Pls help me fast fast fast

Pls Help Me Fast Fast Fast

Answers

Answer 1

The value of ∠E = 31 degrees and the value of ∠G = 149 degrees for the given triangle.

What are similar triangles?

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "."

The two triangles are similar thus the measure of its angle are also equal.

Using the similar triangle we have:

Angle D = Angle A = 82 degrees.

Angle F = 67 degrees

Using the sum of interior angles of triangle we have:

∠D + ∠F + ∠E = 180

82 + 67 + ∠E = 180

∠E = 31

From the figure we observe that,

∠E + ∠G = 180 (straight line)

31 + ∠G = 180

∠G = 149

Hence, the value of ∠E = 31 degrees and the value of ∠G = 149 degrees for the given triangle.

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Related Questions

Alicia's doctor allowed her to eat junk food every fifth day. If Alicia had junk food on Monday and Saturday, what are the next two days that she will be allowed to have junk food?​

Answers

The next two days when Alicia would be allowed to eat junk foods are Thursday and Tuesday.

When would Alicia eat junk food?

The first day after Saturday when Alicia would have junk food can be determined by counting the fifth day after Saturday.

Sunday - first day

Monday - second day

Tuesday - third day

Wednesday - fourth day

Thursday - fifth day

The next day after Thursday when Alicia would have junk food is the fifth day after Thursday.

Friday - first day

Saturday - second day

Sunday - third day

Monday - fourth day

Tuesday - fifth day

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(a) Share £40 in the ratio 1:3:4
(c) Share 88p in the ratio 2:4:5
(d) Share 180° in the ratio 2:2:5
Pls help, if you don't mind
I would rlly appreciate that ​

Answers

£40 is shared as £5, £15 and £20. 88p is shared as 16p, 32p and 40p. 180° is shared as 40°, 40° and 100°

What is an equation?

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

a) Share £40 in the ratio 1:3:4

For the first ratio = (1/8) * £40 = £5

For the second ratio = (3/8) * £40 = £15

For the third ratio = (4/8) * £40 = £20

b) Share 88p in the ratio 2:4:5

For the first ratio = (2/11) * 88p = 16p

For the second ratio = (4/11) * 88p = £32

For the third ratio = (5/11) * 88p = 40p

c) Share 180° in the ratio 2:2:5

For the first ratio = (2/9) * 180° = 40°

For the second ratio = (2/9) * 180° = 40°

For the third ratio = (5/9) * 180° = 100°

The ratios are shown above

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your three circles may not have intersected exactly at a single point. how could you improve your results

Answers

Increase the accuracy of your measurements by using a more precise instrument or tool, such as a protractor or ruler.

The accuracy of the intersection of your three circles may not have been exact due to imprecise measurements taken. To improve the results, you could use a more precise instrument or tool, such as a protractor or ruler. With a protractor , you can measure the angle of the intersection of the circles more accurately. If a ruler is used, make sure that it is a straight edge, and measure the distance between the circles to ensure they intersect at the same point . Once the measurement is taken, draw the circles and their intersection accordingly. Doing this will help improve the accuracy of the intersection of the three circles and yield better results.

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In a recent school newspaper survey, 3,000 randomly selected teenagers were asked to cite their primary transportation method to school. Fifteen of 20 teenagers said they use their own car to get to school. A 90% confidence interval to estimate the true proportion of teenagers who drive their own car to school is found to be (0.5907, 0.9093). Which of the following is a correct interpretation of the confidence level?

Ninety percent of the time, the procedure used to generate this interval will capture the true proportion of teenagers who drive their own car to school.
Ninety percent of all samples of this size would yield a confidence interval of (0.5907, 0.9093).
There is a 90% chance that the true proportion of teenagers who drive their own car to school will be (0.5907, 0.9093).
Ninety percent of all the samples of size 3,000 lie in the confidence interval (0.5907, 0.9093).

Answers

The correct interpretation of the 90% confidence interval is given as follows:

There is a 90% chance that the true proportion of teenagers who drive their own car to school will be (0.5907, 0.9093).

