After evaluation, the resultant value of the function f(2009) is 1.9021.
What are functions?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.
The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Any input for x results in a single output for y.
Considering that x is the input value, we would state that y is a function of x.
So, evaluate f(2009) as follows:
Given that f(x) is a function with all positive real numbers satisfying the requirement that f(x) > 0 and for all x > 0 and also:
[tex]\begin{aligned}&f(x-y)=\sqrt{f(x y)+1} \\&x > 0, y > 0 \\&\text { for, } x=1, \text { and } y=\frac{1}{2} \\&f\left(1-\frac{1}{2}\right)=\sqrt{f\left(1 \times \frac{1}{2}\right)+1} \\&f\left(\frac{1}{2}\right)^2=f\left(\frac{1}{2}\right)+1 \\&f\left(\frac{1}{2}\right)=\frac{1+\sqrt{5}}{2}\end{aligned}[/tex]
Now, consider: x = 2009 and y = 0
[tex]\begin{aligned}&f(2009-0)=\sqrt{f(2009 * 0)+1} \\&f(2009)=\sqrt{f(0)+1} \\&f(2009)=\sqrt{f\left(\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}\right)+1} \\&f(2009)=\sqrt{\sqrt{f\left(\frac{1}{\sqrt{2}} * \frac{1}{\sqrt{2}}\right)+1}+1} \\&f(2009)=\sqrt{\sqrt{f\left(\frac{1}{2}\right)+1}+1} \\&f(2009)=\sqrt{\sqrt{\frac{1+\sqrt{5}}{2}+1}+1} \\&f(2009)=\sqrt{\sqrt{\frac{3+\sqrt{5}}{2}}+1} \\&f(2009)=\sqrt{\sqrt{5.2362}+1} \\&=\sqrt{3.6180} \\&=1.9021\end{aligned}[/tex]
Therefore, after evaluation, the resultant value of the function f(2009) is 1.9021.
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The sampling distribution for a goodness of fit test is the a. Poisson distribution b. t distribution c. normal distribution d. chi-square distribution
The sampling distribution for a goodness of fit test is the
d. chi-square distributionWhat is chi-square distribution?A continuous distribution with degrees of freedom is a chi-square distribution. It is used to describe how a sum of squared random variables is distributed.
When comparing categorical variables from a random sample, the statistical test known as chi-square is used to assess the degree of fit between the predicted and actual results.
We can therefore conclude that chi-square distribution is the sampling distribution for a goodness of fit test
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(A) Prove that the opposite sides of the rectangle are congruent.
Use Distance Formula: v(x2 - x1)^2 + (y2 - y1)^2
(B) Prove the diagonals of your rectangle are congruent.
(C) Using the slopes for each side, prove there are 4 right angles on the rectangle.
**Please Show All Work**
A. Using the distance formula, we can state that the opposite sides are congruent because AD = BC = √10 units and AB = CD = √40 units.
B. The diagonals are equal, AC = BD = √50 units.
C. Based on the slopes of each side, there are 4 right angles on the rectangle.
What is the Distance Formula?The distance formula is used to find the distance that exist between tow points that are on a coordinate plane. The formula is: d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
What is the Slope of a Line?
Slope = change in y / change in x.
A. The coordinates of each of the vertices of the rectangle are:
A(1, 2)
B(7, 4)
C(8, 1)
D(2, -1)
Use the distance formula to find AB, CD, BC, and AD.
AB = √[(7−1)² + (4−2)²]
AB = √40
CD = √[(2−8)² + (−1−1)²]
CD = √40
BC = √[(8−7)² + (1−4)²]
BC = √10
AD = √[(2−1)² + (−1−2)²]
AD = √10
Therefore, the opposite sides are congruent because AD = BC = √10 units and AB = CD = √40 units.
B. The diagonals are AC and BD. Find their lengths using the distance formula:
AC = √(8−1)² + (1−2)²]
AC = √50 units
BD = √[(2−7)² + (−1−4)²]
BD = √50 units
Therefore, the diagonals are equal, AC = BD = √50 units.
C. Find the slope of AB, CD, BC, and AD:
Slope of AB = change in y / change in x = rise/run = 2/6 = 1/3
Slope of CD = 2/6 = 1/3
Slope of BC = -3/1 = -3
Slope of AD = -3/1 = -3
-3 is the negative reciprocal to 1/3, this means that, if the two lines that meet at a corner have these two slope, then they will form a right angle because they are perpendicular to each other.
Therefore, there are 4 right angles on the rectangle.
