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∠E is 74° because it is alternate to the given angle of 74°.

∠E is and the 74° angle are alternate interior angles. Alternate interior angles are a pair of angles on the inner side of two parallel lines. But the angles should be on the opposite sides of the transversal. A transversal line is a straight line that intersects two or more parallel lines.

So here, ∠E and 74° lie on the inner sides of two parallel lines on the opposite sides of the transversal.

Therefore <E = 74°

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Each board must be within how many inches of 15 is l' actual = (15±0.03) inch, l" actual = (15±0.03) inch.

size is the quantification of attributes of an item or occasion, which can be used to evaluate other objects or occasions. In other words, measurement is a system of figuring out how massive or small a bodily amount is compared to a primary reference quantity of the identical kind.

size is the simple idea inside the have a look at of arithmetic and technology. measurement quantifies the traits of an object or occasion, which we can compare with other things or activities. measurement is the most commonly used word, on every occasion we address the department of an amount. dimension gear makes our lives higher and more secure, and they enhance the best and quantity of lifestyles. measurement is a contrast of an unknown quantity with a known fixed amount of the equal kind. The cost received on measuring a quantity is referred to as its value. The value of a quantity is expressed as numbers in its unit.

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aₙ = aₙ₋₁ - 9 is the recursive formula of Arithmetic progression.

Arithmetic progression is a sequence of number in order with same difference .

A fixed number is added to any term of a AP to get next term . That Fixed number is known as common difference.

In the question,

16 , 7 , -2 , -11 . . . .

First term of AP : a₁ = 16

Second term : a₂ = 7

Common difference : d = a₂ - a₁

=> d = 7 - 16

=> d = -9

The recursive formula of AP : aₙ = aₙ₋₁ + d

Here d = -9 , substituting d

The recursive formula of given AP : aₙ = aₙ₋₁ - 9

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(-2 - 2(-1/2))^3

= (-2 + 1)^3

= (-1)^3

= -1

Answer:

y = 2x + 5

Step-by-step explanation:

The slope of 2 parallel line are always the same. This means that we can easily tell that the slope of the equation that we are trying to solve has a slope of 2. To find the "b" in the slope-intercept form, plug in the coordinates given and that's how you get the answer above.

Answer:

Please refer photo for answer

Binomial probability distribution = 0.0231

The following is the probability using the binomial distribution:

P(X = 24) = 0.0231.

In terms of the normal approximation to the binomial, it is discovered that:

Part 2: C. Yes, because np(1-p)≥10, the normal distribution can be used.

Part 3: The likelihood is: 0.0227.

Part 4: The distinction is: 0.0004.

Binomial probability distribution

The following is the mass function for the probability of exactly x successes:

P(X = x) = [tex]C_{n,x}[/tex].[tex]P^{x}[/tex].[tex](1-P)^{n-x}[/tex]

[tex]C_{n,x}[/tex] = [tex]\frac{n!}{x!(n-x)!}[/tex]

In which the following parameters are defined:

The number of trials in the experiment is n.

The probability of success on a single trial of the experiment is given by p.

The values of these parameters are given in the context of this problem as follows:

n = 59, p = 0.3, X = 24.

Hence the probability is:

P(X = x) = [tex]C_{n,x}[/tex].[tex]P^{x}[/tex].[tex](1-P)^{n-x}[/tex]

P(X=24) = [tex]C_{59,24}[/tex].[tex](0.3)^{24}[/tex].[tex](0.7)^{35}[/tex] = 0.0231

In the context of this problem, the condition for the approximation is verified as follows:

np = 59 x 0.3 = 17.7 ≥ 10.

n(1 - p) = 59 x 0.7 = 41.3 ≥ 10.

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The required solution is Option D.

sin 21 = x / 22

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sinθ

sec θ = 1/cosθ

cot θ = 1/tanθ

Given data ,

Let the triangle be ΔABC and ∠B = 90°

The angle ∠A = 21°

θ = 21°

The value of the hypotenuse = 22

The value adjacent to the right angle is BC = x

From the trigonometric functions , we know that

sin θ = opposite / hypotenuse

So ,

sin θ = x / 22

Hence , the required solution is sin 21 = x / 22

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The events that have probability of exactly three-fourths are

(a) not picking a square  ,

(d) picking shape that has only straight edges ,

(e) not picking a circle   .

