Look at the number line below. b fa and b are equal distances from 0, which of the following is true?
A a+b=0
B. a/b=1
C. a-b=0
D. ab = 1​

Using diagonals from a common vertex, 143 triangles could be formed from a13-gon. But there will be 47 distinct triangles in total.

If we choose a common vertex of an n-gon, we can form (n-2) triangles by drawing diagonals from that vertex to each of the other vertices of the polygon. This is because every vertex, except for the adjacent vertices, can be connected to the chosen vertex to form a triangle.

Therefore, for a 13-gon, we can choose any one of the 13 vertices as the common vertex and form (13-2) = 11 triangles using diagonals from that vertex. We can repeat this process for each of the 13 vertices to form a total of 13*11 = 143 triangles.

However, we need to be careful not to count the same triangle multiple times. In the process of forming triangles from a common vertex, we may end up forming some of the same triangles using different vertices. For example, the triangle formed by connecting vertices 1, 6, and 9 is the same as the triangle formed by connecting vertices 9, 6, and 1.

To avoid double-counting, we can divide the total number of triangles by 3, since each triangle is counted 3 times in the process of forming triangles from a common vertex. Therefore, the number of distinct triangles that can be formed using diagonals from a 13-gon is 143/3 = 47.

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Answer:

c

Step-by-step explanation:

The following is true for the t test for independent means:T test for independent means is a parametric inferential test used for making comparisons between two groups' means.

The t test for independent means can only be performed if there are two different groups or conditions.The t test for independent means assumes that the data are approximately normally distributed and that the variances of the two groups are equal.The t test for independent means can be used to examine whether or not there is a significant difference between the means of the two groups.The t test for independent means' null hypothesis is that there is no significant difference between the means of the two groups. If the t statistic obtained from the test is greater than the critical value, the null hypothesis will be rejected, indicating that there is a significant difference between the means of the two groups.The t test for independent means is an excellent way to compare two groups when the data are approximately normally distributed and the variances are equal.

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Among the given statements, statement A is correct, which states that for any term x^a * y^b in the expansion of (x + y)^n, the sum of the exponents a and b is equal to n. The other statements, B, C, and D, are incorrect.

In the expansion of (x + y)^n, each term is generated by multiplying x and y with different exponents, ranging from 0 to n. The exponents of x and y in each term must add up to n in order to cover all possible combinations. This is represented by statement A, which correctly states that a + b = n.

Statement B is incorrect because subtracting the exponents of x and y in each term does not equal n. Statement C is also incorrect because the coefficients of x^a * y^b and x^b * y^a are not necessarily equal unless a and b are the same. Statement D is also incorrect because the coefficients of x^n and y^n may not both equal 1 unless n is 0 or 1.

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Answer:

9:20 AM

Step-by-step explanation:

they spend 4 hours in total doing activities

We get this value by adding up all the time spent

1:30pm - 4 hours =

9:20 AM

The service center is located 90 miles from the 3rd exit and 30 miles from the 10th exit on the highway.

Given, The third exit on a highway is located at milepost 40 and the tenth exit is at milepost 160.

There is a service center on the highway located three-fourths of the way from the third exit to the tenth exit.

To find, The location of the service center.

Solution:First, let's calculate the total length of the highway:Length of the highway = Milepost of the 10th exit - Milepost of the 3rd exitLength of the highway = 160 - 40 = 120 milesNow, let's find the distance

between the 3rd exit and the service center.Using the formula,Distance = Rate x TimeWe know that the distance from the 3rd exit to the service center is three-fourths of the total distance between the 3rd and the 10th exit, i.e.,Distance between 3rd and 10th exit = 160 - 40 = 120 milesDistance from the 3rd exit to the service center = three-fourths of the total distance between the 3rd and the 10th exitDistance from the 3rd exit to the service center = 3/4 x 120Distance from the 3rd exit to the service center = 90 milesNow, let's find the distance between the service center and the 10th exit.Distance between the service center and the 10th exit = total distance between the 3rd and the 10th exit - distance between the 3rd exit and the service centerDistance between the service center and the 10th exit = 120 - 90Distance between the service center and the 10th exit = 30 milesTherefore, the service center is located 90 miles from the 3rd exit and 30 miles from the 10th exit.

swer: The service center is located 90 miles from the 3rd exit and 30 miles from the 10th exit on the highway.

