Which of the following is a statistical question that can result in numerical data?

What is the name of your favorite pizza store?
How many hours this week did you spend on homework?
How many times did you go swimming this year?
How many pink erasers do the students in your class have?

Answer:

(1/2)(x + 4 + 100) = 3x

x + 104 = 6x

5x = 104, so x = 20.8

The mode of the given data set as required to be determined in the task content is; 17.

It follows from the task content that the mode of the given data set is to be determined.

Recall from definition that the mode of a given data set is the observation or data value which occurs most frequently; i.e with the highest frequency.in the data set.

On this note, since 17 appears most frequently in the data set; It follows that the mode is ; 17.

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The command  that bisects and divides angles is: A. Line Command.

You must draw two lines starting at the angle's terminus and extending to any point on the angle in order to bisect an angle using the Line command. Next draw a line through the angle's vertex and the intersection of the two lines you just drew using the "bisector" tool from the "Object Snap" menu.

You can draw a line from the angle's vertex to any point on the angle and then use the "Divide" command to divide that line into the necessary number of segments to divide an angle using the Line command. Angles are divided into equal pieces at the spots where the divided line crosses them.

Therefore the correct option is A.

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Answer:

To find the volume of a rectangular prism, we multiply its length by its width by its height.

Here, the length, width, and height are all 5 yards, so we have:

Volume = length x width x height

Volume = 5 yd x 5 yd x 5 yd

Volume = 125 cubic yards

Therefore, the volume of the rectangular prism is 125 cubic yards.

The value of C(11, 0) is 1.

We have to find C(11, 0)

Using the definition of Combination

C(n, r) = n!/ r1 (n-r)!

Here, n =11 and r= 0

So, C( 11, 0)

= 11! / 0! (11-0)!

= 11! / 1 x 11!

= 1

Thus, the value of C(11, 0) is 1.

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Answer:

y = 2x + 1.5

Step-by-step explanation:

You can find two points and derive an equation.

Two obvious points are (0, 1.5) and (2, 5.5).

Using the form y = mx + b, you can find the slope m by using the formula [tex](y_1-y_2)/(x_1-x_2)[/tex].

m = (1.5-5.5)/(0-2) = -4/-2 = 2.

You can find b by plugging in your m value and one of the two points.

y = 2x + b

1.5 = 2*0 + b

b = 1.5

Thus, your equation is y = 2x + 1.5.

The vectors that describe the translation between the shapes are <-6, -6> and <6, 6>

a) shape R to shape T

We are given shapes R and T

The shape R is translated down by 6 units and translated right by 6 units

As a vector, we have the following representation <-6, -6>

b) shape T to shape R?

This is the reverse of the above transformation

i.e. the shape T is translated up by 6 units and translated left by 6 units

As a vector, we have the following representation <6, 6>

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Jada will receive a prize and what prize she will receive depends on the specific details of the prize allocation process.

If there are exactly 36 prizes available and they are being allocated in sequential order, then Jada will receive a prize because she is the 36th customer.

However, if there are fewer than 36 prizes available or if they are being allocated randomly, then Jada may or may not receive a prize.

It is possible that Jada will receive a specific prize designated for the 36th customer, or she may receive a prize that is randomly allocated to any customer.

It is also possible for Jada to receive more than one prize if the prizes are being allocated in a way that allows customers to receive multiple prizes.

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the equivalent expression of 5^-4 is 1/625

Index forms are defined as mathematical forms that are used in the representation of numbers or variables that are too large or too small.

They are also called scientific notation or standard forms.

They are represented as a number or variable that is raised to an exponent.

Examples of index forms are;

a³, c²

5², 6³

From the information given, we have;

5^-4

Note that equivalent expressions are described as expressions that have the same solution but different arrangement of values

Then, we have;

1/5⁴

Find the fourth root

1/625

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a. The number of degrees of freedom that should be used for finding the critical value to/2 is 49.

b. Using a t-distribution table or a calculator, we get: by/2 = 2.0096 (rounded to four decimal places)

c. The correct option is D. The number of degrees of freedom for a collection of sample data is the number of sample values that can vary after certain restrictions have been imposed on all data values.

a. The number of degrees of freedom that should be used for finding the critical value to/2 is given by the formula df = n - 1, where n is the sample size.