In the question ,

it is given that ,

there are 2 circles , 4 triangles , 2 squares .

(a) probability of not picking a square = ( circles + triangles )/total

= 6/8 = 3/4

(b) probability of picking a square = number of square / total figure

= 2/8 = 1/4

(c) probability of picking up a triangle = 4/8 = 1/2

(d) probability of picking up shape with straight edge = ( triangle + square) / total

= 6/8 = 3/4

(e) probability of not picking a circle = ( triangle + square) / total

= 6/8 = 3/4 .

Therefore , The events that have probability of exactly three-fourths are

(a) not picking a square  ,

(d) picking the shape that has only straight edges ,

(e) not picking a circle   .

The given question is incomplete , the complete question is

A shape is picked at random from the group of 2 circles, 4 triangles, and 2 squares .

Which event has a theoretical probability of exactly Three-fourths? Select three options.

(a) not picking a square

(b) picking a square

(c) picking a triangle

(d) picking shape that has only straight edges

(e) not picking a circle

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Answer:

3 with 1 left over

Step-by-step explanation:

3 * 5 + 1 = 16

Answer:

3 with 1 left over.

Step-by-step explanation:

16÷5=3remainder1

HOPE IT HELPED

By solving a linear equation, we will see that the value of the greater integer is 12.

Let's define x as the smaller integer, then the greater integer is:

x + 2

(is +2 because is the next consecutive even integer)

We know the sum of an integer and 4 times the next consecutive even integer is 58.

So we can write the linear equation:

x + 4*(x + 2) = 58

x + 4x + 8 = 58

5x = 58 - 8

5x = 50

x = 50/5

x = 10

Then the greater integer is x + 2 = 10 + 2 = 12

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Answer: $3.75

Step-by-step explanation:

Answer:

The cost of 6 cans of soup is 3.75

Step-by-step explanation:

12 = 7.50

1 can = x

12x = 7.50

We need to find the cost of 1 can. So we divide 7.50 by 12.

x = 0.625

Then multiply by 6.

0.625 x 6 = 3.75

As a result the cost of 6 cans of sup is $3.75

Answer:

The answer is 0.05556

0.5/9 gives you that

Answer:

b=17/4

x=-3/5

Step-by-step explanation:

This is what i put for the hw and i got 100% on it. If you want you can just write a bunch of random equations that look like they relate to the question and then just write and circle the answer, which is exactly what i did

Answer:

Step-by-step explanation:

1) 3b + 9 - 5b + 3 = -14 + 6b - 8, for b?

→ 3b + 9 - 5b + 3 = -14 + 6b - 8

→ -2b + 12 = 6b - 22

→ -2b - 6b = -22 - 12

→ -8b = -34

→ b = -34/-8

→ [ b = 17/4 ]

Hence, the value of b is 17/4.

2) 2x + 5 - 4x + 8 = 5(5 + 6x) - 12x, for x?

→ 2x + 5 - 4x + 8 = 5(5 + 6x) - 12x

→ -2x + 13 = 25 + 30x - 12x

→ -2x - 18x = 25 - 13

→ -20x = 12

→ x = 12/-20

→ [ x = -3/5 ]

Hence, the value of x is -3/5.

The rate of change between (1,5) and (-5,1) is 0.

What is the rate of change?

The slope is the ratio of the rate of change between two points (also known as the "slope") to (the change in the x coordinate).

Let (x,y)=(1,5), (m,n)=(-5,1)

Rate of change=(n-y)/(m-x)=(-5-(5))/(1-1)=0.

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Answer:

  C.  6 times as many as c is 72

Step-by-step explanation:

You want to know if c = 12, which statement is true.

We can substitute 12 for c in each expression and write it as a math equation. That makes it easier to see if it is true.

  12 = 5×4

  12 = 20 . . . . . false

  27 = 12×3

  27 = 36 . . . . . false

  6×12 = 72 . . . . . TRUE

  8 + 12 = 15

  20 = 15 . . . . . false

Answer: 64/225 is already in simplest form

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator GCD (greatest common denominator) of 64 and 225 

Divide both the numerator and denominator by the GCD

64÷1/225÷1

fraction: 64/225

Therefore, 64/225 simplified to lowest terms is 64/225.

