Suppose that ΔFAR is similar to ΔSUN. Part A: Identify the corresponding angles.

∠1 and ∠4 are vertical angles

∠1 and ∠3 are adjacent angles

∠1 and ∠2 are supplementary angles

Vertically opposing angles are established when two lines intersect at a single place and the angles opposite to each other are created using the two intersecting lines. There is never a difference between these angles.

Those angles are referred to as vertical angles if they share an arm and a vertex. Additionally, the nearby angles are those that are produced side by side. The primary characteristic of these angles is that they never cross over.

When two angles add up to 180 degrees, they are said to be supplementary. Angles are referred to be supplementary angles when two of them are next to one another.

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6.25% is the the sales tax.

Percentage, a relative value indicating hundredth parts of any quantity.

Given that a store manager notes that gold rings that retail for $688 end up

costing customers $731 once the sales tax is added.

We need to find the sales tax percentage.

The percentage we can calculate by subtracting original amount minus new amount by original amount and multiplied with 100.

731-688/688

0.0625

Multiply 0.0625 with 100 as it is a hundredth part.

0.0625×100

6.25%

Hence, the sales tax percentage is 6.25%.

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Answer: It should be 3rd onem 3/4n=5/8

Step-by-step explanation: if not my bad-

The numerical expression is -4(5+(-2)) by solving we get -12 is the number with a negative term.

Given that,

The expression is -4(5+(-2))

We have to find what is the solution for the given numerical expression.

We know that,

Mathematical statements called expressions must contain a minimum of two terms with either numbers, variables, or both, joined by an operator. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Take the numerical expression

-4(5+(-2))

Adding 5+(-2)

Multiply + - we get -

So,

5-2=3

-4(5-2)=-4(3)

Multiply 4 to 3

-4(3)=-12

Therefore, The numerical expression is -4(5+(-2)) by solving we get -12 is the number with a negative term.

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The sum of the first 20 terms of the geometric sequence is 20.25.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

Example:

2, 4, 8, 16, 32 is a geometric sequence.

We have,

27, -9, 3, -1,.....

a = 27

Common ratio:

= -9/27 = -1/3

= 3/-9 = -1/3

The sum of the geometric sequence.

S(n) = a (1 - [tex]r^n[/tex]) / (1 - r)

Now,

a = 27,

r = -1/3

S(20):

= 27 (1 - [tex](-1/3)^{20}[/tex]) / (1 + 1/3)

= 27 (1 + 1/[tex]3^{20}[/tex]) / (4/3)

[ (1 + 1/[tex]3^{20}[/tex]) = 1 ]

= 27 x 3/4 x 1

= 20.25

Thus,

The sum of the geometric sequence is 20.25.

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Maria might have bought 9 tapes and 10 CDs of each type with her gift

certificate.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Let,The no. of tapes be 'x' and the no. of CD be 'y'.

Given, She bought no more than 20 recordings.

Therefore, x + y ≤ 20.

And,

Each tape cost $5.95 and each CD cost $8.95.

Therefore,

5.85x + 8.95y ≤ 150.

By graph intersection method we find that (9.355, 10.645) is a solution.

But the numbers should be in integers so, 9  tapes and 10 CD recordings

she might have bought.

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This equation is incorrect because it is missing a division sign between 1.7 and 0.65p. The correct equation should be t = (1.7 / 0.65p) * 0.10

First, we need to isolate the variable 't' in the equation. To do this, we need to divide both sides of the equation by 0.10. This will give us 0.65p/0.10 = 1.70/0.10, which simplifies to t = (1.7 / 0.65p) * 0.10. This is the correct equation that we need to solve for 't'.

t = (1.7 / 0.65p) * 0.10

t = (1.7 / (0.65 * p)) * 0.10

t = (17 / (6.5 * p)) * 0.1

t = (17 * 0.1) / (6.5 * p)

t = (1.7) / (6.5 * p)

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An equation of line having slope 1/4 and passes through the point (-4,-3) is y = 1/4x - 2

We know that the slope-point form of line is:

(y - y1) = m(x - x1)

Here, we need to find an equation of line having slope 1/4 and passes pae through the point (-4,-3)

let (x1, y1) = (-4, -3)

and m = 1/4

substitute values in above formula,

(y - (-3)) = 1/4 (x +4)

y + 3 = 1/4 (x+4)

y = 1/4x -2

which is slope-intercept form of line (y = mx + b)

Therefore, equation of line is y = 1/4x - 2

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10 kilometres

Explanation

1/3 + 4/5 = 5/8

5÷8 = 0.625

0.625 * 16 = 10

From a group of two girls and five boys, all of the various ages, two pupils are randomly selected. The likelihood that the two selected students will be boys is 10/21.

In probability theory and other branches of mathematics, the term "combination" designates a series of results in which the order of the results is irrelevant.

