water balloon was thrown from a window. The height of the water balloon over time can be modeled by the function y=-16x^(2)+160x+50. What was the maximum height of the water balloon after it was thrown?

Answer: y = -10

Step-by-step explanation:

y = 2(-3) - 4

-6 - 4 = -10

y = -10

The result is 16, which matches the information given in the problem. Thus, our solution is correct. Thao originally had 30 coins.

Let's solve this problem step by step.

Let's assume the number of coins Thao originally had is x.

According to the problem, Thao gives two fifths of her coins to her sister. Two fifths of x can be represented as (2/5)x.

After giving away two fifths of her coins, Thao receives 4 coins for her birthday. So, the number of coins she has now is (2/5)x + 4.

The problem states that she now has 16 coins. Therefore, we can set up the following equation:

(2/5)x + 4 = 16

To solve for x, we need to isolate x on one side of the equation. We can start by subtracting 4 from both sides:

(2/5)x = 16 - 4

(2/5)x = 12

To get rid of the fraction, we can multiply both sides of the equation by 5:

5 * (2/5)x = 5 * 12

2x = 60

Next, divide both sides of the equation by 2 to solve for x:

(2x)/2 = 60/2

x = 30

Therefore, Thao originally had 30 coins.

To verify our answer, we can substitute x = 30 back into the equation (2/5)x + 4 and see if it equals 16:

(2/5) * 30 + 4 = 12 + 4 = 16

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Answer:

3x³ + 13x² + 14x

Step-by-step explanation:

(f × g)(x)

= f(x) × g(x)

= (x + 2)(3x² + 7x)

= x(3x² + 7x) + 2(3x² + 7x) ← distribute parenthesis

= 3x³ + 7x² + 6x² + 14x ← collect like terms

= 3x³ + 13x² + 14x

Answer:

l = 2.25 cm

Step-by-step explanation:

given l is inversely proportional to w² then the equation relating them is

l = \(\frac{k}{w^2}\) ← k is the constant of proportion

(i)

to find k use the condition w = 1.5 , l = 16 , then

16 = \(\frac{k}{1.5^2}\) = \(\frac{k}{2.25}\) ( multiply both sides by 2.25 )

36 = k

l = \(\frac{36}{w^2}\) ← equation of proportion

(ii)

when w = 4 , then

l = \(\frac{36}{4^2}\) = \(\frac{36}{16}\) = 2.25 cm

Answer:

20.57

Step-by-step explanation:

Answer:

Find the mean of the sampling distribution of xC-xT

Calculate and interpret the standard deviation of the sampling distribution. Verify that the 10% condition is met.

Justify that the shape of the sampling distribution

Step-by-step explanation:

2.4 letters. Both distributions of word length are unimodal and skewed to the right. Independent random samples of 40 words

Answer:

35 miles/hour

Step-by-step explanation:

Divide any number of miles by the corresponding number of hours above.

70 miles / 2 hour = 35 miles/hour

Answer: 35 miles/hour

Answer:

Starting with the equation:

(x + 1)^2 = 13/4

We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.

Taking the square root of both sides, we get:

x + 1 = ±√(13/4)

Simplifying under the radical:

x + 1 = ±(√13)/2

Now we can solve for x by subtracting 1 from both sides:

x = -1 ± (√13)/2

Therefore, the solutions to the equation are:

x = -1 + (√13)/2 or x = -1 - (√13)/2

Step-by-step explanation:

(a) P = mt + b

(b) The exact percentage of defective cars cannot be determined without the values of m and b.

(c) The slope (m) represents the rate of change in the percentage of defective cars per unit change in the production rate. Its sign and magnitude determine the direction and steepness of the change.

(a) To write the equation for the percentage of cars P that are defective if t toys are produced an hour, we can use the concept of a linear relationship between the production rate and the percentage of defective cars. The equation can be written as:

P = mt + b

Where P represents the percentage of defective cars, t represents the number of toys produced per hour, m represents the slope of the line (change in percentage per change in production rate), and b represents the y-intercept (the percentage of defective cars when no toys are produced).

(b) Using the equation from part (a), if 2,500 cars are produced an hour (t = 2500), we can substitute this value into the equation to find the percentage of defective cars:

P = m(2500) + b

To calculate the exact percentage, we need the values of m and b. Unfortunately, the values are not provided in the given information. Therefore, without knowing the specific values of m and b, we cannot determine the exact percentage of defective cars.

