A regular octogon is inscribed in a circle with a radius of 14 inches. Find the perimeter of the octogon. Round to 2 decimal places.

Answers

Answer 1

The perimeter of the octagon is:

Perimeter = 8s ≈ 100.16 inches

What is the perimeter?

The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.

To find the perimeter of the regular octagon inscribed in a circle with radius 14 inches, we need to use the formula:

Perimeter of octagon = 8 x length of one side

Since the octagon is regular, all sides are congruent. Let s be the length of one side of the octagon.

The radius of the circle is 14 inches, which is also the distance from the center of the circle to any vertex of the octagon. We can divide the octagon into eight congruent isosceles triangles, each with base s and legs of length 14 inches. We can then use the Pythagorean theorem to find the length of the base s:

s² = 14² - (s/2)²

s² = 196 - s²/4

5s²/4 = 196

s² = 156.8

s ≈ 12.52

Therefore, the perimeter of the octagon is:

Perimeter = 8s ≈ 100.16 inches (rounded to 2 decimal places).

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Related Questions

112+18x14 divided by 14-19 i need help

Answers

the answer to the equation 112+18*14/14-19 is 111.

How to solve the question?

To solve this equation, we need to follow the order of operations (also known as PEMDAS), which is as follows: parentheses, exponents, multiplication and division (performed left to right), and addition and subtraction (also performed left to right).

So let's break down the equation step by step:

18*14 = 252 (multiplication)

252/14 = 18 (division)

112+18 = 130 (addition)

130-19 = 111 (subtraction)

Therefore, the answer to the equation 112+18*14/14-19 is 111.

It's important to note that if we had performed the operations in a different order, we would have gotten a different answer. That's why following the order of operations is crucial in solving mathematical equations.

In general, it's important to have a good understanding of basic arithmetic and algebraic concepts to solve equations like this one. This includes knowing the order of operations, how to perform operations with fractions and decimals, and how to use variables and solve for unknowns. Practicing these skills regularly can help improve your problem-solving abilities in math and other subjects.

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1245+557-45677/88765×345.865​

Answers

Answer:

if question is a fraction then -0.001429, if not then 624.0235948

Which function represents the inverse of function f?
= 3x + 5
O A. T (2)
O B.
O c.
O D.
=-3x - 5
x+ //
– ž
g(x) =
p(x) =
8(x) = 3z +5
x

Answers

The inverse function of f(x) = 3x + 5 is given as follows:

C. p(x) = 1/3x - 5/3.

How to obtain the inverse function?

The function in the context of this problem is defined as follows:

f(x) = 3x + 5.

To obtain the inverse function, first we must exchange the variables x and y, hence:

y = 3x + 5

x = 3y + 5.

Now we must isolate the variable y, hence:

3y = x - 5

y = (x - 5)/3.

p(x) = 1/3x - 5/3.

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The length of a rectangular poster is 2 more inches than two times its width. The area of the poster is 84 square inches. Solve for the dimensions (length and width) of the poster.

Answers

Step-by-step explanation:

w = width

2w + 2 =  Length

Area = W x L  = 84 = w (2w+2)

                          84 = 2w^2 + 2w

                            0 = 2w^2 + 2w - 84        Use Quadratic Formula

                                                                 a = 2    b=2    c = -84

to find  

W = 6      then     L =  14 inches

In Math town,60% of the population are males and 30% of them have brown eyes. Of the total math town population 28 % have brown eyes. What percentage of the females in math town have brown eyes?
A) 20%
B) 24%
C) 25%
D) 28%

thought i would leave this but ⇒ty to whoever answers this, have an amazing day <3

Answers

The percentage of females with brown eyes as follows is 25%.

What is percentage?

Percentage is a way of expressing a number as a fraction of 100. It is represented by the symbol "%". The word "percent" means "per hundred".

According to question:

Let's assume that the total population of Math town is 100 people for the sake of simplicity. Then, we can use the following information to create a table:

Population Males Females

Total         60         40

Brown eyes 18         ?

From the table, we can see that 60% of the population are males, so there are 60 x 0.3 = 18 males with brown eyes.

We also know that the total population with brown eyes is 28%, so there are 100 x 0.28 = 28 people with brown eyes. Therefore, there must be 28 - 18 = 10 females with brown eyes.