What is the interpretation of a x% confidence interval?

It means that it is x% likely that the true population parameter(mean/proportion/standard deviation) is between a and b, which are the bounds of the confidence interval.

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What percentage of the marbles in the jar are white?
O 20%
O 40%
O 60%
O 80%

Answers

The percentage of white marbles on the jar is obtained dividing the number of white marbles by the total number of marbles.

How to calculate a percentage?

A percentage is calculated applying a proportion, dividing the number of total outcomes by the number of desired outcomes, and then multiplying by 100%.

The outcomes for this problem are given as follows:

Desired: number of white marbles.Total: total number of marbles.

Missing Information

The problem is incomplete, hence the standard procedure to obtain the percentage of white marbles was presented.

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32 Ounces of Juice for $7.04. How much per ounce

Answers

Answer:

$0.22.

Step-by-step explanation:

To find the cost per ounce of juice, divide the total cost of 32 ounces of juice by the number of ounces:

7.04 ÷ 32 ounces = 0.22 per ounce

So, the cost per ounce of juice is approximately $0.22.

Answer:

0.22

Step-by-step explanation:

Write a polynomial for the area of the shaded region.

Answers

The polynomial for the shaded area will be 3x² + 15x and x² + 6x + 8.

What is the area of the rectangle?

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L × W square units

19. The area is given as,

A = (x + 5)(3x)

A = 3x² + 15x

19. The area is given as,

A = (x + 4)(x + 2)

A = x² + 6x + 8

The polynomial for the shaded area will be 3x² + 15x and x² + 6x + 8.

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What additional piece of information do you need to prove that ALKN-AKNM by the SAS similarity theorem?
A. MN=1/2
B.MN=1
C. MN/LK||MN
D. LN=2/5

Answers

The additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem is option C, MN/LK||MN.

What is SAS (Side-Angle-Side) similarity theorem?

The SAS (Side-Angle-Side) similarity theorem states that if two triangles have two pairs of corresponding sides that are in proportion, and the included angles are congruent, then the triangles are similar.

In this case, we know that ΔLKN and ΔKNM share the angle at vertex K, and we also know that LN/MN and LK/KN are in proportion.

However, we need to establish that MN/LK||MN, which means that MN is parallel to LK and forms a transversal with LN.

This information is necessary to establish that the included angles between the corresponding sides are congruent, which is required for the triangles to be similar.

Therefore, option C is the correct additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem.

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What are the coordinates of the centroid of ABC? A. (1/2, -2 1/2) B. 2 2/3, -3 1/3) C. (4, -3) D. (7, -5)

Answers

The centroid of the given triangle is [tex]( 2\frac{2}{3} , -3\frac{1}{3} )[/tex], which is option B.

What is a centroid of a triangle?

A place where a triangle's medians coincide is the centroid of the triangle. The line segments that are drawn from a vertex to the midpoint of the vertex's opposite side are known as medians.

A triangle is divided into two smaller triangles with equal areas by each of its medians. The centroid of a triangle is where the medians of the triangle cross. Unlike other points of concurrency in a triangle, the centroid always lies inside one.

The formula of the centroid of a triangle when the coordinates of the vertices are known is:

Centroid = [tex](\frac{x_1 +x_2+x_3}{3} , \frac{y_1 +y_2+y_3}{3})[/tex]

From the graph, we can find the vertices of the triangle

A = (x₁, y₁) = (-3,-7)

B = (x₂,y₂) = (5,1)

C = (x₃,y₃) = (6,-4)

Centroid = [tex](\frac{x_1 +x_2+x_3}{3} , \frac{y_1 +y_2+y_3}{3}) = (\frac{-3+5+6}{3} ,\frac{-7+1-4}{3}) = (\frac{8}{3} ,\frac{-10}{3} ) = ( 2\frac{2}{3} , -3\frac{1}{3} )[/tex]

Therefore the centroid of the given triangle is [tex]( 2\frac{2}{3} , -3\frac{1}{3} )[/tex].

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how does multivariable calculus in college compare with ap calculus bc in high school? is there a significant gap in difficulty?

