Mathematics College

Jim worked 40 regular hours last week, plus 8 overtime houts at the time and a half rate. His gross pay was $1,248.
a.) What was his hourly rate?
b.) What was his hourly overtime rate?

Answers

Answer 1

40 hours regular pay

8 hours at 1.5 = 8*1.5 = 12

40+12 = 52

1248/52 = 24

A) $24 per hour

B) 14*1.5 = $36 per hour for overtime

Answer 2
Answer:

a)  

           His hourly rate= $ 24

b)

         His hourly overtime rate= $ 36

Step-by-step explanation:

Jim worked 40 regular hours last week, plus 8 overtime hours at the time and a half rate.

This means if he is paid $ x per hour working in regular hours.

Then he will be paid $ (1.5x) per hour working overtime.

( Since it is given that: he is paid time and a half rate for overtime)

Now, his gross pay is: $ 1248

i.e.

Amount working at regular hours for 40 hours+ Amount obtained for working 8 hours overtime= $ 1248

i.e.

40x+8(1.5x)=1248

i.e.

40x+12x=1248

i.e.

52x=1248

i.e.

x=24

a)

Hence, his hourly rate is:$ 24

b)

His hourly overtime rate is: $ (24×1.5)

i.e.

His hourly overtime rate is:  $ 36

Related Questions

China's population is 1.446×10^9 . Marshall Islands's population is 6.025×10^4 . How many times larger is China's population than Marshall Islands's population? Drag and drop the values into the boxes to represent the answer in scientific notation.

Answers

(1.446×10^9) ÷ (6.025×10^4)
= 0.24 x 10^5
= 2.4 x 10^4

answer

2.4 x 10^4

China's population is 2.4 x 10^4 times larger than Marshall Islands's population.

How does scientific notations work?

The number is written in the form  [tex]a \times 10^b[/tex] where we have   [tex]1 \leq a < 10[/tex]. The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. Scientific notations have some of the profits as; Better readability due to compact representation. Its value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.

We have given that

China's population = 1.446 × [tex]10^9[/tex]. Marshall Islands's population is 6.025× [tex]10^4[/tex]).

Then ;

(1.446 × [tex]10^9[/tex]) ÷ (6.025 × [tex]10^4[/tex])

= 0.24 x 10 power of 5

= 2.4 x [tex]10^4[/tex]

Therefore, China's population is 2.4 x 10^4 times larger than Marshall Islands's population.

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your bakery is in a large shopping center. The entrie shopping center is 4,500 square feet. Your bakery takes up only 1/10 of that space.How many square feet is your bakery

Answers

So if the bakery is 1/10 of the shopping center's area, and the shopping center's area is 4500 feet, then the bakery's area is 1/10th of 4500 feet. 1/10th of 4500 feet is 450.

A more in-depth explanation:

A fraction is:
x/y
where y would equal how many parts you wanted to split a number into and x would equal how many parts you want to take.

So splitting 4500 into 10 parts and then taking one is basically 1/10 of 4500.

4500 in 10 parts, one would be 450.

The bakery takes up 1/10 of the total shopping center space. Since the shopping center is 4,500 square feet, the bakery is 450 square feet.

To determine the size of the bakery in square feet, we need to calculate 1/10th of the total shopping center's area. The shopping center is 4,500 square feet in total. So, the calculation would be:

Divide the total area by 10 to find 1/10 of the area.Multiply that number by 1 to get the exact area for the bakery.

Here's the step-by-step calculation:

4,500 square feet / 10 = 450 square feet

Therefore, the bakery takes up 450 square feet of space within the shopping center.

how much water will it take to simmer 1 3/4 quarts of barley using a water to barley ratio of 4 to 1

Answers

4 to 1 or 4:1, water to barley, simply means, the water will be 4 times as much as the barley.

well, convert the 1 and 3/4 from mixed to "improper" and check.