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The service center is located at milepost 130 on the highway.

The distance between the third exit and the tenth exit on the highway is 160 - 40 = 120 miles. To find the location of the service center, we need to determine three-fourths of this distance, which is (3/4) * 120 = 90 miles.

To locate the service center, we start at the third exit at milepost 40 and travel 90 miles towards the tenth exit. This brings us to milepost 40 + 90 = 130.

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The slope - intercept form of a line is given by the equation:

In this case, we know that m=2 and y=5. So, the equation of this line will be:

To graph it, we need to plot two points and then join them both. These points could be:

Graphing:

The main difference is interest charged for a payday loan is typically over a short period, whereas  credit card represents the annualized interest rate over a year.

The payday loan interest is a one-time charge, while the credit card APR accumulates over time if the balance is not paid in full.

For a payday loan, the 30% interest is typically charged over a short period, often within a few weeks.

This means that if you borrow $100, you would need to repay $130, including the $30 interest, within that short timeframe.

On the other hand, a 30% APR on a credit card represents the annualized interest rate charged on the outstanding balance. This interest is spread out over a year.

If you have an outstanding balance of $100 on a credit card with a 30% APR, the interest charged over a year would be $30.

In summary, the main difference is that the 30% interest charged for a payday loan is typically applied over a short period, whereas the 30% APR on a credit card represents the annualized interest rate over a year.

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Hourly earnings of call center employees is not a discrete random variable.

The answer is C.

The continuous random variable is not a discrete random variable. Continuous random variables are variables that can take an infinite range of values within a specific range, such as time, length, and weight.

A discrete random variable is a random variable that can only take certain discrete values. A discrete random variable is defined as a variable that takes on a specific set of values or a range of values.

The number of births, number of fives, and number of applicants are all random variables that can only take certain discrete values within a particular range of possible values.

So, the answer is C. The hourly earnings of a call center employee in Boston is not a discrete random variable.

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Answer:

21

Step-by-step explanation:

please pick me as brainliest

Answer:

90=square

72=nonagon

60=hexagon

45=pentagon

40=octagon

I am not entirely sure tho

Answer:

27 is 30% of what number?

D. 90

Step-by-step explanation:

You're welcome.

Answer:

PT = 32

Step-by-step explanation:

From the question, we are told that:

T is the midpoint of PQ

This means:

PT = TQ

PT=3x+8 and TQ = 5x-8

Step 1

We solve for x

3x + 8 = 5x - 8

Collect like terms

8 + 8 = 5x - 3x

16 = 2x

x = 16/2

x = 8

Step 2

We can solve for PT now

PT=3x+8

x = 8

PT = 3×8 + 8

PT = 24 + 8

PT = 32

Therefore, PT = 32

Answer:

∠ N = 40°

Step-by-step explanation:

The opposite angles of a parallelogram are congruent, thus

∠ L = ∠ N , substitute values

3x - 20 = 2x ( subtract 2x from both sides )

x - 20 = 0 ( add 20 to both sides )

x = 20

Thus

∠ N = 2x = 2(20) = 40°

From the given quadrilateral, the value of angle N is 40°

Data;

Opposite angles in a parallelogram are equal to each other.

\(N = L\\2x = 3x - 20\\3x- 2x = 20\\x = 20\)

The value of x is equal to 20.

