Given f(x) = -3(x + 2), what is the value of f(−7)?

Each worker would take home a net pay of $586.71.

What is the net pay?

The net pay is the amount of money that an employee takes home after all deductions have been made from their gross pay. Gross pay is the total amount of money an employee earns before taxes and other deductions are taken out.

To calculate net pay, you need to subtract all the required deductions from the employee's gross pay.

To calculate the net pay for each worker, we first need to determine their gross pay. The gross pay will depend on the number of hours they worked and whether they worked any overtime.

For the first 40 hours worked, each worker earns $15.90 per hour, so their gross pay for those hours would be:

Gross Pay for 40 hours = $15.90/hour x 40 hours = $636

For any hours worked beyond 40, the worker earns time and a half wages. This means they earn 1.5 times their regular hourly wage of $15.90, or $23.85 per hour. So, if they worked, for example, 45 hours in total, the additional 5 hours would be paid at the overtime rate, resulting in an additional gross pay of:

Gross Pay for 5 overtime hours = $23.85/hour x 1.5 x 5 hours = $178.88

Therefore, their total gross pay would be:

Total Gross Pay = Gross Pay for 40 hours + Gross Pay for 5 overtime hours = $636 + $178.88 = $814.88

Now, we need to calculate the deductions, which we are told are 28% of the gross pay. So the total deductions would be:

Total Deductions = 28% x $814.88 = $228.17

Finally, to determine the net pay, we need to subtract the total deductions from the gross pay:

Net Pay = Gross Pay - Total Deductions = $814.88 - $228.17 = $586.71

Therefore, each worker would take home a net pay of $586.71.

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Answer:

11xy(121x²-y²)

Step-by-step explanation:

When factorizing, you should always look for what each term has in common.

First, let's look at the coefficients (numbers) in each term: 1331 and 11. Both are divisible by 11, so let's factorize out 11:

1331x³y-11y³x

11(121x³y-y³x)

Looking at the terms in the bracket, we see they both have 'x's in common (121x³y has three x's multiplied in and y³x has one). Let's factorize out this x:

11(121x³y-y³x)

11x(121x²y-y³)

We can also see both terms in the brackets have 'y's in common (121x²y has one y and y³ has three multiplied in). Let's factorize out this y:

11x(121x²y-y³)

11xy(121x²-y²)

Since there is nothing in common left between the terms, we can say the expression is fully factorized!

Answer:

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

Given inequality:

Consider x ≠ 0 and multiply all terms by x, 4 and 3:

The x-intercepts are:

This quadratic function has a positive leading coefficient and two zeros, and hence is positive when:

The matching choice is C.

The mean of the sampling distribution (p) and The standard error of the mean (o)  are 56 and 2 respectively.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

(a) The mean of the sampling distribution (p) is equal to the population mean, which is 56.

(b) The standard error of the mean (o) is calculated as the standard deviation of the population divided by the square root of the sample size. So for a sample of 36 participants:

o = 12 / √36 = 2

(c) The distribution of the sample means (p) will be approximately normal with a mean of 56 and a standard deviation of 2. To sketch this distribution with M ± 3 SEM, we would plot a normal distribution with mean 56 and standard deviation 2, and shade the region that is 3 standard errors away from the mean on either side.

This region would capture approximately 99.7% of the data if the samples were selected randomly and independently from the population.

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6,000 grams is equivalent to 6 kilograms.

The problem is solved by converting the given dimensions from grams to kilograms. The conversion is from a smaller metric unit to a larger metric unit.

A kilogram is a larger unit of measurement for mass or weight compared to a gram.

The prefix kilo in kilogram means 1000, so one kilogram is equal to 1000 grams.

Therefore, to convert from grams to kilograms, you simply divide the number of grams by 1000.

In this case, 6,000 grams divided by 1000 equals 6 kilograms.

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a) The probability of rolling a 5 or a number greater than 3 is 1/2.

b) The probability of rolling a number less than 4 or an even number is 5/6.

c) The probability of rolling a 4 or an odd number is 2/3.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

In rolling a six-sided die, the total number of outcomes is 6.

The sample space is {1,2,3,4,5,6}

The probability formula is -

Probability = Number of outcomes corresponding to events / total number of outcomes.

(a)  Let A be the event of rolling a 5. Then A = {5}.

Let B be the event of rolling a number greater than 3. Then B = {4,5,6}.

The event of rolling A or B is given by A∪B = {4,5,6}.

So, apply the probability formula -

P(A∪B) = 3/6 = 1/2

Therefore, the probability value is 1/2.

(b)  Let C be the event of rolling a number less than 4. Then C = {1,2,3}.

Let D be the event of rolling an even number. Then D = {2,4,6}.

