Z= v-e/m ; solve for m

The length of the PR is 14 cm by pythagoras theorem

We have to find the length of PR

By using pythagoras theorem we know that In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

PR² + RQ² = 50 ²

PR² + 48² = 50 ²

PR² +2304=2500

PR²=2500-2304

PR²=196

PR=14

Hence, the length of the PR is 14 cm by pythagoras theorem

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The reason that Rachel could give for her proof is given as follows:

<1 ≅ <5 by the Corresponding Angle Theorem.

When two parallel lines are cut by a transversal, corresponding angles are pairs of angles that are in the same position relative to the two parallel lines and the transversal.

Corresponding angles are always congruent, which means that they have the same measure.

A pair of corresponding angles in this problem is given as follows:

<1 and <5.

Hence they are congruent. <8 is opposite by the same vertex with <5, hence they are also congruent, and by the transitive property of congruence, we have that:

<8 ≅ <1, as <8 ≅ <5 and <5 ≅ <1.

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Step-by-step explanation:

Area = 12 ft x 12 ft = 144 ft^2

Cost =  144 ft^2  *  $ 4/ ft^2 = $ 576

2081 is the estimated population of the deer as per the given table.

We assume that the characteristics of the sample of the deer population match the characteristics of the population as a whole. This will be the case if the sample is random: each deer is equally likely to be included in the sample.

So, if 85 of the 110 marked deer show up in the sample, we assume that the sample is 85/110 of the entire population.

For a sample size of 1608 deer, that means the population is estimated to be ...

 1608 = 85/110 × population

 population = 1608 × 110/85 = 2081

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Answer:

The expression πr2h is a monomial because it is a single term that is the product of three variables: π, r2, and h. The term "mono" means "one," and "monomial" refers to a single term in algebraic expressions.

The degree of a monomial is the sum of the exponents of its variables. In this case, the degree of the monomial is 3, because the variables π, r, and h have exponents of 1, 2, and 1 respectively. Therefore, the degree of the monomial is 1 + 2 + 1 = 3.

(a) The height of the larger box is determined as 2 cm.

(b) The volume of the smaller box is determined as 384 cm³.

The height of the larger box is calculated by applying the following formula as follows;

Volume = surface area x height

V = Ah

h = V / A

h = ( 1728 cm³ ) / ( 864 cm²2)

h = 2 cm

The volume of the smaller box is calculated by applying the following formula as follows;

V = Ah

where;

V = 96 cm²  x  4 cm

V = 384 cm³

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The area of triangle UVW to the nearest square inch is approximately 2 square inches.

The area of triangle UVW can use the Heron's formula:

Area = √(s(s-a)(s-b)(s-c))

s is the semiperimeter of the triangle and a, b and c are the lengths of its sides.

First, we can calculate the semiperimeter s:

s = (u + v + w)/2

s = (5.5 + 4.4 + 9.6)/2

s = 9.75

The length of each of the three sides of the triangle:

a = v = 4.4 inches

b = u = 5.5 inches

c = w = 9.6 inches

Then, we can plug these values into the Heron's formula and simplify:

Area = √(s(s-a)(s-b)(s-c))

Area = √(9.75(9.75-4.4)(9.75-5.5)(9.75-9.6))

Area = √(9.75(5.35)(4.25)(0.15))

Area ≈ √(3.296)

Area ≈ 1.81

Rounding this to the nearest square inch, we get:

Area ≈ 2 square inches

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Answer:

[tex]x\leq -5[/tex]

Mia's total profit for the month is given as follows:

$200.

The profit function is obtained as the subtraction of the revenue function by the cost function, as follows:

P(x) = R(x) - C(x).

From the table given in this problem, the revenue and the costs are given as follows:

Hence the profit is given as follows:

9500 - 9300 = $200.

As the profit is positive, it is in fact a profit(gain) and not a loss.

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The probability that more than two out of the twelve automobiles fail the test is approximately 29. 35%.

