Identify the theorem or postulate that is related to the measures of the angles in the pair, and find the unknown angle measures.

m/1 = (5x +15)°, m/4= (30x - 60)°

The sequence in the question may be given as

1, 3, 9, 27

From this, the first term is 1 and the common ration is 3

Common ratio = 3/1 = 9/3 = 27/9

= 3

A unit rate means a quantity at a rate of one of something.

The number of miles Sara can drive on 12.5 gallons of gas is 281.25 miles.

Option D is the correct answer.

A unit rate means a quantity at a rate of one of something.

It is written with a denominator of one. 

We have,

Sara drives 171 miles on 7.6 gallons of gas.

This can be written as:

171 miles = 7.6 gallons

Multiply 12.5/7.6 on both sides.

12.5/7.6 x 171 miles = 12.5/7.6 x 7.6 gallons

281.25 miles = 12.5 gallons

Thus,

The number of miles Sara can drive on 12.5 gallons of gas is 281.25 miles.

Option D is the correct answer.

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First we have to find the volume of the cone so we use the formula:

and we replace pi by 3.14, h by 8 and r by 3 so:

now she sloshes 2/3 of the water, so we need to calculate the remaining 1/3 of the volume so:

the remaining volume of water is 25.12 cubic centimeters

Answer: 25%

Explanation:

Probability is expressed as

number of favorable outcomes/number of total outcomes

From the information given, the spinner has 4 equal spaces. Thus,

number of total outcomes = 4

number of favorable outcomes = number of blue spaces = 1

Thus,

the probability of spinning the spinner and having it land on blue = 1/4 x 100

the probability of spinning the spinner and having it land on blue = 25%

We are told to list all the elements of whole numbers not greater than 8 using both the set notation and the listing method.

SET NOTATION

Let 'x' be used to represent the whole numbers.

LISTING METHOD

The domain can be best described using interval notation. The domain is [1,∞].

A continuous function is graphed here. The function is continuous only on  where it is defined. That is, the graph of the function does not have any discontinuities from 1 to infinity.

The domain of a function is the x-values for which the function is defined. That is for such x-values, the function will attain some y-value, which is called the function value. This function values corresponding to each x-value sketches the graph.

From the figure, the graph is started from x = 1 and is extended to infinity.

So it is better to express the domain in an interval form.

Graph of the function is a curve. So the domain is [1,∞].

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From the ratio given, the number of games won is 77

To solve this problem, we simply need to use the ratio of games won to find the total number of games played.

Let x represent the total number of games played;

The fraction of games won can be written as

[tex]\frac{9}{9 + 2} * x = 63\\\frac{9}{11}* x = 63[/tex]

Let's solve for x here;

[tex]\frac{9x}{11} = 63\\ 9x = 63 * 11\\9x = 693\\x = 77[/tex]

From the calculations above, the chess played a total of 77 games.

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Answer:

the answer to your question is that of 17 1/4

I got the answer of 505 students

First we need to look at the change of signal of the function (it changes from √x to -√x).

This change of signal means the function was reflected over the x-axis.

Then, the value of -3 was added to the function.

An addition of -3 in the function means a translation of 3 units down.

So the transformations from m(x) to p(x) are:

A reflection over the x-axis followed by a translation of 3 units down.

Given:

a function f(x) = (x-2)^2 is given.

Find:

we have to find the function whose graph is a result of horizonal shift of 2 units of the original graph.

Explanation:

Since the given graph of the function is shifted 2 units horizontally,

and we know y is vertical axis, x is horizontal axis.

So put x = x+2 in the given function, we get

Therefore the graph of f(x)=(x-2)^2 is a result of horizontal shift of 2 units of f(x) = x^2.

The graphs are given for the reference

The 28th term of the given arithmetic sequence is 219

any arithmetic sequence can be solved once we identify the aa1 term and the an term because then we have to simply find the common difference and solve further by substituting the value in the below mentioned equation.