The event of rolling C or D is given by C∪D = {1,2,3,4,6}.

So, apply the probability formula -

P(C∪D) = 5/6

Therefore, the probability value is 5/6.

(c)  Let E be the event of rolling a 4. Then E = {4}.

Let F be the event of rolling an odd number. Then F = {1,3,5}.

The event of rolling E or F is given by E∪F = {1,3,4,5}.

So, apply the probability formula -

P(E∪F) = 4/6 = 2/3

Therefore, the probability value is 2/3.

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The x-coordinate of P is given as follows:

x = 4.

The x-coordinate of P is obtained applying the proportions in the context of this problem.

The partition ratio is 2:4, hence the equation to obtain the coordinates is given as follows:

P - A = 2/6(B - A)

P - A = 1/3(B - A).

Then the x-coordinate of P is obtained as follows:

x - 10 = 1/3(-8 - 10)

x - 10 = -6

x = 4.

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Answer:

28

Step-by-step explanation:

IF 20 GALLONS IS EQUIVALENT TO 5 SECONDS WHAT ABOUT 7 SECONDS

CROSS MULTIPLY

Answer:

20 gallons / 5 seconds = 4 gallons / second

Therefore, In 7 seconds you get (7 x 4 ) or 28 gallons.

Step-by-step explanation:

Answer:

2+1=3, 7+8=15, 0+1=1, 8+7=15, 2+9=11, 1+3=4, 2+0=0, 4+5=9, 3+4=7

A function is given net change and the average rate of change between the given values of the variable.

A.   = -  [tex]\frac{4h}{7h + 49}[/tex]

B.  = - [tex]\frac{4}{7h + 49}[/tex]

Examples of average rates of change include: 80 kilometres per hour is the average speed of a bus. At a pace of 100 each week, a lake's fish population grows. For every 1 volt drop in voltage, the current in an electrical circuit reduces by 0.2 amps.

a) The net change is just the difference between g(h) and g(0). This is found below.

g(h) - g(0) = [tex]\frac{4}{h + 7}[/tex] - [tex]\frac{4}{0 + 7}[/tex]

                = [tex]\frac{28 - 4h -28}{7h + 49}[/tex]

               = -  [tex]\frac{4h}{7h + 49}[/tex]

b) The average rate of change is the net change divided by the length of the interval. This is:

[tex]\frac{g(h) - g(0)}{h - 0}[/tex] = - [tex]\frac{{4h}/{7h + 49}}{h - 0}[/tex]

             = - [tex]\frac{4}{7h + 49}[/tex]

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Answer:

784 R 13

Hope this helps!

Step-by-step explanation:

Answer:

To find the probability of Miko taking a red marble first, then a white marble, we can use the formula for joint probability:

P(red, then white) = P(red) * P(white | red)

Where P(red) is the probability of Miko taking a red marble first and P(white | red) is the probability of Miko taking a white marble second, given that he took a red marble first.

P(red) = 3/12 = 1/4

P(white | red) = 4/12 = 1/3

So,

P(red, then white) = 1/4 * 1/3 = 1/12

Therefore, the probability of Miko taking a red marble first, then a white marble is 1/12.

Answer:

2) 47 snow globes (51+8-12) 23) 130 snowballs (46+59+25) 4) 92 penguins (83+69-55)

Answer:

y = 36

Step-by-step explanation:

Given logarithmic equation:

[tex]\log_4(y-9)+\log_43=\log_481[/tex]

[tex]\textsf{Apply the \textbf{log product law}}: \quad \log_ax + \log_ay=\log_axy[/tex]

[tex]\implies \log_4\left(3(y-9)\right)=\log_481[/tex]

[tex]\textsf{Apply the \textbf{log equality law}}: \quad \textsf{If $\log_ax=\log_ay$ then $x=y$}[/tex]

[tex]\implies 3(y-9)=81[/tex]

Divide both sides of the equation by 3:

[tex]\implies \dfrac{3(y-9)}{3}=\dfrac{81}{3}[/tex]

[tex]\implies y-9=27[/tex]

Add 9 to both sides of the equation:

[tex]\implies y-9+9=27+9[/tex]

[tex]\implies y=36[/tex]

Therefore, the solution to the given logarithmic equation is y = 36.

Answer: look at the image for the answer and the solution

Step-by-step explanation:

Using Pythagorean theorem, The value of cos(S) rounded to the nearest hundredth is approximately 0.78.

It is the simplest polygon and a key component in many branches of science and mathematics.

A triangle's three sides can be equilateral, isosceles, scalene, or any other combination of lengths and kinds. An isosceles triangle has a third side that is a different length from the other two sides, while an equilateral triangle has three sides that are all the same length. All three of the sides of a scalene triangle are different lengths.

