Find the value of x in the proportion. Check your answer.
18/x = 6/13

Answer:

Step-by-step explanation:

1) 2^2 + 2^2 = c^2

4 + 4 = c^2

8 = c^2

c = sqrt8

2) 2^2 + 3^2 = c^2

4 + 9 = c^2

13 = c^2

c = sqrt13

3) 10^2 + 4^2 = c^2

100 + 8 = c^2

108 = c^2

c = sqrt108

4) 1^2 + 5^2 = c^2

1 + 25 = c^2

26 = c^2

c = sqrt26

5) 3^2 + 1^2 = c^2

9 + 1 = c^2

10 = c^2

c = sqrt 10

6) 9^2 + 9^2 = c^2

81 + 81 = c^2

162 = c^2

c = sqrt162

There are a total of 42 lightbulbs needed for 7 chandeliers

From the question, the equation of the function is given as

f(x) = 6x

Where

For 7 chandeliers, we have

x = 7

Substitute x = 7 in f(x) = 6x

So, we have

f(7) = 6 x 7

Evaluate the product

f(7) = 42

Hence, the number of lightbulbs needed for 7 chandeliers is 42

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The number of lightbulbs needed for 7 chandeliers would be; 42

An equation is an expression that shows the relationship between two or more numbers and variables.

From the given problem, the equation of the function is;

f(x) = 6x

Where

x be the number of chandeliers and f(x) represents the number of lightbulbs.

For 7 chandeliers, x = 7

Now Substitute x = 7 in f(x) = 6x

Therefore, f(7) = 6 x 7

Evaluate the product;

f(7) = 42

Hence, the number of lightbulbs needed for 7 chandeliers would be; 42

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Answer:

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Step-by-step explanation:

We can use the trigonometric identity:

cos 2a = 1 - 2 sin^2 a

to rewrite 1 + 2cos a as:

1 + 2cos a = 1 + 2(1 - sin^2 a/2)

= 1 + 2 - 2(sin^2 a/2)

= 3 - 2(sin^2 a/2)

Now, using another trigonometric identity:

sin a = 2 sin(a/2) cos(a/2)

we can rewrite sin^2 a/2 as:

sin^2 a/2 = (1 - cos a)/2

Substituting this into the expression for 1 + 2cos a, we get:

1 + 2cos a = 3 - 2((1 - cos a)/2)

= 3 - (1 - cos a)

= 2 + cos a

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

The statement that describes the distribution based on the given information is:

A) The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 98 messages.

The graph shows a normal distribution, as indicated by the shape of the curve. The highest point of the curve (the peak) is at 128, which represents the mean of the distribution.

The standard deviation measures the spread of the data, and based on the information given, it is 98. Therefore, option A accurately describes the distribution.

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The probability that:

First, check if it is appropriate to use the normal approximation to the binomial distribution. The rule of thumb is that this approximation is reasonable if both np and n(1-p) are greater than 5. In this case, p = 0.83 (probability of failure), n = 70 (number of trials).

So,

np = 700.83 = 58.1,

n(1-p) = 700.17 = 11.9.

Both quantities are larger than 5, so use the normal approximation.

Convert this to a problem involving a normal distribution. The mean of this distribution is np = 58.1 and the standard deviation is √(np(1-p)) = √(700.830.17) = 6.35.

(a) within 2 years 47 or more fall:

This corresponds to a Z-score of (47.5 - 58.1) / 6.35 = -1.67. The probability that a standard normal variable is greater than -1.67 is 0.9525.

So the probability that 47 or more products fail is approximately 0.9525.

(b) within 2 years 58 or fewer fail:

This corresponds to a Z-score of (58.5 - 58.1) / 6.35 = 0.063. The probability that a standard normal variable is less than 0.063 is 0.5250.

So the probability that 58 or fewer products fail is approximately 0.5250.

(c) within 2 years 15 or more succeed:

Since the probability of success is 1-p, this is equivalent to fewer than (70 - 15 = 55) failing. This corresponds to a Z-score of (54.5 - 58.1) / 6.35 = -0.567.

The probability that a standard normal variable is greater than -0.567 is 0.7151.

So the probability that 15 or more products succeed is approximately 0.7151.

(d) within 2 years fewer than 10 succeed:

This is equivalent to more than (70 - 10 = 60) failing. This corresponds to a Z-score of (60.5 - 58.1) / 6.35 = 0.377.

The probability that a standard normal variable is less than 0.377 is 0.6478.