The probability of more than two automobiles failing the emissions test would be:

= 1 - Probability that none fails - Probability that 1 fails - Probability that 2 fail

The probabilities are :

P (0 fail) = C (12, 0) x ( 0.08 ⁰) x (0.92 ¹² )

= 1 x 1 x 0. 2785

= 0. 2785

P(1 fail) = C (12, 1) x (0.08 ¹ ) x ( 0.92 ¹¹ )

= 12 x 0. 08 x 0. 3016

= 0. 2899

P (2 fail) = C (12, 2) x (0.08 ² ) x ( 0.92 ¹⁰)

= 66 x 0. 0064 x 0.3259

= 0.1381

The probability that more than two fail is:

= 1 - (0.2785 + 0.2899 + 0.1381)

= 0.2935

= 29. 35 %

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The number of different sodas that can be made is given by "n!" or factorial form.

If the soda tastes different depending on the order in which the flavors are chosen, we can calculate the number of different sodas that can be made without repetition using the concept of permutations.

Let's assume we have "n" different flavors of soda available. To calculate the number of different sodas we can make, we need to find the number of permutations of "n" flavors taken "r" at a time, where "r" is the number of flavors we want to choose for each soda.

The formula to calculate permutations is given by:

P(n, r) = n! / (n - r)!

Here, "n!" represents the factorial of "n," which is the product of all positive integers less than or equal to "n."

In this case, if repetition is not allowed, each soda can have only one flavor. Therefore, we have "r = 1" for each soda.

Applying the formula, we have:

P(n, 1) = n! / (n - 1)!

= n! / (n - 1)

= n

Hence, the number of different sodas that can be made without repetition is "n."

Therefore, the number of different sodas that can be made is given by "n!" or factorial form.

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The solution is: Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1, the following functions is graphed below.

Option C is correct.

Explanation:

We are given a graph of piece-wise function which break at x=1

We need to choose correct option for graph.

Function is break at x=1.

We will get two function

For x≤1 and x>1

As we can see x≤1, graph is linear and x>1 graph is parabolic.

Equation of linear graph, x≤1

Take two point of graph (0,6) and (-6,0)

Equation of line:

y-y1/y2-y1 = x-x1/x2-x1

y = x+1

f(x)=x+6 , x≤1

Equation of parabolic graph, x>1

f(x) = x^2 + 3

Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1

Please see the attached figure.

Hence, The option C is correct.

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The square root of 107.6 is approximately 10.372

To find the square root of 107.6, we can use a calculator or use the following procedure:

Make an initial estimate:

We know that the square root of 100 is 10, so we can estimate that the square root of 107.6 is slightly more than 10.

Use the formula: We can use the following formula to improve our estimate:

x(n+1) = (x(n) + a/x(n))/2

where x(n) is the nth estimate of the square root of a, and a is the number we want to find the square root of.

Apply the formula: Using the estimate of 10, we get:

x(1) = (10 + 107.6/10)/2 = 10.38

Now we use this new estimate to get a better one:

x(2) = (10.38 + 107.6/10.38)/2 = 10.371

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The volume of the figures are;

4.  27. 18 in³

5. 3. 024 m³

6.  23 6/18 yd³

The formula for calculating the volume of a triangular prism is expressed with the equation;

V = Bl

Given that the parameters are;

4.  We have that;

Base area = 1/2 × 2.6 × 4.1

Multiply the values

Base area = 5. 33in²

Then,

Volume = 5.33 × 5.1

Volume = 27. 18 in³

5. Base area = 1/2 × 2. 4 × 1.4

Multiply the values

Base area = 1. 68 m²

Volume = 1.8 ×1.68

Multiply the values

Volume= 3. 024 m³

6. Base area = 1/2 × 10/3 × 14/3

Multiply the values

Base area = 7 14/18yd²

Volume = 140/18 × 3

Multiply the values

Volume = 23 6/18 yd³

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The average cost function for the given total cost function is AC(x) = 2,100/x + 4 - 0.0003x.

To find the average cost function C, we need to divide the total cost function C(x) by the quantity of output produced, which is represented by x.
The formula for average cost (AC) is:
AC(x) = C(x) / x
Plugging in the given values, we have:
AC(x) = (2,100 + 4x - 0.0003x2) / x
Simplifying this expression, we get:
AC(x) = 2,100/x + 4 - 0.0003x
Therefore, the average cost function C(x) is:
C(x) = 2,100/x + 4x - 0.0003x2
This function represents the average cost per unit of output, taking into account fixed costs (2,100) and variable costs (4x - 0.0003x) that increase as output increases.
It's important to note that the cost function C(x) is quadratic, which means that the average cost function C(x) will have a U-shaped curve.