Answers

Multivariable calculus in college is generally more challenging than AP Calculus BC due to the additional complexity of working with functions of several variables.

Multivariable calculus in college typically goes beyond the content covered in AP Calculus BC in high school. While both cover calculus concepts, multivariable calculus adds the complexity of working with functions of several variables, including partial derivatives, multiple integrals, and vector calculus. As a result, the difficulty level of multivariable calculus in college can be significantly higher than AP Calculus BC. However, this can vary depending on the individual student and the rigor of their high school AP course.

AP Calculus AB and BC are two levels of Advanced Placement calculus courses typically offered in high school.

AP Calculus AB covers a wide range of calculus topics including limits, derivatives, integrals, applications of derivatives and integrals, and the Fundamental Theorem of Calculus. The focus is on single-variable calculus, meaning students work with functions of one variable.

AP Calculus BC, on the other hand, covers all the topics included in AB as well as additional concepts such as parametric, polar, and vector functions, series, and sequences. The course is designed to be more challenging and covers more advanced topics in calculus, including applications of calculus in physics and engineering.

Overall, AP Calculus BC is considered to be a more rigorous course than AP Calculus AB, but both courses prepare students for college-level calculus.

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On the windowsill is a plant that is 3 inches tall. It is growing 4 inches per week. A second plant, which is 17 inches tall, is on the coffee table. It is growing 2 inches per week. Eventually the two plants will be the same height. How many weeks will that take? How tall will the plants be?

Answers

The two plants would have the same height in 7 weeks and the height would be 31 inches.

When would the plants have the same height?

The form of the expression that represents the length of the plant on the window sill is:

initial length + (length of growth per week x number of weeks)

3 + (4 x w)

3 + 4w

The form of the expression that represents the length of the plant on the coffee table is:

initial length + (length of growth per week x number of weeks)

17 + (2 x w)

17 + 2w

When the two plants have the same height, the two expressions would be equal:

17 + 2w = 3 + 4w

17 - 3 = 4w - 2w

14 = 2w

w = 14/2

w = 7 weeks

Height of the plant = 3 + 4(7)

3 + 28 = 31 inches

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how do you know how adding a smaller data point will affect the mean or median if its smaller than them

Answers

When the smaller data point is included, the mean will drop when compared to the other values, but the median may increase or decrease depending on whether the collection of numbers is even or odd.

1. Calculate the original set of numbers' mean and median.

2. Include the lesser data point in the collection.

3. Determine the updated median and mean.

4. Evaluate the original mean and median in comparison to the new mean and median. Depending on whether the collection of numbers is even or odd, the median will decline while the mean will increase.

We must first determine the mean and median of the initial set of data in order to evaluate how the addition of a smaller data point will impact those values. Adding together all the values and dividing by the total number of values yields the mean. We place the middle value in the set of integers after sorting them from least to largest to determine the median. We include the new, smaller data point in the set after finding the mean and median. We next perform the same calculations as previously to determine the new mean and median. Finally, we contrast the updated mean and median with the baseline values. The median may stay the same or drop depending on whether the set of numbers is even or odd, while the mean often decreases as it is compared to other values. The mean and median of a set of numbers can therefore be significantly affected by the addition of a tiny data point.

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The complete question is

how do you know how adding a smaller data point will affect the mean or median if its smaller than them other value.

Mr. Schwartz builds toy cars. He begins the week with a supply of 85 wheels, and uses 4 wheels for each car he builds. Mr. Schwartz plans to order more wheels once he has fewer than 40 wheels left.
The inequality that can be used to find the number of cars, x, Mr. Schwartz builds before he places an order for more wheels is

Answers

Answer:

solution: Mr. Schwartz will need to order more wheels after building 12 cars.

explanation:

Mr. Schwartz begins with total number of wheels = 85

he has to order more wheels once he left with less than 40 wheels

so min. no. of wheels he can use before ordering more wheels = 85-40 = 45

Mr. Schwartz uses 4 wheels to build 1 car

Mr. Schwartz uses 45 wheels to build 45÷4 = 11.25 cars

then, if he builds 12 cars then he needs 12×4 = 48 wheels

total supply of wheels he begins with = 85

wheels he used to build 12 cars = 48

so total number of wheels remaining are = 85-48 = 37

since 37 is less than 40 so after building 12 cars Mr. Schwartz need to order more wheels.