Finally, we can calculate the percentage of females with brown eyes as follows:

% of females with brown eyes = (10 / 40) x 100% = 25%

Therefore, the answer is (C) 25%.

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4. The average monthly temperatures in New
Orleans, LA has a mean absolute deviation of
43.5°F. What conclusion can you make about
the average monthly temperatures in New
Orleans, LA?

Answers

The difference between the monthly mean temperature and the average monthly temperature for New Orleans, Louisiana, is typically about 43.5°F.

Explain about the mean absolute deviation of a discrete data:

Assume that the data is n-sized as follows:

x1, x2, x3 .....xn

Let the mean of this data be: x'

The mean of the absolute differences between the observations and the mean of the data to which they belong, then, is the mean absolute deviation of such a data.

It is determined by:

M.A.D = ∑ |xi - x'| / n  (i = 1 ....n)

Hence, mean absolute deviation is the average deviation of the data values, regardless of whether it is above or below the mean.

Due to the fact that:

The mean absolute deviation of the monthly temperatures in New Orleans is 43.5°F, which implies that on average, the temperature deviates 43.5°F from the average monthly temperature.

where mean displays New Orleans, Louisiana's typical monthly temperature.

Thus, the difference between the monthly mean temperature and the average monthly temperature for New Orleans, Louisiana, is typically about 43.5°F.

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A new theater is being built for the city ballet. The balcony has 90 seats. The
floor has 15 rows with x seats in each row. The number of people in the
theater must be under 240 to meet fire safety regulations.
What is the solution of this inequality, and what is its meaning?

Answers

The solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.

What is inequality?

In mathematics, the inequality of two lines refers to the relationship between the slopes and y-intercepts of two different lines on a coordinate plane. Specifically, if the slope of one line is greater than the slope of another line, and their y-intercepts are not equal, then the inequality symbol (< or >) can be used to represent their relationship. For example, if line A has a slope of 2 and a y-intercept of -3, and line B has a slope of 1 and a y-intercept of 1, we can write A > B to represent that line A is steeper than line B.

To solve this problem, we need to use the information given to us to set up an inequality that represents the total number of seats in the theater and then use that inequality to determine the maximum number of people that can be in the theater while still meeting the fire safety regulations.

Let's start by calculating the total number of seats in the theater. We know that there are 90 seats in the balcony and 15 rows on the floor. We don't know the exact number of seats in each row, but we do know that each row has the same number of seats, which we will call x. Therefore, the total number of seats in the theater is 90 + (15 × x)

Now we can set up an inequality to represent the maximum number of people that can be in the theater while still meeting the fire safety regulations. We know that this number must be less than or equal to 240. Therefore, our inequality is 90 + (15 × x) ≤ 240

Now we can solve for x by first subtracting 90 from both sides of the inequality,

15 × x ≤ 150

Next, we can divide both sides of the inequality by 15,

x ≤ 10

Therefore, the solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.

To check this solution, we can plug x = 10 into our expression for the total number of seats,

Total number of seats = 90 + (15 × 10) = 240

This confirms that the maximum number of people in the theater is 240, which is the limit imposed by the fire safety regulations.

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A certain coin is a circle with diameter 18 mm. What is the exact area of either face of the coin in terms of pie?

Answers

Answer:

[tex]81\pi[/tex] [tex]mm^2[/tex]

Step-by-step explanation:

Let's recall the formula for the area of a circle:

[tex]A = \pi r^2[/tex]

We are given the diameter, but the formula uses the radius. Since the radius is equal to one-half of the diameter, we can find the radius by doing this:

[tex]r = \frac{1}{2}d=\\\\r=\frac{1}{2}(18)= \\\\r=9[/tex]

Now that we've found the radius is 9 mm, let's substitute the values into the formula for the area of a circle. We have:

[tex]A = \pi r^2=\\A=\pi (9^2)=\\A=\pi (81)=\\A=81\pi[/tex]

So, we've found that the exact area, in terms of pi, of either face of the coin is [tex]81\pi[/tex] [tex]mm^2[/tex].

To find the area of the coin/a circle use this equation:

(a = area, r = radius, d = diameter)

[tex]\text{a = r}^2[/tex]

So we need to do for the radius.

