A rocket is launched from the top of a building. The flight path is modelled by h = -4t2 + 16t + 24
where h is the height of the rocket from the ground in metres, and t is the time in seconds. What is the initial height of the rocket, when will the rocket hit the ground and what height is the rocket after 4 seconds

The minimum and the maximum values of the function f(x) = ∛(x+1)  on the interval [−2, 0] are

The maximum and minimum values are pointed out from the graph by tracing the lowest point within the range and the highest point within the range to the graph, then to the output of the graph

The minimum point was at -2 and this gave an output of -1

The maximum point was at 0 and this gave an out put value of 1

The graph is attached

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The complete statements are:

As a general rule, an adverbial clause, sometimes referred to as an adverb clause, is a group of words that, together, functions as an adverb.

They are introduced to a statement by words such as although, though, etc

Using the above as a guide, we have the following:

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Yes, as the relative frequency distribution closely resembles the empirical criterion for normal models.

Frequency tables or charts are used to represent frequency distributions. Frequency distributions can display the proportion of observations or the actual number of observations that fall inside each range. The distribution is known as a relative frequency distribution in the latter case.

What is the relative frequency distribution formula?

Subgroup Count / Total Count: Relative Frequency

Because they let us determine how frequent a certain value is in a dataset in comparison to all other values, relative frequency distributions are helpful.

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Answer:

1350

Step-by-step explanation:

A:B = 13:5 = 975:x

x=975/13*5 =375

total =975+375 = 1350

We use the proportional method

Let A = water used in household A.

Let B = water used in household B.

A to B = 13 to 5

A = 260 gal

260 to B = 13 to 5

260/B = 13/5

13B = 5 * 260

B = 100

A + B = 260 + 100 = 360

The total is 360 gallons.

Answer:

Step-by-step explanation:

∠ EGF=180-∠FGH

          = 180-(180-112)

          = 112°

∠LKM= 90= 8X -6

           2(4X-3)=90

             4X-3=45°

3)

22=4X-10

 X=8

NR= 3(8) +6

     = 30

Check the picture below.

since we know the triangle EBD is an isosceles, that means that BE = BD, and twin sides will yield twin angles, so the ∡EBD is simply the difference of 180 - 57 - 57, as far as ∡ABC, well, that's just 19 + 66 + 19.  ∡DBC is 19° because both triangles on left and right are congruent.

a)

g(10) = 62 means at 10 miles from the source, the elevation of the Mississippi river is 62 feet.

b)

The rate of change of the elevation with distance from the source is -2.4.

c)

The elevation of the Mississippi 11 miles from its source is 59.6 feet.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

g(x) is the elevation in feet of the Mississippi river x miles from its source.

a)

g(10) = 62

This means,

At 10 miles from the source, the elevation of the Mississippi river is 62 feet.

b)

g'(10 = -2.4

This means,

The rate of change of the elevation with distance from the source is -2.4.

It is negative because the river flows downward.

The unit is feet per mile.

c)

We can make g(x) = mx + c

m = -2.4

(10 , 62) = (x, g(x))

So,

62 = -2.4 x 10 + c

62 = -24 + c

c = 62 + 24

c = 86

And,

g(x) = -2.4x + 86

So,

At x = 11 miles

g(11) = -2.4 x 11 + 86

g(11) = -26.4 + 86

g(11) = 59.6

Thus,

g(10) = 62 means at 10 miles from the source, the elevation of the Mississippi river is 62 feet.

The rate of change is -2.4.

The elevation of the Mississippi 11 miles from its source is 59.6 feet.

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The percentage rate of change per hour to the nearest hundredth is 3%.

Function to represent decay is A(t)= 150×([tex].97^{t}[/tex]).

Percentage means out of hundred. If we want to calculate percentage the we have to make the fraction out of hundred.

It means that if same thing is distributed among 100 people how much a single person would get.

