Carmen tutors history. For each hour that she tutors , she earns 30 dollars. Let E be her earnings (in dollars) after tutoring for H hours. Write an equation relating E to H. Then use the equation to find Carmen’s earnings after tutoring for 13 hours.

Equation: ______

Carmen’s earnings for 13 hour’s: ____ dollars

The graph of the given equations is (see in attachments). The roots are (-3,-2,3)

From the question, we have

x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12

The roots are (-3,-2,3)

Graph:

A graph is an organized visual representation of any data in mathematics. The relationship between the variable quantities is depicted on the graph. In a graph theory, the set of items that are somehow connected to one another is represented by a graph. The vertices or nodes of the objects are essentially mathematical notions, and the edges between the nodes represent the relationships between the nodes. In mathematics and statistics, there are various types of graphs that are used to visually display data. The study of points and lines is known as graph theory. It is a branch of mathematics that focuses on the investigation of graphs. The mathematical truth is shown visually in this picture. Relationships are studied using graph theory.

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Answer:

A on edge

Step-by-step explanation:

because i said so

Answer:

(x-4)^2  [I assume the (z+4)² option was mistyped.  Who wants zzzzzzzzz?]

Step-by-step explanation:

x² − 8x+16

Lok for a pattern that would allow us to fill in the missing numbers in

(x+a)*(x+b)

We know that a and b must equal +16 when multiplied together.  We also know their sum must be -8.  

a*b = 16

a+b = -8

Is there anything that ties these numbers together?  The number 4 comes to mind:  8 and 16 are known to be friendly to 4.  We need the sum to be -8, so lets make the 4 negative and put it into both expressions.

(-4)+(-4) = -8  YES

(-4)*(-4) = 16  YES

Assinging -4 to both a and b produces the factored expression:

(x-4)*(x-4) = x² − 8x+16    YES

Planet B has the larger mass. The mass of planet B is 50 times as large as the mass of planet A.

Mass of planet A = A = 8 * [tex]10^{23}[/tex]

Mass of planet B = B = 4 * [tex]10^{25}[/tex]

[tex]\frac{A}{B}=\frac{8 * 10^{23} }{4*10^{25} }[/tex]

    = [tex]\frac{2}{100}[/tex]

    = [tex]\frac{1}{50}[/tex]

50A = B

Hence, mass of Planet B is 50 times mass of planet B.

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The periodic interest rate for an account that is billed monthly with an APR of 32.99% will be 2.74%

Periodic interest rate is rate of interest over a short period of time. It is found by dividing APR ( annual percentage rate ) by the period of time given to us.

In this question it is given to us that the account is billed monthly so

periodic interest rate = 32.99 / 12

= 2.74%

Therefore periodic interest rate will be 2.74 for this account.

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The equivalent ratio of Pearls to Pizzas would be 13:2 and 13:4.

What is the ratio?

A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as 1: 3. (for every one boy there are 3 girls)

Luigi uses 39 mozzarella pearls for every 6 pizzas they make.

So the equivalent ratio would be 39/6

                                                     = 13:2

And similarly, Luigi uses 13 mozzarella pearls for every 4 pizzas they make.

So the equivalent ratio would be 13/4

                                                     = 13:4

Hence, the equivalent ratio of Pearls to Pizzas would be 13:2 and 13:4.

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The largest Volume of the box possible is 4000 cm³ .

In the question ,

it is given that

the box has a square base ,

let the length and width of the box = "x" , because it is a square

let the height of the box [tex]=[/tex] h

the total surface area of the box = 1200

also the total  surface area with open top is = x² + 4xh

So , x² + 4xh = 1200

h = (1200 - x²)/4x

According to the question ,

the volume of the box = x²h

Substituting the value of h = (1200 - x²)/4x ,

we get ,

Volume = x² × (1200 - x²)/4x

V = (1/4)(1200x - x³)

to Maximize the volume dV/dx = 0

(1/4)(1200 - 3x²) = 0

1200 - 3x² = 0

3x² = 1200

x² = 400

x = -20 , +20

length cannot be in negative , hence x = 20 ,

So , Volume = (1/4)[1200(20) - 20³]

= 4000 cm³

Therefore , The largest Volume of the box possible  is 4000 cm³ .

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The positive square root, then the negative square root of each of the following numbers are:

4, -4, 0.6,-0.6, 5,-5, 0.8, -0.8, 1.1, -1.1, 0.5, -0.5, 1.2, -1.2, 50, -50.

