Answers
Considering that a fraction is not defined when the denominator is zero, the equation is not defined for an angle of 90º.
When is a fraction not defined?A fraction is not defined when the denominator is zero.
In this problem, the expression is given by:
cos(θ)/(1 - sin(θ)) + cos(θ)/(1 + sin(θ)) = 4.
The denominators are zero in two cases:
1 - sin(θ) = 0 -> sin(θ) = 1 -> θ = 90º.1 + sin(θ) = 0 -> sin(θ) = -1 -> θ = 270º.Hence the equation is not defined for an angle of 90º.
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Related Questions
Can someone help please?
Answers
[tex]r = \frac{15}{7} [/tex]
This pattern follows the rule add 14. What other features do you observe?
13, 27, 41, 55
please help meeeeee
Answers
The above pattern follows an arithmetic sequence with a common difference of 14 and first term of 13
How to solve a pattern?The pattern can be represented as follows:
13, 27, 41, 55
The first term of the sequence is 13 and the common difference is 14.
The above pattern is an arithmetic sequence.
Therefore, the following can be used to find the nth term.
nth term = a + (n - 1)d
where
n = number of termd = common differencea = first termTherefore,
a = 13
d = 27 - 13 = 14
Let's find the next term
5th term = 13 + (5 - 1)14
5th term = 13 +(4)14
5th term = 13 + 56
5th term = 69
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N1=731pˆ1=0. 33 n2=644pˆ2=0. 28 use this data to find the 90onfidence interval for the true difference between the population proportions
Answers
The 90% confidence interval for the true difference between the population proportions is [ - 0.0908, - 0.0092]
Given,
[tex]N_{1}[/tex] = 731
[tex]N_{2}[/tex] = 644
[tex]P_{1}[/tex] = 0.33
[tex]P_{2}[/tex] = 0.28
z score for 90% confidence interval = 1.645
Here, the confidence interval formula :
( [tex]P_{1} -P_{2}[/tex]) ± z [tex]\sqrt{\frac{P_{1}(1-P_{1}) }{N_{1} }+ \frac{P_{2}(1-P_{2}) }{N_{2} } }[/tex]
Substituting the values, we get
(0.33 - 0.28) ± 1.645 [tex]\sqrt{\frac{0.33(1-0.33)}{731}+\frac{0.28(1-0.28)}{644} }[/tex]
= 0.05 ± 1.645 [tex]\sqrt{0.0003024624+0.0003130435}[/tex]
= 0.05 ± 1.645 [tex]\sqrt{0.0006155059}[/tex]
= 0.05 ± 1.645 × 0.0248093914
= 0. 05 ± 0.0408114489
Confidence interval:
- 0.05 - 0.0408114489 = - 0.0908114489 ≈ - 0.0908
- 0.05 + 0.0408114489 = - 0.0091885511 ≈ - 0.0092
The confidence interval for the true difference between the population proportions is [ - 0.0908, - 0.0092]
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Use method of subtitution, will give brainliest, 20 pts
Answers
Answer:
x=3
y = -2
Step-by-step explanation:
2x+5y = -4
y = x-5
We want to use substitution
In the first equation, every time we see y, substitute x-5
2x + 5( x-5) = -4
Distribute
2x + 5x -25 = -4
Combine like terms
7x -25 = -4
Add 25 to each side
7x -25+25 = -5+25
7x = 21
Divide each side by 7
7x/7 = 21/7
x=3
Now we can find y
y = x-5
y = 3-5
y = -2
The answer is x = 3, y = -2 or (3, -2).
We are given that :
2x + 5y = -4y = x - 5Let us substitute the 2nd equation's value of y in the 1st equation.
2x + 5(x - 5) = -42x + 5x - 25 = -47x = 21x = 3Now, substitute for x in the 2nd equation.
y = 3 - 5y = -2determine the quotient of 2/3 divided by 4/5
Answers
explanation:
Given the function w(x) = 9x + 8, evaluate w(5). Explain all steps.
Answers
The value of the function w(5) is 53
How to evaluate the function?The function is given as:
w(x) = 9x + 8
The expression w(5) implies that the value of x is 5
i.e. x = 5
Substitute the known values in the above equation
w(5) = 9 * 5 + 8
Evaluate the product
w(5) = 45 + 8
Evaluate the sum
w(5) = 53
Hence, the value of the function w(5) is 53
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In the Kite Club, there are a total of 21 kids. There are 3 more girls than boys. Write two equations and graph to find the number of girls in the club.