This is because initially, as output increases, fixed costs are spread out over a larger quantity of output, leading to a decrease in average cost.

However, at a certain point, the increasing variable costs will outweigh the decreasing fixed costs, causing average cost to increase again.
Overall, knowing the average cost function can be useful for businesses to make decisions about pricing, production levels, and cost management strategies.

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Answer:

where do you live

Step-by-step explanation:

The possible equation for Nate's line is C) 6x - 5y = 15.

To find the equation of the line perpendicular to Maria's line, we need to determine the slope of Maria's line first.

Maria's line is represented by the equation:

y = -5/6 x + 8

The slope of this line can be determined by comparing it to the slope-intercept form of a linear equation (y = mx + b), where m is the slope. Thus, the slope of Maria's line is -5/6.

The slope of a line perpendicular to Maria's line will be the negative reciprocal of -5/6, which is 6/5.

Therefore, the equation of Nate's line could be in the form:

y = 6/5 x + b

where b is the y-intercept of Nate's line.

To determine which of the given answer choices is the equation of Nate's line, we can substitute the equation y = 6/5 x + b into each answer choice and see which one holds true.

A) 5x - 6y = 15

Substituting y = 6/5 x + b, we get:

5x - 6(6/5 x + b) = 15

5x - 36/5 x - 6b = 15

-11/5 x - 6b = 15

This equation is not equivalent to y = 6/5 x + b, so A is not the answer.

B) 5x + 6y = 15

Substituting y = 6/5 x + b, we get:

5x + 6(6/5 x + b) = 15

5x + 36/5 x + 6b = 15

46/5 x + 6b = 15

This equation is not equivalent to y = 6/5 x + b, so B is not the answer.

C) 6x - 5y = 15

Substituting y = 6/5 x + b, we get:

6x - 5(6/5 x + b) = 15

6x - 6x - 5b = 15

-5b = 15

b = -3

This equation is equivalent to y = 6/5 x - 3, so C could be the answer.

D) 6x + 5y = 15

Substituting y = 6/5 x + b, we get:

6x + 5(6/5 x + b) = 15

6x + 6x + 5b = 15

12x + 5b = 15

This equation is not equivalent to y = 6/5 x + b, so D is not the answer.

Therefore, the possible equation for Nate's line is C) 6x - 5y = 15.

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The probability that a female student chose strawberry ice cream is 7/11 or approximately 0.6364 (rounded to four decimal places).

To calculate the probability that a female student chose strawberry ice cream, we need to consider the total number of female students who made an ice cream choice and the number of female students who chose strawberry ice cream.

From the given information, we have the following breakdown:

         Male    Female   Total

Vanilla 6 4 10

Strawberry 9 14 23

Chocolate 13 4 17

Total 28 22 50

To find the probability, we divide the number of female students who chose strawberry ice cream by the total number of female students:

Probability = (Number of female students who chose strawberry ice cream) / (Total number of female students)

Therefore, the probability of a female student choosing strawberry ice cream is:

Probability = 14 / 22

Simplifying the fraction, we have:

Probability = 7 / 11

Therefore, the probability that a female student chose strawberry ice cream is 7/11 or approximately 0.6364 (rounded to four decimal places).

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Answer:

3(x + y + z) = k

z = k\/3 - x - y

-k + 3 x + 3 y + 3 z = 0

The value of k that makes the equation 3x + 3y + 3z = k equal to 42 is k = 14. When you substitute k = 14 into the equation, you get 3x + 3y + 3z = 42, which satisfies the condition.

To find the value of k that makes the equation 3x + 3y + 3z = k equal to 42, you need to solve for k.

The equation is:

3x + 3y + 3z = k

Now, we want this equation to equal 42, so we substitute 42 for k:

3x + 3y + 3z = 42

Next, we can simplify the equation by factoring out the common factor of 3 on the left side:

3(x + y + z) = 42.