[tex]\text{r} = \dfrac{\text{d}}{2}[/tex]

[tex]\text{r} = \dfrac{18}{2}[/tex]

[tex]\text{r} = 9[/tex]

Then solve

[tex]\text{a = 9}^2[/tex]

[tex]\boxed{\bold{a = 81}}[/tex]

Find the area of the triangle. Round to 2 decimal places.

Answers

Answer:

20 ..............................

How can I solve this math problem within 5 minutes

Answers

The equation a² + b² = c² represents the Pythagorean theorem.

What is the Pythagorean theorem?

This is a theorem that  states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

The Pythagorean theorem is used to find the length of one of the sides of a right-angled triangle when the lengths of the other two sides are known.

To solve the problem, you need to have at least two side lengths given. Then, you can use the equation to find the length of the third side. For example:

If you know the lengths of sides a and b and need to find the length of the hypotenuse (c):

Plug in the known values for a and b into the equation and solve for c.

Example: If a = 3 and b = 4, then 3² + 4² = c², which gives 9 + 16 = c², so c² = 25, and c = sqrt(25) = 5.

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The length of a side of an equilateral triangle is 14 centimeters.

What is the length of the altitude of the triangle?


2√ 7cm


3√ 7 cm


7√ 2 cm

7√ 3 cm

Answers

Answer: The altitude of the triangle is [tex]h = 7 \sqrt{3}.[/tex]

Step-by-step explanation:

Suppose that we separate the equilateral triangle with the altitude of the triangle, as shown in the diagram I attached.

Then the length of the altitude [tex]h[/tex] can be found through the Pythagorean theorem:

[tex]h = \sqrt{14^2-\left( \frac{14}{2} \right)^2} = \sqrt{147} = \boxed{7 \sqrt{3}}.[/tex]

Therefore, the altitude of the equilateral triangle is [tex]h = 7 \sqrt{3}.[/tex]

Solve. Complete the table for the consecuIf the sum of a number and eight is tripled​, the result is four less than twice the number. Find the number.
tive integers.

Answers

We can condense and find n's solution: 3n + 24 = 2n - 4

Since n = -14, the unknowable number is also -14.

What is an algebraic expression?

A mathematical expression called an algebraic expression includes variables, integers, and mathematical operations including addition, subtraction, multiplication, and division. Algebraic expressions can be straightforward, like "2x," or they can be more complicated, like

[tex]3x^2+4y-5[/tex].

Variables are used to represent unknown quantities and have a range of possible values. In problems requiring unknown values or to represent connections between quantities, algebraic expressions are widely used.

A mathematical expression that includes variables, constants, and operations involving algebra (addition, subtraction, etc.) is known as an algebraic expression. Terms comprise expressions.

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You may need to use the appropriate technology to answer this question.
The success of an airline depends heavily on its ability to provide a pleasant customer experience. One dimension of customer service on which airlines compete is on-time arrival. The tables below contains a sample of data from delayed flights showing the number of minutes each delayed flight was late for two different airlines, Company A and Company B.
Company A
34 59 43 30 3
32 42 85 30 48
110 50 10 26 70
52 83 78 27 70
27 90 38 52 76

Company B
45 63 42 32 67
104 45 27 38 84
75 46 32 50 64
41 36 33 65 64
(a)
Formulate the hypotheses that can be used to test for a difference between the population mean minutes late for delayed flights by these two airlines. (Let 1 = population mean minutes late for delayed Company A flights and 2 = population mean minutes late for delayed Company B flights.)

H0: 1 − 2 < 0
Ha: 1 − 2 = 0

H0: 1 − 2 ≤ 0
Ha: 1 − 2 > 0


H0: 1 − 2 ≥ 0
Ha: 1 − 2 < 0

H0: 1 − 2 ≠ 0
Ha: 1 − 2 = 0

H0: 1 − 2 = 0
Ha: 1 − 2 ≠ 0
(b)
What is the sample mean number of minutes late for delayed flights for each of these two airlines?
Company A
min
Company B
min
(c)
Calculate the test statistic. (Round your answer to three decimal places.)

What is the p-value? (Round your answer to four decimal places.)
p-value =

Using a 0.05 level of significance, what is your conclusion?
Do not Reject H0. There is statistical evidence that one airline does better than the other in terms of their population mean delay time.
Reject H0. There is statistical evidence that one airline does better than the other in terms of their population mean delay time.
Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.
Reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.

