Use inverse operations to solve each of the following quadratic equations. Put each of your responses in the simplest radical form possible.

The IQR for both runs is 8 minutes.

If there are outliers or extreme values ​​in the data set, we summarize the typical value using the median instead of the mean. When there are outliers in a data set, the variation is often summarized by a statistic called the interquartile range, which is the difference between the first and third quartiles.

 Based on the given box pairs, we can make the following comparisons:

The average wait time at Thrill Tower is about 5 minutes shorter than the average wait time at River Rapids. That's because the centerline of Thrill Tower is  about 5 units below the centerline of River Rapids.  The IQR (interquartile range) for both times is not  directly in the box. However, we can estimate this by finding the distance between the first quartile (Q1) and the third quartile (Q3) of each run. From the box plot of Thrill Tower, we can see that Q1 is around 6 and Q3 is around 14. Therefore, the IQR for Thrill Tower is:

 Thrill Tower IQR = Q3 - Q1 = 14 - 6 = 8 minutes

From the box plot for River Rapids, we can see that Q1 is about 8 and Q3 is about 16. Therefore, the IQR for River Rapids is:

 River Rapids IQR = Q3 - Q1 = 16 - 8 = 8 minutes

Therefore, the IQR for both runs is 8 minutes.

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Answer: HERE IS THE ANSWER BELOW :)

The surface area of the pyramid is 532m²

A pyramid is a 3D polyhedron with the base of a polygon along with three or more triangle-shaped faces that meet at a point above the base. It is made by connecting each vertex of the base to a common tip or apex giving it its typical shape.

The general formula for the lateral surface area of a regular pyramid is L.S.A.=1/2pl

where

Given that The pyramid is a rectangular,

Therefore the surface area is

L.S.A.=1/2(14*4) *19

Surface area = 28*19 = 532m²

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For a hypothesis testing, [tex]H_0 : µ = µ_0[/tex] ; [tex]H_1 : µ > µ_0.[/tex] the calculated P-value for test statistic value are following a) 0.9906 ; b) 0.9370 ; c) 0.9773; d) 0.9678 ; e) 0.4404.

We are testing the null hypothesis versus alternative hypothesis. Both are defined as [tex]H_0 : µ = µ_0[/tex]

[tex]H_1 : µ > µ_0.[/tex].

We have to calculate the P-value for the following observed values test statistic one by one.

a)z = 2.35

The P -value is calculated for as follows P ( z > Zo) = 1 - P( z≤ z0)

= 1 - P( z≤ 2.35)

Now, using the normal distribution table, the value of P( z≤ 2.35) is equals to 0.009387. So, P( z> 2.35) = 1 - 0.009387

= 0.990613

b) z₀ = 1.53

The P-value is calculated for as follows P ( z > z₀) = 1 - P( z≤ z₀)

= 1 - P( z≤ 1.53)

Now, using the normal distribution table , the value of P( z≤ 1.53) is equals to 0.063008. So, P( z> 1.53) = 1 - 0.063008

=0.936992

c) z₀ = 2.00

The P-value is calculated for as follows, P ( z > z₀) = 1 - P( z≤ z₀)

= 1 - P( z≤ 2.00)

Now, using the normal distribution table , the value of P( z≤ 2.00) is equals to 0.02275. So, P( z> 2.00) = 1 - 0.02275

=0.97725

d) z₀ = 1.85

The P-value is calculated for as follows P ( z > z₀) = 1 - P( z≤ z₀)

= 1 - P( z≤ 1.85)

Now, using the normal distribution table , the value of P( z≤ 1.85 ) is equals to 0.032157. So, P( z> 1.85) = 1 - 0.032157

=0.967843

e) z₀ = -0. 15

The P-value is calculated for as follows P ( z > -z₀) = P( z ≤ z₀)

= P( z≤ 0.15 )

Now, using the normal distribution table , the value of P( z≤ 0.15) is equals to 0.440382. So, P( z > - 0.15) = 0.44038. Hence the required P-value is 0.44038.

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From the attached picture, it is proven that the diagonals of rectangle MNOP are congruent.

To show that the diagonals of rectangle MNOP bisect each other, we need to show that they intersect at their midpoint. Let's label the diagonals as AC and BD, where AC is the diagonal that goes from vertex M to vertex O, and BD is the diagonal that goes from vertex N to vertex P.

