The dot plot displays data from 14 random samples, each consisting of 30 middle school students. Each dot represents the mean number of sports played per year by students in the sample.



Which number best represents the mean number of sports played by middle school students? Write your answer as a decimal to the nearest tenth.

__ sports



Part B
Find and interpret the variability in the distribution. Round the MAD to the nearest hundredth.

The MAD is about_____ sport(s). The majority of the sample means are within ______ sport(s) of the mean. This means our estimate is likely not far off from the true mean.

The value of x is 7.

Two or more angles are said to be vertical angles if only they are formed by same two lines intersecting at a point. Thus the two angles have equal measure of value.

Given that A and B are vertical angles, then this implies that there is a relationship between them i.e they are opposite and equal.

Such that;

m<A = m<B

(x + 27) = (2x + 20)

x + 27 = 2x + 20

collect like terms,

-20 + 27 = 2x - x

7 = x

x = 7

Therefore, the value of x is 7.

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The equation that represent y, the total number of letters Natasha put in an envelope in x hours is y = 42x.

Natasha has a job putting letters to the envelope to be mailed. In one hour she put 42 letters in the envelope.

Therefore, the equation that best represent y, the total number of letters Natasha put in an envelope in x hours if she continue at the same rate can be calculated as follows;

1 hours = 42 envelopes

x hours = ?

cross multiply

Therefore,

y = 42x

where

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The correct symbolic expression for a is option C) [tex]\frac{ma_{1} +F}{m}[/tex]

A symbolic expression, also known as a mathematical expression, is a combination of numbers, variables, and mathematical operators (such as +, -, *, /) that can be evaluated to produce a numerical result.

Symbolic expressions can also contain functions, constants, and mathematical operations like logarithms, trigonometric functions, etc. They can be used to model physical phenomena or to solve mathematical problems.

A logarithmic function is a mathematical function that expresses the power (or exponent) to which a fixed number (the base) must be raised to produce a given value.

It is typically written in the form "logb(x)" where b is the base and x is the value being evaluated. The most common base used is 10 (common logarithm) or e (natural logarithm)

These expressions can be used to represent mathematical concepts, relationships, or equations.

Therefore, The correct symbolic expression for a is option C) [tex]\frac{ma_{1} +F}{m}[/tex].

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A function is defined as a relation between a set of inputs, each with an output. The sketch of the function f(x,y) = 9 - 9x² - y² is given below.

f(x,y) = 9 - 9x² - y²

Let the given function is equal to 0, Then

           9 - 9x² - y² = 0

                         y²  = 9 - 9x²

The function can be written as

                          y²  = 9 - 9x²

A function is a relationship between inputs, each associated with exactly one output. Each function has a domain and a codomain or scope. Functions are commonly denoted by f(x). x is the input. Here's the technical definition of the function:

A relationship from a set of inputs to a set of possible outputs.

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Answer:

36,323-17,000

Step-by-step explanation:

just go to the thousands place and look back one place value

The domain of the ordered pairs {(4, 9), (–6, 1), (–2, 5), (3, 1)} is  (c) {–6, –2, 3, 4}

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

{(4, 9), (–6, 1), (–2, 5), (3, 1)}

Rewrite as

(x, y) = {(4, 9), (–6, 1), (–2, 5), (3, 1)}

The domain is the set of the x values

So, we have the following representation

x = {4,–6, –2, 3}

Remove repeated entries and reorder

x = {–6, –2, 3, 4}

So, the domain is x = {–6, –2, 3, 4}

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6.2353535353535 as a fraction is 623535353535/1000000.

This fraction is written as a mixed number by dividing the numerator by the denominator to get 623,535,353,535/1,000,000. This can be further simplified to 623,535/1,000, which is the same as 623 5/8.

The correct answer is B.

The size of the animal population in year 2004 (t=0) is 200 thousands individuals.

Population is a term used to describe the total number of people that live in a specific geographic area. This can be a country, a state, a city, or any other area of the world. Population size and density are important factors in understanding the landscape of an area and its resources.

The size of the animal population in year 2004 (t=0) can be calculated by substituting t=0 into the given equation:

P(t)=210t+400/(t+2)

P(0)=210 × 0 + 400/(0+2)

P(0)=400/2

P(0)=200
Therefore, the size of the animal population in year 2004 (t=0) is 200 thousands individuals.

