Mathematics College

A. 2 sqrt 3

B. 4

C. 8

D. 4 sqrt 6

E. 12

Please help

Answers

Answer 1

Answer:

Option B. 4

Step-by-step explanation:

From the question given above, the following data were obtained:

Angle θ = 60 °

Opposite (Fe) = 4√3

Adjacent (DE) = x

The value of x can be obtained by using the Tan ratio as illustrated below:

Tan θ = Opposite / Adjacent

Tan 60 = 4√3 / x

√3 = 4√3 / x

Cross multiply

√3 × x = 4√3

Divide both side by √3

x = 4√3 /√3

x = 4

Thus, the length of DE is 4

Related Questions

Consider the probability that exactly 90 out of 147 students will pass their college placement exams. Assume the probability that a given student will pass their college placement exam is 56%.

Approximate the probability using the normal distribution. Round your answer to four decimal places.

Answers

Answer:

Step-by-step explanation:

i didnt do anything bro why u delete my answer

look at the picture

Answers

Answer:

Step-by-step explanation:

x²-9x<-8

x²-9x+(-9/2)²<-8+(-9/2)²

(x-9/2)²<-8+81/4

(x-9/2)²<(-32+81)/4

(x-9/2)²<49/4

|x-9/2|<7/2

-7/2<x-9/2<7/2

add 9/2

9/2-7/2<x-9/2+9/2<7/2+9/2

2/2<x<16/2

1<x<8

Determine the domain and range of the following and show/explain your work.
5 y = - x^4 + 4 Provide a graph to verify your answer.

6 y = 2x^3 - 1 Provide a graph to verify your answer.

7 y = 3√(2x+8) Provide a graph to verify your answer.

Answers

See below for how the domain and the range are calculated

How to determine the domain and the range?

Function, y = -x^4 + 4

The function is given as:

y = -x^4 + 4

See attachment for the graph

From the attached graph, we have:

Domain = Set of all real numbersRange = Set of real numbers less than or equal to 4

Function, y = 2x^3 - 1

The function is given as:

y = 2x^3 - 1

See attachment for the graph

From the attached graph, we have:

Domain = Set of all real numbersRange = Set of all real numbers

Function, y = ∛(2x + 8)

The function is given as:

y = ∛(2x + 8)

See attachment for the graph

From the attached graph, we have:

Domain = Set of all real numbersRange = Set of all real numbers

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Find the critical value needed to construct a confidence interval of the given level with the given sample size. Round the answer to at least three decimal places. Level 95%, sample size 10.

Answers

Using the t-distribution, the critical value needed is: t = 2.2622.

How to find the critical value for the t-distribution?

The critical value is found using a calculator, with two parameters:

The confidence level.The number of degrees of freedom, which is one less than the sample size.

For this problem, we have a confidence level of 95% and 10 - 1 = 9 df, hence the critical value is t = 2.2622.

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A random sample of n D 225 and xN D 21 was drawn from a normal population with a known

standard deviation of 26:8: Calculate the 95% confidence interval of the population mean.

Answers

Using the z-distribution, the 95% confidence interval of the population mean is: (17.5, 24.5).

What is a z-distribution confidence interval?

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

For this problem, the other parameters are:

[tex]\overline{x} = 21, \sigma = 26.8, n = 225[/tex]

Hence the bounds of the interval are:

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 21 - 1.96\frac{26.8}{\sqrt{225}} = 17.5[/tex]

[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 21 + 1.96\frac{26.8}{\sqrt{225}} = 24.5[/tex]

The interval is: (17.5, 24.5).

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log a^x² - 9log a³√x simplify

Answers

Answer:

log(a^x^2-27(radicalx))

Step-by-step explanation:

Assuming you have written your question correctly, this is it.

60 POINTS IF CORRECT AND BRAINLIEST ANSWER FOR COMPLETE ANSWER

Answers

1. The solution to the first percent puzzle is as follows:

75% 66²/₃ 11¹/₉

33¹/₃% 25% 22¹/₅% 3⁷/₁₀%

50% 37¹/₂% 33¹/₃% 5¹/₂%

2. The solution to the second percent puzzle is as follows:

10% 90%

50% 5% 45%

What is a percent puzzle?

A percent puzzle is a puzzle that engages students to practice working with percentages.

