1. Estimate the area of the irregular shape. Explain your method and show your work.

[tex]\textit{Horizontal Range}\\\\ R=\cfrac{(v_0)^2\cdot \sin(2\theta )}{g} ~~ \begin{cases} v_o=\textit{initial velocity}\\ \theta =\textit{initial angle}\\ g=gravity\\[-0.5em] \hrulefill\\ v_o=100\\ \theta =45^o\\ g\approx 32~\frac{ft}{s^2} \end{cases}\implies R\approx\cfrac{(100)^2 \sin(2\cdot 45^o)}{32} \\\\\\ R\approx\cfrac{10000\sin(90^o)}{32}\implies R\approx\cfrac{10000(1)}{32}\implies R\approx 312.5~ft[/tex]

The tangent of the subtraction of angles x and y is defined as follows:

tan(x - y) = (36 - 20π)/(48 + 15π)

The tangent of the subtraction of two angles is obtained according to the identity presented as follows:

tan(x - y) = [tan(x) - tan(y)]/[1 + tan(x)tan(y)]

The tangent of angle x is given as follows:

3/4.

The tangent and cotangent are defined as follows:

Hence the tangent of angle y is obtained inverting the numerator and the denominator of the function, as follows:

tan(y) = 5π/12.

The subtraction of the two tangents is given as follows:

tan(x) - tan(y) = 3/4 - 5π/12 = 9/12 - 5π/12 = (9 - 5π)/12.

The quotient of the two tangents is given as follows:

tan(x)tan(y) = 3/4 x 5π/12 = 15π/48.

Then the denominator of the expression is given as follows:

1 + 15π/48 = (48 + 15π)/48.

Considering the division of the two fractions, the tangent of the subtraction is defined as follows:

tan(x - y) = (9 - 5π)/12 x 48/(48 + 15π)

tan(x - y) = (36 - 20π)/(48 + 15π)

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Since Z and 92 both have vertical angles, they are equal. Subtract from 180 to determine the measure of the other angle, which is 88 degrees since it forms a straight line with the 92-degree angle. Solve the expression by setting the value at 88.

∠AOB + ∠BOC = 180°

92°+( 10x  +  32 )° = 180°

10x + 32° = 180 - 92

10x + 32° = 88

10x = 88 - 32

10x = 56

x = 56 ÷ 10

x = 5.6°

Hence, the value of X is 5.6 and Z is 92.

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Answer:

600 ml

Step-by-step explanation:

One of the rules of ratio includes sorting ratio in order according to the question. In this case, squash is mentioned first, then water. Hence, the ratio is:

squash:water = 1:6

Use cross multiplication:

1       :       6

100  :        ?

Multiply 100 by 6 then divide it by 1: which basically means 100 * 6 = 600 ml.

If you are unfamiliar with cross multiplication, then simply find out how many times did you have to multiply the 1 in the squash ratio to result to 100, which is 100, then multiply 6 by that answer = 6 * 100.

Hope you understood :)

Answer: multiples of 4 are -4,8,12,16,20,24,28,32,36,40,44,48,52

Step-by-step explanation:

4x1=4

4x2=8

4x3=12

4x4=16

4x5=20

4x6=24

4x7=28

4x8=32

4x9=36

4x10=40

4x11=44

4x12=48

4x13=52

Answer:

208

Step-by-step explanation:

52×4=208

Answer:

D

Step-by-step explanation:

the midsegment of a trapezoid is half the sum of the parallel sides, that is

midsegment = [tex]\frac{WT+VU}{2}[/tex] = [tex]\frac{17.5+6.1}{2}[/tex] = [tex]\frac{23.6}{2}[/tex] = 11.8

Answer:

2 [tex]\frac{2}{9}[/tex] days

Step-by-step explanation:

Let d = the number of days.

[tex]\frac{1}{4}[/tex] d = [tex]\frac{1}{5}[/tex]d = 1

[tex]\frac{5}{20}[/tex] d + [tex]\frac{4}{20}[/tex] d = 1

[tex]\frac{9}{20}[/tex] d = 1  Multiply both sides by [tex]\frac{20}{9}[/tex]

([tex]\frac{20}{9}[/tex])([tex]\frac{9}{20}[/tex]) d = 1([tex]\frac{20}{9}[/tex])

d = [tex]\frac{20}{9}[/tex]   I can break 20 into 9 + 9 + 2

d = [tex]\frac{9}{9}[/tex] + [tex]\frac{9}{9}[/tex] + [tex]\frac{2}{9}[/tex]           [tex]\frac{9}{9}[/tex] = 1

d = 1 + 1 + [tex]\frac{2}{9}[/tex]

d = 2 [tex]\frac{2}{9}[/tex]

Answer:

  A, C, D

Step-by-step explanation:

You want the angles in the list that have π/3 as the reference angle.