However, since we want more than 60 failing, the probability that the variable is greater than 0.377, which is 1 - 0.6478 = 0.3522.

So the probability that fewer than 10 products succeed is approximately 0.3522.

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Answer:

Step-by-step explanation:

208

Answer:

C 45

Step-by-step explanation:

Answer:

Answer and explanation

Answer:

Step-by-step explanation:

Sales Revenue:  $800.00

Cost of good sold:  $350,000.00

Subtract:                   $450,000.00

Sales Revenue:         $795,000.00

Cost of good sold:     $600,000.00

Subtract Sales             $195,000.00

Revenue from Cost

of goods sold.

Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) \(\times\)(x + 1/2)

(y - 6) = -1/4 \(\times\)(x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

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Answer:

a) 0.277 = 27.7% probability that a randomly selected tyre lasts between 55,000 and 65,000 miles.

b) 0.348 = 34.8% probability that a randomly selected tyre lasts less than 48,000 miles.

c) 0.892 = 89.2% probability that a randomly selected tyre lasts at least 41,000 miles.

d) 0.778 = 77.8% probability that a randomly selected tyre has a lifetime that is within 10,000 miles of the mean

Step-by-step explanation:

Problems of normally distributed distributions are solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\(\mu = 51200, \sigma = 8200\)

Probabilities:

A) Between 55,000 and 65,000 miles

This is the pvalue of Z when X = 65000 subtracted by the pvalue of Z when X = 55000. So

X = 65000

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{65000 - 51200}{8200}\)

\(Z = 1.68\)

\(Z = 1.68\) has a pvalue of 0.954

X = 55000

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{55000 - 51200}{8200}\)

\(Z = 0.46\)

\(Z = 0.46\) has a pvalue of 0.677

0.954 - 0.677 = 0.277

0.277 = 27.7% probability that a randomly selected tyre lasts between 55,000 and 65,000 miles.

B) Less than 48,000 miles

This is the pvalue of Z when X = 48000. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{48000 - 51200}{8200}\)

\(Z = -0.39\)

\(Z = -0.39\) has a pvalue of 0.348

0.348 = 34.8% probability that a randomly selected tyre lasts less than 48,000 miles.

C) At least 41,000 miles

This is 1 subtracted by the pvalue of Z when X = 41,000. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{41000 - 51200}{8200}\)

\(Z = -1.24\)

\(Z = -1.24\) has a pvalue of 0.108

1 - 0.108 = 0.892

0.892 = 89.2% probability that a randomly selected tyre lasts at least 41,000 miles.

D) A lifetime that is within 10,000 miles of the mean

This is the pvalue of Z when X = 51200 + 10000 = 61200 subtracted by the pvalue of Z when X = 51200 - 10000 = 412000. So

X = 61200

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{61200 - 51200}{8200}\)

\(Z = 1.22\)

\(Z = 1.22\) has a pvalue of 0.889

X = 41200

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{41200 - 51200}{8200}\)

\(Z = -1.22\)

\(Z = -1.22\) has a pvalue of 0.111

0.889 - 0.111 = 0.778

0.778 = 77.8% probability that a randomly selected tyre has a lifetime that is within 10,000 miles of the mean

Answer:

x+2y=13

Step 1: Add -2y to both sides.

x+2y+−2y=13+−2y

x=−2y+13

Answer:

x=−2y+13

Step 1: Add 5y to both sides.

3x−5y+5y=6+5y

3x=5y+6

Step 2: Divide both sides by 3.

3x

3

=

5y+6

3

x=

5

3

y+2

Answer:

x=

5

3

y+2

Step 1: Add -3x to both sides.

3x−5y+−3x=6+−3x

−5y=−3x+6

Step 2: Divide both sides by -5.

−5y

−5

=

−3x+6

−5

y=

3

5

x+

−6

5

Answer:

y=

3

5

x+

−6

5

Step-by-step explanation:

Answer:

(7, 3)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

x + 2y = 13

3x - 5y = 6

Step 2: Rewrite Systems

x + 2y = 13

Step 3: Redefine Systems

x = 13 - 2y

3x - 5y = 6

Step 4: Solve for y

Substitution

Step 5: Solve for x

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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\(\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_{3}(y+5)+\log_3(6)~~ = ~~\log_3(66) \\\\[-0.35em] ~\dotfill\\\\ \log_3[(y+5)\cdot 6]=\log_3(66)\implies (y+5)6=66 \\\\\\ y+5=\cfrac{66}{6}\implies y+5=11\implies \boxed{y=6}\)

Answer:

5)  35 / 100 = X / 74      X = 2590 / 100 = 25.9

or .35 * 74 = 25.9

6) 78 / 95 = X * 100

X = 7800 / 95 = 82.1 %

or X = 78/95 * 100 = 82.1 %

7)  60/100 * X = 28

X = 2800 / 60 = 46.7

Or .6 * X = 28

X = .28 / .6 = 46.7

Answer:

First one- x=0

Second=All real numbers

Step-by-step explanation:

.