Answers

The answers are: A)H0: μ1 − μ2 = 0; Ha: μ1 − μ2 ≠ 0

(b)  Means: Company A___50.6___ min.; Company B___52.75___ min.

c)The t-value is -0.30107., The p-value is 0 .764815.

What is a Hypothesis?

A hypothesis is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon

A)H0: μ1 − μ2 = 0

i.e there is no difference between the means of delayed flight for two different airlines

Ha: μ1 − μ2 ≠ 0

i.e there is a difference between the means of delayed flight for two different airlines

(b)

Company A___50.6___ min.

Company B___52.75___ min.

Mean of Company A = x`1= ∑x/n =34+ 59+ 43+ 30+ 3+ 32+ 42+ 85+ 30+ 48+ 110+ 50+ 10+ 26+ 70+ 52+ 83+ 78+ 27+ 70+ 27+ 90+ 38+ 52+ 76/25

= 1265/25= 50.6

Mean of Company B = x`2= ∑x/n =

=46+ 63+ 43+ 33+ 65+ 104+ 45+ 27+ 39+ 84+ 75+ 44+ 34+ 51+ 63+ 42+ 34+ 34+ 65+ 64/20

= 1055/20= 52.75

Difference Scores Calculations

Company A

Sample size for Company A= n1= 25

Degrees of freedom for company A= df1 = n1 - 1 = 25 - 1 = 24

Mean for Company A= x`1=  50.6

Total Squared Difference (x-x`1) for Company A= SS1: 16938

s21 = SS1/(n1 - 1) = 16938/(25-1) = 705.75

Company B

Sample size for Company B= n1= 20

Degrees of freedom for company B= df2 = n2 - 1 = 20 - 1 = 19

Mean for Company B= x`2=  52.75

Total Squared Difference (x-x`2) for Company B= SS2=7427.75

s22 = SS2/(n2 - 1) = 7427.75/(20-1) = 390.93

T-value Calculation

Pooled Variance= Sp²

Sp² = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22)

Sp²= ((24/43) * 705.75) + ((19/43) * 390.93) = 566.65

s2x`1 = s2p/n1 = 566.65/25 = 22.67

s2x`2 = s2p/n2 = 566.65/20 = 28.33

t = (x`1 - x`2)/√(s2x`1 + s2x`2) = -2.15/√51 = -0.3

The t-value is -0.30107.

The total degrees of freedom is = n1+n2- 2= 25+20-2=43

The critical region for two tailed test at significance level ∝ =0.05 is

t(0.025) (43) = t > ±2.017

Since the calculated value of t=  -0.30107.  does not fall in the critical region t > ±2.017, null hypothesis is not rejected that is there is no difference between the means of delayed flight for two different airlines.

The p-value is 0 .764815. The result is not significant at p < 0.05.

C) Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.

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can someone please help me+explain how to do this step by step, im so confused

Your gross income is $4,520.00/month. Your deductions are FICA (7.65%), federal tax withholding (11.75%), and state tax withholding (8.5%). Your fixed expenses are 30% of your realized income. You saved 5 months' worth in an emergency fund, placing 75% in a 60-day CD at a 5.25% APR and the rest in a regular savings account at a 3.8% APR. What is the total amount of your emergency fund? How much is in the CD and savings account? How much is the total interest earned between both accounts in 60 days?

Answers

1. The total amount of your emergency fund will be $11,403.75.

2. $8,552.81 is in the CD, and $2,850.94 is in the regular savings account.

What is the total amount of your emergency fund?

Your FICA deduction is 7.65% of your gross income:

7.65% of $4,520.00 = $345.98

Your federal tax withholding is 11.75% of your gross income:

11.75% of $4,520.00 = $531.40

Your state tax withholding is 8.5% of your gross income:

8.5% of $4,520.00 = $384.40

Your total deductions are:

= $345.98 + $531.40 + $384.40

= $1,261.78

Your monthly income after deductions is:

= $4,520.00 - $1,261.78

= $3,258.22

Your fixed expenses are 30% of your realized income:

= 30% of $3,258.22

= $977.47

Your monthly savings amount is:

= $3,258.22 - $977.47

= $2,280.75

You saved 5 months' worth in an emergency fund, so the total amount in your emergency fund is:

= 5 x $2,280.75

= $11,403.75

Regenerate response

How much is in the CD and savings account?