Given the arithmetic sequence = 3,11, 19, 27

a₁ = 3

a₂ = 11

a₃ = 19

a₄ = 27

the common difference or d = a₂ - a₁

this implies d = 11 - 3 = 8

Therefore the 28th term of the given arithmetic sequence is

a₂₈ = a₁ + ( n - 1 ) d

a₂₈ = 3 + ( 28 - 1 ) 8

     = 3 + 27 × 8

     = 3 + 216

     = 219

Thus a₂₈ = 219

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ANSWER :

0.529

EXPLANATION :

From the problem, Carl made 37 out of 70 free throws attempt.

Divide the number of free throws made by the total number of free throws attempt

we have the following:

replacing:

17. (1, 0) and (5, 5)

therefore,

19. (0, -1) and (3, -5)

therefore,

21. (1, 9) and (6, 2)

therefore,

Given:

U = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {1,2,3,4,5}

B = {4, 5, 6, 7}

C = {5, 6, 7, 8, 9}

D= {1, 3, 5, 7, 9}

E= {2, 4, 6, 8}

F = {1, 5, 9}

What is the question: Find AUC'.

Recall the following:

A ∩ C (read as A intersection C) - are members that are common to both set A and set C.

A ∪ C (read as A union C) - are members that are in set A or set C or both, combining the members of all sets.

C' (read as C complement) - are members that are not in the universal set.

Since what we are about to find is A ∪ C', let's first determine the members of C'.

We get,

C' = {1, 2, 3, 4}

A = {1,2,3,4,5}

Therefore, AUC' = {1,2,3,4,5}.

For y to be parallel to x,

Thus, the value of x is 9.6.

Given:

The graph shows the XY plane where x shows the number of T shirts bought and Y shows the number of stickers received.

The plotted points on the graph have the coordinates:

Clearly, we can see the y coordinate is double of x coordinate here, so the equation of graph shown will be : y = 2x

Now we will check the points given in tables in the options if they satisfy this equation or not.

Check option (F),we get:

Which doesnot satisfy the equation y=2x hence, option F is wrong.

Now chcek option G ,

These points clearly satisfy y= 2x, hence,

Option (G) is correct.

Similarly, if we check option (H) and (I) they will not satisfy the equation, Hence , option (G) is only correct.

the length of th diagonal is 10√2

side length = 10 inches

We need an illustration to solve the question:

Using pythagoras' theorem:

Hypotenuse² = opposite² + adjacent²

hypotenuse = diagonal

opposite = 10 in, adjacent = 10 in

diagonal² = 10² + 10²

diagonal² = 100 + 100

diagonal² = 200

diagonal = √200

diagonal = 10√2

Hence, the length of th diagonal is 10√2

Looking at f(x) and g(x), we can see that g(x) is made by f(x) multiplied by -6.

Since the function was multiplied by a negative value, that means we had a reflection over the x-axis.

Also, if the function was multiplied by a constant value, that means we had a vertical stretch by a factor equal to the absolute value of the constant.

Therefore the correct options are A and D.

The angle addition postulate is the best justification for m∠XPD + m∠DPE = m∠XPE.

An angle bisector is a line segment that divides an angle into two equal parts.

The angle addition postulate states, if a line segment is in between an angle sum of two smaller angles created by the line segment, is equal to the measure of the larger angle.

We have an ∠XPE that is divided by a line segment PD which creates two smaller angles ∠XPD and ∠DPE.

∴ By angle addition postulate m∠XPD + m∠DPE = m∠XPE.

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The number of cheeseburgers sold was three times the number of hamburgers sold then 79 hamburgers and 237 cheeseburgers were sold on Sunday.

Let h be the number of hamburgers

c be the number of cheeseburgers

A local hamburger shop sold a combined total of 316 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold.  

h + c = 316

c = 3h

h + 3h = 316

simplifying the above equation, we get

⇒ 4h = 316

Dividing both sides of the equation by 4, we get

⇒ 4h / 4 = 316 / 4

⇒ h = 79

Therefore, hamburgers were sold on Saturday is 79.

The number of cheeseburgers sold was three times the number of hamburgers sold then

c = 3h

substitute the value of h in the above equation, we get

⇒ c = 237

Therefore, 79 hamburgers and 237 cheeseburgers were sold on Sunday.

