if two distinct numbers are selected at random from the first seven prime numbers, what is the probability that their sum is an even number? express your answer as a common fraction.

The angle pairs can be classified as follows

∠1 and ∠5       →  Alternate exterior angles

∠2 and ∠10    →  Corresponding angles

∠10 and ∠14   →  Alternate interior angles  

∠6 and ∠7      →  Consecutive interior angles

∠5 and ∠12    →  Consecutive interior angles

∠3 and ∠13    →  Alternate exterior angles

From the question, we are to classify each of the angle pairs as corresponding, alternate interior, alternate exterior, or consecutive interior angles.

Considering the given diagram, and applying the appropriate angle theorems, we can write that

∠1 and ∠5 are alternate exterior angles

∠2 and ∠10 are corresponding angles

∠10 and ∠14 are alternate interior angles  

∠6 and ∠7 are consecutive interior angles

∠5 and ∠12 are consecutive interior angles

∠3 and ∠13 are alternate exterior angles

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We will see that the slope of function B is 2, and the slope of function A is 1. This means that the correct equation is:

Slope of function B = 2*Slope of Function A

First, a general linear equation is:

y = a*x + b

Where a is the slope and b the y-intercept.

Here the function A is:

f(x) = x - 9

Then the slope is equal to 1.

We know that function B is a line that passes through (-1, -3) and (2, 3)

Then the slope is:

s = (3 + 3)/(2 + 1) = 6/3 = 2

So the slope of function B is 2, and the slope of function A is 1. Then the equation is:

Slope of function B = 2*Slope of Function A

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Answer:

9+9b

Step-by-step explanation:

Answer:

9 +9b

Step-by-step explanation:

     Like terms are terms that have same variable with same power.

2b and 7b are like terms.

7 and 2 are like terms (constants).

7 + 2b + 7b + 2 = 7 + 2 + 2b +7b

                           = 9 + 9b

Answer:

ABC =146.5

ACB=67

ACD=127

CAB=146.5

Step-by-step explanation:

ABD=127

ACD=127

BCD=60 ( Being equilateral triangle)

60+x=127

x=67

ACB=67

CAB=CBA=y (let)

y+y+ACB = 360 ( Sum of int angles of triangle)

2y+67=360

2y=293

y=146.5

CAB=146.5

ABC=146.5

Okay, here we have this:

Considering the provided information, we are going to calculate the speed at which he runs, so we obtain the following:

So we have the following equation:

Distance Traveled Walking + Distance Traveled Running = Total Distance

Distance Traveled Walking + Distance Traveled Running = 20 miles

And taking into account that speed is equal to distance over time, if we take speed to which runs as x we have:

((x/2) mi/h * 2h) + (x mi/h* 1.5h) = 20 miles

x mi+ 1.5x mi= 20 mi

2.5x mi=20mi

x = 20mi/2.5mi

x=8

Finally we obtain that he runs at 8 miles per hour.

By evaluating the linear equation in t = 5 seconds, we will see that the distance traveled is 271.93 feet.

Here we know that the line that defines the distance traveled by the ball (y) as a function of time (t) is:

y = 3.98 + 53.59*t

Now we want to predict the distance traveled y the ball if it travels for 5 seconds, so we just need to evaluate the above linear equation in t = 5.

So we will get:

y = 3.98 + 53.59*5  = 271.93

So we conclude that the distance traveled in that time is 271.93 feet.

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Answer: 271.93 feet

Step-by-step explanation:

I took the test

Answer:

Step-by-step explanation:

Adriel’s age if the sum of the square of adriel’s age and 4 times jevonte’s age is 85 is 7 years

Let the ages be x and x + 2 since they're consecutive odd integers.

