Tom earns $12.50 per hour at the Yankee Bowling Alley. He regularly works 40 hours per week. He is paid time and a half for each hour of overtime work. Last week he worked 42 hours. What is his pay for the week?

Step-by-step explanation:

2,300×3÷7=985.71 The amount of money saved

2300×1÷10=230the amount of entertainment

985.71+230=1215.71 total

1215.71÷2300=0.5285 Entertainment money + reserve money ÷ total money

The income that he plan to spend each month on these two items together is 0.5285.

A fraction represents a part of a number or any number of equal parts.

Given; Travis's income is $2300 a month, and he plans to budget 3/7 of his income for savings and 1/10 of his income for entertainment.

We need to find the income that he plan to spend each month on these two items together.

The amount of money saved;

2,300×3÷7 = 985.71

The amount of entertainment;

2300×1÷10=230

The total 985.71 + 230 = 1215.71

Now, Entertainment money + reserve money ÷ total money

1215.71÷2300 = 0.5285

The income that he plan to spend each month on these two items together is 0.5285.

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Explanation:

The three angles add to 180, so x+y+z = 180

The second and third angles add to 3 times the measure of the first, so y+z = 3x

The third angle is 29 more than the second, so z = y+29

----------------------------

The system of equations is

[tex]\begin{cases}x+y+z = 180\\\\y+z = 3x\\\\z = y+29\end{cases}[/tex]

For now, let's focus on the second and third equations only.

Start with y+z = 3x. Replace z with y+29 which is valid because of the third equation.

So we'll have

y+z = 3x

y+y+29 = 3x

2y+29 = 3x

Let's isolate y

2y+29 = 3x

2y = 3x-29

y = (3x-29)/2

y = 3x/2 - 29/2

y = 1.5x - 14.5

We'll use this later.

--------------------------

Go back first equation of the system. Plug in z = y+29

x+y+z = 180

x+y+y+29 = 180

x+2y+29 = 180

Then plug in y = 1.5x - 14.5 we found earlier

x+2y+29 = 180

x+2(1.5x-14.5)+29 = 180

x+3x-29+29 = 180

4x = 180

x = 180/4

x = 45

---------------------------

We can use this x value to find y

y = 1.5x - 14.5

y = 1.5*45 - 14.5

y = 53

and use this to find z

z = y+29

z = 53+29

z = 82

As a check, x+y+z = 45+53+82 = 180 to help confirm the answer. I'll let you check the other equations.

f ' ( x ) = 1 ( x + 1 ) 2

Explanation:

differentiating from first principles

f ' ( x ) = lim h → 0

f ( x + h ) − f ( x ) h

f ' ( x ) = lim h → 0

 x + h x + h + 1 − x x + 1 h

the aim now is to eliminate h from the denominator

f ' ( x ) = lim h =0  

( x + h ) ( x + 1 )− x ( x + h + 1) h ( x + 1 ) ( x + h + 1 )

f ' ( x ) = lim h → 0

 x 2 + h x + x + h − x 2 − h x − x h ( x + 1 ) ( x+h + 1 )

f ' ( x ) = lim h → 0

h 1 h 1 ( x + 1 ) ( x + h +1 )

f ' ( x ) = 1 ( x + 1 ) 2

Answer:

M = 1/18

Step-by-step explanation:

The slope is 1/18 mi/min, which means Sonia walks at a rate of 1 mile every 18 minutes.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

Given that, Sonia is walking 2.5 miles home from school.

She left at 4:00 pm and got home at 4:45 pm. She took 45 minutes to get there.

We can interpret the information as two points, the first one is (0,0) that represents the starting point. The second point is (45, 2.5), which represents the ending point when she arrived home. Let's graph these points and draw a line through them.

To find the slope, divide 2.5 miles by 45 minutes,

Thus, slope =2.5/45

m= 1/18 miles per minute

Therefore, the slope is 1/18 mi/min, which means Sonia walks at a rate of 1 mile every 18 minutes.