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Given the function f(x) = 4x^3 - 4, find the value of f(- 1/2)

Answers

The function [tex]f(x) = 4x^3 - 4[/tex] is a polynomial function. It takes an input value x and returns an output value f(x) based on the expression [tex]4x^3 - 4.[/tex]So the value of f(-1/2) is -4.5.

When we evaluate f(-1/2), we substitute -1/2 for x in the expression for f(x). This gives us:

[tex]f(-1/2) = 4(-1/2)^3 - 4[/tex]

The expression inside the parentheses, [tex](-1/2)^3,\\[/tex] is the cube of -1/2. To simplify this expression, we need to first raise -1/2 to the power of 3:

[tex](-1/2)^3 = (-1/2) * (-1/2) * (-1/2) = -1/8[/tex]

Next, we substitute this value back into the expression for f(-1/2):

f(-1/2) = 4(-1/8) - 4

Now we can simplify the expression by multiplying 4 and -1/8:

f(-1/2) = -1/2 - 4

Finally, we subtract 4 from -1/2 to get the final answer:

f(-1/2) = -4.5

So the value of f(-1/2) is -4.5.

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Given the function f(x) = 4x^3 - 4, find the value of f(- 1/2)?

Franklin’s mountain bike weighs 17,000 grams. How many kilograms does his bike weigh?
A
17 kilograms
B
170 kilograms
C
1700 kilograms
D
17,000 kilograms

Answers

The weight of Franklin’s mountain bike in kilograms which  weighs 17,000 grams is equal to option A. 17 kilograms.

Weight of Franklin’s mountain bike  in grams is equal to 17,000 grams

Convert the grams into kilograms.

One kilograms is equal to one thousand grams

1 kilograms = 1000 grams

⇒ 1 grams = ( 1 / 1000 ) kilograms

⇒ 17,000 grams = ( 17,000 / 1000 ) kilograms

⇒ 17,000 grams = 17 kilograms

Therefore, after converting grams into kilograms the weight of Franklin’s mountain bike whose weight in grams is 17,000 grams  is equal to option A. 17 kilograms.

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in a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the ___________ come from a normal distribution.

Answers

The answer to the given fill in the blanks is "Residual". in a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the Residual come from a normal distribution.

In linear regression, we make several assumptions about the relationship between the predictor variable and the response variable. One of these assumptions is that the residuals (the differences between the predicted values and the actual values) follow a normal distribution with a mean of zero and constant variance. To check this assumption, we can create a normal quantile plot of the residuals. A normal quantile plot is a graphical method that compares the distribution of the residuals to a normal distribution. If the residuals are normally distributed, the plot should follow a straight line. If the plot deviates from a straight line, it suggests that the residuals are not normally distributed. A non-normal distribution of residuals can have several implications, such as indicating the presence of outliers or influencing the accuracy of the model’s prediction. Therefore, checking for normality of residuals is a crucial step in evaluating the model's assumptions and determining whether the model is appropriate for the data.

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how many people have to be in a room in order that the probability that at least two of them celebrate their birthday in the same month is at least assume that all possible monthly outcomes are equally likely.

Answers

The people having to be in a room in order that the probability that at least two of them celebrate their birthday in the same month is at least 1/2 is 5.

X = No of people having same month birth day

We need, P(X 2) ≥ 1/2

= 1-P(X ≤1) ≥ 1/2

1-P(No one having same month birth day) ≥ 1/2

P(No one having same month birth day)≤ 1/2..........................(1)

Now, k = Minimum no of people required to satisfy (1)

P(No one having same month birth day) =

[tex]\frac{11*10*9......*(12-k+1)}{12*12*12......*12}[/tex]

for k= 4

P(No one having same month birth day) =

[tex]\frac{11.10.9}{12.12.12} = 0.572 \geq 0.5[/tex]

for k= 5

P(No one having same month birth day) =

[tex]\frac{11.10.9.8}{12.12.12.12} = 0.38 \leq 0.5[/tex]

Therefore , the people having to be in a room in order that the probability that at least two of them celebrate their birthday in the same month is at least 1/2 is 5.