The number of unit cubes it would take to completely fill the prism with no gaps between unit cubes is 72

From the question, we are to determine how many unit cubes it would take to completely fill the prism with no gaps between unit cubes.

To do this, we will calculate the volume of rectangular prism

Assuming each cube is 1 cubic unit

Then,

From the top view,

The length of the rectangular prism = 9 units

The width of the rectangular prism = 2 units

From the Right-side view,

The height of the rectangular prism = 4 units

Thus,

The volume of the rectangular prism = 9 × 2 × 4

Volume of the rectangular prism = 72 cubic units

Now,

Number of cubes required to fill the rectangular prism = Volume of the prism / Volume of the cubes

Number of cubes required to fill the rectangular prims = 72 / 1

Number of cubes required to fill the rectangular prims = 72

Hence, the number of unit cubes it would take is 72

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Answer:

[tex]x=-\frac{y^{2} }{4}[/tex]

Step-by-step explanation:

This graph is in terms of x.

For the given graph, the gradient of the given blue line in the graph is equal to 2.

As given in the question,

For the given graph,

Consider two pairs of coordinates on the blue line of the given graph,

( x₁ , y₁ ) = ( 2, 2 )

( x₂ , y₂ ) = ( 3, 4 )

Gradient is nothing but slope of the line

Formula to calculate the gradient of the given blue line of the graph is given by:

Gradient = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substitute the value in the formula we get,

Gradient = ( 4 - 2 ) / ( 3 - 2 )

              = 2 / 1

              = 2

Therefore, for the given graph, the gradient of the given blue line in the graph is equal to 2.

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Answer:

A

Step-by-step explanation:

-1/5 j + 3/4 - 5/2 j - 7/8 =

= (-2-25)/10 j + (6-7)/8 =

= -27/10 j - 1/8

According to the combination method, the number of elements in the sample space for this experiment is 3060

Combination method:

Basically, the mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter

Given,

A person eating at a cafeteria must choose 4 of the 18 vegetables on offer.

Here we have to calculate the number of elements in the sample space for this experiment.

While we looking into the given question, we have identified the following things,

They are

Total number of available vegetables = 18

Number of choices we have made = 4

Therefore, here the value of n = 18 and the value of x = 4,

Therefore, according to the ncx formula, it can be written as,

=> ¹⁸n₄ = 18! / 4! (18 - 4)!

=> ¹⁸n₄ = 18! / 4! (14)!

=> ¹⁸n₄ = 3060.

Therefore, there are 3060 number of elements in the sample space for this experiment.

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The length of the rectangle is 7y - 3

What is a Rectangle?

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. The area of  a rectangle A = L×W

Where,

A = Area of the rectangle which is 7y^2 - 3y

L = Length  which is unknown

W = Width of the rectangle which is y

Substituting,

7y^2 - 3y = L × y

divide through by y

(7y^2 - 3y)/y = L

L = 7y - 3

Therefore the length of the rectangle is 7y - 3

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The speed is 20/9 miles per hour.

From the question, we have

In 1/4 hour walked = 5/9 mile

In 1 hour walked = 5/9 *4 mile

=20/9 miles per hour

The speed is 20/9 miles per hour (MPH)

Divide:

Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.

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let thee present age be x.

(x-15)^2=x+15

=>x^2–31*x+210=0

=>(x-21)(x-10)=0

x=10 or x=21

present age can not be 10 as it would result at absurd negative age( -5) 15 years ago.

so present age is 21.

"95% confidence interval" means that there is a 95% chance that the true fraction falls within the computed confidence interval.

Confidence Intervals: Confidence intervals are the range of estimates for unknown parameters.

Confidence intervals are more than just a range of estimated values. It also tells you how stable the estimates are. A stable estimate is an estimate that has approximately the same value if the study is repeated. An unstable estimate is one that would vary from one sample to another.

The confidence interval determines the range that one can be certain that contains the true mean of the population.

This means that, The 95% confidence means, there is a 95% chance that the true proportion will be in the calculated confidence interval or 95 percent confidence interval, you have a 5 percent chance of being wrong.

Hence, the true statement that represents "95% confidence interval" is chance of true fraction of sucess.

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