First, let's find the midpoint of AC. The midpoint of a line segment is the point that is exactly halfway between the two endpoints. The endpoints of AC are M and O, so we can find the midpoint by averaging their x-coordinates and y-coordinates:

midpoint of AC = ((Mx + Ox)/2, (My + Oy)/2)

Similarly, we can find the midpoint of BD:

midpoint of BD = ((Nx + Px)/2, (Ny + Py)/2)

Now we need to show that these midpoints are the same point. That is, we need to show that:

((Mx + Ox)/2, (My + Oy)/2) = ((Nx + Px)/2, (Ny + Py)/2)

To do this, we can set the x-coordinates equal to each other and the y-coordinates equal to each other:

(Mx + Ox)/2 = (Nx + Px)/2

(My + Oy)/2 = (Ny + Py)/2

Now we can solve for the values of x and y. First, we'll solve for x:

Mx + Ox = Nx + Px

2Mx + 2Ox = 2Nx + 2Px

Mx + Ox - Nx - Px = 0

(Mx - Nx) + (Ox - Px) = 0

Similarly, we can solve for y:

My + Oy = Ny + Py

2My + 2Oy = 2Ny + 2Py

My + Oy - Ny - Py = 0

(My - Ny) + (Oy - Py) = 0

Now we can see that the x-coordinate and y-coordinate of the midpoint of AC are equal to the x-coordinate and y-coordinate of the midpoint of BD, respectively. Therefore, the diagonals of rectangle MNOP bisect each other.

To show that the diagonals are congruent, we can use the Pythagorean theorem. Let's label the length of AC as a and the length of BD as b. Then we have:

a^2 = OM^2 + ON^2 (by the Pythagorean theorem in triangle OMN)

b^2 = PN^2 + PO^2 (by the Pythagorean theorem in triangle PON)

But we know that OM = ON and PO = PN, since MNOP is a rectangle. Therefore, we can simplify these expressions:

a^2 = 2OM^2

b^2 = 2PO^2

Since OM = PO (they are opposite sides of a rectangle), we can substitute to get:

a^2 = 2OM^2 = 2PO^2 = b^2

Therefore, a = b, and the diagonals of rectangle MNOP are congruent.

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Answer:

35.00 - (0.85x) = remaining amount

Step-by-step explanation:

To find out how much money she has left, we need to subtract this amount from her starting amount of $35.00:

35.00 - 0.85x

Therefore, the expression that shows how much money Pam has left after buying (x) peaches is:

35.00 - 0.85x

It seems like the answer could be $6,500, but I prefer to wait for a professional tbh☹.

The Orchard Cafe can expect approximately 77 diners to show up out of the 81 reservations made

To determine how many diners can be expected to show up at The Orchard Cafe, we can follow these steps:

1. Identify the percentage of diners who actually show up: Since 4% of diners with reservations don't show up, the percentage of diners who do show up is 100% - 4% = 96%.

2. Calculate the expected number of diners who show up: Multiply the total number of reservations (81) by the percentage of diners who show up (96%).

81 reservations x 0.96 (96% as a decimal) = 77.76

Since the number of diners must be a whole number, you can round the result to the nearest whole number.

In this case, 77.76 can be rounded down to 77.

Your answer: The Orchard Cafe can expect approximately 77 diners to show up out of the 81 reservations made.

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The radian measure of the central angle which intercepts the arc is 6.2 radians.

We can use the formula relating the arc length to the angle and radius of the circle:

arc length = radius x central angle in radians

Plugging in the given values, we get:

148.8 = 24 x central angle in radians

Solving for the central angle, we have:

central angle in radians = 148.8/24

central angle in radians = 6.2 radians

Therefore, the radian measure of the central angle which intercepts the arc is 6.2 radians.

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Answer:

$51,500 in her savings account.

Step-by-step explanation:

If Pamela has $50,000 in a savings account with an interest rate of 3% per year and the interest is not compounded, then in 1 year she will earn an interest of $50,000 * 0.03 = $1,500.

So, after 1 year, Pamela will have a total of $50,000 + $1,500 = $51,500 in her savings account.

Answer: Parallelogram

Step-by-step explanation: A parallelogram is a quadrilateral with opposite sides parallel. If ZL, ZM, ZN, and ZO are approximately equal, it implies that the opposite sides LM and NO are parallel, and the opposite sides LO and MN are also parallel.

It may not be a rectangle: While a parallelogram is a quadrilateral with opposite sides parallel, a rectangle is a special type of parallelogram with additional properties, such as all angles being right angles. The given information does not provide any information about the angles of the quadrilateral, so we cannot conclude that it is a rectangle.

It may not be a rhombus: A rhombus is a special type of parallelogram in which all sides are equal. The given information only states that the angles ZL, ZM, ZN, and ZO are approximately equal, but it does not provide any information about the lengths of the sides LM, LO, MN, or NO. Therefore, we cannot conclude that LMNO is a rhombus based solely on the given information.