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Colton sold a total of 28 t-shirts and sweatshirts as part of a fundraiser for his football team. If t-shirts cost $12 each and sweatshirts cost $20 each and he raised a total of $424, how many †-shirts did he sell?
i need points
Step-by-step explanation:
To determine how American college students feel about commuting, 100 students at a private university were randomly chosen by selecting 50 men and 50 women to participate. They were asked how far they commute each day (in minutes) to campus.
The results of this survey are unreliable primarily because of
voluntary response bias
sampling bias
the absence of a control group
response bias
None of the above
The key reason why this investigation's findings are erroneous is sampling bias. In statistics, sampling bias refers to a bias during which a sample is constructed in a way that makes some members of the intended population less likely than others to be included.
A private university's 100 students, 50 men, and 50 women were randomly chosen to participate in a study on how American college students felt about commuting. They were questioned about their daily commuting distance (in minutes) to college. The key reason why this investigation's findings are erroneous is sampling bias.
When certain individuals of a population are consistently more likely to be chosen in a sample than others, this is known as sampling bias. In the medical sciences, it is also known as ascertainment bias. Because sampling bias jeopardizes external validity, particularly population validity, it restricts the generalizability of findings.
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I WILL OPEN MY ALT AND ANSWER AND GIVE YOU A BRINLIST OPEN IF YOU SHOWED YOUR WORK!!! OPEN THE IMAGE
Answer:
x = 0
Step-by-step explanation:
1. Distribute
2. Add the numbers
3. Rearrange terms
4. Subtract 19 from both sides
5. Simplify
6. Add 5x to both sides
7. Simplify
8. Divide both sides by the same factor
9. Simplify
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Step-by-step explanation:
an airport escalator is designed to move 42 people, 75 kg each, upward at a constant speed of 0.6 m/s at 45o slope. determine the minimum power input needed to drive this escalator.
The minimum power input needed to drive this escalator is
15.59 kw.
What is escalator?
A moving staircase that transports people between floors of a building or other structure is called an escalator. It is made up of a motor-driven chain of separately linked steps on a track that rotates on two other tracks, keeping them horizontal.
Given:
[tex]N_p = 50\\m_p = 7.5 kg\\V = 0.6m/s\\[/tex]
θ = 45°
Total mass = 50 x 75 = 3750 kg
The energy required = Change in potential energy
ΔE = mg ΔZ
Power = ΔE/t = mg(ΔZ/t)
ΔZ/t = vsinθ = 0.6 sin(45°) = 0.4247
Power = mg x 0.4243 = 3750 x 9.8 / 100 x 0.4243
P = 15.59 kw
Hence, the minimum power input needed to drive this escalator is
15.59 kw.
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if you wish to test whether these data are sufficient to indicate that the mean for population 2 is larger than that for population 1, what are the appropriate null and alternative hypotheses? define any symbolys you see
at 0.1 level of significance, we can conclude that these data are sufficient to indicate that the mean for population 2 is larger than that for population 1.
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 10 - 1 = 9
The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (- 3.7 - 0)/(2.71/√10)
t = - 4.32
We would determine the probability value by using the t test calculator.
p = 0.00097
Since alpha, 0.1 > than the p value, 0.00097, then we would reject the null hypothesis. Therefore, at 0.1 level of significance, we can conclude that these data are sufficient to indicate that the mean for population 2 is larger than that for population 1.
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Model Real Life 212 students and
89 teachers are attending a leadership
conference. Each table can seat
16 people. Only one table does not
have 16 people seated. What fraction
of the table is full?
The fraction of table filled is 285/301 or in decimal as 0.946
What is FractionsFractions are expressed in mathematics as a number value that defines a part of a whole or group of objects. Fraction is a component or sector of a given quantity taken from the whole, which might be a number, a specified value, or an item.
In a given fraction, the value on the top is called the numerator, while the value on the bottom is known as the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.
In this question, we have to add the total number of attendees first
212 + 89 = 301
But each seat except 1 is filled by 16 people
Let's subtract 16 from the total number
301 - 16 = 285
The fraction of table filled is 285 ÷ 301 = 285/301 = 0.946
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Trapezoid WXYZ is isosceles. Angle WZY measures (8x – 3) and angle XYZ measures (7x + 2). Find the measure of angle WZY.
The measure of angle WZY of the Trapezoid WXYZ is; 37
How to find the angle of the trapezoid?
We are told that the Trapezoid WXYZ is isosceles. This means that there would be two angles that are equal.
Thus, we can see that Side WZ and XY are equal and as such, it means that Angle WZY is congruent to angle XYZ.