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Answer:

88 square cm

Step-by-step explanation:

Surface area of down rectangular prism:

      l = 6cm ; w = 3 cm & h = 2 cm

   [tex]\sf \boxed{Total \ surface \ area \ of \ rectangular \ prism = 2*(lw + wh+hl)}[/tex]

                                                                       = 2*(6*3 + 3*2 + 2*6)

                                                                        = 2* (18 + 6 + 12)

                                                                         = 2 * 36

                                                                          = 72 cm²

Lateral surface area of the top rectangular prism:

    l = 3 cm

    w = 1 cm

     h =  4 - 2 = 2 cm

         LSA = 2h( l + w)

                = 2*2 *( 3 + 1)

                 = 4 * 4

                 = 16 cm²

Surface area of the shape = 72 + 16

                                              = 88 cm²

Answer:

a = 88 cm2

Step-by-step explanation:

[tex]a=(4)(3)+2(4)(1)+2(5)(2)+2(3)(2)+(1)(3)+6(3)+5(3)=12+8+20+12+3+18+15[/tex]

[tex]a=88cm^{2}[/tex]  

Hope this helps

Answer:

6

Step-by-step explanation:

For dividing fractions it's also useful to know that the first fraction (3/4) is called the dividend and the second fraction (1/8) is called the divisor.

Here is a really quick way to divide fractions. In the divisor (the second fraction) we flip the numerator and the denominator. This is known as the reciprocal and basically it means the reverse of the fraction. When we find the reciprocal, we also have to change the division sign to a multiplication sign:

3/4 times 8/1

Once you've flipped the second fraction and changed the symbol from divide to multiply, we can multiply the numerators together and the denominators together and we have our solution:

So we multiply the numerators: 3x8=24

Then multiply the denominators: 4x1=4

Then we have the inproper fraction 24/4

So we divide 24 by 4 to make the answer a proper fraction

Finally you get your answer 6!

A parallelogram is a quadrilateral with congruent and parallel opposite sides. Thus, to justify that the given quadrilateral is a parallelogram, option E is correct.

One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

Quadrilaterals are shaped with four straight sides. Examples are; square, rectangle, parallelogram, trapezium, etc.

A parallelogram is a type of quadrilateral that has opposite sides to be equal and parallel. It has some distinguishing properties which can be used to differentiate it from other quadrilaterals. Some of the are:

Thus, in the given question the required option is C. consecutive angles are supplementary.

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The equation can be written as a linear combination of the vectors in S:

z = 5*(1, 2, −2) -1*(2, −1, 1)

v = -2*(1, 2, −2) + 7*(2, −1, 1)

w = -12*(1, 2, −2) + 11*(2, −1, 1)

What is the linear combination?

Linear combination is the process of adding two algebraic equations so that one of the variables is eliminated. Addition or subtraction can be used to perform a linear combination.

(a) z = (−3, −1, 1)

We can write z as a linear combination of the vectors in S by using the following equation:

z = as1 + bs2

Here, we can find the values of a and b by solving the following system of equations:

-3 = a1 + b2

-1 = a2 + b(-1)

1 = a*(-2) + b*1

Solving this system of equations, we get:

a = 5

b = -1

Therefore, z can be written as a linear combination of the vectors in S as:

z = 5*(1, 2, −2) -1*(2, −1, 1)

(b) v = (−2, −5, 5)

we can write v as a linear combination of the vectors in S by using the following equation:

v = as1 + bs2

Here, we can find the values of a and b by solving the following system of equations:

-2 = a1 + b2

-5 = a2 + b(-1)

5 = a*(-2) + b*1

Solving this system of equations, we get:

a = -2

b = 7

Therefore, v can be written as a linear combination of the vectors in S as:

v = -2*(1, 2, −2) + 7*(2, −1, 1)

(c) w = (1, −23, 23)

we can write w as a linear combination of the vectors in S by using the following equation:

w = as1 + bs2

Here, we can find the values of a and b by solving the following system of equations:

1 = a1 + b2

-23 = a2 + b(-1)

23 = a*(-2) + b*1

Solving this system of equations, we get:

a = -12

b = 11

Therefore, w can be written as a linear combination of the vectors in S as:

w = -12*(1, 2, −2) + 11*(2, −1, 1)

Therefore, The equation can be written as a linear combination of the vectors in S:

z = 5*(1, 2, −2) -1*(2, −1, 1)

v = -2*(1, 2, −2) + 7*(2, −1, 1)

w = -12*(1, 2, −2) + 11*(2, −1, 1)

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Answer:

0.39 is the answer to this question

x = 2

All the sides are 2 so if the length on the bottom is 2, then it would be the same for the top :)

Answer:

x=2

Step-by-step explanation:

This shape is a regular polygon so all the sides are the same length

Answer:

1/7

Step-by-step explanation:

4/4 is 1 and 28/4 is 7 so 1/7

The answer is 1/7.

