Level 2 Problems
11. Given the similar triangles at right.
Note: Be careful. You do not set up
a. The scale factor from small to big is
b. y=
54
1562-72
C. W=
72
54
162
48
W

Gary's pay before taxes is $218.88.

Gary's pay before taxes can be calculated by multiplying his hourly rate by the number of hours he worked.

Taxes are compulsory payments made by a government organisation, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools.

Step 1: Identify the hourly rate and number of hours worked.
Hourly rate: $9.12
Hours worked: 24

Step 2: Multiply the hourly rate by the number of hours worked.
$9.12 * 24 = $218.88

Step 3: The result is Gary's pay before taxes.
Gary's pay before taxes is $218.88.

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Rounding to the nearest whole number, the tire makes 214 revolutions while traveling 500 feet.

What is Circumference?

Circumference is a term used in geometry to refer to the distance around the edge of a circle or any circular object. It is the total length of the boundary or perimeter of the circle. The circumference is determined by the diameter or radius of the circle, and it is calculated using the formula:

Circumference = π × diameter

The circumference of the tire is equal to the distance it travels in one revolution. Since the diameter of the tire is 28 inches, its radius is 14 inches. Therefore, the circumference of the tire is:

C = 2πr = 2π(14 inches) = 28π inches

To convert the distance of 500 feet to inches, we multiply by the conversion factor 12 inches/foot:

500 feet × 12 inches/foot = 6000 inches

Now we can find the number of revolutions of the tire:

number of revolutions = distance traveled / circumference of tire

number of revolutions = 6000 inches / 28π inches ≈ 214 revolutions

Therefore, rounding to the nearest whole number, the tire makes 214 revolutions while traveling 500 feet.

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By adding the rectangle, the shaded area is [tex]53 in^2[/tex], rοunded tο the nearest whole figure.

The entire area οf a three-dimensional οbject's surface is known as surface area. It is a measurement of an οbject's expοsed surface. Indicating an οbject's surface area typically involves using square measurements like square inches οr square meters. The surface area οf a cube, fοr instance, is equal to the tοtal οf the areas οf each οf its six faces. The calculatiοn fοr a cube's surface area is: Surface Area Equals 6*[tex]side^2[/tex] where "side" denοtes the cube's extent οn οne side.

given:

The bigger semicircle has a radius οf 5 inches and a diameter οf 10 inches. Consequently, the bigger semicircle's area is:

(5 in) * (1/2) * π  = 39.27 in (rοunded tο twο decimal places)

The smaller semicircle has a radius of οf 2 inches and a width of οf 4 inches. Consequently, the smaller semicircle's size is:

(2 in) * (1/2) * π * 6.28 in (rοunded tο twο decimal places)

The rectangle's area is: because it is 10 inches long and 2 inches wide.

10 in + 2 in equals [tex]20 in ^2.[/tex]

We can add the area οf the rectangle tο the area οf the larger semicircle after subtracting the areas οf the smaller and larger semicircles tο determine the area οf the shaded regiοn:

[tex]39.27 in^2 - 6.28 in^2+ 20 in^2 = 52.99 in^2.[/tex]

By adding the rectangle, the shaded area is 53 in2, rοunded tο the nearest whole figure.

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A store has three sizes of cans of nuts. The large size contains 2 pounds of peanuts and 1 pound of cashews. The mammoth size contains 1 pound of walnuts, 6 pounds of peanuts, and 2 pounds of cashews.

The giant size contains 1 pound of walnuts, 4 pounds of peanuts, and 2 pounds of enehews. Suppose that the store recelives be filled with the given sizes of cans?

To solve this problem, let's assign variables to the unknowns. Let G represent the number of giant cans, M represent the number of mammoth cans, and L represent the number of large cans.

We can then write out the system of linear equations:

2L + 1M + 4G = 2 lbs. of peanuts
1L + 6M + 1G = 1 lbs. of walnuts
1L + 2M + 2G = 2 lbs. of cashews

Solving this system of equations can be done with any method, such as substitution, elimination, or graphing.

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The other two roots are x = (9 + √137) / 2 and x = (9 - √137) / 2.