The reference angle is the smallest angle between the angle's terminal side and the x-axis. The cosine and sine of the reference angle have the same magnitude of the cosine and sine of the angle in question.

The attached table shows that 7π/3, 2π/3, and 19π/3 have the same reference angle: π/3.

Answer: [tex]10 \frac{2}{3}[/tex]

Step-by-step explanation:

[tex]5 \times \frac{7}{3}=\frac{5 \times 7}{3}=\frac{35}{3}=10 \frac{2}{3}[/tex]

Answer:

Step-by-step explanation:

Approximately 68% of the data points in a dataset are expected to be within one standard deviation of the mean, assuming that the data follows a normal distribution. This is known as the Empirical Rule or the 68-95-99.7 rule. According to this rule, approximately 95% of the data points are expected to be within two standard deviations of the mean, and approximately 99.7% of the data points are expected to be within three standard deviations of the mean.

Please note that this rule applies only to a normal distribution, if the data is not normally distributed, the proportion may be different.

Answer:

Approximately 68% of the data points in a data set are expected to be within one standard deviation of the mean because of the 68-95-99.7 rule.

Step-by-step explanation:

This rule states that approximately 68% of the data points in a normal distribution fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Answer:

Step-by-step explanation:

82

Solution for the given System of linear equation is:

Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods to solving systems of equations: graphing, substitution, elimination and matrices.

Given,  the system of linear equations on the left with its solution type on the right

For  Y=2x-1 and Y=2x+1

Adding both equation,  we will get y = 4x

Thus, these equations have infinite number of solution

For 2x - y = 7 and 3x + y = 3

Adding these equations

5x = 10

x= 2

Substitute the value in equation 1

y = -3

Thus, solution is (2, - 3)

therefore, the Solution for the given System of linear equation is:

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Complete question:

Answer: Elijah's debt-to-credit ratio is 37%.

Step-by-step explanation:

Elijah's debt-to-credit ratio is the ratio of the amount of money he owes to the total amount of credit he has available.

To calculate the debt-to-credit ratio, we need to divide the amount of debt by the total amount of credit, and then multiply by 100 to get the answer in percentage.

Debt = $2,127.50

Credit = $5,750.00

Debt-to-credit ratio = (Debt / Credit) * 100

Debt-to-credit ratio = (2127.50 / 5750) * 100 = 37.29 ~ 37%

So the answer is: b) 37%

The simultaneous equation 5x + 2y = 9 and x + y = -3 is solved by elimination method as follows

There are various methods of solving simultaneous equation however for this problem we solve with elimination method

The equation is 5x + 2y = 9 and x + y = -3

multiply x + y = -3 by 2

2x + 2y = -6

subtract 2x + 2y = - 6 from 5x + 2y = 9

5x + 2y = 9

2x + 2y = - 6

this will result to 3x = -15

solve for x by dividing by 3

x = -5

substitute x = -5 to x + y = -3

-5 + y = -3

y = -3 + 5

y = 2

hence x = -5 and y = 2

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The equation that can be used to determine the total cost, given the number of movie tickets, is c = 8. 50 c

The equation that shows the total cost when you buy a certain number of tickets, can only be found after you solve for the ticket price.

The ticket price is :
= Cost of tickets / Number of tickets

= 42. 50 / 8

= $ 8. 50

The equation for the total cost would therefore be:

Total cost = Number of tickets x Cost per ticket

c = f x 8. 50

c = 8. 50 f

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Answer:

5

Step-by-step explanation:

Answer:

Solving by Factoring is a strategy used to solve quadratic equations. This strategy involves factoring the quadratic equation. Factoring is breaking an expression down into smaller expressions that when multiplied together will equal the original expression.