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Unit 5 Lesson 4 Practice Problems o
1. Match each equation with a description of the function it represents.
a. f(x) = 2x+4
b. g(x) = 2(x+4)
c. h(x) = 4x+2
d. k(x) = 4(x + 2)
14 Student
1.
To get the output, add 4 to the input, then multiply the
result by 2.
2.
To get the output, add 2 to the input, then multiply the
result by 4.
3. To get the output, multiply the input by 2, then add 4 to
the result.
4. To get the output, multiply the input by 4, then add 2 to
the result.

Answers

On solving the provided question, we can say that equation, k(x) = 4(x + 2) represents the function where you add 2 to the input, then multiply the result by 4.

What is equation?

A mathematical equation is a formula that links two assertions and signifies equivalence with the equals sign (=). In algebra, a mathematical statement that proves the equality of two mathematical expressions is referred to as an equation. The equal sign, for instance, separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14. There is a mathematical formula that explains the link between the two phrases that appear on either side of a letter. Frequently, the symbol and the single variable are the same. like in 2x - 4 = 2, for example.

a. f(x) = 2x+4 represents the function where you multiply the input by 2, then add 4 to the result.

b. g(x) = 2(x+4) represents the function where you add 4 to the input, then multiply the result by 2.

c. h(x) = 4x+2 represents the function where you multiply the input by 4, then add 2 to the result.

d. k(x) = 4(x + 2) represents the function where you add 2 to the input, then multiply the result by 4.

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Find the length of the unknown side of the triangle.
10 ft
5 ft
The length of the unknown side of the triangle is?

Answers

The length of the unknown side is 11.2ft

How to determine the value

Using the Pythagorean theorem which states that the square of the hypotenuse side is equal to the sum of the squares of the other two sides.

From the image shown,we have the parameters as;

Hypotenuse = xOpposite side = 10ftAdjacent side = 5ft

Now, substitute the values, we have;

x² = 10² + 5²

Find the squares

x² = 100 + 25

Add the values

x ² = 125

Find the square root

x = 11.2 ft

Hence, the value is 11.2ft

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Consider the line y : 3x-8.
2
Find the equation of the line that is perpendicular to this line and passes through the point (8,
- 4).
Find the equation of the line that is parallel to this line and passes through the point (8, -4).

Answers

Answer:

Step-by-step explanation:

Perpendicular line will have a slope that is the negative reciprocal so slope of 3 becomes - [tex]\frac{1}{3}[/tex].

then use point slope:

y - y = m(x - x)

Use the 2 points (8, -4)

y - -4 = -[tex]\frac{1}{3}[/tex] (x - 8)

y + 4 = -[tex]\frac{1}{3}[/tex] (x - 8)

y + 4 = -[tex]\frac{1}{3}[/tex]x + [tex]\frac{8}{3}[/tex]

y + 4 - 4 = -[tex]\frac{1}{3}[/tex]x  - [tex]\frac{4}{3}[/tex]

y = - [tex]\frac{1}{3}[/tex]x - [tex]\frac{4}{3}[/tex]

Parallelline will have the same slope m = 3.

use point slope again

y - -4 = 3(x -8)

y + 4 = 3x - 24

y + 4 -4 = 3x - 24 -4

y = 3x -28

I will mark BRAINLIEST. Can someone please answer these two questions for me please.

Answers

The height of the plane is 1023 meters and the height of the tree is 307 feet.

What are the solutions to the trigonometric questions?

Given the data in question 9, this forms a right-triangle.

Angle θ = 12°Opposite to angle θ = xAdjacent to angle θ = 4812mValue of height x = ?

To determine the height of the plane x, we use trigonometric ratio

Tangent = Opposite / Adjacent

tan( 12 ) = x / 4812m

x = tan( 12 ) × 4812m

x = 1023m

Therefore, the height of the plane is 1023 meters.

