A jewelry shop was trying to determine the average age customers get their ears pierced. Each time a customer came in for a piercing that day, the shop recorded the customer's age.

{6, 2, 13, 7, 6, 11, 10, 6, 2}



What is the mean age of customers getting their ears pierced?

Mean =

Answer:

  First "order of operations" mistake: step 2

  First arithmetic mistake: step 4

Step-by-step explanation:

As we understand Rena's work, she wants to simplify ...

  \(\left(\dfrac{x^{-3}y^{-2}}{2x^4y^{-4}}\right)^{-3}\)

for x = -1 and y = 2.

Her work seems to be ...

Step 1

  \(\text{Substitute $x=-1$ and $y=2$ into the expression}\\\\\left(\dfrac{(-1)^{-3}2^{-2}}{2(-1)^42^{-4}}\right)^{-3}\qquad\text{no error}\)

Step 2

  \(\text{Simplify the parentheses}\\\\\left(\dfrac{2^4}{2(-1)^4(-1)^32^2}\right)^{-3}=\left(\dfrac{2^2}{2(-1)^7}\right)^{-3}\qquad\text{order of operations error}\)

Step 3

  \(\text{Evaluate the power to a power}\\\\\dfrac{2^{-6}}{2^{-3}(-1)^{21}}\qquad\text{no error}\)

Step 4

  \(\text{Use reciprocals and find the value}\\\\\dfrac{1}{2^32^6(-1)^{21}}=\dfrac{1}{8\cdot 64\cdot (-1)}=\dfrac{-1}{512}\qquad\text{error: $2^3$ is used instead of $2^{-3}$}\)

_____

So, the first arithmetic error is in Step 4. However, the order of operations requires exponents be evaluated first. Doing that makes step 2 look like ...

  \(\left(\dfrac{-\dfrac{1}{4}}{2(1)\dfrac{1}{16}}\right)^{-3}=(-2)^{-3}\qquad\text{proper Step 2}\)

__

We expect your answer is supposed to be Step 4.

Answer:

D.

Step-by-step explanation:

∠X = 89°, ∠Y = 90°, ∠Z = 40° ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

→ (2b+6)+(3b-1)=90----> 5b+5=90----> 5b=85----> b=17°

→ ∠Z=2b+6---- 2*17+6-----> ∠Z=40°

→ ∠Y=3b-1---> ∠Y=3*17-1---> ∠Y=50°

angle Y and W are supplementary angles

so

→ ∠Y+∠W=180---------> ∠W=180-∠Y------> ∠W=180-50----> ∠W=130°

angle X and Z are supplementary angles

so

→ ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

Therefore, the answer is

The median total of amount Franky earned is A = $81.67 per day.

Given data ,

For the first five days: $(100 + x) per day

For the next two days: $(175 + 2x) per day

For the final three days: $(75 + 2x) per day

Now , the average amount she earns is $80 per day

So , Average earnings = Total earnings / Total number of days

Average earnings = [(100 + x) * 5 + (175 + 2x) * 2 + (75 + 2x) * 3] / 10

Simplifying the equation:

80 = [500 + 5x + 350 + 4x + 225 + 6x] / 10

Multiplying both sides by 10:

800 = 1075 + 15x

Subtracting 1075 from both sides:

15x = -275

Dividing both sides by 15:

x = -18.33

For the first five days: $(100 - 18.33) = $81.67 per day

For the next two days: $(175 + 2*(-18.33)) = $138.34 per day

For the final three days: $(75 + 2*(-18.33)) = $38.34 per day

Arranging the earnings in ascending order: $38.34, $38.34, $38.34, $81.67, $81.67, $81.67, $81.67, $138.34, $138.34

The median is the middle value when the earnings are arranged in ascending order. In this case, the middle value is $81.67

Hence , the median is $81.67

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The surface area of the composite figure is 2005 in².

To find the surface area of the composite figure, we need to calculate the sum of the areas of its individual components.