Step-by-step explanation:

To solve a quadratic equation by factoring we must first get the equation into the form ax^2 + bx + c = 0. From here we must use a strategy of factoring known as Reverse FOIL. By using reverse FOIL we will break the equation down into smaller parts. The four steps to use in reverse FOIL are:

1. Find two factors of “ac” (the coefficient of x^2) that when added together equal “b” (the coefficient of x).

2. Multiply the two factors you found in step one to produce “ac.”

3. Group the two terms with the “ac” terms in the equation.

4. Factor the two terms with “bx” in them.

For example, if we have an equation such as 9x^2 + 15x + 4 = 0  we would look for two factors of 4 (ac) that when added together equal 15 (b). The two factors of 4 that when added together equal 15 are -1 and -4. Therefore our equation would become: (9x^2 -1x -4x +4) and we can group the terms like this: (9x^2 -1x)(-4x +4).

The fourth step is to factor the two terms with “bx” in them. In our equation, the two terms with “bx” in them are -1x and -4x. Factoring these terms give us: (9x^2 -1x)(-4x +4) = (3x -1)(3x -4).

The final step is to find the two solutions, or the “x” values, that make the equation equal zero. To find these two x values, just set each factor to zero, and solve the resulting equations. In this example, setting the first factor, (3x - 1) equal to zero, we get x = (1/3); setting the second factor, (3x - 4) equal to zero, we get x = (4/3).

Therefore, the two solutions to 9x^2 + 15x + 4 = 0 are x = (1/3) and x = (4/3).

Using the strategy of Factoring, we have been able to successfully solve the equation 9x^2 + 15x + 4 = 0.

Answer:

Let x be the number of guppies Percious can purchase.

We know that the total cost of the goldfish, starfish and guppies is less than or equal to $80.

We can use this information to write an inequality:

32 + 12 + 6x <= 80

This inequality represents the total cost of the goldfish, starfish, and guppies.

By solving this inequality we can find the number of guppies Percious can purchase.

To solve this inequality, we can first simplify it by combining like terms:

44 + 6x <= 80

Then we can subtract 44 from both sides:

6x <= 36

And finally, we divide both sides by 6:

x <= 6

So, Percious can purchase a maximum of 6 guppies if she wants to spend all of her money.

x is less than or equal to 6.

Step-by-step explanation:

Let x be the number of guppies Percious can purchase.

We know that the total cost of the goldfish, starfish and guppies is less than or equal to $80.

We can use this information to write an inequality:

32 + 12 + 6x <= 80

This inequality represents the total cost of the goldfish, starfish, and guppies.

By solving this inequality we can find the number of guppies Percious can purchase.

To solve this inequality, we can first simplify it by combining like terms:

44 + 6x <= 80

Then we can subtract 44 from both sides:

6x <= 36

And finally, we divide both sides by 6:

x <= 6

So, Percious can purchase a maximum of 6 guppies if she wants to spend all of her money.

x is less than or equal to 6.

The total interest paid for the period of three months will be $600 on the loan amount of $550000.

The interest is the charges levied on the amount which we borrow from any bank for a particular period of time.

Here in the question given data is

P= $550000

R=2.0%+2.8%=4.8%

T=1/4 years or three months

So from the simple interest formula

SI = PRT / 100

= 550000 x 4.8 x 1/4 / 100

= 6600

Hence, the total interest paid for the period of three months will be $600 on the loan amount of $550000.

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where’s the answer choices??? the picture?? did you finish the question??

Answer:

Step-by-step explanation:

Answer:

The answer is 32

Step-by-step explanation:

We solve this by first finding the angle 3. To do this we subtract 180 (the sum of a triangle) and the two known angles. 180-15-17 = 148.

So now we know that the 3rd angle is equal to 148. Now to find the angle 4 we subtract angle 3 from 180, because a straight line is equal to to 180 degrees; 180-148=32

Hope that helps

The system of inequalities y > x + 2 and y < x - 3. when solved will not have solutions

When the graphs meet at a point, a system of linear equations has just one solution.

No solution, When the graphs are parallel, a system of linear equations cannot have a solution.

examining the system of linear equations y > x + 2 and y < x - 3, the slope of the two linear functions are equal with a value of 1.

Because of this, the equations will not intersect and the lines are said to be parallel and no solution expected

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Answer:

We can use the tangent function to solve for the height of the tower. The tangent of an angle is the ratio of the opposite side to the adjacent side in a right triangle.