Now, we have a simpler equation:

x + y + z = 42 / 3

Divide both sides by 3:

x + y + z = 14

So, to make the equation 3x + 3y + 3z = k equal to 42, k should be equal to 14.

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Answer:

Step-by-step explanation:

You want the amounts invested at 9% and 6% if they total $11,335 and the interest from the 9% investment exceeds the interest from the 6% investment by $865.35.

If we let x represent the amount invested at 9%, the amount invested at 6% is (11335-x). The relation between the values of interest earned is ...

  (x)·9% -(11335-x)·6% = 865.35

  0.15x -680.10 = 865.35 . . . . . simplify

  0.15x = 1545.45 . . . . . . . . add 680.10

  x = 10303 . . . . . . . . . . . divide by 0.15

  11335 -x = 1032

$10,303 was invested at 9%; $1,032 at 6%.

__

Additional comment

It is convenient to use a single variable, and to let it represent the amount invested at the higher rate. If you use a system of 2 equations, you can effectively do this by substituting for the variable representing the amount invested at the lower rate. Using this approach keeps all of the numbers positive, tending to reduce errors.

Answer:

Amount invested at 9% = $6832.15; Amount invested at 6% = $4502.85

Step-by-step explanation:

We'll need a system of equations to find the amounts invested at both 9% and 6% and we'll need to convert the percentages to decimals (i.e., 0.09 and 0.06):

First equation in system:  

We know that the interest earned from the 9% investment is $865.35 greater than the interest earned from the 6% investment.

Thus, one equation we can use is x = y + 865.35

Second equation in system:

We also know that the amount invested at 9% plus the amount invested at 6% equals $11335.00

Thus, our second equation is 0.09x + 0.06y = 11335

Step 1:  We can use substitution to solve.  We must plug in x from the first equation for x in the second equation to solve for y:

0.09(y + 865.35) + 0.06y = 11335

0.09y + 77.8815 + 0.06y = 11335

0.15y + 77.88 = 11335

0.15y = 11257.12

y = 75047.46667

y = 75047.47

Step 2:  Now we can plug in 75047.47 for y into any of the two equations in our system to solve for y.  Because the first equation is simpler, let's use this one:

x = 75047.47 + 865.35

x = 75912.82

Step 3:  We can now find the amount invested by multiplying x by 0.09 and y by 0.06:

0.09x = 0.09(75912.82) = 6832.1538 = $6832.15

0.06y = 0.06(75047.47) = 4502.8482 = $4502.85

Optional Step 4:  We can check that our numbers are correct by substituting 75912.82 for x and 75047.47 for y in the two equations in our system:

Checking solutions for first equation:

75912.82 = 75047.47 + 865.35

75912.82 = 75912.82

Checking solutions for second equation:

0.09(75912.82) + 0.06(75047.47) = 11335

6832.1538 + 4502.8482 = 11335

6832.15 + 4502.85 = 11335

11335 = 11335

Whether the equation 3(x - 5) - 7 = ax + b has a solution depends on the value of a.

To determine if the equation 3(x - 5) - 7 = ax + b has a solution, we need to compare the coefficients of x on both sides of the equation.

In the given equation, the coefficient of x on the left side is 0 (since 3(x - 5) - 7 does not have an x term), and the coefficient of x on the right side is a.

For the equation to have a solution, the coefficients of x on both sides should be equal.

Therefore, we need to equate 0 and a:

0 = a.

If a = 0, then the equation has a solution. However, if a ≠ 0, then there is no solution.

Therefore, whether the equation 3(x - 5) - 7 = ax + b has a solution depends on the value of a.

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The research question is whether there is a significant relationship between GPA and the four variables, and the assumption of normality is tested by creating a descriptive statistics table with skewness and kurtosis values to determine if the variables follow a normal distribution.

Research question: Is there a significant relationship between GPA and the four variables (variable names not provided)?

Null hypothesis (H0): There is no significant relationship between GPA and the four variables.

Alternative hypothesis (Ha): There is a significant relationship between GPA and the four variables.

Step 2: Testing Assumptions - Normality

Research question: Is the assumption of normality violated for the four variables?

Null hypothesis (H0): The distribution of the four variables follows a normal distribution.