You placed 75% of your emergency fund in a 60-day CD at a 5.25% APR:

= 75% of $11,403.75 = $8,552.81

You placed the remaining 25% of your emergency fund in a regular savings account at a 3.8% APR:

= 25% of $11,403.75

= $2,850.94.

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Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.

Answers

The shaded area covers around 0.8664 square feet of space.

What is the typical normal distribution where the standard deviation is 0 and the mean 1?

The mean and standard deviation of the standard normal distribution are 0 and 1, respectively. The standard deviation shows how much a particular measurement deviates from the mean, and the standard normal distribution is centred at zero.

Using a conventional normal distribution table, we must first determine the areas to the left of z= -1.5 and z=1.5, and then subtract those two areas to determine the area of the shaded zone.

Using a standard normal distribution table, we find that the area to the left of z= -1.5 is 0.0668, and the area to the left of z=1.5 is 0.9332. As a result, the darkened region's area is:

0.9332 - 0.0668 = 0.8664

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x f(x) f ′(x) g(x) g′(x)
2 5 1 2 1
4 −2 −6 5 4
5 1 2 4 5
6 5 1 2 −2


The functions f and g have continuous derivatives. The table gives values of f, f ′, g, and g′ at selected values of x.

Part A: Find h′(2) if h(x) = g(f(x)). (5 points)

Part B: Find m′(2) if m(x) = f(x2). (5 points)

Part C: Let k(x) = f(g(x)). Write an equation for the line tangent to the graph of k at x = 4. (10 points)

Part D: Let j of x is equal to g of x divided by f of x. Find j′(2). (10 points)

Answers

Answer:

A.  h'(2) = 5

B.  m'(2) = -24

C.  y = 8x - 31

D.  j'(2) = 3/25 = 0.12

Step-by-step explanation:

When differentiating composite functions, use the chain rule.

[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\$\left[f\left(g(x)\right)\right]'=f'\left(g(x)\right) \cdot g'(x)$\\\end{minipage}}[/tex]

Chain Rule: The derivative of a composite function is the product of the derivative of the outer function evaluated at the inner function and the derivative of the inner function.

Part A

Using the chain rule, if h(x) = g(f(x)) then h'(x) = g'(f(x)) ⋅ f'(x).

To find h'(2), substitute x = 2 into the differentiated equation:

[tex]\begin{aligned}h'(x)& = g'(f(x)) \cdot f'(x)\\\\\implies h'(2)& = g'(f(2)) \cdot f'(2)\\& = g'(5) \cdot 1\\& = 5 \cdot 1\\&=5\end{aligned}[/tex]

Therefore, h'(2) = 5.

Part B

Using the chain rule, if m(x) = f(x²) then m'(x) = f'(x²) ⋅ 2x.

To find m'(2), substitute x = 2 into the differentiated equation:

[tex]\begin{aligned}m'(x) &= f'(x^2) \cdot 2x\\\\\implies m'(2) &= f'(2^2) \cdot 2(2)\\&=f'(4) \cdot 4\\&=-6 \cdot 4\\&=-24\end{aligned}[/tex]

Therefore, m'(2) = -24.

Part C

To find the slope of the tangent line to the graph of k at x = 4, substitute x = 4 into the derivative of k(x).

If k(x) = f(g(x)) then k'(x) = f'(g(x)) ⋅ g'(x).

Therefore, the slope of the tangent line is:

[tex]\begin{aligned}k'(x) &= f'(g(x)) \cdot g'(x)\\\\\implies k'(4) &= f'(g(4)) \cdot g'(4)\\&= f'(5) \cdot 4\\&= 2 \cdot 4\\&= 8\end{aligned}[/tex]

Now calculate k(x) when x = 4:

[tex]\begin{aligned}k(x)&=f(g(x))\\\\\implies k(4) &= f(g(4))\\&=f(5)\\&=1\end{aligned}[/tex]

To write the equation of the tangent line, substitute the found slope m = 8 and point (4, 1) into the point-slope equation:

[tex]\begin{aligned}y-y_1&=m(x-x_1)\\y-1&=8(x-4)\\y-1&=8x-32\\y&=8x-31\end{aligned}[/tex]

Therefore, an equation for the line tangent to the graph of k at x = 4 is:

y = 8x - 31

Part D

To find the derivative of j(x) use the quotient rule.