The conclusion that red is the preferred color of shirt among 7th grade students based on a survey of 6 random students in an art class is not necessarily valid due to the small sample size, sampling bias, and lack of generalizability.

The sample size of six pupils is tiny and may not be typical of the overall seventh-grade population. It's probable that the six students in the art class have different preferences or biases than the other seventh-grade students.

Also, the sample of six pupils is drawn at random from an art class rather than from the total 7th grade population. Students who are interested in art may have different preferences than students who are not. This can add bias into the sample.

Finally, the language of the survey question is critical. If the survey question specifically asks about the most chosen color of shirt among 7th grade kids in general, the conclusion that red is the most preferred color of shirt follows.

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Answer:

p=30 s=30 k=90 x=0

Step-by-step explanation:

000000000000

Answer:

20/8 or 20:8

Step-by-step explanation:

Ok, so we start off with a smaller square with one side being 8.

We then have to go from one side being 8 to one side being 20.

So, the ratio has to be a number larger than 1 to go from smaller to larger, so we can use the ratio of 20/8 (or 2.5).

Check:

2.5x8=20

The cost of the case of air fresheners is $33.25.

Let the cost of the case of air fresheners be represented by the variable a.

Then, the cost of 5 buckets is 5 times $2.89, or 5 x 2.89 = $14.45.

The cost of 10 brushes is 10 times $7.91, or 10 x 7.91 = $79.10.

The cost of 48 towels is 48 times $0.36, or 48 x 0.36 = $17.28.

The total cost of the purchases, including the case of air fresheners, is $144.08.

Therefore, we can write the equation:

14.45 + 79.10 + 17.28 + a = 144.08

Simplifying the left side of the equation, we get:

110.83 + a = 144.08

Subtracting 110.83 from both sides of the equation, we get:

a = 33.25

Therefore, the cost of the case of air fresheners is $33.25.

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Answer:

volume

Step-by-step explanation:

Victoria should use volume measurement to determine how much sand she should buy.

We reject the null hypothesis and conclude that the true average temperature of COVID patients exceeds 100, with a type I error rate of 10% and a p-value of 0.0068 indicating a low probability of obtaining the observed sample mean if the null hypothesis were true.

To test if the true average temperature of COVID patients exceeds 100, we can use a one-sample z-test.

The null and alternative hypotheses are

Null hypothesis: The true average temperature of COVID patients is less than or equal to 100.

Alternative hypothesis: The true average temperature of COVID patients exceeds 100.

We can calculate the test statistic as

z = (x - μ) / (σ / sqrt(n))

where x is the sample mean, μ is the hypothesized population mean (100 in this case), σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get

z = (101.2 - 100) / (6 / sqrt(56))

z = 2.47

We can find that the p-value is 0.0068. This means that if the true average temperature of COVID patients is actually 100, there is only a 0.68% chance of getting a sample mean of 101.2 or higher.

Since the alpha level is 10%, and the p-value is less than 10%, we reject the null hypothesis and conclude that the true average temperature of COVID patients exceeds 100.

The type of error that could have occurred is a type I error, which is rejecting the null hypothesis when it is actually true. The probability of a type I error is equal to the chosen alpha level, which is 10% in this case.

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The solution to the given problem of volume comes out to be the pyramid is 10 cm tall.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Liter and in3 are the symbols for cubic measures.

Here,

The formula: gives the volume of a pyramid.

=> V = base_area * height * (1/3)

The area of the base (base_area) of a pyramid whose base is a rectangle with dimensions of 7.5 cm in length and 2 cm in width can be computed as follows:

base_area equals length * width,

=> 7.5 cm * 2 cm =15 cm².

Additionally, we are informed that the pyramid's (V) volume is 50 cm3.

=> (1/3) * 15 * height = 50

=> height =  (3 * V)/base_area.

When V and base_area's values are entered, we obtain:

=> height = (15/15) / (3*50) = 10 cm

Consequently, the pyramid is 10 cm tall.

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Answer: 7.5

Step-by-step explanation: 2 x 7.5 = 15

Answer:

x = - [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

14 = [tex]\frac{8}{3}[/tex] (x + 6) ← multiply both sides by 3 to clear the fraction

42 = 8(x + 6) ← distribute parenthesis

42 = 8x + 48 ( subtract 48 from both sides )

- 6 = 8x ( divide both sides by 8 )

[tex]\frac{-6}{8}[/tex] = x , that is

x = - [tex]\frac{3}{4}[/tex]

For any value of x, the corresponding value of y will always be 7, and the line will be a horizontal line passing through the point (5,7).

If a straight line is parallel to the x-axis, then it means that the line will have a constant y-value for all values of x. This means that the slope of the line will be zero, because there will be no change in y for any change in x.

