otis paints the interior of a home for $45 per hour plus $75 for supplies. Shireen paints the interior of a home for $55 per hour plus $30 for supplies. The equations give the total cost for x hours of work for each painter. For how many hours of work are Otis's and Shireen's costs equal? what is the cost for this number of hours?

Y= 45x + 75 - Otis
Y= 55x + 30 - Shireen​

(12, 11):

2((12) + 3) - (11) = 7 + (12)

2 • 15 - 11 = 19

2 • 4 = 19

8  [tex]\neq[/tex]  19

(1, 0):

2((1) + 3) - (0) = 7 + (1)

2 • 4 = 8

8 = 8

(-5, 1):

2((-5) + 3) - (1) = 7 + (-5)

2 • -2 - 1 = 2

2 • -3 = 2

-6  [tex]\neq[/tex]  2

Hope this helps.

Answer:

If it is a six-sided die then it has the probability of 1/6 or .16

Step-by-step explanation:

Answer:

531.

Step-by-step explanation:

Let's assume 2(1) + 1 = 3

a = 1 and b = 1

Now we can plug that in

8(1)^3 + (1)^3 + 18(1)(1)

Then we need to multiply together

8^3 + 1^3 + 18

Then do the powers

512 + 1 + 18

Then add them together

531

Hope this helped!

Answer:

27

Step-by-step explanation:

A sum of cubes factors as

a³ + b³ = (a + b)(a² - ab + b²)

Factor the sum of cubes 8a³ + b³

8a³ = (2a)³, thus

8a³ + b³

= (2a)³ + b³

= (2a + b)(4a² - 2ab + b²)

We now have the right side as

(2a + b)(4a² - 2ab + b²) + 18ab ← substitute 2a + b = 3

= 3(4a² - 2ab + b²) + 18ab

= 12a² - 6ab + 3b² + 18ab ← collect like terms

= 12a² + 12ab + 3b² ← factor out 3 from each term

= 3(4a² + 4ab + b²) ← perfect square

= 3(2a + b)² ← substitute 2a + b = 3

= 3 × 3²

= 3 × 9

= 27

Answer:

1 pencil = $0.75

1 eraser = $0.29

Step-by-step explanation:

4p+2e=3.58                                 1p+6(0.29)=2.49

1p+6e=2.49                                   1p+1.74=2.49

p=2.49-6e                                     1p=0.75

4(2.49-6e)+2e=3.58                       p=0.75

9.96-24e+2e=3.58

9.96-22e=3.58

-22e=-6.38

e=0.29

Answer:

C

Step-by-step explanation:

Subtraction Property

10x - 30 = 7x

Subtract 7x from both sides.

3x - 30 = 0

To construct a histogram, you must decide on your interval size by dividing the data range by your desired number of intervals. Then, sketch the graph with scaled axes and intervals consistently to accurately represent the data.

To construct a histogram, you need to determine the interval size for your bins. The interval size depends on the range of your data and the number of intervals you want to use. For instance, if you have data ranging from 32.5 to 100.5 and you want to create five intervals, you subtract the smallest value from the largest and then divide by the number of intervals. So it would be (100.5 - 32.5) ÷ 5, which equals 13.6. This means each interval would be 13.6 units wide.

When constructing the actual histogram, the x-axis would cover from 32.5 to 100.5 and the y-axis would cover the frequency of the data within each interval. An interval's endpoints can be determined successively by adding the interval width to the previous endpoint, starting with 32.5. Moreover, for data with a small range like 1 to 6, you could create six intervals ranging from 0.5 to 6.5 to ensure all data points are included, with a 1 unit interval size for clarity.

Sketch the graph using a ruler and pencil, and carefully scale the axes to accurately reflect the range and intervals for the data you're representing. Consistency in interval size is key when placing data values into each bin.

Final answer:

A histogram is constructed by determining the number of intervals, with a common range being five to 15 intervals. Calculate the interval width by dividing the total range of data by the chosen number of bins. Use a ruler and pencil for a scaled and precise histogram representation.

Explanation:

To construct a histogram, you need to decide on the number of intervals, also known as classes or bins. In this case, the data provided suggests we need to create five to six intervals. The x-axis for our histogram might range from 32.5 to 100.5, representing the data values, and the y-axis records the frequency of the data points.

To calculate the width of each interval, take the range of the data (100.5 - 32.5 = 68) and divide it by the number of intervals (5). This gives us an interval width of 13.6. When scaling the axes, use a ruler and pencil for precision.

For example, if your data set ranges from a smallest value of 1 to a largest value of 6, you might set your bins to start at 0.5 and end at 6.5 to ensure that all values are included. With this range of 6 (6.5 - 0.5), and deciding on six bins, the bin size or interval size would be 1. This is explained in Solution 2.10.