[tex]\textsf{If\;\;$j(x)=\dfrac{g(x)}{f(x)}$\;\;then:}\\\\\\j'(x)=\dfrac{f(x)g'(x)-g(x)f'(x)}{(f(x))^2}[/tex]

To calculate j'(2), substitute x = 2 into the equation:

[tex]\begin{aligned} \implies j'(2)&=\dfrac{f(2)g'(2)-g(2)f'(2)}{(f(2))^2}\\\\&=\dfrac{5 \cdot 1-2 \cdot 1}{(5)^2}\\\\&=\dfrac{5-2}{25}\\\\&=\dfrac{3}{25}\\\\&=0.12\end{aligned}[/tex]

Therefore, j'(2) = 3/25 = 0.12.

Question 6(Multiple Choice Worth 5 points) (Statistical Measurements LC) Which of the following is a statistical question that can result in numerical data? What is the name of your favorite pizza store? How many hours this week did you spend on homework? O How many times did you go swimming this year? How many pink erasers do the students in your class have?​

Answers

The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"

Identifying the statistical question that can result in numerical data?

The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"

This is because the question is asking for a numerical response that can be measured and counted. The other options are not statistical questions that can result in numerical data.

"What is the name of your favorite pizza store?" is a question that asks for a categorical response, "How many times did you go swimming this year?" is a question that asks for a countable response, And "How many pink erasers do the students in your class have?" is a question that asks for a discrete numerical response.

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Evelyn sells 4 bags of popcorn. Her teammate Sidney sells 5 bags of popcorn. How much money do they raise in all?

Answers

how much did the bags cost

A researcher is standing in a corner (point c) of a triangler plot. the angle to point a is S76E the angle to point b is N32E The distance between point c and point a is 210 ft and the distance between point c and point b is 150 ft
find the distance between point a and point b

Answers

Answer:

We can use the Law of Cosines to find the distance between points a and b.

Using the angles given, we can find the angle between points a and b:

Angle C = 180 - (76 + 32) = 72 degrees

Next, we can use the Law of Cosines:

c^2 = a^2 + b^2 - 2ab cos(C)

where c is the distance between points a and b, a is the distance between point c and point a (210 ft), b is the distance between point c and point b (150 ft), and C is the angle between points a and b (72 degrees).

Plugging in the values:

c^2 = 210^2 + 150^2 - 2(210)(150)cos(72)

c^2 ≈ 21069.27

Therefore, the distance between points a and b is approximately:

c ≈ 145.2 ft

Samuel went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 300 mg of sodium and each frozen dinner has 450 mg of sodium. Samuel purchased 5 more frozen dinners than cans of soup and they all collectively contain 6000 mg of sodium. Write a system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased. Define the variables that you use to write the system.

Answers

the system of equations is: [tex]300x + 450y = 6000[/tex]

[tex]y = x + 5[/tex]

What best define about variables?

Let's define the variables:

Let "x" be the number of cans of soup purchased by Samuel.

Let "y" be the number of frozen dinners purchased by Samuel.

According to the given information, each can of soup has 300 mg of sodium and each frozen dinner has 450 mg of sodium. Samuel purchased 5 more frozen dinners than cans of soup, so we can write the following equations:

The total sodium from cans of soup: 300x mg

The total sodium from frozen dinners: 450y mg

The total sodium from both cans of soup and frozen dinners: [tex]6000 mg[/tex]

So the first equation is:

[tex]300x + 450y = 6000[/tex]  (since the total sodium from cans of soup and frozen dinners is 6000 mg)

Since Samuel purchased 5 more frozen dinners than cans of soup, we can write the second equation:

[tex]y = x + 5[/tex] (since y is 5 more than x)

Therefore,  the system of equations is:

[tex]300x + 450y = 6000[/tex]

[tex]y = x + 5[/tex]

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I need help with this

Answers

Answer:

1500

Step-by-step explanation:

Number of boxes = 12

Number of pencils in each box = 125

Total number of pencils

= 12 × 125

= 1500 pencils

50 Points! Multiple choice algebra question. Transform both sides of each equation to determine which is a polynomial identity. Photo attached. Thank you!