Answer:

Cuando 102 se divide por 2/3 la respuesta es 153

Step-by-step explanation:

102 : 2/3 =

102 * 3/2 =

51 * 3 =

The solution is, the profit is 18.

If the profit of a company made by the company is in the form a quadratic expressions but in the different forms as given in the question.

a). The prices that give a profit of zero dollars.

   Expression that is most useful,

   Factored form: -2(p - 3)(p - 9) = 0

   p = 3, 9

b). The profit when the price is zero .

   Standard form:

   Profit = -2p² + 24p - 54 = 0

   -p² + 12p - 27 = 0

   -p² + 3p + 9p - 27 = 0

   -p(p - 3) + 9(p -3) = 0

    (-p + 9)(p - 3) = 0

    p = 3, 9

c). The price that gives the maximum profit.

  Vertex form: -2(p - 6)² + 18

  Vertex of the given expression → (6, 18)

  Maximum profit will be at p = 6.

  Therefore, profit = -2(6 - 6)² + 18 = 18

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complete question:

The profit that a company makes selling an item (in thousands of dollars) depends on the price of the item (in dollars). If p is the price of the item, then three equivalent forms for the profit are

Standard form: - 2 p^2 + 24p - 54

Factored form: -2(p - 3)(y-9)

Vertex form: -2(p-6)^2 + 18.

Which form is most useful for finding a. The prices that give a profit of zero dollars?

b. The profit when the price is zero?

c. The price that gives the maximum profit?​

The students need to earn $182 per month in order to accomplish their goals.

Division is the process of dividing a number by a given number.

Given that, the total cost for the class to go to the observatory is $910 and the students need money in 5 months.

To collect $910 in 5 months, students must earn $910/5 per month.

910/5

= 182

Hence, the students need to earn $182 per month in order to accomplish their goals.

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The maximum APR with quarterly compounding that the borrower will accept from a lender is 16.132%.

To convert the maximum effective monthly rate of 1% into an APR with quarterly compounding, we can use the formula:

\(APR = [(1 + \dfrac{r}{n})^n - 1] \times 4\)

Where r is the effective monthly rate and n is the number of compounding periods per year. In this case, we want to find the maximum APR with quarterly compounding that the borrower will accept, so we can substitute r = 1% and n = 3:

\(APR = ((1 + \dfrac{0.01}{3})^3 - 1) \times 4\)

APR = (1.0100333³ - 1) x 4

APR = 0.04033 x 4

APR = 0.16132 or 16.132%

Therefore, the maximum APR with quarterly compounding that the borrower will accept from a lender is 16.132%.

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The first table represents y as a function of x.

If a table represents a function, each of the x-values will have only one possible y-value that corresponds to it, however, two different x-values can have the same y-value.

All the tables, except the first table, have x-values that have more than one y-value assigned to it.

The first table have exactly one y-value that corresponds to each of the x-values. Therefore, the first table represents y as a function of x.

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Answer:

5x10x9 Is the correct answer meaning that the answer is 450

Brainliest would be very appriciated

Step-by-step explanation:

EDIT: my bad i read the question wrong, the answer is D:450

sorry for any confusion ;^;

Answer:

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

According to the remainder theorem, if we subtract 68 from the given trinomial it should be divisible by x - 4. In other words, one of zero's will be x = 4.

Answer:

\(x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}\)

Step-by-step explanation:

Given trigonometric equation:

\(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

To solve the equation for x in the given interval [0, 2π), first rewrite the equation in terms of sin x and cos x using the following trigonometric identities:

\(\boxed{\begin{minipage}{4cm}\underline{Trigonometric identities}\\\\$\tan \left(\dfrac{\theta}{2}\right)=\dfrac{1-\cos \theta}{\sin \theta}$\\\\\\$\csc \theta = \dfrac{1}{\sin \theta}$\\ \end{minipage}}\)

Therefore:

              \(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

\(\implies 2 \left(\dfrac{1-\cos x}{\sin x}\right)- \dfrac{1}{\sin x}=0\)

  \(\implies \dfrac{2(1-\cos x)}{\sin x}- \dfrac{1}{\sin x}=0\)

\(\textsf{Apply the fraction rule:\;\;$\dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}$}\)

\(\dfrac{2(1-\cos x)-1}{\sin x}=0\)

Simplify the numerator:

\(\dfrac{1-2\cos x}{\sin x}=0\)

Multiply both sides of the equation by sin x:

\(1-2 \cos x=0\)

Add 2 cos x to both sides of the equation:

\(1=2\cos x\)

Divide both sides of the equation by 2:

\(\cos x=\dfrac{1}{2}\)

Now solve for x.