A. 9 girls
B. 10 girls
C. 11 girls
D. 12 girls
I need help thank you.
Answers
5 yd
5 yd
8 yd
5 yd
14 yd
3 yd
9 yd
6 yd
Pleasee help rn
Answers
An airport parking lot charges a basic fee of $2 plus $1 per half-hour parked. what is the total charge from parking in the lot for 72 hours? a. $144 b. $146 c. $74 d. $72 please select the best answer from the choices provided a b c d
Answers
Using a linear function, the total charge from parking in the lot for 72 hours is of:
b. $146.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Both the basic fee, which is the y-intercept, and the hourly fee, which is the slope, are of $2, hence the cost of parking x hours is given by:
C(x) = 2x + 2
Hence the cost for parking 72 hours is:
C(72) = 2 x 72 + 2 = 2 x 73 = $146.
Which means that option b is correct.
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For this item, a non-integer answer should be entered as a fraction using / as the fraction bar.
Simplify the numerical expression.
The expression has a value equal to
Answers
The numerical expression, 2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3 = 67/24 on simplification using the BODMAS rule.
In the question, we are asked to simplify the numerical expression:
2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3.
To simplify the expression, we will follow the BODMAS rule, where B means Brackets, O means Of, D means Divide, M means Multiplication, A means Addition, and S means Subtraction.
2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3
= 2/3 ÷ 16 + (3/4 + 1/6) ÷ 1/3 {Solving 2⁴ = 16, before proceeding BODMAS}.
= 2/3 ÷ 16 + ((9+2)/12) ÷ 1/3 {Solving Brackets by taking LCM}
= 2/3 ÷ 16 + 11/12 ÷ 1/3 {Simplifying}
= 2/3 * 1/16 + 11/12 * 3/1 {Solving divisions by taking reciprocals}
= 1/24 + 11/4 {Multiplying}
= (1 + 66)/24 {Adding using LCM}
= 67/24 {Simplifying}.
Thus, the numerical expression, 2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3 = 67/24 on simplification using the BODMAS rule.
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The provided question is incomplete. The complete question is:
"Type the correct answer in the box. Use numerals instead of words. For this item, a non-integer answer should be entered as a fraction using / as the fraction bar.
Simplify the numerical expression.
2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3
The expression has a value equal to."
Is the following number rational or irrational [tex]Is the following number rational or irrational \sqrt{45\\}[/tex]
Answers
A rational number includes any number that can be expressed as a whole integer; a fraction, a simple full number, and any form of a full number that isn’t a portion of a number. Because the square root of 45 is equal to more than 6 but less than 7, it is represented by a decimal. That decimal that represents it is 6 whole + a portion of another whole, meaning that the square root is not a perfect square. Imperfect squares, or numbers that can be divided to get only one number (such as 36 = 6 x 6), are irrational. Because 45 cannot be divided by a number to get that same quotient of the number being divided by, it is irrational. If you need any help, let me know and I will gladly assist you.
Determine whether the sequence converges or diverges. if it converges, find the limit. (if an answer does not exist, enter dne. ) an = n2 n3 5n
Answers
The sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex] diverges.
For given question,
We have been given a sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex]
We need to determine whether the sequence converges or diverges.
From given sequence we have, [tex]a_{n+1}=\frac{(n+1)^2}{(n+1)^3+5(n+1)}[/tex]
We use Ratio Test.
According to Ratio Test, [tex]r=\frac{a_{n+1}}{a_n}[/tex], where sequence converges if and only if |r| < 1.
Consider,
[tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |\\\\= \lim_{n \to \infty} |\frac{\frac{(n+1)^2}{(n+1)^3+5(n+1)}}{\frac{n^2}{n^3+5n}} |\\\\\\= \lim_{n \to \infty} |\frac{(n+1)^2(n^3+5n)}{n^2[(n+1)^3+5(n+1)]} |\\\\=\infty[/tex]
Since [tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |[/tex] is not defined, the sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex] diverges.
Therefore, the sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex] diverges.
