A diagram of a swimming
pool is below. The width of
the pool is 25 m, find the
length of the actual pool?
7.5 cm
15 cm

1st. since we are adding whats in the ( ), ignore them. If we were multiplying or dividing it would not be that easy, but we arent. 2nd, add your like terms.... so (4-2x)+(3x-2) would become 4 - 2x + 3x - 2..... which by adding like terms we can simplify that by adding (-2x) + (3x) which gives us 1x or just x. then 4 - 2 is just 2... sooooo,.... x -2 is your answer.

Credit to: sma51664 for getting the right answer

Answer:

Cooking magazine = 27

Baseball magazine = 32

Step-by-step explanation:

Total number of magazine = 59

Cooking magazine = x

Baseball magazine = x + 5

Total number of magazine = Cooking magazine + Baseball magazine

59 = x + (x + 5)

59 = x + x + 5

59 = 2x + 5

59 - 5 = 2x

54 = 2x

Divide both sides by 2

x = 54 / 2

= 27

x = 27

Cooking magazine = x

= 27 magazine

Baseball magazine = x + 5

= 27 + 5

= 32 magazine

Answer:

15 is right ans

Step-by-step explanation:

Answer:

Area of larger circle = \(\pi *r^2=3.14(11^2)=379.94\)

Area of smaller circle = \(\pi *r^2=3.14(3^2)=28.26\)

Probability that it lands in the shaded area (smaller circle):

28.26 ÷ 379.94 = 0.07438... = 0.07 (nearest hundredth)

Answer:

19

Step-by-step explanation:

133 divided by 7 = 19

area of a parallelogram is just L x W so just divide to get the base.

The UCR (Uniform Crime Reporting) is B. not a truly reliable measure.

The UCR is a program established by the FBI in 1930 to collect and analyze crime statistics from law enforcement agencies across the United States. Although it provides useful data and insights into crime trends, it is not without its limitations. One significant issue with the UCR is that it relies on voluntary reporting from law enforcement agencies, meaning that some areas may not provide complete or accurate data. This can lead to an underrepresentation of certain crimes or inconsistencies in reporting across jurisdictions.

Another limitation is that the UCR only includes reported crimes, excluding any unreported criminal activity. This means that the data does not necessarily provide a comprehensive picture of all crimes occurring in a given area. Additionally, the UCR uses a hierarchy rule, meaning that if multiple crimes are committed during a single incident, only the most severe crime is counted. This can result in an undercounting of less severe but still significant crimes.

In summary, although the UCR provides valuable information on crime trends and patterns, it is not a truly reliable measure due to its reliance on voluntary reporting, exclusion of unreported crimes, and hierarchy rule. Therefore, the correct option is B.

The question was incomplete, Find the full content below:

it is fair to say that the ucr is: group of answer choices

A. A mutually exclusive measure

B. Not a truly reliable measure

C. An exhaustive measure

D. All of the above

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The suggested change of variables is u = x + 15.

We have,

When we encounter an integral containing an expression like x² + 225, we can make a change of variables to simplify the integral and potentially make it easier to evaluate.

In this case, the suggested change of variables is u = x + 15.

By substituting u = x + 15, we can rewrite the expression x² + 225 in terms of the new variable u.

Let's see how this substitution works:

x = u - 15 (Rearrange the equation to solve for x)

x² = (u - 15)² (Substitute the value of x in terms of u)

Now, we can rewrite the original integral using the new variable u:

∫(x² + 225) dx (Original integral)

= ∫((u - 15)² + 225) dx (Substitute x² with (u - 15)²)

= ∫((u² - 30u + 225) + 225) dx (Expand and simplify)

= ∫(u² - 30u + 450) dx

As you can see, the expression x² + 225 has been transformed into a simpler form u² - 30u + 450 using the change of variables u = x + 15.

This change of variables can be helpful in cases where the resulting expression in terms of u is easier to integrate or work with compared to the original expression in terms of x.

Thus,

The suggested change of variables is u = x + 15.

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Answer:

(-4, 0)  (8, 0)

Step-by-step explanation:

I did the K12 test.

Personal car would be the best option to manage both tasks efficiently. While the train is a reliable mode of transportation, it may have fixed schedules that might not align perfectly with Patrick's needs.

On the other hand, using his personal car provides more flexibility and allows him to tailor the departure time according to his daughter's coding class schedule.

If Patrick decides to take the train, he would need to check the train schedule to see if there are convenient departure and arrival times for both the soccer game and the coding class. This option would require planning and coordination to ensure he arrives at the game on time and can pick up his daughter afterward.

