\binom{40}{5}(0.06)^{5}(0.94)^{35} \approx 0.059\)

Answer:

1) a number squared, reduced by 12

2) the quantity of twice a number divided by 3, increased by 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

The first expression reads "x squared less (or minus) 12."

The second expression becomes "the quotient 2x/3 plus one."    Note that 2x/3 must be computed before "one" is added, due to order of operations rules.

The third expression reads "8 less than the cube of x."

Answer:

The average weight of the chipmunks is 91 grams

Step-by-step explanation:

The mean of a dataset gives the average which is obtained by taking the sun of each data value and dividing by the number of samples. The median however requires the arrangement of data in terms of size ze (ascending) and taking the mid value (value which falls in the 50% mark). For the data above, the most appropriate measure of the average is the mean. Hence, the prediction which matches the data is ; The average weight of the chipmunks is 91 grams.

Based on the data that the Biologists found out, the prediction that best matches the data is The average weight of the chipmunks is 91 grams.

The data shows the weights of the five chipmunks that were recorded and the mean of these weights was 91 grams.

The mean of a dataset is the same as its average which means that the average weight found from the chipmunks was 91 grams.

In conclusion, option D is correct.

Options for this question are:

About one-half of the chipmunks weigh more than 91 grams

The average weight of the chipmunks is 87 grams.

About one-half of the chipmunks weigh more than 87 grams

The average weight of the chipmunks is 91 grams

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