[tex]\bf \cfrac{water}{barley}\qquad 4:1\qquad\cfrac{4}{1}=\cfrac{\stackrel{water}{w}}{\stackrel{barley}{1\frac{3}{4}}}\implies \cfrac{4}{1}=\cfrac{w}{\frac{1\cdot 4+3}{4}}\implies \cfrac{4}{1}=\cfrac{w}{\stackrel{improper}{\frac{7}{4}}} \\\\\\ \cfrac{4}{1}=\cfrac{\quad \frac{w}{1}\quad }{\frac{7}{4}}\implies \cfrac{4}{1}=\cfrac{w}{1}\cdot \cfrac{4}{7}\implies 4=\cfrac{4w}{7}\implies 28=4w \\\\\\ \cfrac{28}{4}=w\implies 7=w[/tex]

Answer:

The water will be 4 times more as compared to the original.

Step-by-step explanation:

What is 9 (3 x 4)??????

Answers

if you are doing order of operations than it would be 108 but if you were doing distributive property it would be 27 x 36 which is 972 

HOPE THIS HELPS!!
Is 108 do what’s in parentheses first (3x4)=12 then you do 9x12 witch is 108. Hope this helps

A family has two cars. During one particular week, the first car consumed 30 gallons of gas and the second consumed 40 gallons of gas. The two cars drove a combined total of 1800 miles, and the sum of their fuel efficiencies was 50 miles per gallon. What were the fuel efficiencies of each of the cars that week?

Answers

Car 1 consumes 30 gallons of gas.Car 2 consumes 20 gallons of gas.

3/4g=-12 I need help solving this

Answers

That is the answer of ur problem
3/4g = -12
/3/4      /3/4
g = -16

Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.
A(n)=-6+(n-1)(6)
A. 0, 18, 54
B. –6, 18, 54
C. 6, 18, 54
D. –6, 12, 48

Answers

the firs term
A(1)=-6+(1-1)(6)
A(1)=-6+(0)(6)
A(1)=-6



The fourh term
A(n)=-6+(n-1)(6)
A(4)=-6+(4-1)(6)
A(4)=-6+(3)(6)
A(4)=-6+18
A(4)=12


The tenth term
A(10)=-6+(10-1)(6)
A(10)=-6+(9)(6)
A(10)=-6+54
A(10)=48

Answer: 
D.  -6,12,48

replace n with 1, 4 and 10 and solve the equations:

 answers would be D. –6, 12, 48


-6+(1-1)*6 = -6

-6+(4-1)*6 = 12

-6+(10-1)*6 = 48

The temperature is changing every day by negative 7 over 18 degrees Fahrenheit. What will be the change in the temperature after 3 days? 21 over 6 degrees Fahrenheit negative 21 over 6 degrees Fahrenheit negative 7 over 6 degrees Fahrenheit 7 over 6 degrees Fahrenh

Answers

negative 7 or 6 degrees

-7

6

taking teeeeesststt not sure id corryect

A local gym offers a trial membership for 3 months. It discounts the regular monthly fee x by $25. If the total cost of the trial membership is less than $100, you will consder signing up. What inequality can yu use to determine whether you should sign up?

Answers

3(x - 25) < $100.  We're not req'd to solve this.


Convert the decimal number 625 to binary using addition/subtraction method

Answers

1001110001=625 in binary hope this helps

What is the product of a number and it’s reciprocal

Answers

The product of a number is always one. Both numbers cancel each other in the numerator and denominator. 

For example: 1/3*3= 1   1/4*4=1
The product of a number and it's reciprocal is simply 1.

Find the average value of the function f(x) = 9 sin2(x) cos3(x) on the interval [−π, π].

Answers

Final Answer:

The average value of f(x) = 9 sin²(x) cos³(x) over the interval [-π, π] is 0.

Explanation:

Integrate and Divide: To find the average value of a function f(x) over an interval [a, b], we calculate the definite integral of f(x) over the interval and divide by the interval's width:

Average value = (1/(b-a)) * ∫a^b f(x) dx

In this case, a = -π and b = π, so b - a = 2π.

Integrate f(x): Unfortunately, integrating f(x) = 9 sin²(x) cos³(x) directly is quite complex. However, we can use the trigonometric identity sin²x = (1 - cos²x) to rewrite the function:

f(x) = 9 sin²(x) cos³(x) = 9 (1 - cos²x) cos³(x)

Integrating this form of f(x) is more manageable, although it still involves integration by parts due to the product of three terms.

Zero Integral: After integrating and simplifying, the definite integral of f(x) over [-π, π] evaluates to 0.