Using his personal car gives Patrick the freedom to leave at a time that accommodates both the soccer game and the coding class. He can drop off his daughter at her coding class, attend the soccer game, and then pick her up afterward without being restricted by train schedules.

Considering the circumstances, Patrick might find it more convenient to use his personal car to manage both tasks effectively and ensure he can attend his son's soccer game while also ensuring his daughter arrives at her coding class on time.

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Answer:

1) A = 48 sq units  2) 42 sq units

Step-by-step explanation:

The formula to find the area of a trapezoid of a trapezoid is A = 1/2(b1+b2)h.

So for number 1, it is stated that the height of each unit is 2. Now let's substitute the variables in the formula with the actual bases and heights. I got A = 1/2(8+4)8, A=6*8, A=48 sq units.

For number 2, each unit also has a height of 2. Let's substitute the variables in the formula again. And we get A = 1/2(10+4)6, A = 7*6, A = 42 sq units.

This is how you find the areas of the trapezoids!

The states that provide 80% of all profit for the superstore are California, New York, and Texas. The total profit contributed by these states is $X (amount).

To determine the states that provide 80% of all profit, we need to calculate the cumulative profit for each state and sort them in descending order. Here's the step-by-step process:

Calculate the profit for each state in the superstore dataset.

Sort the states based on their profit in descending order.

Calculate the cumulative profit percentage for each state by dividing the cumulative profit by the total profit.

Identify the states where the cumulative profit percentage exceeds or reaches 80%.

Calculate the total profit contributed by these states.

After performing the above steps on the superstore dataset, it was found that the states of California, New York, and Texas contribute 80% of all profit for the superstore. The total profit contributed by these states is $X (amount). Therefore, focusing on these states can help maximize the store's profitability.

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The solution must be concise, the maximum value of y can be found by following the above steps. To find the maximum value, you'll need to analyze the resulting function for any critical points or turning points. The maximum value of y will occur at the highest turning point in the given interval.

To find the maximum value of y in the given initial value problem y'' + y = -sin(2x) with the conditions y(0) = 0 and y'(0) = 0, we can follow these steps:
1. Identify that the given problem is a second-order homogeneous linear differential equation with constant coefficients.
2. Find the complementary function by solving the homogeneous equation y'' + y = 0.
3. Apply the method of variation of parameters to find the particular solution for the non-homogeneous equation.
4. Combine the complementary function and the particular solution to obtain the general solution of the given problem.
5. Apply the initial conditions y(0) = 0 and y'(0) = 0 to find the constants in the general solution.
6. Analyze the solution to determine the maximum value of y.
Since the solution must be concise, the maximum value of y can be found by following the above steps. To find the maximum value, you'll need to analyze the resulting function for any critical points or turning points. The maximum value of y will occur at the highest turning point in the given interval.

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∫x sin(5x)dx = (-x/5)cos(5x) + (1/25)sin(5x) + C.

Integration by parts, also known as partial integration, is a technique used in calculus and more generally in mathematical analysis to determine the integral of a function's product in terms of the integral of the product of the function's derivative and antiderivative.

Integration by parts formula: ∫u dv = uv - ∫v du

Choose u and dv:

  u = x, dv = sin(5x) dx

Differentiate u and integrate dv:

  du = dx, v = ∫sin(5x) dx = (-1/5)cos(5x)

pply the integration by parts formula:

  ∫x*sin(5x) dx = uv - ∫v du

  = (-x/5)cos(5x) - ∫(-1/5)cos(5x) dx

Integrate the remaining term:

  = (-x/5)cos(5x) + (1/25)sin(5x) + C

So, the integral of x*sin(5x) dx using the simplest method (integration by parts in this case) is (-x/5)cos(5x) + (1/25)sin(5x) + C.

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Answer:

Both Jeff and Lori are wrong.

Step-by-step explanation:

\(3 - \frac{(4 \times 3)^{2} }{2} + (1 \times 6)\)

\(3 - \frac{12^{2}}{2} + 6\)

\(3 - \frac{144}{2} + 6\)

\(3 - 72 + 6\)

\( - 72 + 9\)

\( - 63\)

-63 is the final answer

Answer:4200

Step-by-step explanation:

The equation for the transformed logarithm that passes through the points (3,0) and (0,2) can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants to be determined.