Now for the given question:

For radioactive decay the mathematical equation is

      A(t) = A(0)[tex](1-r)^{t}[/tex]

where A(0) is the initial quantity = 150 gm. and r is the rate of decay = 51%

For hourly decay,

     A(24)= A(0)(1-0.51) as 1 day has 24 hour and each day substance decay by 51%.

     A(24)= A(0)×0.49

but,

   A(24)= A(0)[tex](1-r)^{24}[/tex]

0.49A(0)=A(0)[tex](1-r)^{24}[/tex]       (we do this to calculate r)

.049= [tex](1-r)^{24}[/tex]

1-r = [tex]\sqrt[24]{.49}[/tex]

1-r= 0.97

r = 1- 0.97

r= 0.03

r = 3%

Function for hourly decay,

A(t) = 150 ×[tex](1-r)^{t}[/tex]

A(t) = 150 ×[tex](1-0.03)^{t}[/tex]

A(t)= 150×([tex].97^{t}[/tex])

Hence, Hourly rate of decay is 3% and the equation for hourly rate o decay is A(t)=150×[tex].97^{t}[/tex].

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The mean number of absences for the sample of 50 students will fall within this range.

The 95% confidence interval for the mean number of absences for the sample of 50 students can be calculated using the formula: X ± z*(σ/√n), where X is the sample mean, z is the critical value of the normal distribution at a 95% confidence level (1.96), σ is the population standard deviation (1.4), and n is the sample size (50). The confidence interval can be calculated as follows: X ± 1.96 (1.4/√50) = X ± 0.246. Therefore, the 95% confidence interval for the mean number of absences for the sample of 50 students is 0.902 to 1.296.

The formula can be interpreted as follows: the sample mean is likely to fall within the interval of 0.902 to 1.296, plus or minus 1.96 times the standard deviation of the population divided by the square root of the sample size. Since the population standard deviation is 1.4 and the sample size is 50, the interval is 0.902 to 1.296. This interval gives us a 95% confidence that the mean number of absences for the sample of 50 students will fall within this range.

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Answer: -5

Step-by-step explanation:

To solve for x, you must use inverse operations.

We must move the 12 from the right, to the left in order to solve for x.

The inverse of addition, is subtraction.

Subtract 12 from both sides

7 - 12 = x + 12 - 12

To subtract a bigger number from a smaller number, flip it around, and make your answer negative

12 - 7 = 5

7 - 12 = -5

Something minus itself is 0

-5 = x + 12 - 12

-5 = x + 0

We like to have x on the left, and the = is symetrical.  Just flip it around

x = -5 + 0

x = -5

Verify

7 = -5 + 12

7 = 12 - 5

7 = 7

true

For the first scenario (choosing 3 balls from 1 to 9):

[tex]_{9}C_{3} = \frac{9!}{3!(9 - 3)!} [/tex]

For the second scenario (choosing 5 potato chips from 20):

[tex]_{20}C_{5} = \frac{20!}{5!(20 - 5)!} [/tex]

For the third scenario (choosing 2 team members as captain and co-captain from 24):

[tex]_{24}P_{2} = \frac{24!}{(24 - 2)!} [/tex]

The first situation is a combination. In a combination, the order of the items does not matter. In this game, it does not matter what order the 3 balls are in, as long as you have the correct numbers in a row. If you choose balls 1, 2, and 3, it's the same as if you choose 3, 2, and 1. A permutation, on the other hand, would require the order of the items to be specific. In this game, the order of the numbers doesn't matter, making it a combination.

The second situation is a combination. In this scenario, you are choosing 5 out of 20 different potato chips, and the order in which you choose them doesn't matter. Whether you choose chips 1, 2, 3, 4, and 5, or chips 5, 4, 3, 2, and 1, the combination is still the same.

The third situation is a permutation. In a permutation, the order of the items matters, meaning the first chosen person will be the captain and the second chosen person will be the co-captain. In this scenario, there are 24 people to choose from, and the order in which they are chosen determines their role as captain or co-captain. A combination, on the other hand, only cares about the items themselves, not the order in which they are chosen. In this scenario, the order matters, making it a permutation.