Given,

In the question:

Find the positive square root, then the negative square root of each of the following numbers:

The numbers are given as:

16, 0.36, 25, 0.64, 1.21, 0.25, 1.44, 2500

Now, According to the question;

Square Root:

The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is \sqrt{ } ​square root of, end square root . Finding the square root of a number is the opposite of squaring a number.

We have to find the Arithmetic Square Root Method

and, Add a minus sign to the Arithmetic root.

a) [tex]\sqrt{16}[/tex] = 4

[tex]-\sqrt{16}[/tex] = -4

b) [tex]\sqrt{0.36}[/tex] = 0.6

[tex]-\sqrt{0.36}[/tex] = -0.6

c) [tex]\sqrt{25}[/tex] = 5

[tex]- \sqrt{25}[/tex] = -5

d) [tex]\sqrt{0.64}[/tex] = 0.8

[tex]-\sqrt{0.64}[/tex] = -0.8

e) [tex]\sqrt{1.21}[/tex] = 1.1

[tex]-\sqrt{1.21}[/tex] = -1.1

f) [tex]\sqrt{0.25}[/tex] = 0.5

[tex]-\sqrt{0.25}[/tex] = -0.5

g) [tex]\sqrt{1.44}[/tex] = 1.2

[tex]-\sqrt{1.44}[/tex] = -1.2

h) [tex]\sqrt{2500}[/tex] = 50

[tex]-\sqrt{2500}[/tex] = -50

Hence, The positive square root, then the negative square root of each of the following numbers are:

4, -4, 0.6,-0.6, 5,-5, 0.8, -0.8, 1.1, -1.1, 0.5, -0.5, 1.2, -1.2, 50, -50.

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If we take any sample from population the mean of sample is approximately population mean always sample mean of 100 babies is 3500.

Statistics is a science concerned with developing and studying methods of collecting, analyzing, interpreting, and presenting empirical data. Statistical research is applicable to virtually all scientific disciplines, and research challenges in various scientific disciplines motivate the development of new statistical methods and theories. Statisticians use a variety of mathematical and computational tools to develop methods and study the theory behind methods. His two basic ideas in the field of statistics are uncertainty and variability. Science (or life in general) often encounters situations where the outcome is uncertain.

Sample mean is unbiased estimator of population mean.

so , if we take any sample from population the mean of sample is approximately population mean always.

therefore, sample mean of 100 babies is 3500.

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Answer:

x=7

Step-by-step explanation:

Use the Distributive Property to simplify the equation.

an=an-1+6, written in explicit formula when a = 9 is aₙ = 9n+5

An explicit formula is given as aₙ= a + (n - 1) d

where,

aₙ = nth term of the arithmetic sequence

a = the first term of the arithmetic sequence

d = the common difference

Given: aₙ = an-1+6 ;a1= 9

Substitute a = 9 into the equation:

aₙ = 9n-1+6

aₙ = 9n+5

Therefore, an=an-1+6, when a = 9 written in explicit formula, is aₙ = 9n+5

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The required ratios: a. Purchasers to non purchasers is 37:13 b. Non Purchasers to purchasers is 13:37 c. Purchasers to total customers is 37:50 d. Non Purchasers to total customers is 13:50

So, based on the information-

Non purchasers = 13

Purchasers = 37

Total customers = 50

Finding ratio by keeping the values as per the requirement -

a. Purchasers to non purchasers = 37:13

b. Non Purchasers to purchasers = 13:37

c. Purchasers to total customers = 37:50

d. Non Purchasers to total customers = 13:50

Hence, the ratios are a. 37:13, b. 13:37, c. 37:50 and d. 13:50.

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A rate of 3.76% per year for 30 years requires an initial principal investment of $281.95 to yield a total return of $600.00,

These considerations include the total amount you borrow from the bank, the loan's interest rate, and the time frame for finishing your mortgage repayment. You should use the following formula to calculate your mortgage:

M = P [i(1 + i)n] / [(1 + i)n - 1].

The first step is to convert R percent to r a decimal, which is 3.76%/100 or 0.0376 per year.

Our equation is solved as follows:

M = 600 / (1 + (0.0376 30)) = 281.95488721805 P = $281.95

A rate of 3.76% per year for 30 years requires an initial principal investment of $281.95 to yield a total return of $600.00,

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a = -2 is the value of linear equation .