Answers

The only equation that is a polynomial identity is (A), (c+d)³ = c³ - d³ + 3cd(c + d).

How to express the value

It should be noted that to determine which equation is a polynomial identity, we need to simplify both sides of each equation and see if they are equal for all values of c and d.

(A) (c+d)³ = c³ + 3c²d + 3cd² + d³

= c³ - d³ + 3cd(c + d)

The left-hand side can be expanded using the binomial formula. The right-hand side is a polynomial of degree 3, so we can see that equation (A) is a polynomial identity.

(B) (c+d) = c + d³ + 3cd(c + d)

= d³ + c³ + 3cd(c + d) + c + d - c³

= d³ + c³ + 3cd(c + d) + c + d

The right-hand side can be simplified, but it is not equal to the left-hand side for all values of c and d. Therefore, equation (B) is not a polynomial identity.

(C) (c+d)³ = c³ + 3c²d + 3cd² + d³

= c³ + d³ + 3cd(c + d) + cd(c - d)

The right-hand side is not equal to the left-hand side for all values of c and d, so equation (C) is not a polynomial identity.

(D) (c+d)³ = c³ + 3c²d + 3cd² + d³

= c³ - d³ + 3cd(c - d) + c³ + d³

= 2c³ + 3cd(c - d)

The right-hand side is not equal to the left-hand side for all values of c and d, so equation (D) is not a polynomial identity.

Therefore, the only equation that is a polynomial identity is (A), (c+d)³ = c³ - d³ + 3cd(c + d).

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An African mousebird is 2 feet tall. A camel is 4 times as tall as the mousebird. How tall is the camel in inches?

Answers

If an African mousebird is 2 feet tall, then the camel is 4 times as tall, which means:

Height of the camel = 4 * Height of the mousebird
Height of the camel = 4 * 2 = 8 feet

To convert the height of the camel from feet to inches, we need to multiply by 12 since there are 12 inches in one foot:

Height of the camel = 8 feet * 12 inches/foot = 96 inches

Therefore, the camel is 96 inches tall.

solve the equation x^2+4x-11=0 by completing the square

Answers

To solve the equation x^2 + 4x - 11 = 0 by completing the square, we can follow these steps:

Move the constant term to the right side of the equation:

x^2 + 4x = 11

Complete the square by adding the square of half the coefficient of x to both sides of the equation:

x^2 + 4x + (4/2)^2 = 11 + (4/2)^2

Simplifying the left side:

x^2 + 4x + 4 = 11 + 4

Factor the perfect square on the left side of the equation:

(x + 2)^2 = 15

Take the square root of both sides of the equation:

x + 2 = ±√15

Solve for x by subtracting 2 from both sides:

x = -2 ± √15

Therefore, the solutions to the equation x^2 + 4x - 11 = 0 by completing the square are x = -2 + √15 and x = -2 - √15.

For this answer the equation would be

2
+
4


1
1
=
0

A skydiver jumps out of a plane from a certain height. The graph below shows their height h in meters after t seconds. How long is the skydiver in the air? Height (in meters) 3000 2500 2000 h 1500 1000 500 0 (0, 2592.1) 2 4 6 8 10 12 14 16 Time (in seconds) 18 20 (23, 0) t 22 24​

Answers

The skydiver is in the air for 23 seconds.

What is graph?

A diagram or pictorial representation that organises the depiction of facts or values is known as a graph.  

The relationships between two or more items are frequently represented by the points on a graph.

The skydiver is in the air as long as their height is greater than zero. From the graph, we can see that the skydiver reaches a height of zero at t = 23 seconds. Therefore, the skydiver is in the air for:

t = 23 seconds - 0 seconds = 23 seconds

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In the year 2000, the population of Mexico was about 100 million, and it was growing by 1.53% per year. At this growth rate, the function f(x) = 100(1.0153)x gives the population, in millions, x years after 2000. Using this model, in what year would the population reach 106 million? Round your answer to the nearest year.