Remember to consistently apply the same method when placing data values within intervals to enable comparability and clarity in your histogram.

Answer:

Step-by-step explanation:

volume =1/3×base area×height

216=1/3× A×6

base area=216/2=108 in²

Answer:

Here is the answer

Step-by-step explanation:

108 in squared

or D

The equation [tex]y=2x+2[/tex] is a function

Explanation:

Given that the graph contains the coordinates [tex](-1,0)[/tex], [tex](0,2)[/tex] , [tex](1,4)[/tex] and [tex](2,6)[/tex]

We need to determine whether the equation [tex]y=2x+2[/tex] is a function.

To determine the equation is a function, let us substitute the coordinates in the equation and check whether it satisfies the equation.

Let us substitute the coordinate [tex](-1,0)[/tex] in the equation [tex]y=2x+2[/tex]

Thus, we have,

[tex]0=2(-1)+2[/tex]

[tex]0=-2+2[/tex]

[tex]0=0[/tex]

Thus, the coordinate [tex](-1,0)[/tex] satisfies the equation [tex]y=2x+2[/tex]

Substituting the coordinate [tex](0,2)[/tex] in the equation, we have,

[tex]2=2(0)+2[/tex]

[tex]2=2[/tex]

Thus, the coordinate [tex](0,2)[/tex] satisfies the equation [tex]y=2x+2[/tex]

Substituting the coordinate [tex](1,4)[/tex] in the equation [tex]y=2x+2[/tex]

[tex]4=2(1)+2[/tex]

[tex]4=4[/tex]

Thus, the coordinate [tex](1,4)[/tex] satisfies the equation [tex]y=2x+2[/tex]

Substituting the coordinate [tex](2,6)[/tex] in the equation, we get,

[tex]6=2(2)+2[/tex]

[tex]6=6[/tex]

Thus, the coordinate [tex](2,6)[/tex] satisfies the equation [tex]y=2x+2[/tex]

Hence, the coordinates [tex](-1,0)[/tex], [tex](0,2)[/tex] , [tex](1,4)[/tex] and [tex](2,6)[/tex] satisfies the equation [tex]y=2x+2[/tex]

Thus, the equation [tex]y=2x+2[/tex] is a function.

Answer:

Step-by-step explanation:

Let w be the width

Length = 3w +15

Perimeter = 94 cm

2*(length + width) = 94

2*(3w+15 + w) = 94

2*( 4w + 15) = 94

4w + 15 = 94/2

4w +15 = 47

        4w = 47 -15

         4w = 32

           w = 32/4

          w = 8 cm

Length = 3w +15 = 3*8 + 15 = 24 +15 = 39

Length = 39cm

Area = length * width = 39*8 = 312

Area = 312 cm²

The area of the rectangle is [tex]\( \boxe{312 \, \text{cm}^2} \).[/tex]

Step 1

Let's denote the width of the rectangle as w cm.

According to the problem, the length of the rectangle is [tex]\( 15 \)[/tex] cm more than three times its width. So, the length [tex]\( l \)[/tex] can be expressed as [tex]\( 3w + 15 \)[/tex]cm.

The perimeter P of a rectangle is given by:

[tex]\[ P = 2(l + w) \][/tex]

Given that the perimeter of the rectangle is [tex]\( 94 \)[/tex] cm, we can write the equation:

[tex]\[ 94 = 2((3w + 15) + w) \][/tex]

Step 2

Now, let's solve for [tex]\( w \)[/tex]:

[tex]\[ 94 = 2(4w + 15) \]\[ 94 = 8w + 30 \]\[ 8w = 94 - 30 \]\[ 8w = 64 \]\[ w = \frac{64}{8} \]\[ w = 8 \][/tex]

Step 3

Now that we have found the width of the rectangle to be [tex]\( 8 \)[/tex] cm, we can find its length:

[tex]\[ l = 3w + 15 \]\[ l = 3(8) + 15 \]\[ l = 24 + 15 \]\[ l = 39 \][/tex]

Step 4

Now that we have the width [tex]\( w = 8 \)[/tex] cm and the length [tex]\( l = 39 \)[/tex] cm, we can calculate the area A of the rectangle:

[tex]\[ A = l \times w \]\[ A = 39 \times 8 \]\[ A = 312 \][/tex]

So, the area of the rectangle is [tex]\( \boxe{312 \, \text{cm}^2} \).[/tex]

Initial equation:

4a / 2 = 5.2

Multiply both sides by 2:

4a = 10.4

Divide both sides by 4:

a = 2.6

Hope this helps!! :)

Answer:

Step-by-step explanation:

2.6 becuase 4a/2= 5.2

4a=10.4

a=2.6

Answer: k = -17

Step-by-step explanation:

K -7= -24

k= -24 + 7

k = -17

When doing absolute value, negatives will always be positive.