We are told Angle WZY measures (8x – 3) and angle XYZ measures (7x + 2). Thus;
(8x – 3) = (7x + 2)
8x - 7x = 2 + 3
x = 5
Thus;
Angle WZY = (8(5) – 3)
Angle WZY = 37°
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Which correctly shows how to use the gcf and the distributive property to find an expression equivalent to ?.
The correct option B. 9(5 + 8) ; is the equivalent expression to 45 + 72 using the GCF and the distributive property.
Explain the distributive property?The distributive property states that multiplying the sum of 2 or more operand by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.A mathematical statement made up of variables, constants, and mathematical operators is called an expression.
The formula is 45 + 72.
45 and 72 divided by one is three and nine.
The GCF is nine.
The largest number that evenly divides two or even more given numbers is known as the greatest common factor.
You can write the phrase as,
9 ( 5 + 8)
45 +72 = 9 ( 5 + 8)
Thus, the Distributive property was used to factor this.
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The correct question is-
Which correctly shows how to use the GCF and the distributive property to find an expression equivalent to 45 + 72?
A. 3(15 + 24)
B. 9(5 + 8)
C. (5)(9) + (2)(36)
D. (3)(15) + (8)(9)
maya drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took hours. when maya drove home, there was no traffic and the trip only took hours. if her average rate was miles per hour faster on the trip home, how far away does maya live from the mountains? do not do any rounding.
Maya drove on the mountains for her trip. Due to traffic, her average rate of miles per hour was faster at the time of coming back to her home than going on her trip. Thus, The distance between where she lives and the mountains is
288 miles .
Let's consider that Maya live x miles from the mountains.
Let her rate to mountains be y miles/h.
we have given that
Driveing time taken by Maya going from home to trip location= 9 hours due to traffic
total return time taken by her = 4 hours
average rate = 40 miles/hour
Using rate formula,
Rate = distance/time
=> distance (d) = rate (r) × time (t)
so, x/y = 9
=> x=9y --(1)
Return trip 4 hours then rate = y+40
=> x/(y+40) =4 --(2)
using Substitution method, x= 3 substitute in (2)
=> 9y/(y+40)=4
=> 9y=4y+160
=> 9y-4y=160
=> 5y=160
=> y= 160/5
=> y=32
Now, x=9y
x=9×32= 288 miles
Hence, distance to the mountain is 288 miles.
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Complete question:
Maria drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 9 hours. When Maria drove home, there was no traffic and the trip only took 4 hours. If her average rate was 40 miles per hour faster on the trip home, how far away does Maria live from the mountains?
Do not do any rounding.
Mr. William thi $40 a month for 7 gallon of water Mr. William pay $40 a month for city water, no matter how many gallon or water he ue in a given month. Let x repreent the number of gallon of water ued per month. Let y repreent the monthly cot of the city water in dollar. What i the equation of the line that repreent thi information? What i the lope of the line? ued in the number of gallon of water ued per month
Answer: y = 40, slope is 0, the line is horizontal
Step-by-step explanation:
find the margin of error of a poll, assuming 95% confidence, a population proportion of 0.360, and sample size n
False, the margin of error of a poll, assuming 95% confidence's measure of an estimate's accuracy.
A measure of an estimate's accuracy that also accounts for the variability of the sampling technique used to produce the estimate is the margin of error of a confidence interval. It doesn't directly take into account sample process bias.
Bias is the term for deliberate mistakes made during the planning or execution of a study that produce outcomes that are not accurate representations of the real population under investigation. Although it is not a precise indicator of bias, bias can have an impact on the margin of error if it causes the sampling technique to be more variable.
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Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
25:5
Answer:
5
Step-by-step explanation:
25/5 = 5/1 = 5
Tim has 1 1/4 kilograms of raisins. He uses 1/6 of the raisins in his trail mix. How many kilograms of raisins did Tim use?
Tim will use 5/24 kilograms of raisins in his trail mix.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Tim has 1(¹/₄) kilogram of raisins. He uses 1/6 of the raisins in his trail mix.
The weight of the raisins will be calculated as,
Weight = 1(¹/₄) x 1 / 6
Weight = ( 5 / 4 ) x ( 1 / 6 )
Weight = 5 / 24 kg
Therefore, Tim will use 5/24 kilograms of raisins in his trail mix.