We want to find Adriel’s age if the sum of the square of adriel’s age and 4 times jevonte’s age is 85. This will be illustrated as:

x² + 4(x + 2) = 85

x² + 4x + 8 = 85

Collect like terms

x² + 4x + 8 - 85

x² + 4x - 77 = 0

x² + 11x - 7x - 77 = 0

x(x + 12) - 7(x + 11) = 0

x - 7 = 0

x = 0 + 7

Therefore, the age is 7 years.

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Answer:

22 cups in total

Step-by-step explanation:

In order to solve this problem we need to know how much money Mimi makes by just selling 1 cup of lemonade. We can find this by dividing

38/19 = 2

Now that we know how much money Mimi makes by just selling 1 cup of lemonade, we can use this to find how many cups she needs to sell in total to earn $44. We can use this equation

2x = 44 (x = cups of lemonade)

Now we solve for x

2x =44

/2    /2

x = 22

So Mimi needs to sell 22 cups in total to earn $44 dollars. Hope this helps :)

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

Bonus: she need to sell 3 more cups lol incase you need to know

Using the conversion of a fractional exponent to a rational expression, the equivalent expression to  x^(2/3) is given by:

K. [tex]\sqrt[3]{x^2}[/tex]

A fractional exponent is converted to a rational expression applying the law of indices, in which the numerator, which is the top term of the fraction, will be the power of the base, while the denominator, which is the bottom term of the fraction, represents the root.

The law of indices is illustrated as follows:

[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]

In the context of this problem, the expression is:

x^(2/3).

Hence the coefficients are n = 2 and m = 3, and thus the equivalent expression is:

[tex]x^{\frac{2}{3}} = \sqrt[3]{x^2}[/tex]

Meaning that option K is correct.

The possible options for the question are missing, and are given by the image at the end of the answer.

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iq scores have a bell shape distribution with a mean of 100 and standard deviation of 15. 81.855%  of the population has an iq score between 70 and 115

What is z-score?

The z score, also referred to as the standard score, serves to calculate how far each data point place is from its mean. In other words, it calculates x's (data point's) deviation in terms of standard deviations.

Using z tables, you may calculate the proportion of the population that is either below or above the score.

Now, according to the question;

IQ scores follow a normal distribution, with a mean of 100 as well as a standard deviation = 15.

A z score is determined as follows:

z = (x - μ)/σ

μ = mean of the distribution

σ = standard distribution of the sampling.

Calculation for the z score for x = 70 and  115

z= (70-100)/15

= -30/15

=-2

and x=115

z = (115 - 100)/15

= 15/15

z = 1.0

Use z-score table, then likelihood that a randomly chosen person's IQ is more than 115 is,

P( -2 < z < 1)= P(z<1) - P(z< -2)

                   =  0.8413 - 0.02275

                  = 0.81855

Therefore, the percent of the population has an iq between 70and 115 is 81.855%.

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Answer: h(x)=-15

Step-by-step explanation: First: We plug in h(6) for x. Gives us -2(6)-3. When we solve -12-3. -15.

Answer:

h(6) = 9

Step-by-step explanation:

h(x) = 2x – 3,

Let x = 6

h(6) = 2*6 -3

      = 12 -3

      = 9

Rising or growing steadily and quickly: a city in exponential expansion. noun. Mathematics the value of the constant e raised to the power of a given expression, represented as the exponential of 3x, e3x. something that is positive and raised in power.

In the biological sciences, exponential functions are frequently employed to simulate the evolution of a certain quantity over time, such as population number. Experimental data graphs are often created with the quantity on the y-axis and the time on the x-axis.

The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour. After x hours, you will have twice as much germs if you start with one and it doubles every hour. F(x) = 2x can be used to express this.

The values of f(x) and g(x) in the table for various values of f(x) = 9x + 7 and g(x) = 5x

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even if an independent variable has an effect on the dependent variable, it fail to reject the null hypothesis and make a type II error

Even if a treatment is effective in the real world (it has an effect), it is still possible to obtain a sample mean that is so similar to the population mean that the sample mean doesn't fall in the critical, or rejection, region. If this happens, you are likely to fail to reject the null hypothesis and make a type II error.