Option A) 1023 meters is the correct answer.

Given the data in question (10)

Angle θ = 62°Adjacent to angle θ = 160ftOpposite to angle θ = xHeight of tool = 6ft

Solve for x using trigonometric ratio,

Tangent = Opposite / Adjacent

tan( 62 ) = x / 160ft

x = tan( 62 ) × 160ft

x = 301ft

Now, height of the tree will be;

Height = x + height of tool

Height = 301ft + 6ft

Height = 307 ft

Therefore, the height of the tree is 307 feet.

Option D) 307 feet is the correct answer.

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Lillian makes 480 sandwiches 25% of them are tuna sandwiches 45% of them are ham sandwiches and the rest are egg sandwiches how many egg sandwiches does Lillian make?

Answers

Answer:

144 egg sandwiches

Step-by-step explanation:

[tex]25\% + 45\% = 70\%[/tex], and [tex]100\% - 70\% = 30\%.[/tex] Thus, [tex]30\%[/tex] of the [tex]480[/tex] sandwiches are egg sandwiches. Since "of" means multiply, we have [tex]30\% \cdot 480.[/tex] We know [tex]30\% = \frac{30}{100} = \frac{3}{10},[/tex] so we can rewrite it as [tex]\frac{3}{10} \cdot 480.[/tex] We cancel [tex]480[/tex] with [tex]10[/tex] which is [tex]480 \div 10 = 48.[/tex] We multiply [tex]48[/tex] by the numerator, [tex]3,[/tex] to get [tex]48 \cdot 3 = 144.[/tex] Thus, Lillian makes [tex]\boxed{144 \text{ egg sandwiches.}}[/tex]

Find the value of each variable show proofs

Answers

The sides of the right triangle are as follows:

x = 18 units

y = 15.6 units

How to find the side of a right triangle?

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the sides of the right triangle using trigonometric ratios

tan 30° = opposite / adjacent

tan 30° = 9 / y

cross multiply

y = 9 / tan 30

y = 15.5884645362

y = 15.6 units

Let's find x

sin 30 = opposite / hypotenuse

sin 30° = 9 / x

x = 9 / 0.5

x = 18 units

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you are flipping 100 coins, putting aside those that come up heads after each flip. how many flips do you expect to make before running out of coins to flip?

Answers

5050 flips expect to make before running out of coins .

Let's approach this problem using the concept of geometric distribution.

The probability of getting heads on any given coin flip is 1/2, assuming a fair coin.

So the probability of getting tails on a given flip is also 1/2.

The number of flips it takes to get the first head is a geometric distribution with a probability of success p = 1/2.

The expected number of flips until the first head appears is 1/p = 2 flips.

After the first head appears, there will be 99 coins left to flip.

The expected number of flips until the next head appears is still 2, since the probability of getting heads on any given flip is still 1/2.

So the expected number of flips until the second head appears (and the number of coins remaining drops to 98) is 2+1 = 3 flips.

Similarly, the expected number of flips until the third head appears (and the number of coins remaining drops to 97) is 2+1+1 = 4 flips.

We can generalize this pattern: after k heads have been obtained, the expected number of additional flips until the next head appears (and the number of coins remaining drops to 100-k) is k+1 flips.

Using this formula, we can calculate the expected number of flips to obtain all 100 heads:

E(number of flips) = (2 + 3 + 4 + ... + 101)

= (1 + 2 + 3 + ... + 100) + 100

= (100 x 101 / 2) + 100

= 5050

Therefore, we expect to make 5050 flips before running out of coins to flip and obtaining all 100 heads.

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Gina's goal is to raise $160 for the school through her ticket sales. if she is selling the tickets for $3 each, what is the minimum number of tickets Gina needs to sell in order to earn $160?

Answers

Answer: All she needs to sell is 53 tickets

Step-by-step explanation: You divide 160 by 3 which gives you 53.3333 so you take the decimal place and get rid of it and it gives you 53. So she needs to sell at least 53 tickets to reach her goal

Answer these two questions, I am having difficulty understanding. Explanation would be nice but it is not required. Spam answers will be reported.