From inspection of the attached unit circle, we can see that the values of x for which cos x = 1/2 are π/3 and 5π/3. As the cosine function is a periodic function with a period of 2π:

\(x=\dfrac{\pi}{3} +2n\pi,\; x=\dfrac{5\pi}{3} +2n\pi \qquad \textsf{(where $n$ is an integer)}\)

Therefore, the values of x in the given interval [0, 2π), are:

\(\boxed{x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}}\)

Answer:

true for all x

Step-by-step explanation:

-2x + 12 = -2(x – 6)

Distribute

-2x+12 = -2x+12

Add 2x to each side

12 =12

Since this is always true, there are infinite solutions

x is all real numbers

The system of inequalities are : C + D ≤ 1300 ; C≥500 and D≥650

The graph can be made using these three inequalities.

How do you describe linear inequality with two variables?

The solution(s) of a linear inequality in two variables like mx + ny > p is value in pair (x, y) that satisfies the inequality when the values of x and y are substituted into that inequality. The graph of that inequality in two variables is the set of points that represents all roots to the inequality.

Let the commercial units be represented by C and Domestic units by D,

Given that both units are not more than 1300.

Means, C + D ≤ 1300

Also Given that, Commercial units are atleast 500 i.e, C≥500

Similarly, for domestic D≥650

a)The system of inequalities are:

C+D ≤1300

C≥500

D≥650

b)Graph for the above inequalities

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Refer to the graph attached with solution.

Answer:

Zach time of reading every weekend forms a sequence with these terms: 10, 20, 40, 80. On the other hand, that of Victoria forms a sequence with terms: 35, 50, 65, 80. By keenly observing the sequences, Zach's sequence is a geometric sequence with a common ratio equal to 2 and Victoria's sequence is an arithmetic or linear sequence with a common difference of 15. Thus, the answer is letter B.

Step-by-step explanation:

Answer: 34.64 m

Step-by-step explanation:

Given: A boat is 60 m from the base of a lighthouse.

The angle of depression between the lighthouse and the boat is 37°.

By using trigonometric ratios :

\(\tan x=\dfrac{\text{Side opposite to }x}{\text{Side adjacent to }x}\)

here x= 37°, side opposite to x = height of lighthouse (h) , side adjacent to x = 60 m

\(\tan 37^{\circ}=\dfrac{h}{60}\\\\\Rightarrow\ 0.57735=\dfrac{h}{60}\\\\\Rightarrow\ h= 60\times0.57735\approx34.64\)

Hence, the lighthouse is 34.64 m tall.

Answer:

the value is 4 i think

Step-by-step explanation:

Using the normal distribution, it is found that there is a

a) 0% probability that the number of calls received at the switchboard will be exactly 578.

b) 0.1586 = 15.86% probability that the number of calls received at the switchboard will be less than 570.

c) 0.9485 = 94.85% probability that the number of calls received at the switchboard will be between 561 and 600.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem:

Item a:

In the normal distribution, the probability of an exact value is 0%, hence, 0% probability that the number of calls received at the switchboard will be exactly 578.

Item b:

The probability is the p-value of Z when X = 570, hence:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{570 - 580}{10}\)

\(Z = -1\)

\(Z = -1\) has a p-value of 0.1586.

0.1586 = 15.86% probability that the number of calls received at the switchboard will be less than 570.

Item c:

This probability is the p-value of Z when X = 600 subtracted by the p-value of Z when X = 561, hence:

X = 600:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{570 - 580}{10}\)

\(Z = 2\)

\(Z = 2\) has a p-value of 0.9772.

X = 561:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{561 - 580}{10}\)

\(Z = -1.9\)

\(Z = -1.9\) has a p-value of 0.0287.

0.9772 - 0.0287 = 0.9485.

0.9485 = 94.85% probability that the number of calls received at the switchboard will be between 561 and 600.

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