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the rocket will be 70 feet above the ground after 1.25 seconds and again after 3.5 seconds.

Factorization, also known as factoring, is the process of expressing a mathematical object (such as a number, polynomial, or matrix) as a product of simpler objects.

To determine when the rocket hits the ground, we need to find the value of t when the height, h, is equal to 0. We can set h(t) = 0 and solve for t:

-16t²+ 76t = 0

-16t(t - 4.75) = 0

So either -16t = 0 or t - 4.75 = 0. The first equation has no solutions, so we solve the second equation:

t - 4.75 = 0

t = 4.75

Therefore, the rocket will hit the ground after 4.75 seconds.

To determine when the rocket is 70 feet above the ground, we need to find the value of t when h(t) = 70. We can set h(t) = 70 and solve for t:

-16t² + 76t = 70

-16t²+ 76t - 70 = 0

We can simplify this equation by dividing each term by -2:

8t² - 38t + 35 = 0

We can factor this equation:

(4t - 5)(2t - 7) = 0

So either 4t - 5 = 0 or 2t - 7 = 0. Solving these equations gives:

4t - 5 = 0

t = 1.25

2t - 7 = 0

t = 3.5

Therefore, the rocket will be 70 feet above the ground after 1.25 seconds and again after 3.5 seconds.

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In this case, the population is children from 6 to 18 years old who had nonlethal scorpion sting; on the other hand, the sample is the 245 children selected.

In a research study, the population is considered as the group of individuals being studied. However, as this number is often high, researchers often select a small random percentage that should be representative of the population, which is known as the sample.

Based on this, the population can be children  from 6 to 18 years old who had nonlethal scorpion sting, while the sample are those children selected (245) to carry out the research study.

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(-2, -4)

Systems of equations are sets of two or more equations that share the same variables.

Graphing

To graph a system of equations, simply graph each line individually. Both of the equations given are linear. Attached is a graph of both equations. As you can see the graphs intersect at (-2, -4).

Solutions to Systems of Equations

The solution to a system of linear equations is the coordinate point that the lines intersect. This is the point where the x and y-values make both equations true. To check the answer, plug the values into the equations. If both remain true, the answer is correct.

First, y = 2x

This is true. Next, y = x - 2

This is also true; thus the answer is (-2, -4).

The set of data that Zoey should use for the linear graph is given as follows:

D the temperature of a water sample increasing 2° every hour.

The graph represents a linear function, meaning that the rate of change of the output variable relative to the input variable must be constant.

The input and output variables of the graph are given as follows:

As the rate of change must be constant, the correct option is given by option d, which has a rate of change of 2º every hour. For the other options, the rate of change is not constant.

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According the Question the value οf x will be 6.

The measurement οf the circle's bοundaries is called as the circumference οr perimeter οf the circle. whereas the circumference οf a circle determines the space it οccupies. The circumference οf a circle is its length when it is οpened up and drawn as a straight line. Units like cm οr unit m are typically used tο measure it.

The circle's radius is cοnsidered while calculating the circumference οf the circle using the fοrmula. As a result, in οrder tο calculate the circle's perimeter, we must knοw the radius οr diameter value.

The side οf the circle JH . JG = JK . JM

JM = 7*16/8 = 14

X = 14-8 =6

Hene the value οf x will be 6.

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Answer:

b

Step-by-step explanation:

The coordinates of its reflection are (4, -10)

A reflection over line is a transformation in which each point of the original figure (the pre-image) has an image that is the same distance from the reflection line as the original point, but is on the opposite side of the line.

Given that point P(4,11) is reflected across the line y=1,

Point P is on x = 4 which will not change after reflection, P is 10 units above line y = 3 so counting down 10 from y = 1, and then we will get on

y = -5'

Hence, the coordinates of reflection of point P = (4, -10)

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The probability that your class of 20 students will have a mean completion time greater than 60 minutes on the unit test is very low.

What is probability ?

Probability cam be defined as ratio of number of  favorable outcomes, total number of outcomes

We can solve this problem by using the central limit theorem. According to the theorem, if we have a large enough sample size, the distribution of sample means will be approximately normal, regardless of the underlying distribution of the population.