Therefore, in this case, df = 50 - 1 = 49.

b. To find the critical value tα/2 corresponding to a 95% confidence level, we need to use a t-distribution table with 49 degrees of freedom.

For a two-tailed test at the 0.025 level of significance (α/2), we find that tα/2 = 2.0096 (rounded to four decimal places).

Therefore, by/2 = 2.0096.

c. The number of degrees of freedom for a collection of sample data is the number of sample values that can vary after certain restrictions have been imposed on all data values.

This restriction is typically imposed when estimating a population parameter from a sample statistic. The number of degrees of freedom is determined by subtracting 1 from the sample size (n-1).

The concept of degrees of freedom is important in statistical inference and hypothesis testing, as it affects the critical value used in determining whether a hypothesis is statistically significant.

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Answer:

Step-by-step explanation:

The sum of angles in a quadrilateral is 360 degrees. So, we have:

x + 2x + 3x + fourth angle = 360

6x + fourth angle = 360

fourth angle = 360 - 6x

To find the value of x, we can use the fact that the angles in a quadrilateral add up to 360 degrees:

x + 2x + 3x + (360 - 6x) = 360

6x + 360 - 6x = 360

360 = 360

This equation is true for any value of x, so we cannot solve for x.

To find the size of the largest angle, we can substitute any value of x into the expression for the fourth angle and then find the largest of the four angles. For example, if we choose x = 30, then the angles are:

x = 30 degrees

2x = 60 degrees

3x = 90 degrees

fourth angle = 360 - (x + 2x + 3x) = 180 degrees

So the largest angle is 180 degrees.

The number of days the family were on vacation is 20 days.

The number of days the family were on vacation is calculated as follows;

Let's consider morning and afternoon as a half day.

From the question we will have the following equation;

12 mornings +  13 afternoons = 25  half days.

25 - 15 days of raining = 10  half days

10  half days = 5  mornings and 5 afternoons with no rain.

The number of days they stayed is calculated as;

15 + 5 = 20  days.

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The equation  that correctly shows the relationship between cups of flour and sugar is  f = 1/2s. Option A

if 1 cup of flour needs 2 cups of sugar.

2 cups of flour need 4 cups of sugar.

3.5 cups of flour need 7 cups of sugar.

5.25 cups of flour need 10.5 cups of sugar.

This only means that the size of sugar is twice the size of flour. Therefore to form our equation, we say

sugar = 2flour. But since the option is not there,

we can also go for

f = 1/2s

3.5 = 1/2 × 7

3.5 = 3.5

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Margo will pay an interest of $17.50.

To calculate the interest that Margo will pay, we first need to find the interest rate for 7 months.

The annual interest rate is 6%, so the monthly interest rate is:

6% / 12 months = 0.5% per month

Now, we can calculate the interest that Margo will pay on the $500 loan:

Interest = Principal x Rate x Time

where Principal is the amount borrowed, Rate is the monthly interest rate, and Time is the time period in months.

Plugging in the values, we get:

Interest = $500 x 0.5% x 7 months = $17.50

Therefore, Margo will pay $17.50 in interest.

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The angle formed between this vector and the positive x-axis measures around 61.26° and goes in a counterclockwise direction.

First, we calculate the components:

u = (80cos(30°), 80sin(30°)) ≈ (69.28, 40.00)

v = (60cos(60°), 60sin(60°)) ≈ (30.00, 51.96)

w = (50cos(120°), 50sin(120°)) ≈ (-25.00, 43.30)

Now, let's find the resultant vector (u+v+w):

u+v+w = (69.28 + 30.00 - 25.00, 40.00 + 51.96 + 43.30) ≈ (74.28, 135.26)

The magnitude of the resultant vector ||u+v+w|| can be found using the Pythagorean theorem:

||u+v+w|| = √(74.28² + 135.26²) ≈ 152.44

To find the direction, we calculate the angle θ:

θ = atan2(135.26, 74.28) ≈ 61.26°

The total size of the composite vector, obtained by adding u, v, and w, amounts to a value close to 152.44.