To simplify : 4/28

To simplify fractions, we should follow these steps:

Here, the given fraction is 4/28.

At first, we need to write the factors of the numerator and the denominator

Factors of the numerator, 4 = 1, 2, 4.

Factors of the denominator, 28 = 1, 2, 4, 7, 14, 28.

So, the common factors are 1, 2 and 4.

Dividing the numerator and denominator by the common factor, 2;

(4/2) / (28/2)   or,

2/14

And,

(2/2) / (14/2)    or,

1 / 7.

Hence, 1/7 is the simplified fraction of 4/28.

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We can conclude that the supplement angle of 89° will be 91°.

Angles that add up to 180 degrees are referred to as supplementary angles.

For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°.

The sum of complementary angles is 90 degrees.

Two angles are complementary if their sum equals 90 degrees, and supplementary if their sum equals 180 degrees.

So, we have an angle of 89°.

We know that the supplement angle is an angle of measure 180°.

Now, the supplement angle of 89° will be as follows:

180 - 89

91°

Therefore, we can conclude that the supplement angle of 89° will be 91°.

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The temperature change that is required is; A reduction in temperature by 8°C.

We are told that;

The freezer should be working at -18°C.

The temperature on the freezer marks -10°C.

Now, what we see here is basic arithmetic because we simply want to find the additional temperature that will make the current reading to be equal to the ideal temperature required for it to wor. Thus, what we will do is to simply subtract the current temperature from the ideal one to find out the temperature required to make it work well.

Thus;

Temperature change = -18 - (-10)

Temperature change = -18 + 10

Temperature change = -8°C.

We see that the freezer still needs its' temperature to be reduced by 8°C.

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Complete question is;

Tom works in the cold food department in a supermarket. The thermometer shows the temperature of one of the freezers. The freezer should be working at -18°C. The temperature on the freezer marks -10 The temperature should increase or decrease by how many °C?

Examining the number line, the value of y is calculated to be 5

The value of RS and ST are 33 and 28 respectively

A number line is a horizontal representation of number parts with equal intervals

The numbers in a number line is arranged to be increasing from left to right , hence drawing a number line will have the smaller values to the left of the bigger values

In the problem, the given data include:

RS = 6y + 3​,

ST = 4y + 8​,

RT = 61.

From the number line we can say that

RT = RS + ST

61 = 6y + 3 + 4y + 8

collecting like terms

61 - 8 - 3 = 6y + 4y

10y = 50

divide through by 10

y = 5

RS = 6y + 3​,

RS = 6 * 5 + 3​ = 30 + 3 = 33

RS = 33

ST = 4y + 8​,

ST = 4 * 5 + 8 = 20 + 8 = 28

ST = 28

​

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Answer:

3x-6 is more than -3

Step-by-step explanation:

3x-6=0

  +6 +6

3x=6

3/   3/

x=3

Therefore , the solution of the given problem of expression comes out to be for addition +2 and subtraction -2.

Multiplying, dividing, adding, and subtracting are necessary math operations. When combined, the following expression would appear: A mathematical operator, some data, and an equation Values, variables, and functions make up a statement of fact's constituent parts, such as additions, deductions, multiplications, divisions, etc. It is possible to contrast and compare words and phrases.

Here,

Given :

So, for addition expression:

=> -5 + 2 = -3

So , for the subtraction expression:

=> -5 -(-2) = -3

Therefore , the solution of the given problem of expression comes out to be for addition +2 and subtraction -2.

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The probability of randomly drawing three consecutive red marbles is  [tex]\frac{27}{512}[/tex]  

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Here Total number of marbles = 3+3+2 = 8.