Given that x = -9 is a root of |(x,3,7)(2,x,2)(7,6,x)| = 0, we can use the determinant of the matrix to find the other roots. The determinant of the matrix is given by:

| (x,3,7)(2,x,2)(7,6,x) | = x(x*x - 2*6) - 3(2*x - 7*2) + 7(2*6 - 7*x)

= x^3 - 12x - 3(2x - 14) + 7(12 - 7x)

= x^3 - 12x - 6x + 42 + 84 - 49x

= x^3 - 67x + 126 = 0

Since x = -9 is a root, we can divide the polynomial by (x + 9) to get:

(x^3 - 67x + 126) / (x + 9) = x^2 - 9x - 14

Now we can use the quadratic formula to find the other two roots:

x = (-(-9) ± √((-9)^2 - 4(1)(-14))) / (2(1))

x = (9 ± √(81 + 56)) / 2

x = (9 ± √137) / 2

Therefore, the other two roots are x = (9 + √137) / 2 and x = (9 - √137) / 2.

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An investment of $1,000 at an annual interest rate of 7.5%, compounded annually, will be worth $1,232.28 after 3 years.

Value is a term used to describe the worth of something, either in terms of money, or in terms of importance or usefulness. Value can be determined in terms of the amount of money something is worth, or the level of importance or usefulness it has to someone. When something has a high value, it means that it is worth a lot of money or has a high level of importance or usefulness.

The value of an investment of $1,000 after 3 years at an annual interest rate of 7.5%, compounded annually, can be calculated using the following formula:

Future Value (FV) = Present Value (PV) × (1 + r)ⁿ

Where PV is the present value of the investment ($1,000 in this case), r is the annual interest rate (7.5%) and n is the number of years (3).

Using this formula, we can calculate the future value of the investment after 3 years as follows:

FV = $1,000 × (1 + 0.075)³

FV = $1,000 × 1.23228

FV = $1,232.28

Therefore, an investment of $1,000 at an annual interest rate of 7.5%, compounded annually, will be worth $1,232.28 after 3 years.

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The number of home-runs LA Dodgers hit is  35.

Given,

Total home runs in Major league = 583

Home - runs accounted by LA Dodgers = 6 %

Number of home-runs by LA Dodgers

                = 6% of 583

                = 6/100 * (583)

                = 0.06 * 585

                = 34.98

                = 35 approximately

Hence, the total number of homeruns that did the LA Dodgers hit are 35 approximately.

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It takes Carys 1/10 οf an hοur, οr 6 minutes, tο earn οne dοllar.

In mathematics, the term linear functiοn refers tο twο distinct but related nοtiοns: In calculus and related areas, a linear functiοn is a functiοn whοse graph is a straight line, that is, a pοlynοmial functiοn οf degree zerο οr οne.

Tο find the number οf hοurs it takes Carys tο earn οne dοllar, we can set E (the amοunt earned) equal tο $1 and sοlve fοr h (the number οf hοurs):

E = 10h

$1 = 10h

h = $1/10

Hence, it takes Carys 1/10 οf an hοur, οr 6 minutes, tο earn οne dοllar.

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Carys earns one dollar in one-tenth of an hour, or six minutes.

The word linear function in mathematics refers to two distinct but related concepts: A linear function in calculus and related fields is a function whose graph is a straight line, Namely, a polynomial function of degree zero or one.

Set E (the amount earned) to $1 and solve for h (the number of hours):

E = 10h

$1 = 10h

h = $1/10

As a result, it takes Carys one-tenth of an hour, or six minutes, to earn one dollar.

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let's convert the mixed fraction to improper fraction first.

[tex]\stackrel{mixed}{3\frac{5}{6}}\implies \cfrac{3\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{23}{6}} \\\\[-0.35em] ~\dotfill\\\\ 3\frac{5}{6}\times 12\implies \cfrac{23}{6}\times 12\implies \cfrac{23}{6}\times \cfrac{12}{1}\implies \cfrac{23}{1}\times \cfrac{12}{6}\implies 23\times 2\implies \text{\LARGE 46}[/tex]

Answer:

59

Step-by-step explanation:

Opposite angles are equal

C or KCG isn121

Straight line angle is 180

YCG + GCK = 180

YCG = 180- 121

Another method

All the four angles at a point is 360

YCH + HCK + KCG +YCG is 360

C is 121

121 + X + 121 + X = 360

2X + 242 =360

Subract 242 from both sides

2X = 118

Divide both sides by 2 = 59

To find out how many minutes it would take Teresa to run 9 miles at the same rate, we can use a proportion.

We know that Teresa took 44 minutes to run 6 miles. This means she was running at a rate of 6 miles per 44 minutes. To solve for how long it would take to run 9 miles, we can set up a proportion with this information.