Answers

The amount of money that is take home pay would be = $3,491.91

The amount of money that is your fix expenses would be = $1,257.09

How to calculate the amount of money for fixed expenses?

The amount of money that you make each month = $3,764.82.

The percentage of deduction made for FICA = 7.25%

That is;

= 7.25/100 × 3,764.82/1

= 27294.945/100

= $272.91

Therefore, the take home pay ;

= $3,764.82-$272.91

= $3,491.91

The percentage of the fixed expenses = 36% of the realised income.

That is, 36/100 × 3,491.91/1

= 125708.76/100

= $1,257.09.

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Determine the equation of the circle graphed below?

Answers

The equation of the circle graphed above is equal to (x - 1)² + (y - 6)² = 9.

What is the equation of a circle?

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²

Where:

h and k represents the coordinates at the center of a circle.r represents the radius of a circle.

By critically observing the graph of this circle, we have the following parameters:

Radius, r = 3 units.

Center, (h, k) = (1, 6).

Substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - 1)² + (y - 6)² = 3²

(x - 1)² + (y - 6)² = 9.

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Which function has a simplified base of 4RootIndex 3 StartRoot 4 EndRoot?

f(x) = 2(RootIndex 3 StartRoot 16 EndRoot) Superscript x
f(x) = 2(RootIndex 3 StartRoot 64 EndRoot) Superscript x
f(x) = 4(RootIndex 3 StartRoot 16 EndRoot) Superscript 2 x
f(x) = 4(RootIndex 3 StartRoot 64 EndRoot) Superscript 2 x

Answers

The function that has a simplified base of (4∛4) is 4(∛16[tex])^({2x)[/tex].

What is Exponential Function?

Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread.

From the general formula of an exponential function, we know that;

f(x) = a[tex](b)^x[/tex]

Now, we have;

f(x) = (4∛4[tex])^x[/tex]

4(∛16[tex])^({2x)[/tex], the base is (∛16)²

(∛16)²

= √(16^(⅔))

=256^(⅓)

= 4∛4

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Answer:

C.

Step-by-step explanation:

Took the test. :)

a stairway with three steps has three risers that are each 8 inches high and three treads that are each 10 inches deep. what is the area, in square inches, of this figure that is the side panel of the stairway?

Answers

The area of the side panel of the stairway is 360 square inches.

The side panel of the stairway is essentially a right triangle with the three steps forming the three horizontal segments (treads) and the three risers forming the three vertical segments (risers).

The height of the side panel would be the total height of the three risers, which is -

3 risers x 8 inches/riser = 24 inches

The length of the side panel would be the total length of the three treads, which is -

3 treads x 10 inches/tread = 30 inches

Now, we can calculate the area of the side panel using the formula for the area of a right triangle:

Area = (base x height)/2

we have the base as the length of the side panel (30 inches) and the height is the total height of the three risers (24 inches).

Substituting these values into the formula we get,

Area = (30 inches x 24 inches)/2

Area = 360 square inches

Therefore, the area of the side panel of the stairway is 360 square inches.

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Which of the following statements about f(x)= -(x-4)² -1 are true? Select all that apply.
a) Vertex: (4, -1)
b) y-intercept: (0, -17)
c) x-intercept: (5, 0)
d) Axis of Symmetry: x = 4
e) x-intercept: (3, 0)
f) no x-intercepts

Answers

The following statements are true about the function f(x) = -( x-4) ² -1

1. The y intercept is (0,-17)

2. The axis of symmetry x = 4

3. The x intercept is (3,0)

What are quadratic function?

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.

The equation f(x) = -(x-4)² -1 can be expanded as

f(x) = -x²+8x-16-1 = -x²+8x-17

therefore when x = 0

the y-intercept = -17

therefore the y intercept = (0,-17)

The x intercept of the function,

when y = f(x) and y = 0

-(x-4)² = 1

-(x-4) = 1

-x+4 = 1

-x = -3

x = 3

the x intercept of the function is (3,0)

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