The mean of the sample means will be equal to the population mean, and the standard deviation of the sample means (also known as the standard error) will be equal to the population standard deviation divided by the square root of the sample size.

In this case, we have a sample size of 20, which is not very large, but we can still use the central limit theorem as an approximation. The population mean is 48 minutes, and the population standard deviation is 15 minutes. The standard error of the sample mean is:

SE = σ / sqrt(n) = 15 / sqrt(20) = 3.354

To find the probability that the mean completion time for the sample is greater than 60 minutes, we need to standardize the sample mean using the formula:

z = (x - μ) / SE

where x is the sample mean, μ is the population mean, and SE is the standard error of the sample mean.

Plugging in the values, we get:

z = (60 - 48) / 3.354 = 3.57

We can now look up the probability of getting a z-score greater than 3.57 in a standard normal distribution table (or use a calculator). The probability turns out to be very small, approximately 0.0002 or 0.02%.

Therefore, the probability that your class of 20 students will have a mean completion time greater than 60 minutes on the unit test is very low.

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Answer: 85.5

Step-by-step explanation: divide 855 by ten or move the decimal to the left one place for every zero

By solving the increase in percentage, the projected number of students in an associate degree program in 2024-2025 is approximately 7,897,500.

What is an increase in percentage?

An increase in percentage is a measure of the change in a quantity expressed as a percentage of the initial value. It is calculated by subtracting the initial value from the final value, dividing the result by the initial value, and then multiplying the quotient by 100 to express the result as a percentage. The formula for calculating the percentage increase is:

percentage increase = (final value - initial value) / initial value * 100

To find the increase in the number of students enrolled in an associate degree program from 2014-2015 to 2024-2025, we can first calculate the amount of increase as a percentage of the initial enrollment:

Increase = 21.5% * 6,500,000 = 1,397,500

Therefore, the increase in the number of students is approximately 1,397,500.

To find the projected number of students in an associate degree program in 2024-2025, we can add the increase to the initial enrollment:

Projected enrollment = 6,500,000 + 1,397,500 = 7,897,500

Therefore, the projected number of students in an associate degree program in 2024-2025 is approximately 7,897,500.

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The values that complete the table would be: $140, $160, $180, $200, $220, $240, $260. This is a linear relationship because the data on the graph would show an ascending line with a constant slope.

To complete the table we must take into account the information, in this case Erick saves $20 per week, so we would have to add $20 to his initial budget of $120 and add $20 each week. Based on this information, the data that completes this table would be:

The graph with this data would be a linear expression, so the line would go up from $120 to $260 constantly, with a difference of $20 each week.

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Answer:

y=4sin(1/2πx)

Step-by-step explanation:

A = 4

Period for y=sin(x) is 2pi

Since the graph shows the period is 4. Then b must be 1/2pi

Answer:

4[tex]\frac{3}{8}[/tex]

Step-by-step explanation:

Answer:

4 3/8

Step-by-step explanation:

4*8=32 35-32=3

Answer: 113.2 - 10.8x=70

Step-by-step explanation:

Answer:

A. 24 in, 32 in, 40 in

Step-by-step explanation:

To determine whether a set of measurements could be the side lengths of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the lengths of the other two sides.

Using this theorem, we can check each set of measurements:

A. 24 in, 32 in, 40 in

Here, 40 in is the longest side, so it could be the hypotenuse. If we square the other two sides and add them together, we get:

24^2 + 32^2 = 576 + 1024 = 1600

And if we square the length of the hypotenuse, we get:

40^2 = 1600

So this set of measurements satisfies the Pythagorean theorem and could be the side lengths of a right triangle.

B. 24 in, 36 in, 40 in

Again, 40 in is the longest side and could be the hypotenuse. Squaring and adding the other two sides gives:

24^2 + 36^2 = 576 + 1296 = 1872

And squaring the length of the hypotenuse gives:

40^2 = 1600

So this set of measurements does not satisfy the Pythagorean theorem and cannot be the side lengths of a right triangle.

C. 24 in, 32 in, 48 in

Here, again, we can take 48 in as the hypotenuse. Squaring and adding the other two sides gives:

24^2 + 32^2 = 576 + 1024 = 1600

And squaring the length of the hypotenuse gives:

48^2 = 2304

So this set of measurements does not satisfy the Pythagorean theorem and cannot be the side lengths of a right triangle.