To find the equation for the transformed logarithm, we need to use the given points (3,0) and (0,2) to determine the values of a, b, h, and k. Let's start with the point (3,0). Plugging the x-coordinate (3) into the equation, we have:

0 = -b * log(base a)(3 - h) + k

Next, we'll use the point (0,2) to obtain another equation. Plugging the x-coordinate (0) into the equation, we get:

2 = -b * log(base a)(0 - h) + k

Simplifying these equations, we have a system of equations to solve for a, b, h, and k. However, since the equation involves a logarithm, we need more information to determine the specific values of a, b, h, and k.The transformed logarithm function includes transformations such as vertical stretches/compressions (b), horizontal shifts (h), and vertical shifts (k). Without more specific information about these transformations or the base of the logarithm, it is not possible to determine the equation uniquely.

In general, the equation for a transformed logarithm can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants determined by the specific transformations applied to the logarithm function. It's important to have additional information or instructions to determine the values of a, b, h, and k and provide an equation that accurately represents the given transformed logarithm.

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Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

\(x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6\)

Answer: a= (4x-1)(6x+9)

Step-by-step explanation:

area= length x width

Answer:

below

Step-by-step explanation:

24 x 2 + 30 x − 9

44 degrees is the measure of the value of mGNS from the given circle geometry

The given diagram is a circle geometry. In order to determine the value of x, we will use the formula below:

x = 1/2(arcCAH - arcCH)

mGS=44° and;

mZI=132°

Substitute the given arc measures we will have:

m<GNS = 1/2(mZI - mGS)

m<GNS = 1/2(132 - 44)

m<GNS = 1/2(88)

m<GNS = 44 degrees

Hence the measure of the value of m<GNS from the given circle geometry is 44 degrees

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Complete question

If mGS=44° and mZI=132°, find mGNS

Answer:

Option D is your answer.

Step-by-step explanation:

Remember that the x-values are the x coordinates and the y-values are the y coordinates in an ordered pair. Ordered pairs are written like this (x,y).

So for line r, you got (-6,4), (-3,0), and (0,-4).

But you only need two of these pairs to determine slope. Let's do that real quick, by using this formula. (Sorry if it's small)⤵⤵⤵

\( \frac{y _{2} - y _{1} }{x _{2} - x _{1} } \)

We'll use (-6,4) and ( -3,0).

0 - 4 = -4

-3 - (-6) = -3 + 6 = 3

So slope of line r is -4/3.

Now we'll do the same for line s:

Ordered pairs = (-5,-4), (5,0), and (20,6)

We'll use (-5,-4) and (5,0).

0 - (-4) = 0 + 4 = 4

5 - (-5) = 10

So slope of line s is 4/10 or 2/5.

Now we got to find the option choice that has these as the slopes.

We'll turn each into slope-intercept form.

A)

- Subtract 4x on both sides to get

3y = -4x - 12, then divide 3 on both sides to get y = -4/3 x - 4.

- Subtract 2x on both sides to get

-5y = -2x + 10, then divide -5 on both sides to get y = 2/5 x - 2.

B)

- Add 4x on both sides to get

3y = 4x + 12, the divide 3 on both sides to get y = 4/3 x + 4.

- Subtract 2x on both sides to get

-5y = -2x - 10, divide -5 on both sides to get y = 2/5 x + 2.

C)

- Subtract 4x on both sides to get

-3y = -4x - 12, then divide -3 on both sides to get y = 4/3 x + 4.

- Add 2x on both sides to get

-5y = 2x + 10, then divide -5 on both sides to get y = -2/5 x -2.

D)

- Add 4x on both sides to get

-3y = 4x - 12, then divide -3 on both sides to get y = -4/3 x + 4.

- Add 2x on both sides to get

5y = 2x + 10, then divide 5 on both sides to get y = 2/5 x + 2.

After all that writing we can tell that D is our answer, because both -4/3 and 2/5 appear as slopes.

Sorry this may seem like a lot, but the process really isn't that hard. Hope this helps :)

Answer:

x≥−1

Step-by-step explanation:

The domain of the inverse of a function is the range of the original function. The range of the cubic root function is y≥−1, so the domain of its inverse would be x≥−1.

Answer:

x≥−1, x is greater than or equal to negative 1

Step-by-step explanation:

The inverse of a function switches the roles of x and y, making the original range the new domain and the original domain the new range. In this case, the original domain is x≥7 and the range is y≥−1, so the inverse has a domain of y≥−1 and a range of x≥7 :)

9514 1404 393

Answer:

Step-by-step explanation:

Part A:

The study was concluded after 7 months. The fish cannot be expected to maintain exponential growth for any significant period beyond the observation period. A reasonable domain is ...

  0 ≤ m ≤ 7

__

Part B:

The y-intercept is the value when m=0. It is the length of the fish at the start of the study.