What are examples of linear equations?

Step 1 - Write the equation.

3/a + 2 - 6a/a² - 4 = 1/a - 2

Step 2 - rewrite the equation.

3/a + 2 - 6a/a² - 4 = 1/a - 2

Step 3 - Take the LCM.

3(a- 2) - ( a + 2 )/a² - 2² = 6a/a²-4

Step 4 - Further simplify the above expression

3a - 6 - a - 2/a² - 4 = 6a/a² - 4

Step 5 - Cancel out the denominator of both sides and then further simplify.

2a - 8 = 6a

a = -2

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The complete question is -

A student solves the following equation and determines that the solution is −2. Is the student correct? Explain.

3/a + 2 − 6a/a2 − 4 = 1/a − 2

Answer:

If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then the triangles are congruent.

Answer:

∠ ADC = 113° , ∠ ABC = 85°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , then

∠ ADC + ∠ ACD + ∠ CAD = 180° , that is

∠ ADC + 39° + 28° = 180°

∠ ADC + 67° = 180° ( subtract 67°  from both sides )

∠ ADC = 113°

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

DA is an angle bisector of ∠ BAC , then

∠ BAD = ∠ CAD = 28° , then ∠ BAC = 56° , then

∠ ABC + ∠ BAC + ∠ ACB = 180° , that is

∠ ABC + 56° + 39° = 180°

∠ ABC + 95° = 180° ( subtract 95° from both sides )

∠ ABC = 85°

The percentage increase in the price of a technology stock is 1.69%.

According to the question,

We have the following information:

The price of a technology stock was $9.45 yesterday. Today, the price rose to $9.61.

We know that following formula is used to find the percentage increase:

Percentage increase = 100*(final price- initial price)/initial price

Percentage increase for the technology stock = 100*(9.61-9.45)/9.45

Percentage increase for the technology stock = 100*0.16/9.45

Percentage increase for the technology stock = 16/9.45

Percentage increase for the technology stock = 1.69%

Hence, the percentage increase in the price of a technology stock is 1.69%.

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Answer:

45c−20c2

Step-by-step explanation:

have great day

The number is -2. By using the concept of Linear Equation we get the number -2 as Answer of this question.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

Let the number be ‘x’

So According to the Question,

The number that is 11 times less than 21 which results in seven times of the number decreases by 29 can be written in the numerical form as

11x – 21 = 7x- 29

11x – 7x = -29+21

4x = -8

x = -8/4

x = -2

So that’s how we got the value of the x = -2

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Using the normal distribution, the probability that the sample proportion of households spending more than $125 a week is less than 0.3 is 30.29%.

Normal distribution refers to a continuous probability distribution wherein values lie in a symmetrical fashion mostly centered around the mean. In a normal distribution, the probability is calculated using the z-score of a measure X. A Z-score refers to a numerical measurement that defines a value's relationship to the mean (of a group of values).

In order to determine the probability of the sample proportion, the z-score of a measure X is determined.

z-score = (X - µ)/σ where µ is the mean and σ is the standard deviation.

The standard deviation σ = √(p(1-p)/n

From the given data:

n = no of random sample = 145

p = probability of success (household spending more than $125) = 0.32

Hence,

σ = √((0.32(1-0.32)/145) = 0.0387

Calculating the z-score when X = 0.3

z-score = (0.3 – 0.32)/0.0387 = -0.516

From the table, the probability of z = -0.516

P(X<z) = 0.30293 or 30.29%

The probability that the sample proportion of households spending more than $125 a week is less than 0.3 is 30.29%.

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Answer:

d

Step-by-step explanation:

angles on the circle subtended by the same arc are congruent

54° and x° are subtended by the same arc y , then

x = 54°

the measure of an inscribed angle is half the measure of its intercepted arc.

x and 54 are inscribed angles intercepted by arc y , then

y = 2 × 54° = 108°

Answer:

Why does each perfect square have two square roots?

Step-by-step explanation:

Why does each perfect square have two square roots?

The length of line segment is 10 units.

Writing the start and end points of line segment in (x, y) axis. First point = (-5, 5) and second point = (3, -1).