(c) The slope of the equation represents the rate of change in the percentage of cars that are defective per unit change in the production rate. It quantifies how the percentage of defective cars increases or decreases as the production rate varies.

Unfortunately, the value of the slope (m) is not provided in the given information, so we cannot determine it directly. However, we can make some general observations about the slope:

If the slope is positive, it means that as the production rate increases, the percentage of defective cars also increases.

If the slope is negative, it means that as the production rate increases, the percentage of defective cars decreases.

The magnitude of the slope indicates the rate at which the percentage of defective cars changes with the production rate. A larger magnitude indicates a steeper change, while a smaller magnitude indicates a gentler change.

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In the excerpt, Li's crush gave his girl   friend a rose. The text states: Li's crush gave his girl   friend a rose. She was so happy!

Li's mother was upset about the gift later because she thought it was too expensive.

The text states: Li's mother was upset when she found out how much the rose cost. She thought it was too much money to spend on a gift.

Li's mother's reaction is understandable. Roses are expensive flowers, and it is possible that Li's mother did not have the money to spend on such a gift. However, it is also important to remember that Li's crush was trying to do something nice for his girl friend, and the rose was a symbol of his love for her. In the end, it is up to Li and his girl friend to decide whether or not the rose was worth the money.

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Answer:

The answer is 0.01

Step-by-step explanation:

so in order to round it you have to know after the decimal it goes: tenths, hundreds, thousands (0 tenths, 0 hundreds, 0 thousands)

So 0.007492, take the first 3 numbers after the decimal, 0.007, since it will be in the hundreds place, lets see if we can round the 0 up. If the number behind 0 is greater then or equal to 5 round up, if the number is less then 5 then it stays the same. Since 7>5 it rounds up, so the 0 becomes 1. So your new number will be 0.01

Hoped this helped :D

By rounding 0.007492 to the nearest hundredth, we get 0.01.

The number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

Example: 0.3879 rounded to the nearest hundredth is 0.39.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

Example: 0.3823 rounded to the nearest hundredth is 0.38.

Given number is 0.007492.

Rounding to nearest hundredth, we get:

0.00749 ⇒ 0.01.

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Answer:

Please help me important question in image

Step-by-step explanation:Please help me important question in image

Please help me important quePlease help me important question in image

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Please help me important question in image

Please help me important question in image

Answer:

The equation a=0.003x^2+21.3 models the average ages of women when they first married since the year 1940 in the United States. In this equation, a represents the average age and x represents the years since 1940. To estimate the year in which the average age of brides was the youngest, we need to find the minimum value of the quadratic function a=0.003x^2+21.3. This can be done by using the formula x=-b/2a, where b is the coefficient of x and a is the coefficient of x^2. In this case, b=0 and a=0.003, so x=-0/(2*0.003)=0. This means that the average age of brides was the lowest when x=0, which corresponds to the year 1940. The value of a when x=0 is a=0.003*0^2+21.3=21.3, so the average age of brides in 1940 was 21.3 years old. This is consistent with the historical data, which shows that the median age of women at their first wedding in 1940 was 21.5 years old. The average age of brides has been increasing since then, reaching 28.6 years old in 2021.

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We want to study the angle of an arc given that the length of the said arc is smaller than the radius of the circle.

The correct option is:

"it is less than pi radians"

A circle of radius R has a circumference:

C = 2*pi*R

An arc defined by an angle θ has a length:

L = θ*R

Now, we know that the length of the arc is smaller than the radius, then we have:

θ*R < R

Dividing both sides by R we get:

θ < 1

So we can see that the correct option is:

"it is less than pi radians"

Because it is smaller than 1.

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According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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Answer:

1.74

Step-by-step explanation:

0.58*(12/4) = 0.58*3 = 1.74

Answer:

1.74

Step-by-step explanation:

Multiply 0.58 times 3 to get your answer.

Answer:

Below

Step-by-step explanation:

-40 -(-12/5) =  -200/5   +   12/5   = -188/5 =  - 37  3/5

There are 20 students who do not study any language.

To determine the number of students who do not study any language, we need to subtract the total number of students who study at least one language from the total number of students in the group.

Given the information provided, we can use the principle of inclusion-exclusion to calculate the number of students who study at least one language.