D. 20 in, 32 in, 40 in

Once more, we can take 40 in as the hypotenuse. Squaring and adding the other two sides gives:

20^2 + 32^2 = 400 + 1024 = 1424

And squaring the length of the hypotenuse gives:

40^2 = 1600

So this set of measurements does not satisfy the Pythagorean theorem and cannot be the side lengths of a right triangle.

In conclusion:

A set of measurements that could be side lengths of a right triangle is A) {24in,32in,40in}. The other sets do not satisfy Pythagorean theorem and cannot be sides of a right triangle.

Answer:

Third choice
π = 1/2 and 1 - π = 1/2

Step-by-step explanation:

Formula for binomial distribution is
[tex]P(x) = \dfrac{n!}{x!(n-x)!} \pi^x (1-\pi)^{n-x}[/tex]

where
x is the number of successes

n = number of trials

π = probability of success on a single trial

The variance of the binomial distribution is
[tex]\sigma^2 = n \cdot \pi(1-\pi)[/tex]

The maximum variance occurs when
[tex]\pi = (1- \pi) = 1/2[/tex]

Hence the correct choice is the third choice
π = 1/2 and 1- π = 1/2

The answer of the question based on graph function is given below, graph is a reflection of the parent function y = x² about the x-axis, horizontally compressed by a factor of 2, and vertically shifted downward by 4 units.

A graph  is visual representation of data or functions. It is way to display information in  visual format, usually with  use of coordinates and shapes.

The given equation is:

y = (-1/4 x)² - 4

To transform the graph of the parent function y = x², we can apply the following transformations:

Horizontal compression by a factor of 2: This will compress the graph horizontally, making it wider and shorter. The coefficient -1/4 in front of the x² indicates this compression.

Reflection across the x-axis: This will flip the graph of y = x² upside down. The negative sign after the x² in the equation indicates this reflection.

Vertical shift downward by 4 units: This will shift the entire graph downward by 4 units. The constant -4 at the end of the equation indicates this shift.

Using these transformations, we can graph the equation as follows:

Start with the graph of the parent function y = x²:

Apply the horizontal compression by a factor of 2 by multiplying the equation by -1/4:

y = (-1/4 x)²

Apply the reflection across the x-axis by negating the equation:

y = -(1/4 x)²

Apply the vertical shift downward by 4 units by subtracting 4 from the equation:

y = -(1/4 x)² - 4

The resulting graph is a reflection of the parent function y = x² about the x-axis, horizontally compressed by a factor of 2, and vertically shifted downward by 4 units.

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Answer:

Step-by-step explanation

I:

Answer:

B

Step-by-step explanation:

The function that models the situation is an exponential decay function of the form:

t(m) = a(1 - r)^m

where:

t(m) is the number of trees after m months

a is the initial number of trees (5,500 in this case)

r is the monthly rate of decrease (3.2% or 0.032 as a decimal)

Substituting the values given in the options, we get:

A) t(m) = 5,500(0.032)^m

B) t(m) = 5,500(1-0.032)^m = 5,500(0.968)^m

C) t(m) = 5,500(1.032)^m

D) t(m) = 5,500(1-0.968)^m = 5,500(0.032)^m

Option B is the correct answer as it correctly models the situation with exponential decay with a starting value of 5,500 trees and a monthly rate of decrease of 3.2%.

Answer: The formula for exponential decay is given by:

t(m) = a(1-r)^m

where

a = initial value

r = decay rate

Here, the initial value is 5,500 and the monthly decay rate is 3.2% or 0.032. So the function that can be used to find the number of trees in the forest at the end of m months is:

t(m) = 5,500(1 - 0.032)^m

t(m) = 5,500(0.968)^m

Therefore, the answer is (D) t(m) = 5,500(0.968)^m.

Your welcome (;

Answer:

A) 1080º

Step-by-step explanation:

I remember learning this in math class. The octagon has 8 interior angles and 8 exteriors angle. The sum of the interior angles of an octagon is 1080º

Answer:

The sum of the interior angles of an octagon can be found using the formula: (n-2) x 180 degrees, where n is the number of sides of the polygon.