First, we'll find the opposite side (the height of the tower) using the angle of elevation:

tan(21°) = opposite / 300

opposite = 300 * tan(21°)

Then we'll find the opposite side (the depth of the base of the tower below the window) using the angle of depression:

tan(20°) = opposite / 300

opposite = 300 * tan(20°)

Now we can add the two opposite sides we found to get the total height of the tower

height = opposite(elevation) + opposite(depression)

height = 300 * tan(21°) + 300 * tan(20°)

The angle should be converted to radians before using the tangent function, and the final answer should be rounded to 2 decimal places.

Step-by-step explanation:

Answer:

27/7

Step-by-step explanation:

First, note that 3 6/7 is a mixed number, also know as mixed fraction. It has a whole number and a proper fraction. The numbers in the mixed fraction are defined as follow:

3 = whole number

6 = numerator

7 = denominator

To convert mixed number 3 6/7 to improper fraction, you follow these steps:

Multiply the whole number by the denominator

3 × 7 = 21

Add the product from Step 1 to the numerator

21 + 6 = 27

Write answer from Step 2 over the denominator

27/7

The mixed number 3 6/7 converted to improper fraction is therefore :

27/7

Answer:

27/7

Step-by-step explanation:

Value of the expression 10z + 5w is 40.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.

For example, x + y is an expression, where x and y are terms having an addition operator in between.

Given expression

10z + 5w

z = 3

w = 2

Substituting value of z and w in the expression

10z + 5w = 10(3) + 5(2)

⇒ 10z + 5w = 30 + 10

⇒ 10z + 5w = 40

Hence, 40 is the value of the expression 10z + 5w.

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The cost of both the shirt and pants each is $10, solved using elimination method.

Let s stand for shirt and p for trousers.

Then we may solve the following equations:

1st Equation:

2s + 3p = 50

2nd Equation:

3s +1p = 40

Our initial aim is to determine the cost of one shirt. To get rid of the pants, we might artificially multiply the second equation by -3. This is what it would look like:

2s + 3p = 50

-3(3s +1p) = -3(40) (40)

———————————————

2s + 3p = 50

-9s - 3p = -120 We can obviously remove the pants (p) now.

—————————————

-7s = -70

Divide both sides by -7 to isolate s, and we get:

s = 10 -> As a result, one shirt costs $10.

Pants = 2(10) + 3p = 50

p = $10

Let us calculate the cost of 5 shirts.

As a result, we will perform 5 x $10 = $50.

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Complete question:

You buy 2 shirts and 3 pairs of pants for $50. Your friend buys 3 shirts and 1 pair of pants for $40. how much does the shirts cost?

The average of the numbers 11, 20, 13, and 16 is 15

The average may be calculated by dividing the total number of values by the sum of all the numbers. An average of the values in a sample of data may be used to determine a mean. In other words, the arithmetic mean is another name for an average. A mean is a term used to describe the average.

Finding an average helps us understand a general pattern of behavior or trend. For example, knowing Mrs. Mansell's average shopping expenditure helps us understand whether she typically spends a lot or little money, and knowing Keiran's average spelling score helps us understand how proficient he typically is.

In the above question:-

The average of the numbers 11, 20, 13, and 16  is

15

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Answer:

Step-by-step explanation:

The number of new jobs that would be created would be 1,120,000. This is calculated by multiplying the number of workers (16,000,000) by the projected job growth rate (7%) which equals 1,120,000.

The equivalent equation to Paolo's equation is,

w = Start Fraction uppercase P minus 2l Over 2 End Fraction.

What is algebraic operation?

A basic algebraic operation in mathematics is any of the common arithmetic operations, such as addition, subtraction, multiplication, division, raising to a whole number power, and taking roots (fractional power).

Multiplication and division tasks should be completed first from left to right, followed by addition and subtraction tasks from left to right.

Given:

uppercase P = 2 (l + w)

Simplifying this,

uppercase P = 2l + 2w

Subtract 2l from both sides,

uppercase P - 2l = 2l  + 2w - 2l

uppercase P - 2l = 2w

Divide both sides by 2,

(uppercase P - 2l) / 2 = 2w / 2

(uppercase P - 2l) / 2 = w

Hence, the equivalent equation to Paolo's equation is,

w = Start Fraction uppercase P minus 2l Over 2 End Fraction.

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