Let x = the number of minutes it would take Teresa to run 9 miles.

6/44 = 9/x

Cross-multiply to solve for x: 44x = 54

Divide both sides by 44 to find the solution: x = 54/44 = 1.227 minutes

Therefore, it would take Teresa 1.227 minutes to run 9 miles at the same rate.

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Option C multiplies one and demonstrates that the result is one, proving that one has the attribute of multiplicative identity.

Any number multiplied by one is equal to itself, according to the multiplicative identity condition of 1. Hence, the following equation illustrates the multiplicative identity feature of 1.

C) 1/4 x 4 = 1

Adding 1/4 to 4 results in: 1/4 x 4 = (1 x 4) / 4 = 4/4 = 1

This demonstrates that when we multiple any number by 1, the result is always the same. Because they involve multiplying many numbers, not just 1, Options A, B, and D do not demonstrate the multiplicative identity characteristic of 1. Option C, on the other hand, multiplies one and demonstrates that the result is one, proving that one has the attribute of multiplicative identity.

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The condensed form of the given logarithmic expression ln(3) + ln(x) + ln(y) is: ln(3*x*y)

To condense the given logarithmic expression to a single logarithm with a leading coefficient of 1, we can use the product property of logarithms.

The product property states that the sum of two logarithms with the same base is equivalent to the logarithm of the product of the two numbers.

Using this property, we can combine the three logarithmic terms in the given expression: ln(3) + ln(x) + ln(y) = ln(3*x*y)

Therefore, the condensed form of the given logarithmic expression is:
ln(3*x*y). This is a single logarithm with a leading coefficient of 1, as required.

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As you have two side lengths but no angle measures, the Pythagorean Theorem should be used to obtain the value of x.

Then the value of x is given as follows:

x = 36.3.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The parameters for this problem are given as follows:

Hence the value of x is obtained as follows:

x² + 19² = 41²

x = sqrt(41² - 19²)

x = 36.3.

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Three rational expressions that simplify to (x)/(x+1) are:

1) (x+2-2)/(x+1)
2) (2x-3x+3)/(2x+2-3x+1)
3) (3x+5-5-2x)/(x+2+1-2)

To simplify these expressions, we can combine like terms in the numerator and denominator:

1) (x+2-2)/(x+1) = (x)/(x+1)
2) (2x-3x+3)/(2x+2-3x+1) = (-x+3)/(-x+3) = (x)/(x+1)
3) (3x+5-5-2x)/(x+2+1-2) = (x)/(x+1)

As shown, all three expressions simplify to (x)/(x+1), fulfilling the requirements of the question.

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The area of the shaded diagonal plane is  17.5 square units.

The area of the shaded diagonal plane is calculated as follows:

Using Pythagoras' theorem, let the hypotenuse formed by the diagonal be x

x² = 3² + 5²

x² = 9 + 25

x² = 34

x = √34

The shape of the shaded plane is a rectangle.

The area of the rectangle will be:

Area = length * width

Area = √34 * 3

Area do the shaded plane = 17.5 square units

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The percentage of customers who put chocolate creamer in their coffee during the hour is 70%.

To find the required percentage, find the number of customers that chose chocolate creamer and total the number of customers who came to choose the creamer in the hour.

Divide the number of customers that chose chocolate creamer by the total number of customers and multiply by 100.

Here we have

The manager of a coffee shop recorded the number of customers who put vanilla creamer or chocolate creamer in their coffee during one hour

The bale given is

                          Vanilla      Chocolate    

Age 18 - 30            2               6

Age 30 +                4               8      

Here, number of customers = 2 + 4 + 6 + 8 = 20

No of customers that choose chocolate creamer = 6 + 8 = 14

The percentage of customers that put chocolate creamer

=  [ 14/20 ] × 100 =  70%

Therefore,

The percentage of customers who put chocolate creamer in their coffee during the hour is 70%.

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Answer: 70%

Step-by-step explanation:

Answer:2

Step-by-step explanation:

20 divided by 10 equals 2

Answer:

x=25°

Step-by-step explanation:

please mark as brainliest

Answer:

See below.

Step-by-step explanation:

We are asked to find the value of x, and what these 2 angles are.

We know that these angles are Vertical Angles.

Vertical Angles are angles that are opposite of each other and are equal. They're equal due to the two straight lines crossing over each other at the same angle.

These angles aren't Adjacent Angles because they aren't next to each other. These angles don't share a common side. (Ray)

Since Vertical Angles are equal:

[tex]75 = 4x - 25[/tex]

Simplify for x:

[tex]100=4x\\25 = x[/tex]

x will equal 25°.