Using the inclusion-exclusion principle, we can calculate the number of students who study at least one language as follows:

Students studying at least one language = Students studying Spanish + Students studying German + Students studying French - Students studying Spanish and German - Students studying Spanish and French - Students studying German and French + Students studying all three languages

Substituting the given values from the question:

Students studying at least one language = 28 + 30 + 42 - 8 - 10 - 5 + 3

Students studying at least one language = 80

Now, we can calculate the number of students who do not study any language:

Students not studying any language = Total number of students - Students studying at least one language

Students not studying any language = 100 - 80

Students not studying any language = 20

20 students do not study any languages, as a result.

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Answer:

it is 237

Step-by-step explanation:

Answer: 237

Step-by-step explanation:

You do not to do order of operations for this problem

2 x 100 = 200

200 + 18 = 218

218 - 1 = 217

217 + 20 = 237

Hope it helps!

The maximum height of the golf ball on Mars is about 48.8 meters.

To find how much longer it would take for the golf ball hit on Mars to reach the ground, we can use the given equation h = -1.9t² + 26t, where h is the height of the object and t is the time in seconds. First, we need to find the time it takes for the golf ball to reach the ground on Mars. Setting h = 0, we get:

0 = -1.9t² + 26t

Solving for t using the quadratic formula, we get t = 13.684 or t = 0.856. Since the golf ball is launched upward, we need the positive value of t, so it takes about 13.7 seconds for the golf ball to reach the ground on Mars. Therefore, it takes 13.7 − 5.4 = 8.3 seconds longer for the golf ball hit on Mars to reach the ground than the golf ball hit on Earth.

To find the maximum height of the golf ball on Mars, we can use the formula h = -1.9t² + 26t, where t is the time when the height is maximum. Since the formula is a quadratic equation, the maximum height occurs at the vertex of the parabola, which is at t = -b/2a.

In this case, a = -1.9 and b = 26, so the time at maximum height is t = -26 / 2(-1.9) = 6.842. Plugging this value into the equation for h, we get:

= -1.9(6.842)² + 26(6.842) ≈ 48.8 meters

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Answer:

Step-by-step explanation: 1.587401052

Answer:

8

Step-by-step explanation:

this means

\( \sqrt{ {4}^{3} } \)

4³ = 4×4×4 = 64

the square root of 64 is 8.

Answer:θ ≈ 2.57 radians

θ ≈ 0.58 radians

Step-by-step explanation:We can solve this quadratic equation in sin(θ) by factoring:

4sin^2(θ) + 7sin(θ) - 5 = 0

(4sin(θ) - 1)(sin(θ) + 5) = 0

Therefore, either:

4sin(θ) - 1 = 0

sin(θ) = 1/4

or:

sin(θ) + 5 = 0

sin(θ) = -5 (not possible, since sin(θ) is between -1 and 1)

So, we have sin(θ) = 1/4. Since 0 ≤ θ < 2π, we can find the two solutions in the interval [0, 2π) by using the inverse sine function:

θ = arcsin(1/4)

Using a calculator, we find:

θ ≈ 0.2531 or θ ≈ 2.8887

Therefore, in radians, the solutions for θ are approximately:

0.2531 (which is less than 2π)

2.8887 (which is greater than 2π)

So the only answer that satisfies 0 ≤ θ < 2π is:

Answer:

The actual change in the car's value is $\(1700\) and the relative change is \(7.20\)%.

Step-by-step explanation:

It is given that the value of a car is dropped from $\(23600\) to $\(21900\).

So, the change in the value is the drop in the value of car, which is, \(23600-21900=1700\).

So, the actual change in this car's value is $\(1700\).

The relative change can be given by the expression,

\(\dfrac{\:\rm{Actual Change}}{\:\rm{Original Value}}\times100\)

Substituting values, the relative change can be given by,

\(\begin{aligned}\dfrac{1700}{23600} \times 100&=\dfrac{1700}{236}\\&=7.20\end{aligned}\)

Answer:

it is also the main set it is the real answer

Answer:

B

Hope this helps!

explanation:

we solve the inequality and to do that we must first subtract 12 from both sides, which gets us -x<-4, then we divide both sides by -1, which gives us x>4, since we have to flip the sign when we divide by a negative. when we graph this, there will be a circle around 4 and the arrow pointing to the right, since it's greater than.