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If the 6am temperature in Durango, Colorado was -8° F and the temperature rose 15° by 2pm, then what would the temperature be at 2pm?
Answers
-8° + 15° = temperature at 2pm
• When adding a positive to a negative, we are subtracting the numbers and taking the sign of the greater number. The equation is represented as so:
(-) + (+) = (+)
The general rule corresponding to this equation is that the answer acquires the sign of the greater number. In this case, because 15 is greater than 8, our answer will be a positive number.
-8 + 15 = 7
From 6am to 2pm, the temperature would have risen from -8° Fahrenheit to 7° Fahrenheit. If you need any extra help, let me know and I will gladly assist you.
Can anyone tell me how you could describe this answer to the equation?
[tex]f(x)=\frac{5x}{x-25}[/tex]
Answers
The end behavior of the given polynomial is that as x → -∞ or x → ∞, then, f(x) → 5
What is the end behavior of the Polynomial?We are given the polynomial;
f(x) = 5x/(x - 25)
Now, we want to find the limits as x → ±∞. Let us rearrange the given polynomial to get; f(x) = 5/(1 - (25/x))
Thus, applying limits we have;'
lim x → ±∞ [5/(1 - (25/x))]
From algebraic limit laws we know that;
If f(x) = k, then;
lim x → +∞ [f(x)] = k
Also, lim x → -∞ [f(x)] = k
Thus, applying limits at infinity to our polynomial gives;
lim x → ±∞ [5/(1 - (25/x))] = 5/(1 - 0) = 5
This is because lim x → ∞ for 1/x is 0.
Thus, f(x) has horizontal asymptotes at y = 5
Thus, we conclude that the end behavior is that as x → -∞ or x → ∞, then, f(x) → 5
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Which function is the inverse of f(x) = 2x + 3?
05²¹(x) = -1/2 x 1/2
s^²(x) = { x = 1/
2
O f¹(x) = -2x + 3
O f¹(x)=2x+3
Answers
Answer: Option 2
Step-by-step explanation:
Let f(y)=x.
[tex]x=2y+3\\\\x-3=2y\\\\y=\frac{1}{2}x-\frac{3}{2}\\\\f^{-1}(x)=\frac{1}{2}x-\frac{3}{2}[/tex]
The inverse of the function is,
⇒ f ⁻¹(x) = 1/2 (x - 3)
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
⇒ f (x) = 2x + 3
Now,
We can find the inverse of function as;
⇒ f (x) = 2x + 3
Put y = f (x);
⇒ y = 2x + 3
Solve for x;
⇒ y - 3 = 2x
⇒ x = 1/2 (y - 3)
⇒ f ⁻¹(x) = 1/2 (x - 3)
Thus, The inverse of the function is,
⇒ f ⁻¹(x) = 1/2 (x - 3)
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What is the period of y=−5 cos( 8 π x)+3? Give an exact value. units PLEASE MAKE IT QUICK
Answers
Answer:
Maximum/Minimum Value: (0,−2) is a local minima (1/8,8) is a local maxima
Explanation: Use the derivative to find the maximum and minimum
Answer:
Period = ¹/₄
Step-by-step explanation:
The cosine function is periodic, meaning it repeats forever.
Standard form of a cosine function:
f(x) = A cos(B(x + C)) + D
where:
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shiftGiven function:
[tex]y=-5 \cos (8 \pi x)+3[/tex]
Comparing the given function with the standard form:
A = 5B = 8πC = 0D = 3[tex]\implies \sf Period=\dfrac{2 \pi}{B}=\dfrac{2 \pi}{8 \pi}=\dfrac{1}{4}[/tex]
Therefore, the period of the given function is ¹/₄.
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1. Tanya determined that the dimensions of a painted barn quilt needed to be 1 1/3 ft by 2 1/4 ft. What will be the area of the barn quilt?
2. Mrs. Smith oatmeal cookie recipe calls for 2/5 of a cup of sugar. How much sugar would she need to make 1/2 of a batch of cookies?
3. At the park, 6 boys are practicing throwing, catching, andhitting a baseball. Of those 6 boys, 2/3 of them are working on hitting. How many boys are practicing hitting the ball.