Option A's absolute value is 140.

Option B's absolute value is 104.

Option C's absolute value is also 104.

Option D's absolute value is 204.

Therefore, the option with the greatest absolute value would be D. |-204|

Answer:

A because is positive and highlights numbers

Answer:

12x⁴ + 2x³ + x² - 7x + 14

Step-by-step explanation:

(5x^4-3x^3+2x^2-15x+27) + (7x^4+5x^3-x^2+8x-13)

(5+7)x⁴ + (-3+5)x³ + (2-1)x² + (-15+8)x + (27-13)

12x⁴ + 2x³ + x² - 7x + 14

The chances of winning the grand prize in this game are approximately 0.089, whereas the chances of winning the consolation prize are 0.01.

The subject of this question is Probability, which is a branch of Mathematics. To calculate the probability, we'll need to determine the total number of outcomes and the count of the favorable outcomes.

a) To win the grand prize, all three balloons popped have to have 'Winner' slips. The probability of each dart hitting such a balloon will decrease as the total number of balloons decreases. First dart probability would be 5/8 (5 'Winner' balloons out of 8 total), the second one 4/7 (as one 'Winner' balloon is already popped), and 3/6 for the third. Multiply these probabilities together to get the overall probability: (5/8) * (4/7) * (3/6) = 0.089 (rounded to the third digit).

b) Similarly, for the consolation prize, we would have to hit all three balloons with blank slips. The process is equivalent, resulting in a probability of (3/8) * (2/7) * (1/6) = 0.01 (rounded to the third digit).

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Answer:

The change in total amount of money the cashier are paid each week will be $331.5.

Step-by-step explanation:

16 store cashiers work average 21 hours per week and paid $8.25 per hour.

Now, the store manager hires 2 additional cashiers each cashier will be paid 0.25 more per hour and will work an average of 1.5 fewer hours per week.

Therefore, the two additional cashiers will be paid $8.50 per hour and will work an average of (21 - 1.5) = 19.5 hours per week.

So, the change in the total amount of money the cashiers are paid each week will be (2 × 19.5 × 8.5) = $331.5. (Answer)

The account balance will be $6642 after seven years.

Step-by-step explanation:

To find the amount after seven years, a certain formula is used.

Amount = [tex]P( 1+r/n)^{n\times t}[/tex]

where,

P is the principal amount that is invested in the account.

Therefore, P = 4500 dollars.

r is the rate of interest. (r = 5.5 %)

Therefore, r = 5.5/100 = 0.055

n is the number of time the interest is compounded per year which is n= 4.

t is the time period which is t = 7 years.

Now, substituting all the above values in the formula,

Amount = [tex]4500(1+0.055/4)^{4\times 7}[/tex]

⇒ [tex]4500(4.055/4)^{28}[/tex]

⇒ [tex]4500(1.014)^{28}[/tex]

⇒ [tex]4500\times1.4759[/tex]

⇒ 6641.55 (which is approximately equal to 6642)

⇒ 6642 dollars.

The account balance after 7 years is $6642.

Answer:

Step-by-step explanation:

a) (5,5) ;    (10,6);  slope = 1/5

  (x1,y2);    (x2,y2)

y-y1 = m (x-x1)

[tex]y-5=\frac{1}{5}*(x-5)\\\\y-5=\frac{1}{5}*x-\frac{1}{5}*5\\\\y-5=\frac{1}{5}x-1\\y=\frac{1}{5}x-1+5\\\\y=\frac{1}{5}x+4[/tex]

d) (√2,7)    ; (√2,-7)

  (x1,y1)    ; (x2,y2)

[tex]slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{-7-7}{\sqrt{2}-\sqrt{2}}\\\\=\frac{-14}{0}=0[/tex]

Equation: y =7 or y = -7

Answer:

4x - 12

Step-by-step explanation:

Distribute the 4 to the x and -3.

4 × x = 4x

4 × -3 = -12

4x - 12

Answer:

the height is 3

the with is also 3 because

1.5+1.5=3

Answer: 373/50

Step-by-step explanation:

Step 1: convert to a fraction

746% = 746 ÷ 100 = 7.46

7.46 = 373/50

Step 2: Write the number as a fraction of one: 7.46 = 746/100

Step 3: use a common divisor of 2 to reduce the numbers, we have

(746÷2)= 373

(100÷2)=50

when reduced to the simplest form= 373/50

Therefore, 746/ 100 = 373/50 when expressed as a mixed number.

Answer: 373/50

Step-by-step explanation:

Step 1) Since 746% is a percent, it is written over the denominator of 100. So first convert it to a fraction, which would be 746/100.