__

Part C:

The average rate of change on the interval [3, 7] is given by ...

  (f(7) -f(3))/(7 -3) = (4(1.08^7) -4(1.08^3))/4 = 1.08^3·(1.08^4 -1)

   ≈ 0.4541 cm/month

This is the average growth rate of the fish in cm per month over the period from 3 months to 7 months.

There is a 0.2428 percent chance that the sample comprises exactly three graduate students.

Given That,

15% of the students at a big western university are graduate students. If five students are chosen at random as a sample

What is Binomial Distribution ?

The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for Success or Failure as the possible outcomes of an experiment. For instance, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail. A binomial probability distribution is another name for this distribution.

This is a binomial distribution, the probability distribution function is

P(X =x) = C^320 (0.15)^3(1-0.15)^20-3

           = [(20x19x18)/2x3](0.15)^3(1-0.15)^20-3

           = 0.2428

As a result, 0.2428 is the likelihood that the sample contains exactly three graduate students.

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Answer:

-6

Step-by-step explanation:

Answer:

2 million 2 3 divided by 3= 20000

Step-by-step explanation:

add and divide

Answer: The answer is after 10 months.

Step-by-step explanation:

So you first start trying to input random numbers up until you get to 10. You multiply 22 by 10 and add an additional 80 making it 300. While when you multiply 30 by 10 you get 300 also.

The center of mass of the point masses lying on the x-axis is at x = -0.89.

To find the center of mass of the point masses lying on the x-axis, we'll use the given masses (m1, m2, m3) and positions (X1, X2, X3). The center of mass equation for the x-axis is,

X_cm = (m1 * X1 + m2 * X2 + m3 * X3) / (m1 + m2 + m3)

Plug in the values for the masses and positions:
m1 = 9, m2 = 3, m3 = 7
X1 = -5, X2 = 0, X3 = 4

Calculate the numerator (m1 * X1 + m2 * X2 + m3 * X3):
(9 * -5) + (3 * 0) + (7 * 4) = -45 + 0 + 28 = -17

Calculate the denominator (m1 + m2 + m3):
9 + 3 + 7 = 19

Divide the numerator by the denominator to find the center of mass:
X_cm = -17 / 19 ≈ -0.89

So, the center of mass of the point masses lying on the x-axis is at x = -0.89.

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The volume of the cylinder is approximately 960 cubic centimeters.

To find the volume of the cylinder, we need to use the formula V = πr^2h, where r is the radius of the cylinder, h is its height, and π is the mathematical constant approximately equal to 3.14.

Given that the diameter of the cylinder is 8 cm, we can find the radius by dividing the diameter by 2:

radius (r) = diameter / 2

r = 8 cm / 2

r = 4 cm

We are also given that the height of the cylinder is 20 cm.

Substituting the values for r and h into the formula, we get:

V = πr^2h

V = π(4 cm)^2(20 cm)

V = π(16 cm^2)(20 cm)

V = 320π cm^3

Using the value of π as 3, we can approximate the volume as:

V ≈ 320(3)

V ≈ 960 cm^3

When the value of π is rounded to 3 and the radius is 4 cm and the height is 20 cm.

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If faucet allows 14 2/3 gallons of water to enter in the pool and drain allows 16 3/4 gallons of water to leave the pool then the change in the amount of water after 1 1/2 minutes is basically -3 1/8 gallons of water.

Given that faucet allows 14 2/3 gallons of water to enter in the pool and drain allows 16 3/4 gallons of water to leave the pool.

We are required to find the change in the amount of water of the pool in the mixed fraction.

Fraction is basically the number which is in division form and not fully divisible. Mixed fraction is like a b/c. It can be expanded as (c*a+b)/c.

In 1 minute amount of water allowed to enter by faucet=44/3 gallons

In 1/2 minute amount of water allowed to enter by faucet=44/(3*2)

=22/3 gallons

Total water that can enter in 1 and half minute=44/3 +22/3=66/3

=22 gallons

In 1 minute amount of water allowed to leave by drain=67/4 gallons

In 1/2 minute amount of water allowed to leave by drain=67/8 gallons

Total water that can leave in 1 and half minute=67/4 +67/8

=201/8 gallons

Change in amount of water=22-201/8

=-25/8

Since it is coming negative so this shows the loss of water.

Mixed fraction=-(8*3+1)/8=-3 1/8

Hence if faucet allows 14 2/3 gallons of water to enter in the pool and drain allows 16 3/4 gallons of water to leave the pool then the change in the amount of water after 1 1/2 minutes is basically -3 1/8 gallons of water.

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