To calculate the line segment the formula to be used is -

d = ✓([tex] x_{2}[/tex] - [tex] x_{1}[/tex] )² + ([tex] y_{2}[/tex] - [tex] y_{1}[/tex] )²

Keep the values in formula

d = ✓(3 - (-5))² + (-1 - 5)²

d = ✓(3 + 5)² + (-6)²

Performing subtraction and addition based on sign

d = ✓8² + 36

Taking square on Right Hand Side of the equation

d = ✓64 + 36

Performing addition on Right Hand Side of the equation

d = ✓100

Taking square root on Right Hand Side of the equation

d = 10 units

Hence, the distance is 10 units.

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All of the ways to write this time are:

.A.

10 minutes before 7

.D.

50 minutes after 6

.E.

6:50

What is a Clock?

This is a device or timepiece used to tell or measure time. It is a 24-hour measurement instrument. it reads in am(the morning time) and pm (afternoon/night time).

The morning time starts at the midnight (1 am) and ends in the mid-day(12 noon). The afternoon time starts mid-day (1 pm) and ends at the midnight(12 midnight).

Hence, 12mid night -11 in the morning is designated am. 12 noon- 11 pm in the night is designated pm.

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Answer:

C. 34 - 16 = 18

ALSO

D. -4 - (-22)

   -4 + 22 = 18

Step-by-step explanation:

This is the REAL Question!

Which expressions have a value of 18?

Choose all answers that are correct.

A. –3 – 21 B. 7 – (–25) C. 34 – 16  D. –4 – (–22)

The expansion of the series will be 16 + 64 + 256 + 1024.

How to expand the series?

The expansion of a function into a series, or infinite sum, is known as a series expansion in mathematics. It is a technique for calculating a function that cannot be represented using just basic operators (addition, subtraction, multiplication and division).

The series is given as:

When n = 1, we have:

The series is given as S = (n=1,4)∑ [tex]4^{n+1}[/tex]

S = [tex]4^{2}+4^{3} +4^{4}+4^{5}[/tex]

S = 16 + 64 + 256 + 1024

Hence, the expansion of the series is 16 + 64 + 256 + 1024

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Answer:

-11[tex]x^{2}[/tex] + 13x- 13

Step-by-step explanation:

(x - 8x² - 15) + (2 + 12x - 3x²)

(x + 12x) + (- 8x² - 3x²) + (- 15 + 2) [Combine like terms]

-11[tex]x^{2}[/tex] + 13x- 13

The final polynomial equation after synthetic division is [tex]x^5-3x^4-81x+243[/tex]

We need to solve;

Put the solution in the appropriate spot on the grid after using synthetic division to divide the following polynomial. Respond with descending powers of x.

The polynomial equation given is;

[tex]\left(x^4-81\right)\left(x-3\right)[/tex]

By using synthetic division;

⇒ [tex]x^4x+x^4\left(-3\right)-81x-81\left(-3\right)[/tex]

    [tex]x^5-3x^4-81x+243[/tex]

→ The required final equation in descending powers of x is [tex]x^5-3x^4-81x+243[/tex] .

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First Dave picks his swimming day, then his running day, and then his biking day. Since each activity is different, the order in which he selects the days matters. Therefore the number of selections is P(7, 3).

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't. It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability. For instance, the theoretical chance of getting a head when tossing a coin is 1/2.

Here,

He does 3 activities in 7 days,

P(7,3) is the ways to select the schedule.

Dave chooses his swimming, running, and biking days in that order. The sequence in which he chooses the days is important because each activity is distinct. Consequently, P is the number of choices (7, 3).

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By using normal distribution, it is obtained that  the probability that a car has a gas mileage of between 29.8 and 30.2 miles per gallon is 0.2128

What is normal distribution?

Normal distribution is a continuous type probability distribution whose probability density function is

[tex]\frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{z^2}{2}[/tex]

where,  z = [tex]\frac{x - \mu}{\sigma}[/tex]

[tex]\mu[/tex] is the mean and [tex]\sigma[/tex]  is the standard deviation

For x = 29.8, z = [tex]\frac{29.8-30}{0.75}[/tex] = -0.27

For x = 30.2, z = [tex]\frac{30.2-30}{0.75}[/tex] = 0.27

so, P(29.8 < x < 30.2) = P(-0.27 < z < 0.27)

= 2 [tex]\times[/tex] P(z < 0.27)

= 2 [tex]\times[/tex] 0.1064

= 0.2128

Probability that a car has a gas mileage of between 29.8 and 30.2 miles per gallon is 0.2128

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