4. Rachel works at a lemonade stand at the park. On Monday she used 1 2/5 bags of lemons. On tuesday she used 1 1/4 times as many lemons as on Monday. How many bags of lemons did Rachel use on Tuesday?
Answers
The area of the barn quilt is 3 sq.ft.
The amount of sugar needed to make 1/2 of a batch of cookies is 1/5 of a cup.
Number of boys are practicing hitting the ball = 4
Number of bags of lemons used by Rachel on Tuesday = 1[tex]\frac{3}{4}[/tex]
1. A painted barn blanket needed to be 1 1/3 feet by 2 1/4 feet in size.
Area of the barn quilt = 1 1/3*2 1/4
= 4/3*9/4
= 3 sq. ft.
2. The recipe for Mrs. Smith's oatmeal cookies asks for 2/5 cups of sugar.
Sugar needed for making 1/2 of a batch of cookies = 1/2*2/5
= 1/5 of a cup
3. Six boys are practicing baseball throwing, catching, and hitting in the park. Two thirds of those six youngsters are practicing hitting.
Number of boys practicing hitting the ball = 6*2/3 = 4
4. At the park's lemonade kiosk, Rachel works. She used 1 and 2/5 bags of lemons on Monday. She used 1 and 1/4 times as many lemons on Tuesday as she did on Monday.
Number of bags of lemon used on Tuesday = 7/5*5/4
= 7/4
= 1 and 3/4 bags
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What is the sum of the geometric sequence -3, 18, -108,
if there are 8 terms?
Answers
Step-by-step explanation:
using gp formula
tn=ar^n-1
which our a which is the first term is = -3
our r which is t2/t1=-6
t8=(-3)(-6)^8-1
=(-3)(-6)^7
=(-3)(-279936)
=839808
27. Write down the co-ordinates of the points where the line y = 4x - 3 cuts the x-axis
Answers
Step-by-step explanation:
it is a line, so that is 1 point, where it cuts the x-axis.
in general that means y = 0.
so,
0 = 4x - 3
4x = 3
x = 3/4
the point, where the line cuts the x-axis is
(3/4, 0)
What is the surface area of a rectangular prism that has a length of 12 mm, a width of 15 mm, and a height of 16 mm?
Answers
Mark me brainliest
Jeri finds a pile of money with at least $\$200$. If she puts $\$80$ of the pile in her left pocket, gives away $\frac{1}{3}$ of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away $\$200$ of the original pile and kept the rest. What are the possible values of the number of dollars in the original pile of money? (Give your answer as an interval.)
Answers
Based on the amount of money that Jerl had and then the amount that she put away, the possible values of the number of dollars in the original pile of money was ( 200, 440).
What was the amount in the original pile?The amount that was above $200 that she found can be x which means that the greater side of the inequality is:
= 200 + x
She then gave away $80:
= 120 + x
She gave away 1/3 of the money so the amount left is:
= 2/3 x (120 + x)
The lesser side of the inequality:
(x + 2) - 200 = x
So then:
((120 + x) x 2) / 3 > x
240 + 2x > 3x
240 > x
x < 240
The interval that shows the possible values of the original pile of money is therefore:
( 200, 440)
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The time allotted for the Math test for 2 3/4 hours. Emma completed the test 1/2 of an hour earlier. How long did it take Emma to complete the test?
Answers
1/2h=0.5h
2.75h-0.5h=2.25
2.25h=2 1/4h
Or
1/2h•2=2/4h
2 3/4h-2/4h=2 1/4h
It took Emma 2 1/4 hours to complete the test.
Identify the area of the figure rounded to the nearest tenth.
Please give an Explanation :)
Answers
Answer:
67.5 cm²
Step-by-step explanation:
The figure can be decomposed into figures whose area formulas you know.
DecompositionAs the attached figure shows, one way to decompose the figure is by extending the horizontal line. This divides the figure into an upper trapezoid and a lower rectangle.
TrapezoidThe area of a trapezoid is given by the formula ...
A = 1/2(b1 +b2)h
where b1 and b2 are the parallel bases, and h is the height.
The bases of the trapezoid in this figure are 6 and 3 cm, and the height is 5 cm. Its area is ...
A = 1/2(6 cm +3 cm)(5 cm) = 22.5 cm²
RectangleThe area of a rectangle is given by the formula ...