Since that sample mean is so similar to the population mean, the treatment effect may not be detected on analysis even though it is in fact significant, this will cause the research to erroneously concluded that the treatment effect is zero and accept the null hypothesis when it is actually not zero. This is a type II error. Type II error in statistics means the non-rejection of a false null hypothesis and type I error is the rejection of a correct null hypothesis.

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James took 97 minutes to clean his house. there were 12 rooms in the house, and it took him the same amount of time to clean each room. time  left after he finished cleaning is 4 hour 36 minutes

James took 97 minutes to clean his house.

there were 12 rooms in the house,

and it took him the same amount of time to clean each room

how much time did he have left after he finished cleaning?

one room clean =97 minutes

12 room clean = 97*12 amount of minutes

                        = 1164 minutes

                       = 19hour 24 minutes

James took 19 hour 24 minutes to clean 12 room

amount of time left = 24 hour - 19 hour 24 minutes

             = 4 hour 36 minutes

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The ratio of the number of words Li Zhen typed to the number of words Kara typed to the number of words Rose typed = 8 : 4 : 1

Total numbers of words Li Zhen, Kara and Rose typed = 156 words

What is Ratio ?

A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Since, it's given that

    the number of words Kara typed = 48

number of words Li Zhen typed = 2 x 48

                                                      =96words

a)  The ratio of the number of words Kara typed to the number of words Rose typed = 4:1

Since, it's given that

    the number of words Kara typed = 48

let, the number of words Rose typed = x

then, by equating them we get,

4/1 = 48/x

       4x = 48

          x = 48/4

          x = 12

The ratio of the number of words Li Zhen typed to the number of words Kara typed to the number of words Rose typed :

=  96 : 48 : 12

= 8 : 4 : 1

b) Now we know that,

  The number of words Li Zhen typed = 96words

  The number of words Kara typed = 48words

  The number of words Rose typed = 12words

Then, the total numbers of words Li Zhen, Kara and Rose type altogether

                               = 96 + 48 + 12

                               = 156 words

Hence, the total numbers of words Li Zhen, Kara and Rose type altogether is 156 words

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[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-6)}}} \implies \cfrac{2 +1}{-4 +6} \implies \cfrac{ 3 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{\cfrac{3}{2}}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y +1= \cfrac{3}{2} (x +6) \end{array}}[/tex]

They have not a proportional relationship.

The equation that represents a proportional relationship, or a line, is y = k x , where is the constant of proportionality. Use k = y x from either a table or a graph to find k and create the equation. Proportional relationships can be represented by tables, graphs and equations.

From table 1.

temperature ( ∘ C)                    temperature ( ∘ F)

20                                                           68

4                                                              39.2

175                                                           347

converted by using equation   F=[tex]\frac{9}{5}[/tex]C+32

From table 2.

length (in)                                    length (cm)

10                                                             25.4

8                                                               20.32

[tex]3\frac{1}{2}[/tex]                                                              8.89

Converted by using equation c = 2.54n where c represent length (in cm) and n represent length in inches.

Now,

we will check the proportionality by [tex]\frac{c}{F}[/tex]  if all the values of this ratio is same for the tables then they are showing proportionality .

From the table they are not showing proportionality.

Hence, They have not a proportional relationship
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The absolute value inequality represents the difference between the rope lengths cut and the specifications are | x - 10 | ≤ 0.5.

Modulus value always outputs a positive value irrespective of the input value sign.

Julian needed to cut ropes for her school project and their length should be 10 inches long with a difference of 0.5 inches.

∴ The maximum allowable length of the rope should be (10 + 0.5) = 10.5 inches and the minimum allowable length of the rope should be

(10 -0.5) = 9.5 inches.

The absolute value of inequality that represents this condition is,

| x - 10 | ≤ 0.5.

x - 10 ≤ 0.5.

x ≤ 10.5, And

- ( x - 10) ≤ 0.5.