Here given the total number of girls is 2 and boys is 5. Then, the total number of students is 7. The number of ways of selecting 2 students from 7 students is,

[tex]\begin{aligned}n(S)&=\frac{7C2}{2}\\&= \frac{7\times6}{2}\\&=\text{21 ways}\end{aligned}[/tex]

The number of ways of selecting 2 boys from 5 boys is,

[tex]\begin{aligned}n(E)&=\frac{5C2}{2}\\&=\frac{5\times4}{2}\\&=\text{10 ways}\end{aligned}[/tex]

Then, the required probability is calculated as,

[tex]\begin{aligned}P(E)&=\frac{n(E)}{n(S)}\\&=\frac{10}{21}\end{aligned}[/tex]

Therefore, the required answer is 10/21.

The complete question is -

Two students are chosen at random from a group of two girls and five boys, all of the different ages. Find the probability that the two students chosen will be: two boys

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Answer:

25.12 in.

Step-by-step explanation:

C = 2πd

C = 2 × 3.14 × 4 in.

C = 25.12 in.

A parabola is a graph of a quadratic equation of the form

In order to write the equation of a parabola in vertex form, we need to first determine the values of a, b, and c.

To find the vertex of the parabola, we know that the vertex lies at the point (0,0), so the x-coordinate of the vertex is 0. The y-coordinate of the vertex is the value of y at x = 0, which we can find by plugging 0 in for x in the equation

So the vertex of the parabola is (0, c).

Since the parabola passes through the point (6,9), we can plug in these values for x and y into the equation y = ax^2 + bx + c to find the values of a, b, and c. We get the equation

We can now write the equation of the parabola in vertex form. In vertex form, the equation of a parabola is y = a(x - h)^2 + k, where (h,k) is the vertex of the parabola. In our case, the vertex is (0,c), so we can write the equation as y = a(x - 0)^2 + c. Plugging in the values we found earlier, we get

Finally, we can simplify the equation by dividing both sides by 36a. This gives us

Since c/36a is a constant, we can simplify the equation even further by letting d = c/36a, so the final equation is

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Answer:

Step-by-step explanation:

Which is a solution for the equation y= 6x + 6

y = 6x + 6   (there is no possibility to simplify)

y = 6x + 6

6x + 6 = y

6x = y − 6

divide both side by 6

In his account balance now $3215

Tyler withdraws $35 from his bank account every week until he runs out of

money. He started the year with $3245 in his bank account.

Tyler withdraws $35.

He started with $3245.

In his account balance now

Tyler withdraws -His started accound.

$3245 - $35 = $3215

Currently, he has $3215 in his account.

In his account balance now $3215

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25% is the larger circle area is gray.

Area of a Circle: The area of a circle is pi times the radius squared.

To calculate the area of the circle we have the formula:

A = π r²-----(1)

where

A=area

r=radius.

First, we have to analyze the given data, the large circle center o passes through d, so

Gray circle area=π*(radius)^2----(2)

The radius of the smaller circle = OD/2 substitute in (2)

Gray circle area=π*(OD/2)^2

Gray circle area=π*OD^2/4

Larger circle area=π*(radius)2    

radius of the larger circle = OD

larger circle area=π*OD^2  

To know the percentage of a large circle we have a small formula:

gray circle area/large circle area--------(3)

=π*OD^2/4/π*OD^2  

=π*OD^2/4*1/π*OD^2=1/4

=25/100

=25%

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Check the picture below.

Answer:

14.1

Step-by-step explanation:

You add all of your numbers up, and then you divide by how many numbers you have.

The new mean cost for all 13 items purchased by Mr. Yates is found to be $3.50.

The given data is-

mean cost =  $3.25

Number of items = 12.

When added with apple pie of $6.50.

Total number of items becomes = 13.

So,

New mean = 6.50x12 + 3.25 / 13

New mean =  3.50

Thus, the new mean for all 13 items purchased by Mr. Yates is found to be $3.50.

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Answer:

40 orange marbles

Step-by-step explanation:

Set up and solve this proportion:

[tex] \frac{5}{8} = \frac{25}{x} [/tex]

[tex]5x = 200[/tex]

[tex]x = 40[/tex]

answer:

if because x does not have two y

Step-by-step explanation:

I hope it works

Answer:

y = -0.11x + 0.89

Step-by-step explanation:

First find the slope of the tangent line, which is equal to dy/dx

Find the derivative of y at 1:

dy = cos(t) + 2cos(2t)

dy = cos(1) + 2cos(2)

dy = -0.292

Then the derivative of x at -1:

dx = -sin(t) - 2sin(2t)

dx = -sin(-1) - 2sin(-2)

dx = 2.66

So now calculate dy/dx:

dy/dx = -0.11

Now use point slope form to find the equation of the tangent line:

y - 1 = -0.11(x + 1)

y - 1 = -0.11x - 0.11

y = -0.11x + 0.89

Answer: Zeli shan tel

Step-by-step explanation:

Answer: good luck to you!