For an octagon, n = 8, so the sum of the interior angles is (8-2) x 180 = 6 x 180 = 1080 degrees.

Therefore, the correct answer is A) 1080º.

Answer:

-5 and 13.

Step-by-step explanation:

We will kick off by calling the first unknown x.

To get the expression for the larger number:

'23 more than twice the smaller number'

twice the smaller number (x) = 2x.

Thus, the bigger number = 2x+23.

We were told that the sum of these two = 8

Therefore,

x+2x+23=8

=> 3x+23=8

3x=-15

x = -5 (smaller number).

The larger number is 2x+23

= 2(-5) + 23

= 13.

Hope this helps! :)

Answer:

C). 8/9n - 1 1/3

Step-by-step explanation:

Answer:

[tex]\frac{8}{9} n - 1\frac{1}{3}[/tex]

Step-by-step explanation:

Using the distributive property [tex]\frac{4}{9}[/tex] times 2 equals [tex]\frac{8}{9}[/tex] and [tex]\frac{4}{9}[/tex] times 3 equals [tex]\frac{4}{3}[/tex] which simplifies to [tex]1\frac{1}{3}[/tex]

Answer:

To determine whether Kyle will arrive in time for the baseball game, we need to calculate how long it will take him to travel the 130 miles to the baseball field.

Using the formula:

distance = rate × time

We can rearrange the formula to solve for time:

time = distance / rate

Plugging in the given values, we get:

time = 130 miles / 50 miles per hour

time = 2.6 hours

This means that it will take Kyle 2.6 hours to travel the 130 miles to the baseball field at the speed limit of 50 miles per hour.

Since Kyle has 2 hours to get to the baseball game, he will not arrive in time if he drives at the speed limit. He would need to drive faster than the speed limit to make it to the game on time. However, it's important to note that speeding is illegal and dangerous, so Kyle should not exceed the speed limit. He may need to consider leaving earlier or finding alternative transportation to ensure that he arrives at the baseball game on time.

Step-by-step explanation:

The function is positive on the interval (-1, 1)," is the only answer that is accurate. Due to the fact that the function accepts positive values for x between -1 and 0, accepts 0 at x = 0, and then accepts positive values.

When a function is specified at each point along an interval without any gaps, leaps, or interruptions, the interval is said to be continuous for that function.

When we examine the function's graph, we can observe that:

Because the function accepts negative values for x > 1 and positive values for x -1, it does not have a maximum value of 0.

The function does not approach as x approaches. Instead, as x rises, the function alternates between positive and negative values.

There are times when the function increases. Rather, it is rising on the interval (1, ) and falling on the intervals (-, 1). At x = -1, it has a local minimum, while at x = 1, it has a local maximum.

Due to the fact that it accepts negative values for x between -1 and 0, the function is not positive on the range (-1, 1).

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Therefore, the area of the polygon is 22 cm². The correct answer is A) 22 cm².

Another option is to plot the shape on a grid and count the squares: The rectangle's surface area is 15. Example: If each square is one meter in size, the area is 15 m2 (15 square meters).

To find the area of the polygon, we need to use the formula:

Area = (1/2) x Base x Height

We are given that the base of the polygon is 11 cm and the height is 4 cm. Therefore, we can substitute these values in the formula to get:

Area = (1/2) x 11 cm x 4 cm

Area = 22 cm²

Therefore, the area of the polygon is 22 cm². The correct answer is A) 22 cm².

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Answer:

-2yz

Step-by-step explanation:

To simplify the expression -5yz + yz + 2yz, we can combine the yz terms that have the same coefficient:

-5yz + yz + 2yz = (-5 + 1 + 2)yz

Simplifying the coefficients gives:

= -2yz

Therefore, the simplified expression is -2yz.

Answer:

[tex]-2yz[/tex]

Step-by-step explanation:

[tex]-5yz + yz + 2yz = (-5 + 1 + 2)yz[/tex]

[tex](-5 + 1 + 2)yz = -2yz[/tex]

Therefore, the simplified expression is:

[tex]-2yz[/tex]

The points on line segment in  Question 1 is C (52, 3)( 5 2 , 3) and the answer to Question 2 is A (112, 3)( 11 2 , 3).