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Answer:

Distance= 6.6 miles

Bearing= N 62.854°W

Step-by-step explanation:

Let's determine angle b first

Angle b=20° (alternate angles)

Using cosine rule

Let the distance between the liner and the port be x

X² =8.8²+2.4²-2(8.8)(2.4)cos20

X²= 77.44 + 5.76-(39.69)

X²= 43.51

X= √43.51

X= 6.596

X= 6.6 miles

Let's determine the angles within the triangle using sine rule

2.4/sin b = 6.6/sin20

(2.4*sin20)/6.6= sin b

0.1244 = sin b

7.146= b°

Angle c= 180-20-7.146

Angle c= 152.854°

For the bearing

110+7.146= 117.146

180-117.146= 62.854°

Bearing= N 62.854°W

Answer:

22.5 cm3

Step-by-step explanation: i took thy test

The volume of the rectangular prism is 22.5 cm³

A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here. Due to its shape, a rectangular prism is also called a cuboid.

Given here A right rectangular prism has a length of 10 centimeters, a width of 2.5 centimeters and a height of 0.9 centimeters.

Now we know the volume of the rectangular prism is given by

The volume of a rectangular prism = Length x Width x Height cubic units.

∴ V= 10×2.5×0.9

     = 22.5 cm³

Hence, the volume of the rectangular prism is 22.5 cm³

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Answer:

the answers are

a) Area of triangle is 15 square inches

Perimeter of triangle is 18.5 inches.

b) Area of trapezium is 210 square cm.

Perimeter of trapezium is 61.5 cm.

c) Area of parallelogram is 21 square yards

perimeter of parallelogram is 22 yards

Step-by-step explanation:

Area of triangle is 1/2( base × height)

Area of trapezium is 1/2(p1 + p2)×height

Area of parallelogram is base × height

Answer:

C

Step-by-step explanation:

So we have a cylinder with a hole the shape of a rectangular prism through it.

Therefore, our total volume would be the cylinder minus the volume of the rectangular prism.

The volume of a cylinder is given by the formula:

[tex]V=\pi r^2h[/tex]

Use 3.14 for π, 10 for radius, and 15 for the height. Thus:

[tex]V=(3.14)(10)^2(15)\\V=4710[/tex]

So the volume of the cylinder is 4710 cubic feet.

Now, find the volume of the rectangular prism.

The formula for the volume of a rectangular prism is given by:

[tex]V=lwh[/tex]

The length is 5, width is 3, and height is 15. Thus:

[tex]V=(5)(3)(15)\\V=225[/tex]

So, the total volume is:

[tex]V_{\text{Total}}=V_{\text{Cylinder}}-V_{\text{Rectangle}}\\V_{\text{Total}}=4710-225=4485\text{ feet}^3[/tex]

Our answer is C

Answer:

17y^2+19

Step-by-step explanation:

sum means add

Answer:

19+ 17y²

Step-by-step explanation:

Step-by-step explanation:

A no. is divisible by four if the last two digits is a multiple of 4

04 is a multiple of four

All numbers between -8 and 2 are integers except 0

All the integers between - 8 and 2 are,

{- 7, - 6, - 5, - 4, - 3, - 2, - 1, 1 }.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The numbers is,

⇒ - 8 and 2

Now, All the numbers between - 8 and 2 are,

⇒ - 7, - 6, - 5, - 4, - 3, - 2, - 1, 1

Thus, All the integers between - 8 and 2 are,

{- 7, - 6, - 5, - 4, - 3, - 2, - 1, 1 }.

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We can solve this problem in two ways.

1. From the description we conclude that the described sequence is a geometric sequence where the first term a₁ = 2 and common ratio r = 3, so:

[tex]\boxed{a_n=2\cdot3^{n-1}}[/tex]

Answer D.

2. The easiest way. We know that a₁ = 2, so let's substitute n = 1 for each of the possible answers:

A. 3·2ⁿ = 3·2¹ = 3·2 = 6 - Wrong

B. 2·3ⁿ = 2·3¹ = 2·3 = 6 - Wrong

C. 3·2ⁿ⁻¹ = 3·2¹⁻¹ = 3·2⁰ = 3·1 = 3 - Wrong

D. 2·3ⁿ⁻¹ = 2·3¹⁻¹ = 2·3⁰ = 2·1 = 2 - Correct.

Answer:

45

Step-by-step explanation:

Answer:

Step-by-step explanation:

15 + 10 = 25

HI = 25

Answer: 5

Step-by-step explanation:

Answer: It's 176/25 or 7 remainder 1/25

Answer:

Step-by-step explanation:

-3 is the difference

Answer:

157

Step-by-step explanation:

First, let's subsitute a and f.

6(2)^2 + 4(4) - 3

Remeber the order of operations. Paranthesis, exponents, multiply, divide, add, subtract.