Let's break down the figure into its different parts and calculate the surface area step by step:

Rectangular Prism: The rectangular prism has dimensions of 20 in, 11 in, and 5 in. The surface area of a rectangular prism can be found by adding the areas of its six faces. The total surface area of the rectangular prism is given by:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(20)(11) + 2(20)(5) + 2(11)(5) = 440 + 200 + 110 = 750 in²

Rectangular Prism: Another rectangular prism has dimensions of 19 in, 12 in, and 12 in. Following the same process as above, we can calculate the surface area of this rectangular prism:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(19)(12) + 2(19)(12) + 2(12)(12) = 456 + 456 + 288 = 1200 in²

Base: The base is a rectangle with dimensions 11 in and 5 in. The surface area of a rectangle is given by the formula:

Surface Area of Rectangle = lw

Plugging in the values, we have:

Surface Area of Rectangle = (11)(5) = 55 in²

Finally, to find the total surface area of the composite figure, we add the surface areas of the individual components:

Total Surface Area = Surface Area of Rectangular Prism + Surface Area of Rectangular Prism + Surface Area of Rectangle

Total Surface Area = 750 in² + 1200 in² + 55 in² = 2005 in²

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The Vertex is : (-6, -30)

The X-intercepts are : Approximately (-10.89, 0) and (-1.11, 0)

The Y-intercept is : (0, 6)

The Axis of symmetry is : x = -6

The functions Domain: is All real numbers

The Range is : All real numbers greater than or equal to -30.

To sketch the graph of the quadratic function \(f(x) = x^2 + 12x + 6,\) we can start by identifying the vertex, x-intercepts, y-intercept, axis of symmetry, domain, and range.

To find the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in standard form\((ax^2 + bx + c).\)

In this case, a = 1, b = 12, and c = 6.

Applying the formula, we get x = -12/(2 \(\times\) 1) = -6.

To find the y-coordinate of the vertex, we substitute this x-value into the equation:\(f(-6) = (-6)^2 + 12(-6) + 6 = 36 - 72 + 6 = -30.\)

So, the vertex is (-6, -30).

To determine the x-intercepts, we set f(x) = 0 and solve for x. In this case, we need to solve the quadratic equation \(x^2 + 12x + 6 = 0.\)

Using factoring, completing the square, or the quadratic formula, we find that the solutions are not rational.

Let's approximate them using decimal values: x ≈ -10.89 and x ≈ -1.11. Therefore, the x-intercepts are approximately (-10.89, 0) and (-1.11, 0).

The y-intercept is obtained by substituting x = 0 into the equation: \(f(0) = 0^2 + 12(0) + 6 = 6.\)

Thus, the y-intercept is (0, 6).

The axis of symmetry is the vertical line that passes through the vertex. In this case, it is the line x = -6.

The domain of the function is all real numbers since there are no restrictions on the possible input values of x.

To determine the range, we can observe that the coefficient of the \(x^2\) term is positive (1), indicating that the parabola opens upward.

Therefore, the minimum point of the parabola occurs at the vertex, (-6, -30).

As a result, the range of the function is all real numbers greater than or equal to -30.

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Answer:

Step-by-step explanation:

a) The formula for the regression function is:

Maintenance Cost = 54.7757 + 120.689 x Age of Car

b) The slope of the regression equation is 120.689. This means that on average, for every one year increase in the age of a car, the maintenance cost is expected to increase by $120.689.

c) To construct a 95% interval to predict the maintenance cost for a car that is 7 years old, we can use the formula:

Y = a + bX ± tα/2 * SE

where Y is the predicted maintenance cost, a is the intercept, b is the slope, X is the age of the car, tα/2 is the t-value for the 95% confidence level with n-2 degrees of freedom (11 in this case), and SE is the standard error of the estimate.

Plugging in the values, we get:

Y = 54.7757 + 120.689 * 7 ± 2.201 * 11.8442

Y = 923.167 ± 26.010

Therefore, we can be 95% confident that the maintenance cost for a car that is 7 years old will be between $897.16 and $949.17.

d) The null hypothesis is that there is no significant linear relationship between the average maintenance cost and the age of a car in years. The alternative hypothesis is that there is a significant linear relationship between the average maintenance cost and the age of a car in years.

To test the hypothesis, we can perform a t-test on the slope coefficient using the t-statistic and the p-value provided in the output. The t-statistic is 10.1898, which is much greater than the critical t-value at the 0.05 level of significance for a two-tailed test with 11 degrees of freedom (2.201). The p-value is 0.0000, which is less than the significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that there is a significant linear relationship between the maintenance cost and the age of the car in years.

Based on the time it takes to patrol one neighborhood, the number of neighborhoods that the sheriff can patrol in 5/8 of an hour is 3.125 neighborhoods

The number of neighborhoods that the sheriff can patrol in 5/8 hours depends on the number of hours that it takes the sheriff to patrol one neighborhood.