Answers

Answer:

2004

Step-by-step explanation:

I need help with this problem it's is
8x+5+3x+8=90

Answers

Answer:

x = 7

Step-by-step explanation:

8x + 5 + 3x + 8 = 90

11x + 5 + 8 = 90

11x + 13 = 90

11x = 77

x = 7

Let's Check

8(7) + 5 + 3(7) + 8 = 90

56 + 5 + 21 + 8 = 90

61 + 21 + 8 = 90

82 + 8 = 90

90 = 90

So, x = 7 is the correct answer!

Answer:

7

Step-by-step explanation:

First, collect common factors. This means put the x's together and the regular numbers together.

8x+3x=11x

5+8=13

11x+13=90

Subtract 13 from both sides

11x+13=90

    -13  -13

11x=77

Divide 77 by 11

x=7

Hope this helps! :)

a camel can drink 15 gallons of water in 10 minutes. at this​ rate, how much water can the camel drink in 5 ​minutes?

Answers

In 5 minutes, the camel can drink = 1.5 x 5 = 7.5 gallons of water.

So, the camel can drink 7.5 gallons of water in 5 minutes.

What is unitary method?

The unitary method is a mathematical technique used to solve problems related to proportionality.

It involves finding the value of a single unit and using it to determine the value of a given quantity or multiple quantities.

The unitary method is useful in solving problems that involve direct proportion or inverse proportion.

To find out how much water the camel can drink in 5 minutes, we can use the unitary method.

We know that the camel can drink 15 gallons of water in 10 minutes.

So, in 1 minute, the camel can drink = 15/10 = 1.5 gallons of water.

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Determine the amount of taxes owed on a taxable income of $51, 100.
A) $5,310.00
B) $6,919.00
C) $11,682.00
D) $12,744.40

Answers

The amount of taxes owed on a taxable income of $51, 100 is $6,919.00. The correct option is B.

What is the taxable amount?

To determine the amount of taxes owed on a taxable income of $51,100, we need to use the federal income tax brackets and rates for the tax year in question.

For the tax year 2021, the federal income tax brackets and rates for single filers are:

10% on taxable income from $0 to $9,950

12% on taxable income from $9,951 to $40,525

22% on taxable income from $40,526 to $86,375

24% on taxable income from $86,376 to $164,925

32% on taxable income from $164,926 to $209,425

35% on taxable income from $209,426 to $523,600

37% on taxable income over $523,600

To calculate the taxes owed on a taxable income of $51,100, we need to determine the amount of income that falls into each tax bracket, and then apply the corresponding tax rate to each portion of income.

Income up to $9,950 is taxed at 10%. This gives us a tax of 0.10 x $9,950 = $995.

Income from $9,951 to $40,525 is taxed at 12%. This gives us a tax of 0.12 x ($40,525 - $9,951) = $3,384.48.

Income from $40,526 to $51,100 is taxed at 22%. This gives us a tax of 0.22 x ($51,100 - $40,526) = $2,312.72.

Adding these three amounts together, we get the total tax owed:

$995 + $3,384.48 + $2,312.72 = $6,692.20

Therefore, the closest answer choice is B) $6,919.00.

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The amount of taxes owned on a taxable income of $51100 is $11242 which is approximately equal to option (c).

What is an income?

An income refers to the money that an individual or organization receives on a regular basis from various sources, such as employment, investments, or business activities. It is typically reported as gross income before taxes and other deductions are taken out.

Define tax?

Tax is a mandatory financial charge imposed by the government on individuals, businesses, and other entities, based on their income or property value. The revenue generated from taxes is used to fund public services and infrastructure.

=$51100* 22/100

=$11242

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If P(x,y) is the point on the unit circle defined by real number 8, then cscg =
OA.
OB.
y
B. 1
O C.
-|X
y
OD. V
X

Answers

The value of Cscθ is 1/y.

What is a trigonometric function?

The right-angled triangle's angle and the ratio of its two side lengths are related by the trigonometric functions, which are actual functions. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here, we have

Given: if p(x,y) is the point on the unit circle defined by the real number theta.

We have to find the value of the csc theta.

P(x,y) is the point on the unit circle  (the unit circle has a radius of 1 and center (0,0))

Now in a diagram, we can see that

OA= x

AP= y

radius OP =1

∠POA =θ

Now in ΔAOP

Cscθ = hypotenuse/opposite side

Cscθ = OP/AP

Cscθ = 1/y

Hence, the value of Cscθ is 1/y.

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