Average Value: Dividing the integral by the interval's width (2π) confirms the average value of f(x) on [-π, π] is 0:

Average value = (1/2π) * 0 = 0

Therefore, the average value of f(x) = 9 sin²(x) cos³(x) on the interval [-π, π] is 0, despite the function's non-zero values within the interval.

A consumer group claims that the mean annual consumption of high fructose corn syrup by a person in the U.S. is 48.8 pounds. A random sample of 120 people in the U.S. has a sample mean annual consumption of high fructose corn syrup of 49.5 pounds. Assume the population standard deviation is 3.6 pounds. evidence to support the group’s claim? 1). State the hypothesis: H0 : Ha : 2). Specify the level of significance   3). Sketch the sampling distribution 4). Calculate the test statistic At = 0.05, is there enough 5). Find the P-value and shade this in the distribution in (3): 6). Decision (using the P-value): 7). Write a statement to interpret the decision in the context of the original claim 2

Answers

Part 1:

The null hypothesis (H0) represents the claim to be tested while the alternative hypothesis (Ha) is the opposite of the claim.

Given that a consumer group claims that the mean annual consumption of high fructose corn syrup by a person in the U.S. is 48.8 pounds.

The null and alternative hypothesis are:

[tex]H_0:\mu=48.8 \\ \\ H_a:\mu\neq48.8[/tex]



Part 2:

From the question, we are testing the hypothesis at a level of significance [tex](\alpha=0.05[/tex]



Part 3:

Because the sample size is big enough (i.e 120), we can assume that the distribution is normally distributted.

Recall that the central limit theorem states that given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population all of the samples will follow an approximate normal distribution pattern.
The shape of a nomal distribution curve is attached.



Part 4:

The test statistics is calculated as follows:

[tex]z= \frac{X-\mu}{ \frac{\sigma}{\sqrt{n}} }\\ \\= \frac{48.8-49.5}{\frac{3.6}{\sqrt{120}}}\\ \\ = \frac{-0.7}{\frac{3.6}{10.95}} = \frac{-0.7}{0.3286}\\ \\ =\bold{-2.13} [/tex]



Part 5:

The P-value is obtained as follows:

[tex]P(-2.13)=0.01659[/tex]

Since the test is a two tailed test, the P-value for the test is given by

2(0.01659) = 0.03318



Part 6:

Since, the P-value is 0.033 and is less than the level of significance 0.05, we reject the null hypothesis.


Part 7:

We conclude that there is enough evidence to reject the consumer group's claim that the mean annual consumption of high fructose corn syrup by a person in United Sates is 48.8 pounds at the level of significance α = 0.05.

A money market fund advertises a simple interest rate of 88​%. Find the total amount received on an investment of ​$4000 for 15 months.A money market fund advertises a simple interest rate of 88​%. Find the total amount received on an investment of ​$4000 for 15 months. The total amount received on an investment of ​$4000 for 15 months is ​$ . ​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

Answers

[tex]\bf \qquad \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\to& \$4000\\ r=rate\to 88\%\to \frac{88}{100}\to &0.88\\ t=years\to \frac{15}{12}\to &\frac{5}{4} \end{cases} \\\\\\ I=4000\cdot 0.88\cdot \cfrac{5}{4}[/tex]

which regular polygon has a minimum rotation of 45 to carry the polygon onto itself

Answers

In order for the regular polygon to map onto itself by a rotation of 45°, it should have a central angle of 45° between lines that connect the vertices to the center.

If the regular polygon has n side, then
360°/n = 45°
n = 360/45 = 8

Answer:  An octagon

The library is 0.96 mile away from Theo’s home. Write this distance as a fraction in simplest from.

Answers

24/25 in fraction and simplest form. Hope this helps!

The base of a pyramid has n sides.
Write an EXPRESSION for the number of faces of the pyramid.

Answers

Answer: The expression for number of faces of a pyramid =1+n


Step-by-step explanation:

A Pyramid is a polyhedron or a three dimensional shape having a polygon base and all lateral faces are triangles .

Its base describe the number of other faces of it.

For example a triangular pyramid has a triangular base which gives rise to 3 lateral faces , and a rectangular pyramid has a rectangular base which give rise to 4 lateral faces and so on.....

So the total number of faces in a pyramid = base + lateral faces

If a pyramid has n sides therefore it give rise to n lateral faces such that

The total number of faces in a pyramid= 1+n .