The number of neighborhoods she can patrol can therefore be found by the formula:

= Number of hours sheriff has / Number of hours required to patrol one neighborhood

= 5/8 ÷ 3/15

= 5/8 x 15/ 3

= 75 / 24

= 3.125 neighborhoods

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Answer:

192 is the missing number

Step-by-step explanation:

4 times 8 times 8 = (192 times 8) + (2 times 8)

Answer:

p > 34

He wrote more than 34 pages before today.

Step-by-step explanation:

Eduardo wrote 16 more pages, increasing his total number of pages above 50.

p = pages he wrote before today

p + 16 > 50

p > 50 - 16

p > 34

He wrote more than 34 pages before today.

Answer: Approximately 0.00004597583714

===================================================

Explanation:

Four-of-a-kind is when you get four cards of the same value. One example is if we got four aces. Any four-of-a-kind already has two pairs built into it. I'm assuming your teacher wants four-of-a-kind and another different pair (we'll have 6 pairs all together).

In any suit there are 13 unique cards. So there are 13 choices to fill the first four slots to set up the four-of-a-kind.

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

After the four-of-a-kind is formed, we have 13-1 = 12 unique cards left in any given suit. Once that fifth card is chosen, we then have 4 C 2 = 6 ways to select that final card such that we get another pair. I'm using the nCr combination formula since order doesn't matter. The steps to calculating this value (and the other nCr value mentioned later) is shown in the attached image below.

Multiplying those values gets us 13*12*6 = 936 different six card hands such that we get four-of-a-kind and a different pair.

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

This is out of 52 C 6 = 20,358,520 different six card hands.

Divide the two values found

936/(20,358,520) = 0.00004597583714

An equation for the total cars and trucks for dealership A is: x + y = 164.

An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.

The number of cars that dealership A sold is: 98 cars.

The number of trucks that dealership B sold is: 66 trucks.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:

Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;

x + y = 164.

Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;

2x + 0.5y = 229.

By solving the systems of linear equations simultaneously, we have:

2x + 0.5(164 - x) = 229

1.5x + 82 = 229

x = 98 cars.

For the y-value, we have;

2(98) + 0.5y = 229

0.5y = 229 - 196

y = 33/0.5

y = 66 trucks.

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Answer:

x = - 104, y = - 130

Step-by-step explanation:

the quotient of the 2 numbers is

\(\frac{x+26}{x}\) = \(\frac{4}{5}\) ( cross- multiply )

5(x + 26) = 4x

5x + 130 = 4x ( subtract 4x from both sides )

x + 130 = 0 ( subtract 130 from both sides )

x = - 130

First number is - 130 + 26 = - 104

second number is - 130

Explanation:

The slope of the line is found by the method: rise/run

You calculate how much the slope rises(goes up) and divide it by run(goes horizontal).

One more thing to note is that: the slope is negative BECAUSE ITS DECREASING.

Your answer:   -3/2

Answer:

(i) The factors of the given polynomial is (x – 22) and (x + 10)

(ii) If she purchase 5kg papaya then she pays 110

Step-by-step explanation:

Now,

x² – 12x – 220 = 0

Splitting the middle term

x² – 22x + 10x – 220 = 0

x(x – 22) + 10(x – 22) = 0

(x – 22) + (x + 10) = 0

x – 22 = 0 or x + 10= 0

x = 22 or x = -10

Here, (-10) is the negative value hence it is not possible

So, The value of x is 22

The factors of the given polynomial is (x – 22) and (x + 10)

if she purchase 5kg papaya then,

we know the price of 1 kg papaya i.e., 22 per kg

So,

5 × 22 = 110

Thus, if she purchase 5kg papaya then she pays 110

-TheUnknownScientist 72

Answer:

1)$15000

2)0.55%

3)0.55

4)3

5)24.75

Step-by-step explanation:

5)1500×0.55×3/100

Answer

\(\pink\sf{y=-1}\)

Step-by-step explanation

I'm assuming that this exercise is asking us to simplify the equation \(\sf{y=0.5(6)-4}\).

We know that 0.5 (6) means 0.5 multiplied by 6. That is the same as 6 divided by 2, which is 3:

\(\sf{y=3-4}\)

And now we just simplify the last part:

\(\sf{y=-1}\)

∴ answer: y = -1

By using the substitution method, the value of x is equal to -1 and the value of y is equal to 1.

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:

2x - 3y = -5      .......equation 1.

3x + y = -2          .......equation 2.