The percent puzzle involves a matrix format, in which students multiply the column percent by the row percent to find the percent they must put in the missing boxes to complete the puzzle.

The multiplication results for the missing boxes can be either stated in decimals, fractions, or a combination.

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The sum of three consecutive integers is -15.
If 1 is added to each integer, what is the product.
of the three resulting integers?

Answers

-18 maybe not to sure

-18 not sure buddy but tryit’s really good

Graph the function f(x) = x3 – 3x – 2. Based on the graph, which value for x is a double root of this function?

–2
–1
1
2

Answers

The value for x that is a double root of this function is x = -1

How to determine the double root?

The function is given as:

f(x) = x^3 - 3x - 2

From the graph of the above function (see attachment), we have the following highlights:

The curve crosses the x-axis at x = 2The curve touches the x-axis at x = -1

The point that it touches the x-axis is the double root point

Hence, the value for x that is a double root of this function is x = -1

Answers

6 years!
Divide 72 by your rate and you get the amount of years.

Suppose Mai places $3500 in an account that pays 19% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
S
(b) Find the amount in the account at the end of 2 years.

Answers

Answer:

a.$4165

b.$4956.35

Step-by-step explanation:

a)19% × 3500 = 665.

3500+665 =4165

b)19% × 4165 = 791.35

4165+791.35= 4956.35

I need to see the steps to the problem for me to fully get it

Answers

The matrix [tex]\vec C[/tex] resulting from the multiplication between matrices [tex]\vec B[/tex] and [tex]\vec A[/tex] is equal to the matrix [tex]\left[\begin{array}{ccc}37&55&- 20\\23&11&- 20\\25&28&-9\end{array}\right][/tex]. (Correct choice: C)

How to find the result of a multiplication of two matrices

In this question we must apply the operation of multiplication of two matrices, whose definition is shown below:

[tex]\vec B\, \cdot \, \vec A[/tex], where [tex]\vec B \in \mathbb {R}_{n \times p}[/tex] and [tex]\vec A \in \mathbb{R}_{p \times n}[/tex] (1)

Where each element of the resulting matrix is equal to the following expression:

[tex]c_{(i, j)} = b_{(i, p)} \,\bullet\, a_{(p, j)}[/tex] (2)

Where the operator "[tex]\bullet[/tex]" represents a dot product.

Now we proceed to calculate each element of the matrix:

[tex]c_{(1, 1)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]

5 · 1 + 7 · 5 + 3 · (- 1)

[tex]c_{(1, 2)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]

5 · 7 + 7 · 2 + 3 · 2

[tex]c_{(1, 3)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]

5 · (- 3) + 7 · 1 + 3 · (- 4)

- 20

[tex]c_{(2, 1)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]

(- 3) · 1 + 7 · 5 + 9 · (- 1)

[tex]c_{(2, 2)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]

(- 3) · 7 + 7 · 2 + 9 · 2

[tex]c_{(2, 3)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]

(- 3) · (- 3) + 7 · 1 + 9 · (- 4)

- 20

[tex]c_{(3, 1)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]

2 · 1 + 5 · 5 + 2 · (- 1)

[tex]c_{(3, 2)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]

2 · 7 + 5 · 2 + 2 · 2

[tex]c_{(3, 3)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]

2 · (- 3) + 5 · 1 + 2 · (- 4)

- 9

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Evaluate bh for b = 12 and h = 2. Type a numerical answer in the space provided.

Answers

The value of bh for b =12 and h = 2 is 24

How to evaluate the expression?

The expression is given as:

Where

b = 12 and h = 2

So, we have:

bh = 12 * 2

Evaluate

bh = 24

Hence, the value of bh for b =12 and h = 2 is 24

Answers

The number of board game sorted is 14

How to find the number of games?

The games have been sorted into video games and board games.

The number of video games is 28 less than 6 times the number of board games.

Therefore,

the number of board games = x

number of video game = 6x - 28

The games are 80% video games. Hence,

80 / 100 × x + 6x - 28 = 6x - 28

4 / 5 × 7x - 28 = 6x - 28

4 / 5 (7x - 28) = 6x -28

28 / 5 x - 112 / 5 = 6x - 28

28 / 5 x - 6x = -28 + 112 / 5

28x - 30x / 5 = - 28 + 112 / 5

-2x / 5 = -28 / 5

-10x = -140

x = 14

Therefore, the number of board game sorted is 14.