-x + 10 ≤ 0.5.

- x ≤ - 9.5.    ( think of moving the terms on either side to make x positive).

x ≥ 9.5.

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Answer:

Image result for the government

The Federal Government is composed of three distinct branches: legislative, executive, and judicial, whose powers are vested by the U.S. Constitution in the Congress, the President, and the Federal courts, respectively.

Step-by-step explanation:

By probability , An average rate of one mutation per 12,400 A.A geneticist is examining a strand of DNA .

Describe probability using an example?

Suppose that, in a strand f DNA ,mutations occur randomly and independently of other mutations .

at an average rate of one mutation per 12,400 A.A geneticist is examining a strand of DNA .

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Answer:

8

Step-by-step explanation:

Let the number be “X"

Solution:

4 + (X/2) = 8

(X/2) = 8-4

(X/2) = 4

X = 4×2

X = 8

THEREFORE THE ANSWER IS “8”

Answer:

This is a simultaneous equation.

Step-by-step explanation:

let the first number be x and second be y

Lets make an equation first:

3x-y = 8 .....(1)

x+y = 12........(2)

Solve by elimination.

Dass

3x+x= 8+12

4x=20

x=5

find y

x+y=12

5+y=12

y=12-5

y= 7

Therefore the two numbers are 5 and 7

The x-intercept of the equation is: (8, 0)

The y-intercept is of the equation is: (0, -2)

The x-intercept is the point on the x-axis where the line cuts across the x-axis, while the y-intercept is the point on the y-axis that the graph intercepts.

The value of the x-intercept is the value of x when the value of y is equal to zero, while the y-intercept of a graph is the value of y when the value of x is zero.

Given the equation of the linear graph as, x - 4y = 8, to find the x-intercept, substitute y = 0 into the equation:

x - 4(0) = 8

Solve for x:

x - 0 = 8

x = 8

The x-intercept is: 8.

(8, 0)

To find the y-intercept, substitute x = 0 into the equation, x - 4y = 8 and solve for the value of y:

0 - 4y = 8

-4y = 8

-4y/-4 = 8/-4

y = -2

The y-intercept is: -2.

(0, -2)

The graph for x - 4y = 8 is shown in the attachment.

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Answer:

308

Step-by-step explanation:

Based on the given conditions, formulate: 7 x 572/13

Cross out the common factor: 7 x 44

Calculate the product or quotient: 308

Answer:

308

Step-by-step explanation:

572 divided by 13 is 44 which means there is 44 miles per gallon. So multiply 44 x 7 and you get 308 miles.

The most appropriate choice for matrix will be given by-

The position number of all the matrix entries are

[tex]a_{11} = 0\\a_{12} = -1\\a_{13} = 3\\a_{14} = 5\\a_{15} = -2\\a_{21} = 7\\a_{22} = -8\\a_{23} = 6\\a_{24} = -4\\a_{25} = -9\\a_{31} = 1\\a_{32} = 2\\a_{33} = -3\\a_{34} = -5\\a_{35} = 8[/tex]

What is a matrix?

Any arrangement of numbers in the form of rows and columns are called matrix. The numbers inside a matrix is known as elements of the matrix.

The position number of a matrix entry is denoted by [tex]a_{mn}[/tex] where m denotes the row position and n denotes the column position.

We can do addition, subtraction, multiplication on matrix but two matrices cannot be divided.

Here,

The position number of a matrix entry is denoted by [tex]a_{mn}[/tex] where m denotes the row position and n denotes the column position.