In triangle STU, right angled at T, we have:

[tex]ST = 6UT = \sqrt{(22)}[/tex]

We can use the Pythagorean theorem to find the length of TU:

[tex]TU^2 = ST^2 + UT^2\\TU^2 = 6^2 + (\sqrt{(22)})^2\\TU^2 = 36 + 22\\TU^2 = 58\\TU = sqrt(58)\\[/tex]

Now, we can use the definition of cosine:

cos(S) = adjacent/hypotenuse

In this case, the adjacent side to angle S is ST and the hypotenuse is TU. Therefore:

[tex]cos(S) = ST/TU\\cos(S) = 6/\sqrt{(58)}[/tex]

To round to the nearest hundredth, we can divide 6 by the rounded value of sqrt(58):

cos(S) ≈ 0.78 (rounded to the nearest hundredth)

Therefore, the value of cos(S) rounded to the nearest hundredth is approximately 0.78.

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The equation cos (π/6 + β) is solved to get

From the question it was given that sine β = -0.8

solving for β

sine β = -0.8

β = arc sine ( -0.8 )

β = -0.9273

β ≈ -π/3

substituting the value into cos (π/6 + β)

cos (π/6 + β)

cos (π/6 - π/3)

cos (π/6 - π/3)

= √3 / 2

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Answer:

Step-by-step explanation:

Step 1: Define each variable

Let's define some variables to make the calculations easier:

t1 = the median monthly rent in 1990, which is $447

t2 = the median monthly rent in 2002, which is $658

Δ = the change in median monthly rent, which is t2 - t1

Step 2: Calculate the change in median monthly rent

Δ = t2 - t1 = $658 - $447 = $211

This means that the median monthly rent increased by $211 from 1990 to 2002.

Step 3: Divide the change by the original amount

To find the percentage increase, we need to divide the change by the original amount and multiply by 100:

Δ / t1 * 100 = ($211 / $447) * 100 = 47.2%

This means that the median monthly rent increased by 47.2% from 1990 to 2002.

Step 4: Round to the nearest tenth of a percent

The final answer is 47.2%, rounded to the nearest tenth of a percent.

The percent increase in the median monthly rent prices from 1990 to 2002 was 47.2%.

Answer:

To solve it, you need to use probability. Let me show you how.

We can use a tree diagram to represent the possible outcomes of the last ball. Here is the diagram:

```

Haris Rauf

/        \

yorker   full toss

0.8       0.2

/  \      /  \

boundary no boundary boundary no boundary

0.2  0.8  0.9  0.1

```

The probability of a boundary is the sum of the probabilities of the branches that end with a boundary. To find the probability of each branch, we multiply the probabilities along the branch. For example, the probability of a yorker and a boundary is 0.8 × 0.2 = 0.16.

So, the probability of a boundary is:

0.8 × 0.2 + 0.2 × 0.9 = 0.16 + 0.18 = 0.34

Therefore, the probability that a boundary will be scored of the last ball is 0.34 or 34%.

Step-by-step explanation:

The surface area of the pyramid is 116.4 sq. ft.

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.

For each three-dimensional geometrical shape, surface area and volume are determined. The area or region that an object's surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has.

The surface area of the pyramid is calculated by adding the area of all the faces of the pyramid.

The area of the triangle is given as:

A = 1/2 (b)(h)

For the face of the pyramid:

b = 12 and h = 9

Substituting the values we have:

A = 1/2 (12)(9)

A = 54 sq. ft

The pyramid consists of three faces thus,

A = 3(54) = 162 sq ft

For the base of the pyramid:

b = 12 and h = 10.4 ft

A = 1/2(12)(10.4)

A = (6)(10.4)

A = 62.4 sq ft

The surface area of the pyramid is:

SA = 54 + 62.4

SA = 116.4 sq. ft

Hence, the surface area of the pyramid is 116.4 sq. ft.

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Answer:

14 cm

Step-by-step explanation:

The formula for circumference of a circle is 2πr, where r is the radius. In this problem, the circumference would be 2π * 7cm = 14 cm

Answer:

2. 56°

4. 56°

For number 6, it is not shown on the photo, sorry!

Step-by-step explanation:

2. The square at the corner means that it is 90°, so 90 - 34 = 56

4. The line is straight, so it means that it is 180°, so 180 - 124 = 56

The solution is, the value is, x = 49.6.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

given that,

There is a pair of vertical angles where ∠1=106° and ∠2=3x−75

so, 1 + 2 = 180

or, 106 + 3x - 75 = 180

or, 3x = 149

or, x = 49.6

Hence, The solution is, the value is, x = 49.6.