From equation 2, we have:

y = -3x - 2

By using the substitution method to substitute equation 3 into equation 1, we have the following:

2x - 3(-3x - 2) = -5

2x + 9x + 6 = -5

11x = -5 - 6

x = -11/11

x = -1

For the value of y, we have:

y = -3x - 2

y = -3(-1) - 2

y = 1.

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Answer:

C

Step-by-step explanation:

3^5 = 3*3*3*3*3

You are multiplying 5 3s

Answer:

multiply 3 factors of 5

Step-by-step explanation:

it means you're multiplying 3 five times

Answer:

Step-by-step explanation:

Given the profit made by a company modeled by the function

p = -n² + 300n + 100,000

The company breaks even when p = 0

To get the number of boxes sold when the company breaks even, we will substitute p = 0 into the equation.

0 = -n² + 300n + 100,000

multiply through by -1

0 = n² - 300n - 100,000

n² - 300n - 100,000 = 0

(n² - 500n) + (200n - 100,000) = 0

n(n-500)+200(n-500) = 0

(n+200)(n-500) = 0

n+200 = 0 and n-500 = 0

n = -200 and n = 500

Since n cannot be negative

Hence n = 500

This means that the company breaks even when it sells 500 boxes

Answer:

Positive relationship exists

Linear trend line

R² = 0.3522

Step-by-step explanation:

Given the data :

Promote (X) :

77

110

110

93

90

103

95

103

89

97

100

96

88

109

109

Sales (Y) :

85

103

102

109

85

112

96

93

97

92

94

81

92

108

103

A.) From the resulting plot, tbe slope of the graph is positive, hence, we can conclude that there exist a positive relationship between the variables 'promote' and 'sale'.

The linear trend line gives the best fit for the data with a correlation Coefficient, R value of 0.5935

The R² value is 0.3522. R² is the Coefficient of determination which gives the percentage of explained variation. For this data, about 35% of variation in sales is given by the best fit line.

Step-by-step Answer/Explanation(answers are underlined and bolded):

okay, first you want to identify all the numbers and what they mean:

lawyers:235  (within the main number of lawyers: Criminal lawyers: 74)

Family doctors: 87

Sergeons: 30

From there, add up all of said numbers (ignore the Criminal lawyers for now):

235 + 87 + 30 = 352

(352 is going to be the denominator or the number that we are going to be dividing from.)

Next, we start answering the questions!

the first one is asking for the percent of sergeons.

To do this, we need to take the number of sergeons listed, 30, and divide 352 from it:

30/352 = .0852

then multiply this by 100:

.0852 x 100= 8.52%

So the percent of sergeons is 8.52%

Next question: the percent of Family Doctors

so like the last question, we identify the number of doctors, 87, and divide 352 from it, then multiplying it by 100 after:

87/352 = .2472

.2472 x 100 = 24.72%

Meaning the percent of family doctors is 24.72%

Criminal Law is next:

repeat the steps in the last couple of problems:

72/352 = .2045

.2045 x 100 = 20.45%

Family Law:

Okay, so now, we need to take that 235 from earlier and subtract it from 72 (the criminal law students) to get the number of students going into family law.

235 - 72 = 163

now repeat the steps from the earlier problems:

163/352 = .3864

.3864 x 100 = 38.64%

(I don't particularly understand what the rest is asking...I figure you can probably figure out from here...? I hope this helps!!)

Answer:

\(x = \frac{17}{18}\)

\(y = \frac{23}{6}\)

Step-by-step explanation:

Given

\(y = 3x + 1\)

\(Points = (0,0)\ to\ (-3,4)\)

Required

Determine (x,y) equidistant from the equation and the given point

This question will be answered using distance formula;

\(d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)

Considering The first Point \((0,0)\ to\ (x,y)\)

\((x_1 ,y_1) = (0,0)\)

\((x_2,y_2) = (x,y)\)

The distance is:

\(d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)

\(d = \sqrt{0 - x)^2 + (0 - y)^2}\)

\(d = \sqrt{(- x)^2 + (- y)^2}\)

\(d = \sqrt{x^2 + y^2}\)

Considering the second point: \((x,y)\ to\ (-3,4)\)

\((x_1,y_1) = (x,y)\)

\((x_2,y_2) = (-3,4)\)

The distance is:

\(d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)

\(d = \sqrt{(x - (-3))^2 + (y - 4)^2}\)

\(d = \sqrt{(x + 3)^2 + (y- 4)^2}\)

\(d = \sqrt{x^2 + 6x + 9 + y^2- 8y + 16}\)

\(d = \sqrt{x^2 + 6x + y^2- 8y + 16 + 9}\)