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Answer:

Step-by-step explanation:

80 / 100 × x + 6x - 28 = 6x - 28

4 / 5 × 7x - 28 = 6x - 28

4 / 5 (7x - 28) = 6x -28

28 / 5 x - 112 / 5 = 6x - 28

28 / 5 x - 6x = -28 + 112 / 5

28x - 30x / 5 = - 28 + 112 / 5

-2x / 5 = -28 / 5

-10x = -140

x = 14

The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65° E, and the two towers are 31 kilometers apart. A fire spotted by rangers in each tower has a bearing of N 80° E from the Pine Knob and S 70° E from Colt Station (see figure). Find the distance of the fire from each tower. (Round your answers to two decimal places.)
From Pine Knob:

Answers

The equation that can be used to find the height of the tree is as follows:

[tex]\frac{h}{sin 29} =\frac{40}{sin147}[/tex]

The height of the tree is 35.6 m

How to use sine rule to find height of the tree?

Th equation that can be used to find the height of the tree uses the principle of sine rule.

Therefore,

[tex]\frac{h}{sin 29} =\frac{40}{sin(180-4-29)}[/tex]

[tex]\frac{h}{sin 29} =\frac{40}{sin147}[/tex]

Therefore,

[tex]\frac{h}{sin 29} =\frac{40}{sin147}[/tex]

cross multiply

h sin 147 = 40 sin 29°

h = 40 sin 29° / sin 147

h = 19.3923848099 / 0.54463903501

h = 35.6015636045

h = 35.6 m

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Describe the function over each part of its domain. State whether it is constant, increasing, or decreasing, and state the slope over each part.

Answers

The function is illustrated below based on the information.

How to describe the function?

When x <= 8000

The cost remains constant at 0.35 when x increases from 0 to 8000. The slope of the cost function over this part is 0

When 8000 < x <= 20000

The cost remains constant at 0.75 when x increases from 8000 to 20000 and the slope of the cost function over this part is 0.

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Mike, Luke, and Alex each own a white hat marked with the first letter of their name. Winter owns a plain red hat, which is not marked with any letter.

How many ways can the four people wear these four hats so each person is wearing a different hat, and no one is wearing a hat marked with the first letter of their name?

Answers

Answer:switch mikes Luke’s and Alex in between each other and let winter keep her own

Step-by-step explanation:

20) Chester bought a new car with a sticker price of $18,675. He paid 25% of the cost as a down payment. What
amount did he finance?
O a.) $14,016.25
Ob.) $14,126.25
O c.) $14,006.25
Od.) $14,106.25

Answers

Answer:

B is correct

necesito ayuda con estas operaciones
3x=12
3x= -5=0
x+4=17
9y+3=21
5(x-2)=20
x÷2=4
2x÷=4
5÷x=2
4x+5=3x-6
3(x-2) =0
x÷3-4=0
5(7-x) =31-x
3(2x-2) =2(3x+9)

Answers

The expressions are illustrated below.

How to compute the expression?

3x = 12

x = 12/3

x = 4

x + 4 = 17

x = 17 - 4

x = 13

9y + 3 = 21

9y = 21 - 3

9y = 18

y = 18/9

y = 2

x ÷ 2 = 4

x = 4 × 2

x = 8

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PLEASE help me with this question, and preferably leave your handwritten answer
(Easier for me to understand) but typed is also ok :)

Help is greatly appreciated!!

Answers

Using a system of equations, it is found that there were 100 students at the bus stop.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Variable x: Number of boys in the bus stop.Variable y: Number of girls in the bus stop.

Considering the first paragraph, the equation is:

[tex]\frac{x}{y - 25} = \frac{3}{2}[/tex]

Considering the second paragraph, the equation is:

y - 25 = x - 15.

Hence:

y = x + 10.

Replacing on the first equation:

[tex]\frac{x}{x - 15} = \frac{3}{2}[/tex]

3x - 45 = 2x

x = 45.

y = x + 10 = 55.

The total number was:

45 + 55 = 100.

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Any ideas for this graph

Answers

It’s a parabola;
(X+1)(X+3) = 0

X intercepts are at x=1 and x=3
Y intercept is at y=3

It’s neither odd one even function.