The angle formed between this vector and the positive x-axis measures around 61.26° and goes in a counterclockwise direction.

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The three vectors are in two-dimensional space and have the following components:

u = (80cos(30°), 80sin(30°))

v = (60cos(60°), 60sin(60°))

w = (50cos(120°), 50sin(120°))

What are the magnitude and direction is u+v+w? ||v|= 60 ||w||=50 ||u||= 80

$2,835 is invested at 14% and $1,193 is invested at 7%.

We have,

Let x be the amount invested at 14% and y be the amount invested at 7%.

We know that x + y = 4,028 and that the interest earned from the amount invested at 14% exceeds the interest earned from the amount invested at 7% by $313.39.

The interest earned on x is 0.14x and the interest earned on y is 0.07y.

We can set up an equation based on the given information:

0.14x - 0.07y = 313.39

We can solve for one of the variables in terms of the other:

y = 4,028 - x

Substitute this into the equation we just created:

0.14x - 0.07(4,028 - x) = 313.39

Simplify and solve for x:

0.14x - 281.96 + 0.07x = 313.39

0.21x = 595.35

x = 2,835

Now we can find y:

y = 4,028 - x = 4,028 - 2,835 = 1,193

Therefore,

$2,835 is invested at 14% and $1,193 is invested at 7%.

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The initial value of the function is 81.

The growth factor, or growth rate of the function is 2.25%.

An exponential function is a type of function which involves exponents. The general form of the exponential function is f(x) = a(1 + r)ˣ.

Where a is the initial value of the function and r is growth factor, or growth rate of the function.

We have the exponential growth function f(x) = 81(1.0225)ˣ.

Comparing f(x) = 81(1.0225)ˣ with f(x) = a(1 + r)ˣ. We can say:

a = 81

Thus, the initial value of the function is 81.

comparing again, we can say:

1 + r = 1.0225

r = 1.0225 - 1

r = 0.0225

r = 0.0225 * 100

r = 2.25%

Thus, the growth factor, or growth rate of the function is 2.25%.

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The object will hit the ground after 4 seconds.

We have,

The object will hit the ground when its height is zero.

So we need to solve the equation:

h = -16t² + 48t + 64 = 0

We can simplify this equation by dividing both sides by 16:

-t² + 3t + 4 = 0

To solve for t, we can use the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

where a = -1, b = 3, and c = 4.

Plugging in these values, we get:

t = (-3 ± √(3² - 4(-1)(4))) / 2(-1)

t = (-3 ± √(9 + 16)) / -2

t = (-3 ± √(25)) / -2

t = (-3 ± 5) / -2

We get two possible solutions:

t = -1 and t = 4.

Since time cannot be negative, we can discard the negative solution.

Therefore,

The object will hit the ground after 4 seconds.

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The value of the variable is 11

To determine the value of the variable, we need to know the triangle sum theorem.

The triangle sum theorem states that the sum of the angles in a triangle is 180 degrees.

From the diagram shown, we have that;

The angles are;

90 degrees

60 degrees

2x + 8

add the values

90 + 60 + 2x + 8= 180

collect the like terms, we get;

158 + 2x = 180

then,

2x = 22

Make 'x' the subject

x = 11

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The domain of the function is, (-4, +∞) - {6}

And the range of the function is, R - [-2,0).

Since, The domain of a function is the set values of x for which the function is defined.

And, The range of a function is the set values of y for which the function is defined.

As we can see that the graph of the function can be defined everywhere except on 6 at the x-axis, and between 0 to -2 on the y-axis. therefore,

Domain = (-4, +∞) - {6}

Range = R - [-2,0)

Hence, the domain of the function is (-4, +∞) - {6} and the range of the function is R - [-2,0).