The given matrix is

[tex]\left[\begin{array}{ccccc}0 & -1 & 3 & 5 & -2\\7&-8&6&-4&9\\1&2&-3&-5&8\end{array}\right][/tex]

The position numbers of all the matrix entries are given below

[tex]a_{11} = 0\\a_{12} = -1\\a_{13} = 3\\a_{14} = 5\\a_{15} = -2\\a_{21} = 7\\a_{22} = -8\\a_{23} = 6\\a_{24} = -4\\a_{25} = -9\\a_{31} = 1\\a_{32} = 2\\a_{33} = -3\\a_{34} = -5\\a_{35} = 8[/tex]

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The value of the expression y³ = 1 is y = 1.

Expression:

An expression also known as algebraic expression consisting of variables, numbers and an arithmetic operation between them.

Given,

Here we have the expression y³ = 1.

Now, we need to find the value of y.

While we looking into the expression, when we have to find the value of y then we have to move the cube vale to the other side.

When we move the cube to the other side then it will be the cube root of the number.

While we simplify the cube root of the number then we get the result.

Therefore,

y³ = 1

Move the cube to the other side,

y = ∛1

We know that,

∛1 = 1

So, the value of y = 1.

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The product of factor 83.5 with 0.01 will be 0.835

What are mathematics operations?

• A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.

• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.

Here, the given statement is :

The product of a factor and 0.1 is 8.35

Let the factor be a then :

a x 0.1 = 8.35

a = 8.35/0.1

a = 83.5

The factor is 83.5

Now, the product of this with 0.01 will be :

83.5 x 0.01 = 0.835

Therefore, The product of factor 83.5 with 0.01 will be 0.835

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The woodworker should make atmost 4 rocking kitchen chair and 3 simple kitchen chair to maximize the profit under given conditions of 192 woodworking hours and 21 painting hours.

Profit maximization is a process that businesses go through to make sure the best levels of output and prices are realized in order to maximize their returns. The company modifies important variables like sale price, production costs, and output levels in order to achieve its profit objectives.

inequality, A mathematical statement expressing an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to etc.

Given,

Time needed to woodwork a rocking kitchen chair= 30 hours

Time needed to paint a rocking kitchen chair=3 hours

Time needed to woodwork a simple kitchen chair= 24 hours

Time needed to paint a simple kitchen chair=3 hours

Maximum time given by worker= 192 hours for woodwork and 21 hours to paint

Let x and y be the maximum number of chairs created by woodworker of both the types.

so the system of inequality would be,

30x+24y<192      ......(1)

3x+3y<21             ......(2)

To find x and y,

multiply the (2) by 10

30x+30y<210

subtract (1) from (2)

30x+24y-(30x+30y)<192-210

-6y<-18

y<3

3x+3y<21

3x+3*3<21

3x<12

x<4

By this, he can make maximum 4 rocking and 3 simple kitchen chair to earn the maximum profit.

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Answer:

The answer is 3, but here’s how I got that answer.

Step-by-step explanation:

As we know the trifle recipe requires 1 ½ cups of sugar, and the chocolate cake requires double the amount of sugar.

You have two options.

Multiply 1½ by 2

1½ x 2 = 3

———————————

Or add 1½ + 1½

1½ + 1½ = 3

———————————-

Wasn’t sure what you were asking for with this this question, but hope it helped.

Answer: 3

Step-by-step explanation:

Since the trifle cake uses 1 ½ cups of sugar and the chocolate twice as much sugar as the trifle cake you should multiply 1 ½ x 2 which would equal 3. So, 3 cups of sugar should go into the cake. (This is my first answer to a question so I'm sorry if I'm confusing)

Answer:

Step-by-step explanation:

[tex]\stackrel\ell{\boxed{\boxed{\begin{minipage}{7cm}\\\begin{aligned}\sf{3k-8=7}\\\downarrow\\\sf{3k=7+8}\\\downarrow\\\sf{3k=15}\\\downarrow\\\boxed{\boxed{\sf{k=5}}}\end{aligned}\end{minipage}}}}}[/tex]

I hope this helps!!

Answer:

5

step by step explaination

first side change -8=+8

7+8

now divide 15 by 3

Then

K=5