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The area to be recarpeted is 361 sq. m.

What is area?

The measurement that describes the size of a location on a horizontal or contour is called area. Surface area refers to the area of an extended surface or the border of a tri object, whereas the area of a horizontal region or flat area corresponds to the area of a form or planar laminate. Area can be interpreted as both the amount of substance with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat. It is the two-dimensional equivalent of the volume of a solid or the length of a curve, both of which are one-dimensional concepts (a three-dimensional concept).

given the area is in form of square

So, the area of floor = 19x19 = 361 sq. m.

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Answer: x^2+4x-45

Step-by-step explanation:

Multiply (x-5)(x+9)

Using the FOIL Method.

Multiply

x and x

x and -5

x and 9

-5 and 9

You should get x^2-5x+9x-45

Subtract -5x and 9 and you get your answer

x^2+4x-45

From the information given in the word problem, the oldest child of Mrs. Danforth must be 13 years old.

Given:

Since the bags are distributed according to the proportion of their ages, then, we say

5 bags x 16 candies =80 candies.

80 / 4 = 20 candies per child

Given that his 4-year-old sister gets 20 -12 = 8 candies, then:

8/4 = 2 candies per year for each child's age.

Given that Cameron will gain 20 + 2 =22 candies, then:

22 / 2 = 11 years is Cameron's age.

22 candies of Cameron + 8 candies for youngest sister=30

80 - 30 = 50 candies for the remaining older children.

Since Cameron is the 2nd youngest, it means the remaining 2 siblings must be 12 and 13 years respectively:

So that: 12 x 2 = 24 candies for the 3rd oldest

And 13 x 2 = 26 candies for the oldest child. So, the total allocations of all the candies would be:

8 + 22 + 24 + 26 = 80 candies.

Therefore, the most senior child must be 13 years old.

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Full Question

Mrs. Danforth packed 5 bags of fun-sized candies for her family's picnic. Each bag contains 16 pieces. She had intended to pass out the same number of candies to each of her 4 children. But Cameron, her second-youngest, argues that she should instead distribute the candies in proportion to the children's ages. All of the children have different ages. If Cameron can convince his mother to give out the candies his way, he will gain two candies while his four-year-old sister will lose twelve. How old is Mrs. Danforth's oldest child?

Answer:

Step-by-step explanation:

g

u

Out of 30 students, the probability of one student winning the top prize is 1/30.

Since the student who won the top prize cannot be the student who wins the second prize, then the probability of a student winning the second prize is 1/29.

So, the probability that you will win the top prize and your best friend wins the second prize is:

Answer:

The probability that you will win the top prize and your best friend wins the second prize is 1/870.

In decimal form, this is 0.001149.

In percent form, this is approximately 0.11%.

Given:

The scale is 15 ft = 1 in

Height = 80 ft

Length = 200 ft

Find-:

The required dimensions of the paper

Explanation-:

The scale is:

The required dimension of paper is:

The length is:

So the demission is height 5.33 in and length 13.33 in

The sheet demission is

So, Adoncia's drawing will not fit on the sheet of paper.

We are given the improper fraction

And told to express it as a mixed number. To do so, we take the denominator (4) and look for the closes multiple of it that is less than the numerator (11).Then, we write the numerator as the sum of that multiple of the denominator and another number.

In this case, note that 4*2 = 8 and 4*3=12. So 8 is the multiple of 4 that is the closest to 11, such that it is less than 11.

In this case, we can write the following

Then, we can split the sum as follows

We see that there is one number that is not a fraction. This is the whole number of the mixed number. So we have

Finally, we add the negative sign, so we get

Answer:

Humanities ---> 3%

Social/ Behavioural sciences ---> 8%

Mathematics and Science ---> 16%

Explanation:

The percentage for each value can be calculated by dividing the number of students in that field by the total number of students in college and then multiplying it by 100, so for each field of study, we get

Therefore, the answers are

Humanities ---> 3%

Social/ Behavioural sciences ---> 8%

Mathematics and Science ---> 16%