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Multiply (4m - 9)(3m - 11) using tabular/grid method or foil method or distributive property
Answer:
[tex]12m^2-71m+99[/tex]
Step-by-step explanation:
I will use distributive property
(4m-9)(3m-11)
4m(3m)+4m(-11)-9(3m)-9(-11)
12m^2-44m-27m+99
Combine like terms
12m^2-71m+99
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In tryouts for the olympics, a speed skater had times of 44. 64, 43. 45, 42. 79, and 42. 28 seconds. Find the average time. (hint: add the numbers and divide by 4. ).
The average time of the Olympic speedskated is 43.29 units.
What do we mean by average?An average, which is frequently the sum of the numbers divided by the total number of the numbers in the group, is a single number that is selected to describe a group of numbers in simple English.
For example, the average of the numbers 2, 3, 4, 7, and 9 is 5.
The four sorts of averages that we recognize are mean, mode, median, and range.
Although the others are our most popular "measures of central tendency," range is actually a measure of spread or distribution.
So, the average time is calculated as follows:
We have: Time: 44.64,43.45,42.79 and 42.28
The formula for average mean: ∑ₓ/n
Where ∑ₓ is the sum of observations and n is the number of observations.
Now, calculate the average time:
Average = 44.64+43.45+42.79+42.28/4
Average = 173.16/4
Average = 43.29
Therefore, the average time of the Olympic speedskated is 43.29 units.
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simplify (−4r5)(2r8)
Answer: -8r^13
Step-by-step explanation: We just need to take those numbers multiplied by each other. -4 timed 2 = -8. r^5 timed r^8 = r^13, we just add both because they have the same base and multiple a square is the same as adding them together.
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a business major needs 3 humanities courses to graduate. they can be selected from 29 courses offered. how many ways can the 3 courses be selected?
The number of ways 3 courses can be selected is 3654.
What are the Permutation and Combination?
Permutations and combinations are the various ways in which objects from a set can be selected to form subsets, generally without replacement. When the order of selection is a factor, this selection of subsets is called a permutation; when it is not, it is called a combination.
Total no. of courses available = 29
Courses needed to graduate = 3
No of ways these courses can be selected:
= ²⁹C₃
= 29!/ [(29-3)! - 3!]
= 29! / 26! 3!
= 29 * 28 * 27 * 26!/ 26! 3*2
= 29* 14* 9
= 3654
So, the number of ways 3 courses can be selected is 3654.
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the angle θ is 7.2 degrees, and the circle arc s is 800 km. knowing that there are 360 degrees in a full circle what is the circumference of the surface of the earth? round to the closest 10,000 km. please explain how you came about your final solution.
The earth is 40000 kilometers around. There is no need to round off because the circumference already contains significant figures.
How do I calculate a circle's circumference?
A circle's diameter is multiplied by to determine its circumference (pi). You can also determine the circumference by multiplying 2radius by pi (=3.14).
Given: theta angle (central) = 7.2°; arc length S = 800 km
This indicates that an 800 km long arc is extending a circle with a 7.2° center angle ( earth in this case).
By definition, "An arc's length is a portion of a circle's diameter."
Therefore, we must first establish what percentage of the circle the specified arc length represents.
360° is a complete circle.
Thus, the fraction equals 7.2°/360°, or 1/50.
As a result, the stated arc length (800km) with a 7.2° central angle is 1/50th of the entire circle.
Thus, the whole circumference is 800 x 50, or 40000 km.
Alternately, you can calculate circumference using the formula below:
360° center angle x arc length as the circumference (theta)
Values substituted: circumference 800 = 360° 7.2°
circumference = 360°, 800°, and 7.2°, or 40000 kilometers
Therefore, the earth is 40000 kilometers around. There is no need to round off because the circumference already contains significant figures.
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30 points Please get it Right lol
Graph the piecewise function.
Answer:
see attached
Step-by-step explanation:
You want a graph of the piecewise function ...
[tex]f(x)=\begin{cases}x&\text{if $x\le -1$}\\-3x+2&\text{if $-1 < x < 4$}\\4&\text{if $x\ge 4$}\end{cases}[/tex]
GraphThe graph is attached.
For x ≤ -1, the graph is a line with slope 1. If it were allowed to continue, it would pass through the origin. It terminates in a closed dot at (-1, -1)
For -1 < x < 4, the graph is a line with slope -3 through point (0, 2) on the y-axis. It has open circles at both ends, at points (-1, 5) and (4, -10).
For x ≥ 4, the line is horizontal at y=4. It has a closed dot at (4, 4).
__
Additional comment
The dot at the end of an interval is closed if the "or equal to" case is included (≤ or ≥). If it is not (< or >), then the dot is an open circle.