Answer:

6

Step-by-step explanation:

[tex]1\frac{1}{2}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{2}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{2}[/tex] × [tex]\frac{4}{1}[/tex] = [tex]\frac{12}{2}[/tex] = 6  

Answer:

True

Step-by-step explanation:

Plug in x = 1 into the function expression. You should get  f(xx) = 4

Plug in x = 2 and you will get f(x) = 13

So the function value has increased from 4 at x = 1 to 13 at x = 2

or, just plot it and see it visually

Using synthetic division, the value of g(1) is 37.

To find g(1) using synthetic division, we need to divide the polynomial g(z) by the binomial (z - 1). The process of synthetic division is as follows:

1. Write down the coefficients of the polynomial g(z): 28, -9, -26, 10, 34
2. Write down the value of z that we are plugging in, which is 1, in the leftmost column.
3. Bring down the first coefficient, which is 28, to the bottom row.
4. Multiply the value in the bottom row by the value of z, which is 1, and write the result in the next column.
5. Add the value in the top row to the value in the bottom row and write the result in the bottom row.
6. Repeat steps 4 and 5 until all the columns are filled.
7. The last value in the bottom row is the remainder, and the values in the bottom row before the remainder are the coefficients of the quotient polynomial.

The synthetic division table looks like this:

1 | 28  -9  -26  10  34
|       28   19   -7   3
 | 28  19    -7   3   37

The remainder is 37, so g(1) = 37.

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Ben is incorrect because, all of Ben's expressions are erroneous since none of them equal the number 108 degrees. The correct equation is (n-2) x 180 / n.

A polygon is a geometric shape with a limited number of sides and two dimensions. The sides or edges of a polygon are formed by joining end-to-end segments of a straight line to form a closed shape. The intersection of two line segments, which results in an angle, is referred to as a vertex or corners.

The formula for calculating an interior angle in a regular polygon with n sides is (n-2) x 180 / n.

An internal angle in a pentagon has a measure of (5-2) x 180 / 5 = 108 degrees.

Substituting the angle in Ben's expression:

xᵒ + (x + 40)° + (2x - 30)° + 3(x - 40)° + 3x°

9x - 27° = 108

We observe that none of the value of x results in 108 degrees.

Hence, all of Ben's expressions are erroneous since none of them equal the number 108 degrees.

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Answer:

Step-by-step explanation:

There are four methods of sampling namely Random sampling,Stratified sampling, Cluster sampling and Multistage sampling. Let’s look at them one by one.

Random sampling - When each subject of the population is equally likely to be included in the sample, the sampling method is called random sampling.

Stratified sampling- Under this, the data are first divided into stratas. Each stratum consists of homogeneous subjects and strata are heterogeneous among themselves. Samples are randomly taken from each strata. Example- In an investigation of mortality rate of the insured, we can first subdivide the data into males and females and then take sample from each group. Here, male and female groups represent stratas.

Cluster sampling- Under this we first divide the data into clusters that are homogeneous among themselves and then select few of them and sample all observations from the randomly selected clusters. For example- suppose we want to take a sample of people's weight in a specific city. We observed that the areas in that city are similar to each other , so instead of travelling to each area and collecting data we can select few areas and then take observations from all people of those areas.

Multistage sampling - This adds one more stage to cluster sampling. Unlike cluster sampling where we sample all observations from the selected clusters, In multistage sampling we randomly sample observations from each selected cluster.

I hope this helped.

Answer:

It is D

Step-by-step explanation:

Its D it has to be 5 and bigger than 5

The value of x is 9.75

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Therefore, the other side of the small triangle = √12²+9² = √ 144+81 = √225 = 15

15/9+x = 12/15

225 = 12(9+x)

225/12 = 9+x

18.75 = 9+x

x = 18.75 -9

x = 9.75

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The correct classification for 11+8i is a complex number.√−81 can be expressed as the complex number 9i.

The number 11+8i is a complex number. This is because it has both a real part (11) and an imaginary part (8i). A complex number is any number that can be expressed in the form a+bi, where a and b are real numbers and i is the imaginary unit. Therefore, the correct classification for 11+8i is a complex number.

To express √−81 as a complex number, we can use the fact that √−1 = i. So, √−81 = √(81)*√(−1) = 9*i = 9i. Therefore, √−81 can be expressed as the complex number 9i.

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