Alternative hypothesis (Ha): The distribution of the four variables does not follow a normal distribution

Next, you are instructed to create a descriptive statistics table in statistical software to assess normality. The table should include the four variables, along with their skewness and kurtosis values. Once you have created the table, you should paste it into the DAA Template.

After pasting the table, you will interpret the skewness and kurtosis values. Skewness measures the symmetry of the distribution, where a skewness value of 0 indicates perfect symmetry.

Positive skewness indicates a right-skewed distribution, while negative skewness indicates a left-skewed distribution. Kurtosis measures the peakedness or flatness of the distribution, with a kurtosis value of 3 indicating a normal distribution.

Positive kurtosis indicates a more peaked distribution (leptokurtic), while negative kurtosis indicates a flatter distribution (platykurtic).

Based on the skewness and kurtosis values, you will determine whether the assumption of normality is violated or not violated for the four variables.

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To make both triangles equal, their corresponding angles must be equal and when x = 106 degrees, the second angle in triangle 2 is equal to the third angle in triangle 1, which refutes Terry's claims.

To determine the value of x that refutes Terry's claims, we need to examine the angles of the triangles and find a valid configuration where triangle 1 is similar to triangle 2.

In triangle 1, the given angles are 18 degrees and 96 degrees. The third angle can be found using the property that the sum of the angles in a triangle is always 180 degrees:

Third angle in triangle 1 = 180 - (18 + 96) = 180 - 114 = 66 degrees.

let's find the value of x that will make both triangles similar to one another or their corresponding angles to be equal.

Since we already know one angle in triangle 2 is 8 degrees, we can find the second angle as follows:

Second angle in triangle 2 = 180 - (8 + x) = 180 - 8 - x = 172 - x degrees.

To refute Terry's claims, we need to find a value of x such that the second angle in triangle 2 (172 - x degrees) is equal to the third angle in triangle 1 (66 degrees).

Setting up the equation:

172 - x = 66

Solving for x:

172 - 66 = x

106 = x

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The exact value of sec(θ) is 8√(39)/39.

Given information:

In a right triangle,

Perpendicular side = 5, Hypotenuse side = 8.

Then to find exact secθ:

We can use the definition of secant, which is the reciprocal of cosine:

sec(θ) = 1/cos(θ)

In a right triangle, the cosine of an angle is equal to the adjacent side length divided by the hypotenuse length. Therefore, we first need to find the length of the adjacent side of the angle θ.

Let's label the sides of the right triangle as follows:

the hypotenuse side is H, with a length of 8

the perpendicular side is P, with a length of 5

the base side (adjacent to the angle theta) is B

Using the Pythagorean theorem, we can find the length of the base side B:

B² + P² = H²

B² + 5² = 8²

B² + 25 = 64

B² = 64 - 25

B² = 39

B = √(39)

Now we can use the cosine function to find cos(theta):

cos(θ) = B/H

cos(θ) = √(39)/8

Finally, we can find sec(θ) by taking the reciprocal of cos(θ):

sec(θ) = 1/cos(θ)

sec(θ) = 8/√(39) x √(39)/√(39)

sec(θ) = 8√(39)/39

Therefore, the exact value of sec(θ) is 8√(39)/39. This is the simplified form of the expression and cannot be further reduced because the square root of 39 is not a perfect square.

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Answer:

so do i get brainiliest???

Step-by-step explanation:

The total surface area of the given pyramid is: 95 ft²

To get the surface area of the given pyramid, we will find the individual areas of all surfaces and add up to get the total surface area.

Formula for area of a triangle is:

A = ¹/₂bh

where:

b is base

h is height

Formula for area of a rectangle is:

A = Length * Width

Thus:

Total surface area of pyramid = 4(¹/₂ * 5 * 7) + (5 * 5)

Total surface area of pyramid = 70 + 25

Total surface area of pyramid = 95 ft²

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Answer:

x+116

Step-by-step explanation:

add the expressions.

have a great day and thx for your inquiry :)

Answer:

0.1429

Step-by-step explanation:

The formula for the average rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex]. a = 0, b = 7, f(a) = 2, and f(b) = 3, We plus the numbers into the formula and get 0.1429 as our answer.