What is a line segment?

A line segment is a straight line that is bounded by two distinct endpoints. It is the shortest distance between two points and is usually represented by an arrow. Line segments are an essential part of geometry, as they form the basis for many shapes, such as triangles and rectangles.

A line segment can be divided into two parts in a given ratio if the difference of the coordinates of the end points of the line segment is divided in the same ratio.

For Question 1, the ratio of the line segment is 1:3. To find the point on the line segment, we will divide the difference of the coordinates of the end points of the line segment into the ratio 1:3. The coordinates of the end points of the line segment PQ are (10,2) and (14,6). The difference of the coordinates of the end points of the line segment PQ is (14-10, 6-2) = (4,4). The difference of the coordinates (4,4) is divided into the ratio 1:3. After dividing the difference of the coordinates into the ratio 1:3, we get the coordinates of the point on the line segment PQ as (52,3).

For Question 2, the ratio of the line segment is 3:1. To find the point on the line segment, we will divide the difference of the coordinates of the end points of the line segment into the ratio 3:1. The coordinates of the end points of the line segment PQ are (10,2) and (14,6). The difference of the coordinates of the end points of the line segment PQ is (14-10, 6-2) = (4,4). The difference of the coordinates (4,4) is divided into the ratio 3:1. After dividing the difference of the coordinates into the ratio 3:1, we get the coordinates of the point on the line segment PQ as (112,3).

In conclusion, the point on the line segment PQ that divides the line segment into the ratio of 1:3 is C (52, 3)( 5 2 , 3) and the point on the line segment PQ that divides the line segment into the ratio of 3:1 is A (112, 3)( 11 2 , 3).

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Option D is correct as 16% and 26% results in a percentage of 42%, in line with percentages in the "At least one vitamin" row of the table of random sample.

In random sample:

The student is incorrect. To determine the proportion of participants taking vitamins, we need to add up the percentages in the "At least one vitamin" row of the table. Adding 23.5% and 48.2%, we get a total of 71.7%, which is not more than half. Therefore, option A is incorrect.

Option B is also incorrect, as adding 27.4% and 49.5% gives a total of 76.9%, which is more than half but does not match the percentages in the table.

Option C is incorrect, as adding 11.4% and 23.5% gives a total of 34.9%, which is lower than the percentages in the table.

Option D is correct, as adding 16% and 26% gives a total of 42%, which matches the percentages in the "At least one vitamin" row of the table. Therefore, the correct answer is D.

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According to the given information, measure of angle FNL is given by 234 - 13x.

What is angle ?

In geometry, an angle is a figure formed by two rays, or line segments, that share a common endpoint, called the vertex of the angle. The two rays are called the sides or legs of the angle.

line FN || line EM || line DL,

line FD and line NL intersects line FN,line EM and line DL at pts F,E,D and N,M,L respectively

FE = ED ,NM = ML

angle FNL = (9x-40)deg

angle FDL = (4x-14)deg

Since line FN is parallel to line EM, we have:

angle FNM = angle FEL (corresponding angles)

Since line FN is parallel to line DL, we have:

angle FNL = angle FLD (alternate interior angles)

Similarly, since line FD intersects line FN and line EM at points F and E, we have:

angle FEL + angle FED = 180 degrees (linear pair)

Since FE = ED, we have:

angle FEL = angle FED (opposite angles of a parallelogram are equal)

Combining the above equations, we get:

angle FNL = angle FLD = angle FED = 180 - angle FEL

Also, since NM = ML, we have:

angle NML = angle MLM

Now, applying the angle sum property in triangle FNL, we get:

angle FNL + angle FLD + angle FEL = 180 degrees

Substituting the given values, we get:

(9x-40) + (4x-14) + (180 - angle FEL) = 180

Simplifying, we get:

13x - 54 + 180 - angle FEL = 180

13x - angle FEL = 54

Solving for angle FEL, we get:

angle FEL = 13x - 54

Substituting this value in the equation we derived earlier, we get:

angle FNL = angle FLD = angle FED = 180 - angle FEL

= 180 - (13x - 54)

= 234 - 13x

Therefore, measure of angle FNL is given by 234 - 13x

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