How many more people attended from the 40-60 class than the 60-80

Answers

Answer:7 people

Step-by-step explanation:

Answer:

Step-by-step explanation:

Membership selection. A town council has members, Democrats and Republicans.

(A)

If the president and vice-president are selected at random, what is the probability that they are both Democrats?

(B)

If a 3-person committee is selected at random, what is the probability that Republicans make up the majority?

The probability that they are both Democrats is approximately

enter your response here.
(Type a decimal. Round to three decimal places.)

Answers

Using the hypergeometric distribution, the probabilities are given as follows:

a) 0.2 = 20%.

b) 0.5539 = 55.39%.

What is the hypergeometric distribution formula?

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.

Researching this problem on the internet, it is found that the council has 15 members, of which 7 are Democrats and 8 are Republicans.

Item a:

The parameters are:

N = 15, n = 2, k = 7.

The probability is P(X = 2), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,15,2,7) = \frac{C_{7,2}C_{8,0}}{C_{15,2}} = 0.2[/tex]

Item b:

At most one Democrat, with n = 3, hence:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

In which:

[tex]P(X = 0) = h(0,15,3,7) = \frac{C_{3,0}C_{8,3}}{C_{15,3}} = 0.1231[/tex]

[tex]P(X = 1) = h(1,15,3,7) = \frac{C_{3,1}C_{8,2}}{C_{15,3}} = 0.4308[/tex]

Then:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1231 + 0.4308 = 0.5539[/tex]

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16. Describe the type of solution for the linear system of
equations given below.
2x + 3y = 15
6y=-4x + 12
F.
no solution
G. infinite solutions
H.
one solution
J. two solutions

Answers

Answer:

Step-by-step explanation:

2x+3y=15

multiply by 2

4x+6y=30 ...(1)

6y=-4x+12

4x+6y=12 ...(2)

(1) and (2) represent parallel lines.

Hence no solution.

root of polynomial function f(x)=(x-3)^4(x+6)^2

Answers

28832883838828999888

the domain of f(x)= logb x is the set of all real numbers true or false pls need now

Answers

Answer: False

Step-by-step explanation:

The only number that makes this impossible to solve is x = 0

24g ____ 1,679mg?
Complete the inequality statement

Answers

Answer:

24g > 1,679mg

What is the volume of this prism if a scale factor of 1.25 is applied to its dimensions?

A. 17.00 cubic units

B. 33.20 cubic units

C. 21.25 cubic units

D. 13.60 cubic units

Answers

Answer: B

Step-by-step explanation:

1: 5 × 1.25 = 6.25

2 × 1.25 = 2.5

1.7 × 1.25 = 2.125

2: L × W × H = 6.25 × 2.5 × 2.125 = 33.20 cubic

Tyler wants to have $250,000 in his retirement account by the time he retires in 30 years. The interest rate is 5%. Use the annuity formula to calculate the amount Tyler needs to deposit on a monthly basis in order to reach his goal. When solving, round numbers to the nearest hundred-thousandth. Round your final answer to the nearest cent.

Answers

Using the monthly payment formula, he needs to deposit A = $1,342.12 a month to reach his goal.

What is the monthly payment formula?

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

P is the initial amount.r is the interest rate.n is the number of payments.

For this problem, the parameters are:

P = 250000, r = 0.05, n = 12 x 30 = 360.

Then:

r/12 = 0.05/12 = 0.004167.

Then:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 250000\frac{0.004167(1+0.004167)^{360}}{(1+0.004167)^{360} - 1}[/tex]

A = $1,342.12

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the equation y=ax describes the graph of a line.if the value of a is negative,the line

Answers

If the value of a is negative, the line is reflected across any of the axis

How to describe the line?

The equation is given as:

y = ax

The new line is given as

y = -ax

The above implies that y = ax is transformed to y = -ax

The transformation can be any of:

reflection across the x-axisreflection across the y-axis

Hence, if the value of a is negative, the line is reflected across any of the axis

A. 2 sqrt 3 B. 4 C. 8 D. 4 sqrt 6 E. 12 Please help

Answers

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A. 2 sqrt 3

B. 4

C. 8

D. 4 sqrt 6

E. 12

Please help