12^2 + 16 - 3

144 + 16 - 3

157 is the answer. Hope this helps!!!!!!

Answer:

1. 0.3

2. Relative frequency

Step-by-step explanation:

We would be calculating for p(A) which is the probability of A. With A being that public buildings would be found to be insulated with same materials that causes same issues

n = sample space of public buildings = 10

F = frequency = 3

P(A) = 3/10 = 0.3

Therefore 0.3 is the approximate probability of another building having same issues

Question 2 says we should find method used to assign probability

The method used is relative frequency method and it is determined by:

P(A) = frequency(f)/total number of data values(n).

Answer:

A. y = 0.8x + 4

Step-by-step explanation:

i just took the test

The equation of the linear model shown is A. y = 0.8x + 4

A linear model refers to a model where a response variable is being described. It should be noted that the response should be a continuous variable

The linear model is the framework for the set of models that predict a quantitative dependent variable through the independent variables given.

Based on the diagram, the equation of the linear model shown is y = 0.8x + 4

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Answer:

  a) y-intercept = 17; initial design strength percentage

  b) slope = 2.8; increase in that percentage each day

  c) 29.6 days to 100% design strength

Step-by-step explanation:

a, b) The equation is in the form called "slope-intercept form."

  y = mx + b

where the slope is m, and the y-intercept is b.

Your equation has a slope of 2.8 and a y-intercept of 17.

The y-intercept is the percentage of design strength reached 0 days after the concrete is poured. The strength of the concrete when poured is 17% of its design strength.

The slope is the percentage of design strength added each day after the concrete is poured. The concrete increases its strength by 2.8% of its design strength each day after it is poured.

__

c) To find when 100% of design strength is reached, we need to solve for x:

  100 = 2.8x +17

  83 = 2.8x

  83/2.8 = x ≈ 29.6

The concrete will reach 100 percent of its design strength in about 30 days.

Answer:

(6, -7)

Step-by-step explanation:

(x, y)=(4, -1)

(x1+x2)/2=4

(y1+y2)/2=-1

-----------------

x1+x2=8

2+x2=8

x2=8-2=6

---------------

y1+y2=-2

5+y2=-2

y2=-7

---------------

(6, -7)

9+5=14 bx8=8b  Hope this helps sir or miss!

Answer:

25

Step-by-step explanation:

We can use the Pythagorean Theorem to find the value of x,

The Pythagorean Theorem states that [tex]a^2 + b^2=c^2[/tex], where a and b are the legs and c is the hypotenuse.

We already know a and b’s value so we can substitute inside the formula to find the length of the hypotenuse.

[tex]24^2+7^2=c^2\\\\576+49=c^2\\\\625=c^2\\\\c=25[/tex]

Hope this helped!

Full question attached

Answer:

UCL for x bar chart=7.145

LCL for x bar chart=4.874

Explanation:

Please find answer attached

Answer:

y = 10 CDs

Step-by-step explanation:

30 divided by 3 equals 10

10 times 3 equals 30

Answer:

first blank is y/3

second blank is 10

Step-by-step explanation:

Answer:

70,523

Step-by-step explanation:

This is standard form there no way to show.

Answer:

Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.

Step-by-step explanation:

Just took the test.

Both the steps performed by Mark to determine ,the houses the carrier can deliver mail to in 7.5 minutes at this rate is correct .

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

According to the question

A mail carrier can deliver mail = 36 houses

Time taken to deliver mail in 36 houses = 30 minutes

Mark wants to determine , the houses the carrier can deliver mail to in 7.5 minutes at this rate.

By using unitary method :

Step1: First divide 36 houses by 30 minutes to find a unit rate  

[tex]rate = \frac{36}{30}[/tex]

rate = 1.2 houses in a minute  

Step2: Then multiply the rate to the required time

i.e  1.2 * 7.5  = 9 houses

Hence , Both the steps performed by Mark to determine ,the houses the carrier can deliver mail to in 7.5 minutes at this rate is correct .

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Answer:

37 7/33 or 37.212

Step-by-step explanation:

6j + 23 + k/l - 3

If j = 3, k = 7, and l = 33:

6 × 3 + 23 + 7/33 - 3

= 18 + 22 + 7/33 - 3

= 40 + 7/33 - 3

= 40 7/33 - 3

NOTE: Because 40 and 3 are whole numbers, 3 will be subtracted from 40.

= 37 7/33 or 37.212