A = LW
where L and W represent the length and width, respectively.
The dimensions of the rectangle in this figure are 15 cm long by 3 cm wide. Its area is ...
A = (15 cm)(3 cm) = 45 cm²
Total areaThe total area of the figure is the sum of the areas of the trapezoid and rectangle:
A = (22.5 cm²) + (45 cm²) = 67.5 cm²
The are of the figure is 67.5 cm².
A shop is having a 10% off sale. Find the sale price of a cap which normally costs $12?
Answers
Answer: $10.8
Step-by-step explanation: To do this, we need to find 90% of $12 because the cap is 10% off. We can do this by multiplying 12 by 0.9. 12 x0.9 = 10.8.
A cell phone company wants to determine the average amount of data that their smart phone customers use each month. which group would best represent a sample of the population?
Answers
The group that would best represent a sample of the study population is: C: one thousand of their customers with a current smart phone data plan.
What is a Representative Sample of a Population?A sample that best represents a population under study is a sample that is a subset of the entire population, that is, research subjects that are drawn as samples should reflect the general characteristics of the entire population without leaving out any part of the population. Also, a good sample should enable a researcher make generalization.
A sample that is a subset of a population and reflects the characteristics of the general population would not be biased.
Given the situation above, the population of the study are smart phone customers that use dat in the cell phone company. So, a sample that would better represent this general population would be customers that currently have a smart phone plan, since the average amount of data they use is what the cell pone company wants to ascertain.
Therefore, the group that would best represent a sample of the study population is: C: one thousand of their customers with a current smart phone data plan.
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Which of the following relationships will have a positive slope? Select all that apply.
Answers
Reason
Number of people and amount of trash = more people equals more trash so the slope will go up.
Distance to your destination and time = further distance traveled will show an increase in time so an upward slope.
Number of squirrels and number of acorns hidden. The more squirrels there are, the more acorns will be hidden showing an upward slope.
The other two have no relationship to each other.
Samantha and mia each left julia’s house at the same time. mia walked north at 7 kilometers per hour. samantha ran west at 11 kilometers per hour. how far apart were they after one hour? round the answer to the nearest tenth. a right triangle. a point at the angle with measure 90 degrees is labeled julia's house. a line drawn north is labeled 7 kilometers and a line drawn west is labeled 11 kilometers.
Answers
Samantha and Mia are 13 km apart from each other.
What is Pythagorean ?A right triangle's squared sides add up to the hypotenuse's squared length, according to the Pythagorean Theorem.
Mia is 7 kilometers north of Julia's home as she walked at a speed of 7 kilometers per hour.
Samantha walked at an average speed of 11 km/h, and she is now 11 kilometers west of Julia's home.
A right-angled triangle is formed by Julia's house, Mia and Samantha's locations after one hour, and the figure's points.
Hypotenuse of the triangle, which measures distance between the females
the Pythagorean theorem,
H² = P² + B²
H² = 7² + 11²
H² = 49 + 121
H = √170
H = 13.038
H = 13km
Between them, there is a 13 kilometer distance.
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On the day after my birthday this year, I can truthfully say: "The day after tomorrow is Monday". On which day is my birthday?
Answers
Answer: Friday
Step-by-step explanation:
the weights of cars passing over a bridge have a mean of 3550 pounds and standard deviation of 870 pounds. assume that the weights of the cars passing over the bridge are normally distributed. use a calculator to find the approximate probability that the weight of a randomly selected car passing over a bridge is between 2800 and 4500
Answers
Answer:
Using the usual notations and formulas,
Using the usual notations and formulas,mean, mu = 3550
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculate
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000=P(X < 3000) = 0.2636 (to 4 decimals)
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000=P(X < 3000) = 0.2636 (to 4 decimals)Probability that a car randomly selected is greater than 3000
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000=P(X < 3000) = 0.2636 (to 4 decimals)Probability that a car randomly selected is greater than 3000=1 - P(X < 3000) = 1 - 0.2636 (to 4 decimals) =0.7364 (to 4 decimals)
Clark earns $31 per hour. Calculate his weekly wage if he works 38 hours per week.
Answers
Answer:
1178 because 31 dollars an hour for 38 hours you would multiply or times 31 and 38 and get 1178 for total money earned