Step 2) Find the GCF (greatest common factor). In order to find the GCF start by writing all the factors of

100:

1, 2, 4, 5, 10, 20, 25, 50, 100

Step 3) Now test every number there and see if any go into 746. Start at the highest number, which in this case is 100. (Example, ask yourself, “does 100 go into 746? No.” Then try with 50, and continue until you get to a number that goes into 746 evenly.)

Step 4) The GCF from the previous step is 2. So now divide 746 by 2 (answer is 373) and 100 by 2 (answer is 50).

Step 5) Now put 373/50 and that’s your answer! Congratulations you finished it!

Answer:

4

Step-by-step explanation:

we add them then divide 2

(11/2+2 1/2)/2

Circumference of the circle = 94.2 yd

Solution:

Given data:

Diameter of the circle = 30 yd

The value of π = 3.14

To find the circumference of the circle:

Circumference of the circle = πd

Substitute the diameter value in the formula, we get

Circumference of the circle = 3.14 × 30

                                              = 94.2

Circumference of the circle = 94.2 yd

Probability of distinct 3-digits is 1/6.

Probability of both the first digit and the last digit are even numbers is 1/5.

Step-by-step explanation:

Given set of numbers {1,2,3,5,8,9} = 6

Total number of 3-digits can be formed = 6[tex]\times[/tex]5[tex]\times[/tex]4 = 120.

Probability  of the three-digit numbers with distinct digits :

The number of 3-digit numbers with distinct digits = (6[tex]\times[/tex]5[tex]\times[/tex]4) / (3[tex]\times[/tex]2[tex]\times[/tex]1) = 20.

P(distinct 3-digits) =  no. of distinct 3-digits / Total no.of 3-digits

⇒ 20/120

⇒ 1/6

Probability that both the first digit and the last digit of the three-digit number are even numbers :

The even numbers in the set are 2 and 8 = 2 possibilities.

The number of 3-digits with 1st and 3rd digit are even = (2[tex]\times[/tex]6[tex]\times[/tex]2) = 24.

P(1st and 3rd digits even)= no. of 1st and 3rd digit even/Total no. of 3-digits.

⇒ 24/120

⇒ 1/5

The slope represents the rate of change. Then the rate of change will be 4.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

y = 4x + 60

The slope is 4 and the y-intercept is 60.

The slope represents the rate of change. Then the rate of change will be 4.

More about the linear equation link is given below.

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The rate of change in the equation y = 4x + 60 is 4, which is the coefficient of x. This means for each unit increase in 'x', 'y' will increase by 4 units.

In mathematics, the rate of change in an equation like y = 4x + 60 is represented by the coefficient of the variable x. This is because, in such an equation which is in the form of y = mx + b (a standard linear equation), 'm' represents the rate of change or the slope of the line.

So, in your specific equation y = 4x + 60, the rate of change or slope is 4. This means that for each increment of 1 in 'x', 'y' will increase by 4 units. This value - 4 - is your rate of change in this case.

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Answer:

The answer should be 45

Step-by-step explanation:

To get the whole are you would have to multiply the lenght with the Width and then take that answer and multiply it with the height

BUT

because you want the surface area, it would be just the lenght and width

15x3=45

so 45 is your answer.

Answer:

Part A - 4x + 8 dollars

Part B - $45

Step-by-step explanation:

Answer:

When I calculated this I got: 4.2857142857143 but I don't know if that's the correct answer.

Step-by-step explanation:

Answer:

This question would be related to slopes so the answer is [tex]y=-\frac{7}{2}x+\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]\mathrm{Slope-Intercept\:form\:of}\:\\x2+y2+12x+2y-1=0:\quad y=-\frac{7}{2}x+\frac{1}{4}[/tex]

[tex]\mathrm{Domain\:of\:}\:-\frac{7}{2}x+\frac{1}{4}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]

[tex]\mathrm{Range\:of\:}-\frac{7}{2}x+\frac{1}{4}:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<f\left(x\right)<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]

[tex]\mathrm{Parity\:of}\:-\frac{7}{2}x+\frac{1}{4}:\quad \mathrm{Neither\:even\:nor\:odd}[/tex]

[tex]\mathrm{Axis\:interception\:points\:of}\:\\-\frac{7}{2}x+\frac{1}{4}:\quad \mathrm{X\:Intercepts}:\:\left(\frac{1}{14},\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:\frac{1}{4}\right)[/tex]

[tex]\mathrm{Inverse\:of}\:-\frac{7}{2}x+\frac{1}{4}:\quad -\frac{4x-1}{14}[/tex]

[tex]\mathrm{Slope\:of\:}-\frac{7}{2}x+\frac{1}{4}:\quad m=-\frac{7}{2}[/tex]

Hope this helps you!

Have a good night!

Answer:

4,212

Step-by-step explanation:

Step 1:  Add

23 + 4189

4,212

Answer:  4,212