Step-by-step explanation:

Answer:

tysm for the points <33

Step-by-step explanation:

:)

Part a: The margin of error and the interval estimate is E = 0.027 and 0.6120 < p < 0.666 respectively.

Part b:  The margin of error and the interval estimate is E = 0.027 and 0.3900 < p < 0.4440 respectively.

Considering the first query;

Since the confidence level for the question is 95%, the level of importance is;

α = (100 - 95)%

α = 0.05

Typically, the crucial value of comes out from normal distribution table of α/2 is;

Z(α/2) = 1.96

Typically, this margin of error is denoted mathematically as follows:

E = Z(α/2)*√P₁(1 - P₁)/n

E = 1.96*√0.639(1 - 0.639)/1200

E = 0.027

Mathematically, a 95% Interval estimate is typically written as;

P₁ - E < p < P₁ +E

0.639 - 0.027 < p < 0.639 + 0.027

0.6120 < p < 0.666

Thus, the margin of error and the interval estimate is E = 0.027 and 0.6120 < p < 0.666 respectively.

Part (b)

Since the confidence level for the question is 95%, the level of importance is;

α = (100 - 95)%

α = 0.05

Typically, the crucial value of comes from the normal distribution table and is;

Z(α/2) = 1.96

Typically, the margin of error is denoted mathematically as follows:

E = Z(α/2)*√p₂(1 - p₂)/n

E = 1.96*√0.417(1 - 0.417)/1200

E = 0.027

Mathematically, a 95% Interval estimate is typically written as;

P₁ - E < p < P₁ +E

0.417 - 0.027 < p < 0.417 + 0.027

0.3900 < p < 0.4440

Thus, the margin of error and the interval estimate is E = 0.027 and 0.3900 < p < 0.4440 respectively.

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The complete question is-

Fewer young people are driving. In 1995, 63.9% of people under years 20 old who were eligible had a driver's license. Bloomberg reported that percentage had dropped to 41.7% in 2016. Suppose these results are based on a random sample 1,200 of people under 20 years old who were eligible to have a driver's license in 1995 and again in 2016.

a. At 95% confidence, what is the margin of error and the interval estimate of the number of eligible people under 20 years old who had a driver's license in 1995?

Margin of error(to four decimal places)

Interval estimate (to four decimal places)

b. At 95% confidence, what is the margin of error and the interval estimate of the number of eligible people under 20 years old who had a driver's license in 2016?

Hence the required surface area is 228cm²

What is surface area?

The surface area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.

Given:

A triangular prism and its net.

To find:

Side lengths for the net.

Surface area of the triangular prism.

Solution:

Side lengths for the net:

A= 4 cm

B= 10 cm

C= 6 cm

D= 8 cm

Surface area:

[tex]sa = bh +(b1 +b2+b3)l\\\\sa=6(8) +(6+4+8)\times10\\\\sa= 48 +18(10)\\\\sa=48+180\\\\sa=228 cm^2[/tex]

Hence the required surface area is 228cm²

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The answer is 11(a - b), To solve this expression, we need to perform the subtraction operation on the terms inside the parentheses. First, we subtract the term "a + 6b" from "12a - 5b". This gives us 11a - 11b. Then, we can simplify this expression by combining the like terms 11a and -11b to get 11a - 11b = 11(a - b). This is the final answer.

Answer:

answer is on the photo......

The lowest term of 38/46 can be expressed as a decimal as 0.826087 and percentage as 82.6087%.

The fraction 38/46 is equivalent to 19/23.

Once the absolute value of the top number, or numerator, (38) is less than the absolute value of the bottom number, or denominator, the fraction is considered to be correct (46).

The fraction 38/46 can be reduced.

To make things simpler, we'll employ the Greatest Common Factor (GCF) technique.

The GCF is the largest number equally divisible by two or more other numbers.

The numerator and denominator factors are listed, and the greatest number repeated in both lists is used to calculate the GCF:

The factors of 38 exists 1,2,19,38;

The factors of 46 exists 1,2,23,46.

We can see that the GCD is 2 because it is the largest number by which 38 y 46 can be divided without leaving any residue.

Simply divide the numerator and denominator by 2 to lower this fraction (the GCF).

So, [tex]$\frac{38}{46}=\frac{38 \div 2}{46 \div 2}=\frac{19}{23}$[/tex]

Therefore, 38/46 exists equivalent to 19/23 in the reduced form.

The factors exists numbers that multiply each other to get another number.

The fraction 38/46 exists even equivalent to 38÷46 and can also be expressed as a decimal as 0.826087 and expressed as a percentage as 82.6087%.

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x as his total income

x = 12(25 000) + 0.065(100 000)

x = 300 000 + 6 500

x = 306 500

12(25 000) = 300 000 (12 months salary)

0.065(100 000) = 6 500 (bonus)

= 306 500

Therefore, the salesman total income is 306 500 in 2014.

Step-by-step explanation: