if 3/8=24c, then c=9 true or false

The dimensions that will produce the maximum enclosed area for two adjacent rectangular safe play areas of equal size with 200 feet of fencing is 100 feet by 100 feet.

To solve this problem, use the area of a rectangle formula A = lw, where l is the length and w is the width.

Since the two play areas must be of equal size, let's call the length and width l and w, respectively.

We know that the total length of fencing is 200 feet, so l + w = 200 feet.

We can then solve for l by rearranging the equation as l = 200 - w.

We then substitute this into the area equation to get A = (200 - w)w.

To maximize the area, differentiate this equation to get A' = w - 200.

Set this to 0 and solve for w to get w = 100. Since l + w = 200, l = 100 as well.

Therefore, the maximum enclosed area is produced by dimensions of l = 100 feet and w = 100 feet.

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The average change in population each year is -70. This negative value indicates a decrease in population over the five-year period. On average, the population decreased by 70 students per year.

To find the average change in population each year, we can use the expression (N - P) / 5, where N represents this year's population and P represents the previous population.
Given that the previous population was 1,600 students and this year's population is 1,250 students, we can substitute these values into the expression:

Average change in population each year = (N - P) / 5 = (1,250 - 1,600) / 5 = (-350) / 5 = -70

Therefore, the average change in population each year is -70. This negative value indicates a decrease in population over the five-year period. On average, the population decreased by 70 students per year.

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Answer:

(4,4)

Step-by-step explanation:

The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.

x^2 - 6x + 12 = 2x - 4

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.

y = 2x - 4 = 2(4) - 4 = 4

Therefore, the solution of this system of equations is (4, 4).

Therefore, the correct answer is (4, 4).

The value of k such that the vertical line x = k divides region R into two regions of equal area is approximately 0.7227.

What is Area?

Area is defined as the amount of two-dimensional space that a shape occupies. It can be calculated by multiplying two lengths of a shape, such as the length and width of a rectangle. Area units are always length units squared.

To find the area of region R, we need to integrate the function that defines the upper boundary of the region with respect to x. In this case, the upper boundary is given by y = 3sin(x/2).

To determine the area of R, we can integrate the function from x = 0 to x = (2pi)/3:

A = ∫[0, (2pi)/3] 3sin(x/2) dx

Using the integral property ∫sin(ax) dx = -1/a * cos(ax), we can rewrite the integral as:

A = -6 ∫[0, (2pi)/3] cos(x/2) dx

Evaluating the integral, we get:

A = -6 * [sin(x/2)]|[0, (2pi)/3]

Now we substitute the upper and lower limits into the equation:

A = -6 * [sin((2pi)/6) - sin(0)]

Since sin(0) = 0, the equation simplifies to:

A = -6 * sin((2pi)/6)

Simplifying further:

A = -6 * sin(pi/3)

Using the value of sin(pi/3) = sqrt(3)/2, we get:

A = -6 * (sqrt(3)/2)

A = -3sqrt(3)

However, area cannot be negative, so we take the absolute value:

|A| = 3sqrt(3)

Therefore, the area of region R is 3sqrt(3).

To find the value of k such that the vertical line x = k divides region R into two equal areas, we need to find the x-coordinate of the line of symmetry.

Let's assume the line of symmetry intersects x = k. We want the areas on both sides of the line to be equal, so the areas from x = 0 to x = k and from x = k to x = (2pi)/3 should be equal.

The total area of region R is 3sqrt(3), so the area on each side of the line of symmetry should be (1/2) * 3sqrt(3) = (3/2)sqrt(3).

Let's set up the equation to find k:

∫[0, k] 3sin(x/2) dx = (3/2)sqrt(3)

Using the same integral and evaluating it, we get:

-6 * [sin(x/2)]|[0, k] = (3/2)sqrt(3)

-6 * sin(k/2) = (3/2)sqrt(3)

Dividing both sides by -6 and multiplying by 2/3, we have:

sin(k/2) = -sqrt(3)/4

Taking the inverse sine (arcsin) of both sides, we get:

k/2 = arcsin(-sqrt(3)/4)

To find the value of k, we need to consider the range of the arcsine function. The range of arcsin(x) is -pi/2 ≤ arcsin(x) ≤ pi/2.

Since we're looking for the positive value of k, we need to consider the positive range of arcsin. Thus:

k/2 = arcsin(-sqrt(3)/4)

k = 2 * arcsin(-sqrt(3)/4)

Evaluating this expression using a calculator, we find:

k ≈ 0.7227

Therefore, the value of k such that the vertical line x = k divides region R into two regions of equal area is approximately 0.7227.

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Answer:

x =~ 31.2

y =~ 18

z =~ 9

Step-by-step explanation:

cos 30º = 27 / x

0.8660 = 27 / x

x = 27 / 0.8660

x =~ 31.18

w = height (smaller trinagle w, y, z)

tg 30º = w / 27

0.5774 = w / 27

w = 27 * 0.5774

w = 15.5898

tg 30º = z / 15.5898

0.5774 = z / 15.5898

z = 0.5774 * 15.5898

z = 9.00155052

cos 30º = 15.5898 / y

0.8660 = 15.5898 / y

y = 15.5898 / 0.8660

y =~ 18

Answer:

1.75 gallons of paint

Step-by-step explanation:

A student in the construction trades program has 4 1/2 gallons of paint

If the student uses 2.75 gallons in one room then the gallons of paint that are left can be calculated as follows

= 4 1/2 - 2.75

= 9/2 - 2.75

= 4.5 - 2.75

= 1.75

Hence 1.75 gallons of paint are left

Answer:

69

Step-by-step explanation:

Answer:

=5

Step-by-step explanation:

have a nice day, please give me brainliest

Answer:

X=5

Step-by-step explanation:

3x-x+2=12

2x+2=12

2x=10

X=5

Answer:

Step-by-step explanation:

so  49.8004 is what it is 0.001 left. 1  x or divide it stay the same

exp: 1\(1\sqrt{2}\)

Explanation:

Whenever you divide by a fraction, you multiply by the reciprocal of that fraction, so 49.8004 / 0.001 would be 49.8004 / 1/1000, which would be 49.8004 * 1000/1, which is 49,800.4.

If you think about it, the problem translated into words is "How many 0.001's fit into 49.8004", which is a big number, because a lot of 0.001's can fit inside 49.8004.

Answer:

$3

Step-by-step explanation:

If the markup for both swing sets is 20 1/4% . The school decides to buy the Adventurers swing set. The selling price of the swing set they are buying is:  $3,674.84.

Selling price can be defined as the amount a person intend to sell his/her product or the amount a buyer intend to buy a product.

Given data:

Adventurers  selling price = $3056

Thunder Ridge = 4,125

Markup 20 1/4% = 20.25 %

First  step is to find markup  

Markup = 20.25% × 3056

Markup =  $618.84

Now let find the selling price of the swing

Selling price = $3056 + $618.84

Selling price = $3,674.84

Therefore the selling price is the amount of $3,674.84.

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The complete question is:

An elementary school wants to purchase a new swing set. The table shows the selling price of the swing sets they are interested in buying

Swing Set

Wholesale Price ($)

Adventurers 3,056

Thunder Ridge 4,125

The markup for both swing sets is 20 1/4%. The school decides to buy the Adventurers swing set. What is the selling price of the swing set they

are buying? Round to the nearest cent if necessary,

well, the table has 5 points in it, let's pick any two hmmm say let's  use hmmm (2 , 7) and (6 , 17)

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{17}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{17}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}}\implies \cfrac{10}{4}\implies \cfrac{5}{2}\)

when x = 0, from the table, y = 2, so there's the y-intercept.

Answer:

2n + 1 = 157

2n = 157 - 1

2n = 156

n = 156/2

n = 78

Step-by-step explanation:

hope this helps

Using it's concept, there is a 0.726 = 72.6% probability that all 4 cards have distinct characters (letters or numbers).

A probability is given by the number of desired outcomes divided by the number of total outcomes.

A standard deck is given by 4 suits of 13 cards, each with either a number from 1 to 10 or one letter from A, Q or K, hence:

Hence the probability is given by:

p = 48/51 x 45/50 x 42/49 = 0.726.

0.726 = 72.6% probability that all 4 cards have distinct characters (letters or numbers).

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Question 1: P(X < 5) is approximately 0.9166 or 91.66%

Question 2: The advertised duration of the trip should be approximately 139.74 minutes to ensure that the ferry management is not late on more than 5% of the trips while minimizing the advertised duration.

Question 1:

To find the distribution of X, the smallest of the three numbers selected from {0, 1, ..., 9}, we need to determine the possible values and their probabilities.

The possible values for X are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. We can calculate the probabilities by considering the number of ways each value can be the smallest of the three selected numbers.

P(X = 0): The number 0 will be the smallest if the other two numbers selected are any two from {1, 2, 3, 4, 5, 6, 7, 8, 9}. There are 9 choose 2 ways to select the other two numbers. So, P(X = 0) = C(9, 2) / C(10, 3) = 36 / 120 = 0.3

Similarly, we can calculate the probabilities for the other values of X:

P(X = 1) = C(8, 2) / C(10, 3) = 28 / 120 = 0.2333

P(X = 2) = C(7, 2) / C(10, 3) = 21 / 120 = 0.175

P(X = 3) = C(6, 2) / C(10, 3) = 15 / 120 = 0.125

P(X = 4) = C(5, 2) / C(10, 3) = 10 / 120 = 0.0833

P(X = 5) = C(4, 2) / C(10, 3) = 6 / 120 = 0.05

P(X = 6) = C(3, 2) / C(10, 3) = 3 / 120 = 0.025

P(X = 7) = C(2, 2) / C(10, 3) = 1 / 120 = 0.0083

P(X = 8) = 0

P(X = 9) = 0

Therefore, the distribution of X is:

X | Probability

0 | 0.3

1 | 0.2333

2 | 0.175

3 | 0.125

4 | 0.0833

5 | 0.05

6 | 0.025

7 | 0.0083

8 | 0

9 | 0

To find P(X < 5), we sum the probabilities for X = 0, 1, 2, 3, and 4:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= 0.3 + 0.2333 + 0.175 + 0.125 + 0.0833

= 0.9166

Therefore, P(X < 5) is approximately 0.9166 or 91.66%.

Question 2:

The ferry trip duration is normally distributed with a mean of 2 hours and a standard deviation of 12 minutes.

To find the advertised duration of the trip that ensures the ferry management is not late on more than 5% of the trips, we need to find the z-score corresponding to the 95th percentile of the normal distribution.

Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 95th percentile is approximately 1.645.

The z-score formula is given by:

z = (x - μ) / σ

Where z is the z-score, x is the duration in minutes, μ is the mean duration in minutes (2 hours = 120 minutes), and σ is the standard deviation (12 minutes).

Rearranging the formula to solve for x, we have:

x = z * σ + μ

= 1.645 * 12 + 120

= 19.74 + 120

= 139.74

Therefore, the advertised duration of the trip should be approximately 139.74 minutes to ensure that the ferry management is not late on more than 5% of the trips while minimizing the advertised duration.

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Answer: x = 560/3

Step-by-step explanation:

First! We are going to be using the PEMDAS method! If you have any questions about this method please go ahead and ask below! The first step in our equation is the P - parenthesis, so we are going to multiply \(\frac{3}{5}\)  to everything inside of the parenthesis (x and -710)!

\(\frac{3}{5} (x -710) = -314\)

\(\frac{3}{5}x+(\frac{3}{5}*-710)=-314\)

\(\frac{3}{5}x -426 = -314\)

Now, we are going to add 426 to both sides of the equation, to single out the "x" variable!

\(\frac{3}{5}x= 112\)

Finally, let's multiply both sides by \(\frac{5}{3}\) to cancel out the \(\frac{3}{5}\) fractions, to get the "x" variable alone.

\(x=\frac{560}{3}\)

↑This is our answer!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

The month for the same plan to be the same for Settle City and Text Turf is 3 months.

It should be noted that Settle city charges $15 plus 5 per month for unlimited text messages text turf. This will be represented as 15 + 5m

It should be noted that when they charge $30 plus $10 per month for the same plan, this will be represented as 30 - 10m

It should be noted that m = number of months.

It should be noted that the number of months that you can take from here to company and pay the same price will be:

15 + 5m = 30 + 10m

15 - 30 = 10m - 5m

-15 = 5m

m = -15 / 5

m = -3

The value can't be negative. The information isn't properly written. It should give a positive value of 3.

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To find the range for the measure of the third side of a triangle given the measures of the two sides, we can use the triangle inequality theorem.

According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's apply this theorem to the given measures of the two sides: 10 ft and 16 ft.

For the triangle to be valid, the sum of the lengths of the two sides must be greater than the length of the third side. Mathematically, we can express this as:

10 ft + 16 ft > third side

Simplifying the inequality:

26 ft > third side

Therefore, the range for the measure of the third side of the triangle is any value greater than 26 feet.

In other words, the third side must be longer than 26 feet to form a valid triangle.

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A graph that passes the horizontal line test represents a function. This is because if a horizontal line can only intersect the graph at one point, it means that each input value (x) has a unique output value (y), which is the definition of a function. This is true.

I agree with Lionel, the graph should show a continuous line because age increases gradually like time. Also, age is usually not a discrete variable, it's a continuous variable that can have fractional values, so a line graph is more appropriate to represent the relationship between age and gas mileage.

Let's take f(x) = 3x - 7 and g(x) = -2x + 5 as two linear functions.

f(x) - (-g(x)) = 3x - 7 - (-2x + 5) = 3x - 7 + 2x - 5 = 5x - 12

f(x) + g(x) = 3x - 7 + (-2x + 5) = x - 2

So f(x) - (-g(x)) is not equivalent to f(x) + g(x). This result would not apply to every function, as the properties of addition and subtraction of functions depend on the specific functions being used.

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Answer:

26

Step-by-step explanation:

The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.

To convert the given equation from standard form to vertex form, we need to complete the square.

The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.

Given equation: y = x² - 6x + 14

Move the constant term to the right side:

y - 14 = x² - 6x

Complete the square by adding and subtracting the square of half the coefficient of x:

y - 14 + 9 = x² - 6x + 9 - 9

Group the terms and factor the quadratic:

(y - 5) = (x² - 6x + 9) - 9

Rewrite the quadratic as a perfect square:

(y - 5) = (x - 3)² - 9

Simplify the equation:

y - 5 = (x - 3)² - 9

Move the constant term to the right side:

y = (x - 3)² - 9 + 5

Combine the constants:

y = (x - 3)² - 4

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A random sample  is a sample in which the chosen elements are removed from the population once they are chosen.

A sample is a smaller group of the population that has the desired elements of the population. A sample is sometimes necessary because it might not be feasible or cost effective to access the whole population.

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Answer:

24 runners finish the race

Step-by-step explanation: 1/5 of 75 =15

75 - 15 =60

3/5 of 60 = 36

60 -36 =24

Answer:

$165

Step-by-step explanation:

10%=$15

Answer:

Gail going to pay $165 for his new camera.

Step-by-step explanation:

10% Sales tax+Camera Price=$165

The value of the unknown number x is 8.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

The given numbers include:

The sum of the given numbers is calculated as follows:

\(2 + 4 + \text{x} + 6 = 12 + \text{x}\)

The mean of the given 4 numbers is calculated as follows:

\(\dfrac{12+\text{x}}{4} =5\)

\(12+\text{x}=20\)

\(\text{x}=20-12\)

\(\text{x}=8\)

Thus, the value of the unknown number x is 8.

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Answer:

73567374, even

Step-by-step explanation:

80,986,061 - 7,418,687

73567374

The events are mutually exclusive and the probability of drawing a card from a standard deck and choosing a 7 or a 9 is 2/13

The given parameters are:

Standard deck = 52

n(7) = n(9) = 4

The probability of choosing a 7 or a 9 is calculated as:

P(7 or 9) = P(7) + P(9)

So, we have:

P(7 or 9) = 4/52 + 4/52

Evaluate

P(7 or 9) = 8/52

Simplify

P(7 or 9) = 2/13

Hence, the probability of drawing a card from a standard deck and choosing a 7 or a 9 is 2/13

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The determined value of the number of nickels and the number of dimes that Grayson has is

This is further explained below.

Generally, The following phrase represents Jayden's complete financial worth:

Nickels are worth $0.05 each.

The dime value is equal to $0.10

The total value is equal to the sum of the values of the nickels and dimes.

where;

\(1.20= (0.05*2 x) +(0.1*x)\)

0.1 x+0.1 x=1.2

0.2 x=1.2

\(x=\frac{1.2}{0.2}\)

x=6

y=2

In conclusion, the Total number of dimes=6

Total number of nickels=12

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At year 2, you will have approximately $25,915.13 in your bank account, assuming an initial investment with a 5% interest rate compounded annually. The correct answer is (a).


To find out how much money you will have in your bank account at year 2, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (in this case, $30,000)
P = Principal amount (initial investment)
R = Annual interest rate (5% or 0.05)
N = Number of times interest is compounded per year (assumed to be once per year)
T = Number of years (in this case, 3)
Let’s solve for P, the principal amount at year 0:
30,000 = P(1 + 0.05/1)^(1*3)
30,000 = P(1.05)^3
Dividing both sides of the equation by (1.05)^3:
P = 30,000 / (1.05)^3
P ≈ 25,915.13
Therefore, at year 2, you will have approximately $25,915.13 in your bank account.
The correct answer is (a) $25,915.13.

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