Let's substitute that into N

\(N = 2x \\N = 2(20)\\N = 40^0\)

The value of angle N is 40°

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Answer:

If it's zero it's neither of them because zero is not a number to multiply with because it will always be zero when multiplying with zero

Answer:

1/4x-7/4

Step-by-step explanation:

Answer:

$23780

Step-by-step explanation:

Given data

Let the original price be x

discount= 20%

price= $19,024

so that

20/100*x=x-19,024

0.2x= x-19,024

19,024=x-0.2x

19,024=0.8x

x= 19,024/0.8

x=23780

Hence the original price is $23780

Here's the deal. The definition of congruent triangles requires 6 things to be congruent. 3 corresponding sides and 3 corresponding angles. That's a lot.

But the triangle congruence postulates (SSS,SAS,ASA, AAS) only require 3 congruent pairs to prove triangle congruence.  

Rafe and Ashley used approximately 5353.2 square inches of canvas to make the lamp.

Let's call the length of the base rectangle "L" and the width "W." From the picture, we can see that the base rectangle measures 18 inches by 18 inches. Therefore, the area of one base rectangle is given by:

Area of a rectangle = Length × Width

Area of one base rectangle = L × W = 18 in × 18 in = 324 square inches

Since there are two identical base rectangles, the combined area of both rectangles is:

Total area of base rectangles = 2 × Area of one base rectangle = 2 × 324 square inches = 648 square inches

Let's calculate the perimeter of the base rectangle first:

Perimeter of a rectangle = 2 × (Length + Width)

Perimeter of the base rectangle = 2 × (18 in + 18 in) = 2 × 36 in = 72 inches

Now, the height of the triangular prism is given as 20.1 inches. Therefore, the area of each lateral face rectangle is given by:

Area of a rectangle = Length × Width

Area of one lateral face rectangle = Perimeter of base rectangle × Height = 72 in × 20.1 in = 1447.2 square inches

Since there are three identical lateral face rectangles, the combined area of all three rectangles is:

Total area of lateral face rectangles = 3 × Area of one lateral face rectangle = 3 × 1447.2 square inches = 4341.6 square inches

The height of the triangular face is the same as the height of the prism, given as 20.1 inches. Therefore, the area of each triangular face is given by:

Area of a triangle = (Base × Height) / 2

Area of one triangular face = (18 in × 20.1 in) / 2 = 181.8 square inches

Since there are two identical triangular faces, the combined area of both triangles is:

Total area of triangular faces = 2 × Area of one triangular face = 2 × 181.8 square inches = 363.6 square inches

Now, to find the total surface area of the lamp, we sum up the areas of all the faces:

Total surface area = Total area of base rectangles + Total area of lateral face rectangles + Total area of triangular faces

Total surface area = 648 square inches + 4341.6 square inches + 363.6 square inches

Total surface area = 5353.2 square inches

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Complete Question:

Marius and his dad build a lamp in the shape of a triangular prism, open on the top and bottom. How many square inches of canvas did Marius and his dad use to make the lamp?

Answer:

\(\huge \fbox \pink {A}\huge \fbox \green {n}\huge \fbox \blue {s}\huge \fbox \red {w}\huge \fbox \purple {e}\huge \fbox \orange {r}\)

\( \sqrt{2 \times 2 } \\ = \sqrt{4} \\ = 2\)

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

\( \huge\blue{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}\)

\( \huge \frak \red{question}\)

square root of 2 times 2

\( \huge \frak \green{answer}\)

→\( \sqrt{2 \times 2} \)

→\( \sqrt{4} \)

→ 2

The square root of 2 times 2 is "2"

With lower extreme as 3, upper extreme as 16, median as 11, lower quartile as 8 and upper quartile as 13, the box and whiskers plot is drawn.

The given data set is 3, 5, 5, 8, 9, 10, 10, 12, 12, 12, 13, 14, 14, 16.

A box and whisker plot is a visual tool that is used to graphically display the median, lower and upper quartiles, and lower and upper extremes of a set of data.

From the given data set: 3, 5, 5, 8, 9, 10, 10, 12, 12, 12, 13, 14, 14, 16

Lower extreme = 3

Upper extreme = 16

Median = (10+12)/2 = 11

Lower quartile = 8 (Median of first half of data set)

Upper quartile = 13 (Median of first half of data set)

A box and whiskers plot for the given set of data is given below.