\(d = \sqrt{x^2 + 6x + y^2- 8y + 25}\)

Equate both values of d

\(\sqrt{x^2 + 6x + y^2- 8y + 25} = \sqrt{x^2 + y^2}\)

Square both sides

\(x^2 + 6x + y^2- 8y + 25 = x^2 + y^2\)

Collect Like Terms

\(6x - 8y + 25 = x^2 -x^2+ y^2 -y^2\)

\(6x - 8y + 25 =0\)

Recall that \(y = 3x + 1\)

\(6x - 8(3x + 1) + 25 = 0\)

\(6x - 24x - 8 + 25 = 0\)

\(-18x+ 17 = 0\)

\(-18x=- 17\)

Solve for x

\(x = \frac{-17}{-18}\)

\(x = \frac{17}{18}\)

Substitute \(\frac{17}{18}\) for x in \(y = 3x + 1\)

\(y = 3 * \frac{17}{18} + 1\)

\(y = \frac{17}{6} + 1\)

\(y = \frac{17 + 6}{6}\)

\(y = \frac{23}{6}\)

Answer:

a = c2 +b2

Step-by-step explanation:

18=10000 + 784

10784 ÷ 18

599.111111 BUT ROUNDED WOULD BE 600.00

The horizontal and vertical asymptotes for the function f(x) =6/(-2x +1) is equal to y = 0 and x = 1/2 respectively.

Graph is attached.

As given in the question,

Given function is :

f(x) =6 /(- 2x +1)

f(x) = y

Degree of the numerator is zero

Degree of the denominator is 1.

Degree of denominator is greater than the degree of numerator.

Function represent the horizontal asymptotes for y =0

To get the vertical asymptotes equate denominator equals to zero

(- 2x +1) = 0

⇒2x = 1

⇒x = 1/2

Vertical asymptotes is given by x =1/2.

Graph is attached.

Therefore , the horizontal and vertical asymptotes for the given function is equal to y=0 and x =1/2 respectively.

The above question is incomplete, the complete question is:

Graph the rational function. f(x) =6 /(- 2x +1) Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button X.

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Answer:   v = yx/-w + u

Step-by-step explanation:

cancel -w by dividing and cancel u by dividing

Travis' famous letter, addressed to "The People of Texas and All Americans in the World," in which he passionately appealed for reinforcements and vowed to "never surrender or retreat," has become a symbol of the fortitude and sacrifice displayed by the Texan defenders at the Alamo.

The commander of the Texan forces at the Alamo during the famous battle in 1836 was Colonel William B. Travis. Travis, a lawyer and soldier, was chosen as the leader of the Texan garrison at the Alamo, a former mission turned fortress in San Antonio, Texas. He assumed command of the Texan forces in early 1836 and played a crucial role in the defense of the Alamo against the Mexican army led by General Santa Anna.

Travis and his men, along with notable figures such as James Bowie and Davy Crockett, bravely defended the Alamo against overwhelming odds for thirteen days. Despite their courage and determination, the Texan defenders were ultimately overrun by the Mexican forces on March 6, 1836, and suffered heavy casualties, including the deaths of Travis, Bowie, and Crockett.

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Therefore, Brittany paid a total of $497.05 for the 20 yards of mulch and the delivery.

In mathematics, an equation is a statement that two expressions are equal. Equations are written using an equals sign (=), which means that the expressions on both sides of the equals sign have the same value. Equations can have many different forms and types, depending on the variables and operations involved. Some common types of equations include linear equations, quadratic equations, exponential equations, trigonometric equations, and many others. Equations are used in many areas of mathematics and science, such as algebra, calculus, differential equations, physics, and engineering, to model and analyze the behavior of systems and phenomena. They are also used in computer programming and data analysis to solve problems and make predictions based on data.

Here,

Brittany paid for 20 yards of mulch, and the cost of the mulch is based on the amount of mulch delivered. We are given that for every 4 yards of mulch, the cost is $37.95. Therefore, the total cost for 20 yards of mulch can be found by multiplying the cost per 4 yards by 5, since 20 yards is 5 times 4 yards:

Cost of 20 yards of mulch = $37.95 x 5 = $189.75

In addition to the cost of the mulch, Brittany paid $307.30 for the delivery. Therefore, the total amount that Brittany paid for the mulch and the delivery is the sum of the cost of the mulch and the cost of the delivery:

Total amount paid = Cost of 20 yards of mulch + Cost of delivery

= $189.75 + $307.30

= $497.05

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