The total number of faces of the pyramid is [tex]n+1[/tex].

A pyramid is a three-dimensional structure whose lateral sides converge to a single step at the summit, roughly forming a pyramid in the geometric sense. A pyramid's base can be trilateral, quadrilateral, or any other polygon shape.

For a pyramid having triangular base then, the total number of faces will be [tex]3+1=4[/tex].

In a similar way, if a pyramid has four sides at the base then, the total number of faces will be [tex]4+1=5[/tex].

Hence, in the given question the pyramid has [tex]n[/tex] sides at the base so, the total number of faces of the pyramid is [tex](n+1)[/tex].

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Solve the simultaneous equations 2x+3y=13
4x-y=-2

Answers

2x + 3y = 13
4x - y = -2

In the second equation, subtract 4x from both sides.

-y = -2 - 4x

Divide both sides by -1.

y = 2 + 4x

Put this into the first equation in place of y.

2x + 3(2 + 4x) = 13

Multiply everything in the parenthesis by 3.

2x + 6 + 12x = 13

Combine like terms.

14x + 6 = 13

Subtract 6 from both sides.

14x = 7

Divide 14 on both sides.

x = 7 / 14

x = 0.5

Put this into the second equation in place of x.

4(0.5) - y = -2

2 - y = -2

Subtract 2 from both sides.

-y = -4

Divide both sides by -1.

y = 4

So x = 0.5 and y = 4.

Hope this helps!

The value of x and y are 0.5 and 4 respectively.

2x+3y=13 ..... i

4x-y=-2 ...... ii

Multiply equation i by 4

Multiply equation ii by 2

8x + 12y = 52 ..... iii

8x - 2y = -4 ...... iv

Subtract iv from iii

14y = 56

Divide both side by 14

14y/14 = 56/14

y = 4

Since 4x-y=-2

4x - 4 = -2

4x = -2 + 4.

4x = 2

x = 2/4 = 0.5

Therefore, x = 0.5 and y = 4

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on a suspension bridge the roadway is hung from cables hanging between support towers. the cable of one bridge segment of the parabola y=.1x^2-7x +150 where y is the height of the cable in feet above the roadway at the distance x feet from a support tower. what is the closest the cable comes to the roadway? how far from the support towers does this occur

Answers

The parabola opens upward and is symmetric to the y-axis. Its general form is: . y \;=\;ax^2 + c Its y-intercept is (0, 10) . . . Hence: . y \;=\;ax^2 + 10 It passes through (200, 100). We have: . 100 \:=\:a\cdot200^2 + 10 \quad\Rightarrow\quad a \:=\:\frac{9}{4000} Hence: . y \;=\;\tfrac{9}{4000}x^2 + 10 When x = \pm50,\;\;y \:=\:\tfrac{9}{4000}(50^2) + 10 \:=\:\frac{125}{8} Therefore, 50 feet from the center, the cable is 15\tfrac{5}{8} feet high.

Which graph represents the solution set of the system of inequalities?

Answers

The given inequalities are
y < (2/3)x
y ≥ -x + 2

The line y = (2/3)x  has a positive slope of 2/3, and it passes through the origin.
This line is shown as a dashed line segment in both graphs.
Because the inequality requires that y < (2/3)x, therefore the shading for the first graph is incorrect. It is correct for the second graph.

The line y = -x + 2 has a negative slope of -1, and a y-intercept of 2. 
This line also appears in both graphs.
Because the inequality requires that y ≥ - x + 2, the shading for the first graph is incorrect. It is correct for the second graph.

Answer: The second graph is correct (and it is shown below).

Assume ABC=DEF. if AB=18, BC=10, and AC=25, what is the length of DF?

Answers

The answer is D. 25

It’s easiest to find the solution by drawing out the triangles side by side with the lengths. It is what I did to find the answer

The length of DF is equal to 25 units. Then the correct option is D.

What is a triangle?

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

The two triangles ABC and DEF are congruent to each other and all the sides of one triangle will be the same as all the sides of the other triangle. The value of DF is equal to AC. AC is 25 so DF is equal to 25.

Hence, option D is correct.

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100 equals 15 minus a number all divided by 5

Answers

100 = (15 - x)/5

100(5) = (15-x/ 5)5

500 = 15 - x

500 - 15 = 15 (-15) - x

485/-1 = -x/-1

x = -485

hope this helps

The table represents a linear function.