Now probability of randomly drawing three consecutive red (R) marbles is

=> P(3 consecutive red) = P(red)×P(red)×P(red)

=> P(3 consecutive red) = [tex]\frac{3}{8}\times \frac{3}{8}\times \frac{3}{8}[/tex] = [tex]\frac{27}{512}[/tex]

Hence the probability of randomly drawing three consecutive red marbles is  [tex]\frac{27}{512}[/tex]  .

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hello my friend if i am being helpful please please please rate my work and give me a like

The cubic function of the given expression would be = (2x + 4). That is option A.

Cubic function is defined as the multiplication of variables by itself into three different times.

The factors of the given cubic function f(x) = 8x³ +64 can be calculated using the following steps:

(2x + 4)³ = X

(2x)³ = 8x³

(4)³ = 64

Therefore the cubic function of the given equation is (2x + 4).

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the best deal for holly to do shopping from the first store.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, Holly needs to buy some cloth to make masks. The following deals are available at various stores.

For the first store:

Price per yard = 16.52/6$

Price per yard = 2.7533$

For the second store:

Price per yard = 13.85/5$

Price per yard = 2.77$

therefore, it is best for her to buy from the first store.

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Complete question:

The following deals are available at various stores. Choose the best deal.

a

$16.52 for 6 yd

b

$13.85 for 5 yd

c

Neither

In order to find the magnitude of a vector, we use the Pythagorean theorem. The magnitude, also known as the length or the norm, of a vector, is the square root of the sum of the squares of its components.

In this case, we are given two vectors A and B, which are defined as

A = 5i + 7j

B = 2i + 3j.

The i and j components represent the x and y values of the vector respectively.

To find the magnitude of vector A-B, we need to first find the difference between the two vectors. This can be done by subtracting the components of vector B from the corresponding components of vector A. So,

A-B = (5i + 7j) - (2i + 3j) = 3i + 4j.

Now we can use the Pythagorean theorem to find the magnitude of this vector. The square root of the sum of the squares of the x and y components of the vector is the magnitude of the vector. So, the magnitude of

A-B = √(3^2 + 4^2)

A-B = √(9 + 16)

A-B= √25

A-B = 5. Therefore, the answer is (b) 5.

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Subtract the sum that appears on the same side of the equation as the "x" to isolate the "x" on one side of the algebraic equation. For instance, rewrite the equation "x + 5 = 12" as "x = 12 - 5" and then find "x" in the new equation. The answer is "x = 7"

Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.

A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the numbers m and b provide the line's slope (m) and the value of y. (b). Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.

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Integration by parts can only be used to integrate functions that include either polynomials or exponential functions is False.

What is integration ?

Integration is a process of finding an antiderivative of a function, it is the reverse process of differentiation. It can be thought of as the area under the curve of the function or the accumulation of the function over a certain interval.

Integration by parts is a technique that can be used to integrate a wide variety of functions, not only functions that include polynomials or exponential functions. In fact, integration by parts can be used to integrate any function that can be expressed as the product of two functions, where one of the functions is the derivative of the other function. In other words, integration by parts allows us to evaluate an integral of the form ∫u(x)dv(x)dx by expressing it in terms of an integral of the form ∫v(x)du(x)dx.

It's just that those types of functions are more commonly used when applying this technique.

Hence , Integration by parts can only be used to integrate functions that include either polynomials or exponential functions is False.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{n^2 - 5n + 8}[/tex]

[tex]\mathsf{= 2^2 - 5(2) + 8}[/tex]

[tex]\mathsf{= 2\times 2 - 10 + 8}[/tex]

[tex]\mathsf{= 4 - 10 + 8}[/tex]

[tex]\mathsf{= -6 + 8}[/tex]

[tex]\mathsf{= 2}[/tex]

[tex]\huge\text{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\mathsf{2}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The solution set x<-5.2 or x>5.2 is true for the inequality |x|>5.2.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides.

The given inequality is |x|>5.2.

So, the value of x should be greater than 5.2.

For example take x=6, then the given inequality will be -

|6|>5.2 = 6>5.2, so this is true.

Now take x=-6, then the given inequality will be -

|-6|>5.2 = 6>5.2, so this is also true.

Similarly, among the different choices x<-5.2 or x>5.2

The condition x>5.2 is already true.

Also, the condition x<-5.2 is also true for x if the value is lower than -5.2.

Therefore, the inequality x<-5.2 or x>5.2 is true.

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