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The mortgage of A is $110158.2.

The mortgage of B is $137494.8.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Mortgage A:

15 years at 4.5% with monthly payments of $611.99.

15 years = 15 x 12 = 180 months

Total paycheck.

= 180 x 611.99

= $110158.2

Mortgage B:

30 years at 4% with monthly payments of $381.93

30 years = 360 months

Total paycheck.

= 360 x 381.93

= $137494.8

Thus,

Mortgage A = $110158.2

Mortgage B = $137494.8

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The length of segment YS within the square QRST is equal to 6.

Squares are quadrilaterals with four sides of equal length and two diagonals of equal length, in that order, diagonals QS and RT are the diagonals of square QRST. Besides, we have the following information:

VY = 13, RV = 19

The length of segment YS can be found by means of the following formula:

RV = VY + YS

YS = RV - VY

YS = 19 - 13

YS = 6

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The company will be able to purchase enough pens while staying within the budget by purchasing 10 mugs only not more than that.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

A company has a budget of $305

Company needs to purchase either a mug or a pen for each of its 100 clients.

Price per Mug $5.55 Price per Pen $2.50

Now,

Price of pen = 100*2.50=250

When the number of employees are 10

=10*5.50=55.0

Mugs can be purchased

When the number of employees are 15

=15*5.50=82.5

Mugs cannot be purchased

Therefore, by algebra the answer will be 10 mugs only.

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1. The Venn diagrams are attached

2. When the statistics students number = 10·x + 3, we have;

The number of students that study

When the statistics students number = 2·x + 3, we have;

The number of students that study

The parameters given are;

Total number of students = 30

Therefore;

The number of students that study either algebra or statistics = n(A∪B)

From set theory we have;

n(A∪B) = n(A) + n(B) - n(A∩B)

n(A∪B) = 30 - 3 = 27

Therefore, we have;

The number of students that study

a. Algebra

n(A) = 18/11 + 10 = 128/11

b. Statistic

n(B) = 213/11

Hence, we have;

n(A - B) = n(A) - n(A∩B) = 128/11 - 4 = 84/11

Similarly, we have;

n(B - A) = n(B) - n(A∩B) = 213/11 - 4 = 169/11

However, assuming n(B) = (2·x + 3), we have;

n(A∪B) = n(A) + n(B) - n(A∩B)

n(A∪B) = 30 - 3 = 27

Therefore, we have;

n(A∪B) = x + 10 + 2·x + 3 - 4 = 27

2·x+3 + x + 10= 27 + 4 = 31

3·x = 18

x = 6

Therefore, the number of students that study

a. Algebra

n(A) = 16

b. Statistics

n(B) = 15

Hence, we have;

n(A - B) = n(A) - n(A∩B) = 16 - 4 = 12

Similarly, we have;

n(B - A) = n(B) - n(A∩B) = 15 - 4 = 11

The Venn diagrams can be presented as follows;

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The number of hours Maria rent the kayak for the paid amount of $40 when hourly rate is $5.50 is equal to 6 hours.

Fees of renting charges paid for kayaks from a local shop = $7

Hourly rate = $5.50

Let 't' be the number of hours Maria rent kayak.

Total fees paid by Maria for renting kayak for 't' hours is equal to $40

Required equation to represents the above condition is

$40 = $7 + $5.50t

Simplify the expression to get the value of 't'

⇒ 5.50t = 40 - 7

⇒ t = 33 / 5.50

⇒ t = 6 hours

Therefore, for the number of hours Maria rent kayak by paying total of $40 is equal to 6 hours.

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Answer:

2nd choice  y = 1/2x - 5

Step-by-step explanation:

y = 1/2x - 5  is the only function listed that if you graph it, it makes a straight line.   A linear function forms a straight line when it is plotted on a graph.

The first and last choices are number values of x.

The 3rd choice, if you graph it, makes a parabola.

Answer:

Second option:

[tex]y = \dfrac{1}{2}x -5[/tex]

Step-by-step explanation:

A linear function should have y as a function of x (or x as a function of y) and the degree of the function (the highest power has to be 1)

Both x and y must be present to make it a linear function

General slope intercept form is y = mx + b where m = slope, b = y-intercept

With these restrictions the second option is the correct one
[tex]y = \dfrac{1}{2}x -5[/tex]

This line is in slope intercept form y = mx + b where m = slope(in this case 1/2) and y-intercept b(in this cae -5)

Option 1:  x = 3 is a straight vertical line parallel to the y-axis. Such a line has a slope of ∞

Option 3 is a function with degree 2 and is a quadratic function

Option 4 : 3x - 6 = 4==> 3x = 6 + 4 = 10 or x = 10/3, again another vertical line with slope = ∞