The slope is the ratio of "rise" to "run". It is the number of grid squares the line moves up (+) or down (-) for each grid square to the right.
two times a number is divided by 3 more than the number. if the result is 7, then what was the original number?
The original number is -21/5 or -4.2 which is divided by 3 more than the number.
What is an equation?In mathematics, an equation is a statement or formula which shows two expressions having equal value and connected by an equal sign. The two expressions consist of variables and/or numbers.
For solving the question we have to form an equation.Let the number be 'x' Two times the number = 2x3 more than the number = x + 3
According to the question,two times a number is divided by 3 more than the number is equal to 7 which means 2x / (x+3) = 7
By applying cross multiplication,2x = 7 × ( x+3)2x
= 7x + 7×32x
= 7x + 212x - 7x
= 21-5x = 21x = 21/ (-5)x
= -4.2
Hence the original number is -4.2
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243 divided by 15 and I need to show my work
Answer:
16.2
Step-by-step explanation:
use long division so:
Use the fact that the trigonometric functions are periodic to find the exact value of the given expression. Do not use a calculator.
sec.(25π/4)
Subtract full rotations of 2π until the angle is greater than or equal to 0 and less than 2π
sec(π4) – trigonometry value
The exact value of trigonometry - sec(π4) is 2√2.
Multiply 2√2 by √2.
2⋅√2⋅2
Combine and simplify the denominator.
2√2
Cancel the common factor of 2.
√2
There are various ways to display the outcome.
Exact Form:
√2
Decimal Form:
1.41421356…
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For the function ƒ(x) = 5 (x³ – 6), find ƒ−¹(x).
○ ƒ˜¹(x) = (²16) ³
○ f−¹(x) = 2³+6
○ ƒ˜¹(x) = ( ² + 6) ³
○ ƒ−¹(x) = (x+6)³
5
Submit Answer
Guide
A chemist mixes Chemical A and Chemical B to make a solution. She uses the same ratio of chemicals for each batch she
makes.
Drag numbers to complete the table.
?
4
6
12
Chemical A (ML) Chemical B (mL)
3
36
48
84
36
96
108
132
168
7
9
When chemist mixes Chemical A and Chemical B to make a solution
Part A
When the quantity of chemical B = 48 ml, then the quantity of chemical A = 4 ml
Part B
When the quantity of chemical A = 9 ml, then the quantity of chemical B = 108 ml
A chemist mixes Chemical A and Chemical B to make a solution
She uses the same ratio of chemicals for each batch
The solution A and B are in linear relationship
y = kx
Where y is the quantity of chemical A
x is the quantity of chemical B
k is the constant
Substitute the values in the table and find k
36 = k × 3
k = 36 /3
k = 12
Part A
When chemical B = 48 ml
48 = 12 × x
x = 48 / 12
x = 4 ml
Part B
When chemical A = 9 ml
y = 12 × 9
y = 108 ml
Therefore, when Chemical B = 48 ml, chemical B is 4ml . When chemical A = 9 ml, Chemical B = 108 ml
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2. consider the trapezoid in the previous problem. locate the center of mass of the trapezoid. remember to again break the trapezoid into horizontal or vertical strips.
Calculations in mechanics involving masses dispersed in space, such as the linear and angular momentum, benefit from using the centre of mass as a reference point.
The centre of mass of the trapezoid can be found by breaking it into two trapezoids and finding the centre of mass of each. The centre of mass of the first trapezoid is located at (3, 5). The centre of mass of the second trapezoid is located at (9, 5). Therefore, the centre of mass of the trapezoid is located at (6, 5).
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find the perimeter of the window to the nearest hundredth
The perimeter of the window to the nearest hundredth will be;
⇒ 102.8 cm
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The shape of window is semicircle.
And, The radius of window (r) = 20 cm
Now,
We know that;
The perimeter of semicircle = πr + 2r
Here, The radius of window (r) = 20 cm
So, We get;
The perimeter of the window = πr + 2r
= 3.14 x 20 + 2 x 20
= 62.8 + 40
= 102.8 cm
Thus, The perimeter of the window to the nearest hundredth will be;
⇒ 102.8 cm
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One week, magan earned $162. 00 at his job when he worked for 9 hours. If he is paid the same hourly wage, how much would he make the next week if he worked 19 hours?.
Answer: $342
Step-by-step explanation:
We take 162.00 divided by 9 = $18 / h
To find the salary of 19 hours we just need to take 18 times 19 = $342
What is the slope of the line in this graph?
Answer:
it is b 5/7
Step-by-step explanation:
bc you rise 5 and run 7
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