Therefore, with lower extreme as 3, upper extreme as 16, median as 11, lower quartile as 8 and upper quartile as 13, the box and whiskers plot is drawn.

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It is reasonable for Stacy to use a normal model for the sampling distribution of the sample proportion. This is because, according to the Central Limit Theorem,

when the sample size is large enough (typically considered to be at least 30), the sampling distribution of the sample proportion will be approximately normal, regardless of the shape of the population distribution.

In Stacy's case, she plans on surveying a random sample of students, which implies that she will have a sufficiently large sample size. Therefore, the conditions for using a normal model are satisfied.

In conclusion, Stacy can use a normal model for the sampling distribution of the sample proportion in her survey for the final project.

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Answer:

y=-x+6

Step-by-step explanation:

For linear graphs, the slope of perpendicular lines must be of equal value but opposite in sign: (\(m_1=-m_2\)).

The slope of y=x+1 is 1, therefore the slope of the perpendicular line must be -1.

Given (x,y)=(-2,8) the equation of the perpendicular line can be obtained by substituting these values into the slope-intercept form y=mx+b.

8=(-1)(-2)+b

8=2+b

6=b

So, the perpendicular line has a slope-intercept form of y=-x+6 or y=6-x.

The areas under the curve y = 1/x between x = 1 and x = 2, x = 2 and x = 3, and x = 1 and x = 3. Concludes that ln(2) < 1 < ln(3) based on the comparison of these areas.

We can use the fact that the natural logarithm function is strictly increasing to compare the values of ln(2), 1, and ln(3).

Consider the area under the curve y = 1/x between x = 1 and x = 2, x = 2 and x = 3, and x = 1 and x = 3. We can approximate these areas using rectangles with a width of 1 and a height equal to the value of the function at the left endpoint of the interval.

For the area under the curve between x = 1 and x = 2, we have:

Area ≈ base × height = 1 × 1/2 = 1/2

For the area under the curve between x = 2 and x = 3, we have:

Area ≈ base × height = 1 × 1/3 ≈ 1/3

For the area under the curve between x = 1 and x = 3, we have:

Using the properties of the natural logarithm, we can see that:

Therefore, we have:

ln(2) < 1 < ln(3)

as desired.

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Answer; present value of $12,200 to be received 4 years from today, with a discount rate of 5 percent, is $10,027.51.

The present value of $12,200 to be received 4 years from today can be calculated using the formula for present value. The formula is:

Present Value = Future Value / (1 + Discount Rate)^n

Where:
- Future Value is the amount to be received in the future ($12,200 in this case)
- Discount Rate is the interest rate used to discount future cash flows (5 percent in this case)
- n is the number of periods (4 years in this case)

Plugging in the given values into the formula:

Present Value = $12,200 / (1 + 0.05)^4

Calculating the exponent first:

(1 + 0.05)^4 = 1.05^4 = 1.21550625

Dividing the future value by the calculated exponent:

Present Value = $12,200 / 1.21550625

Calculating the present value:

Present Value = $10,027.51

Therefore, the present value of $12,200 to be received 4 years from today, with a discount rate of 5 percent, is $10,027.51.

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Hope This Helps!!!

Hope This Helps!!!Have A Great Day!!!

Answer:

\(1\frac{1}{5}\)

Step-by-step explanation:

3 = 3/1

(multiply top and bottom separately for fractions)

\(\frac{3}{1}\) × \(\frac{2}{5}\) = \(\frac{6}{5}\)

\(\frac{6}{5} = \frac{5}{5}+\frac{1}{5}= 1\frac{1}{5}\)

Answer:

Step-by-step explanation:

multiplying three (3) and two(2) and express the product of three and two over five.

five can enter in six three times , remainder 1

The fraction in lowest terms is one whole number , one over five.