Answers

Answer:

the slope of the function is -6

Step-by-step explanation:

Hello

You could  use the slope formula to find the slope of this linear function.  

just two points are needed,let´s take these ones

p1(-1,2)  and p2(0,-4)

[tex]s=\frac{y2-y1}{x2-x1} \\s=\frac{-4-2}{0-(-1)} \\s=\frac{-6}{1} \\s=-6[/tex]

so, we have that the slope of the line is -6

I hope it helps you

Have a fantastic day

The slope of the line is -6, the first option.

What is the slope?

If a line has two points (x₁, y₁) and (x₂, y₂), then the slope of the line is given by:

a = (y₂ - y₁)/(x₂ - x₁)

Here we can use the first two points (-2, 8), (-1, 2) to get:

a = (2 - 8)/(-1 + 2) = -6

The correct option is the first one.

  What is the volume of the pyramid? 
11*11*12 are the missing dimensions 
 
       A. 420 cm3   B. 139 cm3   C. 142 cm3   D. 484 cm2

Answers

always use y=mx+b !!!! 11= 11x +12 

[tex]3/2y+12=7/5y-20[/tex]

Answers

[tex]\bf \cfrac{3}{2y}+12=\cfrac{7}{5y}-20\impliedby \begin{array}{llll} \textit{now, let's multiply both sides by 10y}\\ \textit{thus, getting rid of the denominators} \end{array} \\\\\\ 10y\left( \cfrac{3}{2y}+12 \right)=10y\left( \cfrac{7}{5y}-20 \right)\implies 15+120y=14+200y \\\\\\ 1=200y-120y\implies 1=80y\implies \boxed{\cfrac{1}{80}=y}[/tex]

Help asap pleaaaaaaaaase

Answers

5 books at $4 each is a multiplication.
You need to multiply 5 * $4.
Then to include the tote, you need to add its price, $6.
The final expression is
5 * $4 + $6

What is the solution to the proportion 6-10 = 9-x

Answers

First 6-10=-4
So then you get -4=9-X
Now you subtract 9 on both side
-4=9-X
-9. -9
----------
-13= -X
Now make the X positive basically get rid of the negative on both sides
x=13
Check by substituting in 13 for X
9-13= -4
6-10= -4

Sergei says that 10%10% of a number will always be less than 20%20% of any other number. Complete one inequality to support Sergei's claim and one to show that he is incorrect

Answers

That statement is only true sometimes.  If you use 500 and 10, 10% of 500 is 50, while 20% of 10 is only 2.  Clearly, 50 is larger than 2.

Answer:

Step-by-step explanation:

Please help. Should only have two terms, this means you have to combine like terms and simplify. Take a look at photo.

Answers

The yard is a rectangle, and the shed is also a rectangle.
You need to find the areas of the two rectangles.
Then, subtract the area of the shed from the area of the yard.
Yard: length = 13x - 4; width = 5x
Shed: length = 2x + 4; width = 2x

Area of yard:
A = LW = (13x - 4)(5x) = 65x^2 - 20x

Area of shed:
A = LW = (2x + 4)(2x) = 4x^2 + 8x

Area of lawn = area of yard - area of shed

Area of lawn = (65x^2 - 20x) - (4x^2 + 8x)
                     = 65x^2 - 20x - 4x^2 - 8x
                     = 61x^2 - 28x

The area of the lawn is 61x^2 - 28x

The number of feet between 2 objects varies directly as the number of miles. If the distance between 2 objects is 2 1/2 miles or 13,200 feet how many feet are equivalent to a distance of 7 miles

Answers

[tex]\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------[/tex]

[tex]\bf \stackrel{feet}{f}=k\stackrel{miles}{m}\textit{ we also know that } \begin{cases} m=2\frac{1}{2}\\ f=13200 \end{cases}\implies 13200=k\cdot 2\frac{1}{2} \\\\\\ 13200=k\cfrac{5}{2}\implies \cfrac{13200\cdot 2}{5}=k\implies 5280=k \\\\\\ \boxed{f=5280m} \\\\\\ \textit{when m = 7, what is \underline{f}?}\qquad \qquad f=5208(7)[/tex]
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