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The area of the given square is 10 cm².

Given that,

The one square grid is of 1 cm²

Now labeling the figure

Since length of each side of square are equal

Therefore the length of sides of square is nothing but distance between the points (2,5) and (3,2).

Use distance formula

⇒[tex]\sqrt{(3-2)^{2} +(2-5)^{2} }[/tex]

⇒√10

So side of square = √10 cm

Thus area of square = side x side

                                  =  √10 x √10

                                  =  10 cm²

Hence area = 10 cm²

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The correct statement about the area and perimeter of Triangle 2 is true is:

The perimeter is 4.1 times the perimeter of Triangle 1, and the area is 16.81 times the area of Triangle 1.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

Triangle 1 is dilated by a scale factor of 4.1 using the origin as the center of dilation to create Triangle 2.

Now, We get;

The Triangle 1 is dilated by a scale factor of 4.1 using the origin as the center of dilation to create Triangle 2.

Hence, The perimeter of triangle 2 is 4.1 times the perimeter of Triangle 1.

And, We know that;

Area of triangle = 1/2 x Base x Height

So, The area of triangle 2 is 16.81 times the area of Triangle 1.

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The missing options are:

A. The perimeter is 4.1 times the perimeter of Triangle 1, and the area is 4.1 times the area of Triangle 1.

B. The perimeter is 8.2 times the perimeter of Triangle 1, and the area is 8.2 times the area of Triangle 1.

C. The perimeter is 4.1 times the perimeter of Triangle 1, and the area is 16.81 times the area of Triangle 1.

D. The perimeter is 16.4 times the perimeter of Triangle 1, and the area is 16.81 times the area of Triangle 1,

Answer:

118 degrees because it’s opposite of angle M which is also 118

Step-by-step explanation:

pls mark brainliest

The value of angle S and angle R is 95⁰ and 110⁰ respectively.

The value of angle S and angle R is calculated as follows;

11y + 7y = 180 (opposite angles of cyclic quadrilateral are supplementary)

18y = 180

y = 180/18

y = 10

(3x - 5) + (3x + 5) = 180 (opposite angles of cyclic quadrilateral are supplementary)

6x = 180

x = 180/6

x = 30

Angle S = 3x + 5

= 3(30) + 5

= 95⁰

Angle R = 11y

= 11 x 10

= 110⁰

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[tex]f(x)=2(3)^{x+1} \\\\[-0.35em] ~\dotfill\\\\ f(2)=2(3)^{(2)+1}\implies f(2)=2(3)^3\implies f(2)=2(3^3) \\\\\\ f(2)=2(27)\implies f(2)=54[/tex]

Answer:

---------------------

Use the formula for compound interest:

where,

Plugging in the values given, we get:

To find the interest earned, subtract the principal from this amount:

The smaller of the triangle’s two acute angles is 34 degrees

From the question, we have the following parameters that can be used in our computation:

In a right triangle, cos(7x) = sin(5x−6)

As a general rule in a right triangle,

if cos(a) = sin(b), then

a + b

Using the above as a guide, we have the following:

7x + 5x - 6 = 90

So, we have

12x = 96

Divide

x = 8

Next, we have

Angles = 7x and 5x -  6

So, we have

Angles = 7 * 8 and 5 * 8 -  6

Evaluate

Angles = 56 and 34

Hence, the smaller of the triangle’s two acute angles is 34 degrees

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The surface area of this cuboid is 130 cm^2

Cuboid is a closed three-dimensional structure surrounded by rectangular faces, which are rectangle plane sections.

How to determine this

The surface area of cuboid is the total area of all its 6 faces.

SA = 2{(Length * Height) + (Width * Length) + (Width * Height)

Where Length = 10 ft

Width = 5 ft

Height = 1 ft

SA = 2{(10*1) + (5*10) + (5*1)

SA = 2(10 + 50 + 5)

SA = 2(65)

SA = 2 * 65

SA = 130 ft^2

Therefore, the surface area of cuboid is 130 ft^2

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