To find the equation of a straight line passing through the point (5,7) that is parallel to the x-axis, we need to find the equation in the form of y = mx + b, where m is the slope of the line and b is the y-intercept.

Since the slope of the line is zero, we can write the equation as:

y = 0x + b

where b is the y-intercept.

To find the value of b, we can use the point (5,7) that the line passes through. Substituting x = 5 and y = 7 in the equation, we get:

7 = 0(5) + b

Simplifying, we get:

b = 7

Therefore, the equation of the straight line passing through the point (5,7) that is parallel to the x-axis is:

y = 7

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Answer:

3/5 = 60% = 0.6

In the bottom row, 3/5 is the wrong fraction. 2/3 is the correct fraction.

Let's the weight of Case C = "x" grams.

From the information:

Case A = 12 times heavier than Case B,

Therefore, the weight of Case B = 1/12 of Case A's weight:

Weight of Case B = (1/12) * Weight of Case A

Case B = 16 times heavier than Case C,

so, weight of Case C = 1/16 of Case B's weight:

Weight of Case C = (1/16) * Weight of Case B

The weight of Case A = 8,640g,

Let's substitute the value into the equations to find the weight of Case C:

Weight of Case B = (1/12) * 8,640 = 720g

Weight of Case C = (1/16) * 720 = 45g

Thus, the weight of Case C is 45 grams.

Answer:5

Step-by-step explanation: you divide 15 by 3 which gives you 5

Answer: A and D as for angle 24 deg, we are using the sin=opp/hyp and for angle 66 we are using cos=adj/hyp.

To find angle 66, you just subtract all 180 by the angles we know. 180-24-90.

4 is the correct value from the set {1, 2, 3, 4} which is the solution to the equation 3x + 3 = 15.

A solution of an equation refers to a value or values that satisfy the given equation. It is the value or values that make the equation true when substituted for the variable(s) in the equation. Equations are mathematical expressions that contain an equals sign and can have one or more variables. A solution is typically represented as a number, but it can also be a set of numbers, a range of values, or an expression. Finding the solutions of an equation is an important part of solving mathematical problems and has many practical applications in fields such as engineering, physics, and finance.

Solution of the given equation 3x + 3 = 15 means when we put a value in x we should get the result as 15, that is left hand side of the equation should be equal to the right hand side of the equation.

Solving the equation we get,

3x + 3 - 3 = 15 - 3

3x = 12

x = 4

Therefore, the value 4 is a solution to the equation.

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The solution of the system of equations in this problem is given as follows:

(4,0).

The equations that compose the system in this problem are given as follows:

We solve the system graphically, hence the solution is given by the point of intersection of the graphs of the two functions.

From the graph given by the image presented at the end of the answer, the solution to the system is given as follows:

(4,0).

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The documentation provided with the procedure states that the procedure will display the value of (x + y) / x.

This means that the result of the calculation will be shown to the user, and it will be the value obtained by adding x and y, then dividing the result by x.

However, the documentation also includes a very important requirement for the parameter x: it must not be 0. This is because dividing by zero is not a valid mathematical operation, and will result in an error. Therefore, it is crucial to ensure that the value of x passed to the procedure is a non-zero integer.

To summarize, the "calculate" procedure takes two integer parameters, x and y, and displays the value of (x + y) / x.

It is important to note that the value of x must not be 0, as dividing by zero is not a valid mathematical operation.

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A measure of relative fit for a simple regression line is called the r² or coefficient of determination.

A regression line, or line of best fit, is a straight line used to model the relationship between two variables in a data set. It is drawn through the data points to minimize the distance between the line and the points, representing the best fit. The line's equation is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept. The slope represents the rate of change of y with respect to x, and the y-intercept represents the value of y when x is equal to 0. The line is often used to predict the dependent variable based on the independent variable, and the accuracy of the predictions depends on how well the line fits the data.

The coefficient of determination, also known as r², is a statistical measure used to determine the relative fit of a simple regression line. This measure represents the proportion of variance in the dependent variable that can be predicted by the independent variable. The calculation involves squaring the correlation coefficient (r) between the two variables. The resulting value of r² ranges from 0 to 1, where 0 indicates that the independent variable has no explanatory power over the dependent variable, while 1 implies that the independent variable explains all the variability in the dependent variable.

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Answer: 15.

Step-by-step explanation: If one-third of the students are girls, then two-thirds of the students are boys:

number of boys = (2/3) * 30 = 20

Three-quarters of the boys play basketball, so the number of boys in the class who play basketball is:

number of boys who play basketball = (3/4) * 20 = 15

Therefore, the number of boys in the class who play basketball is 15.