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The rule of translation is: (x, y) → (x - 5, y - 3)

Option A is the correct answer.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

The coordinates are:

S = (1, 5)

T = (1, 1)

U = (4, 1)

And,

S' = (-4, 2)

T' = (-4, -2)

U' = (-1, -2)

We see that,

(1, 5) = (1 - 5, 5 - 3) = (-4, 2)

(1, 1) = (1 - 5, 1 - 3) = (-4, -2)

(4, 1) = (4 - 5, 1 - 3) = (-1, -2)

This is a translation of 5 units to the left and 3 units down.

Thus,

(x, y) → (x - 5, y - 3) is the rule of translation.

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Perimeter of quadrilateral is 26.39 unit.

Distance between two points with coordinates (x₁ , y₁)  and (x₂ , y₂). is given by

D = √[(x₁ - x₂)² + (y₁ - y₂)²]

This formula is derived from the Pythagoras Theorem, as the points form a right triangle in plane, with the hypotenuse representing the distance between them.

Given,

Quadrilateral ABCD

A(-3,2)

D(0,-6)

B(6,-2)

C(3,-6)

Perimeter = distance between A and B + distance between B and C + distance between C and D + distance between D and A

Perimeter =

√[(-3 -6)² + (2 - -2)²] + √[(6 - 3)² + (-2 - -6)²] +

√[(3 - 0)² + (-6 - -6)²] + √[(0 - -3)² + (-6 - 2)²]

Perimeter = √[(-9)² + (4)²] + √[(3)² + (4)²] + √[(3)² + (0)²] + √[(3)² + (-8)²]

Perimeter = √[81 + 16] + √[9 + 16] + √[9 - 0] + √[9 + 64]

Perimeter = √[97] + √[25] + √9 + √[73]

Perimeter = 9.85 + 5 + 3 + 8.54

Perimeter = 26.39 unit

Hence, 26.39 unit is the perimeter of quadrilateral ABCD.

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The measurement scale for "age in years" is ordinal, meaning the values have a specific order or ranking, but no notion of equal distances between them.

The "age in years" measurement scale is ordinal. An ordinal scale is a type of measurement scale that has a specific order or ranking to its values, but there is no notion of equal distances between the values. In the case of "age in years," the values have a clear order (e.g., 25 years old is younger than 30 years old), but it doesn't make sense to say that a difference of 5 years is the same as a difference of 1 year. This is why age in years is considered to be measured on an ordinal scale.

Additionally, with an ordinal scale, the values can only be compared in terms of their order or ranking, and not in terms of the actual differences between them. For example, we can say that someone who is 25 years old is younger than someone who is 30 years old, but we cannot say that a person who is half as old as someone who is 50 years old at the age of 25. This is because an ordinal scale does not have a meaningful zero point and does not allow for meaningful comparisons of the absolute size of differences between values. An ordinal scale is the second highest measurement scale, below interval and ratio scales, which provide more information about the magnitude of the values being measured.

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Answer:

a + c = 1250

$7.00a + $5.50c = $7979

Step-by-step explanation:

Making the system of equations for the number of tickets involved how many attended and who attended

It's showing 1250 attended and children and adults showed up. Let's a = adults and c = children

a + c = 1250 <--- that's saying adults + children equal 1250

For $ earned, it involves how much each ticket was and the total cost

Looks like we have prices for a and c and the total cost which was 7979. Since adults were 7.00, we'll call that 7.00a. And for children it was 5.50, we'll call that 5.50c

Putting it together 7.00a + 5.50c = 7979 because all the $7.00 tickets plus all the $5.50 tickets cost $7979

Answer:

The probability of landing on purple is equal to the probability of landing on blue.

This is because each color covers the same number of sections (2 for purple, 3 for blue) and each section has the same size, so the probability of landing on each color is equal.

Probability = Number of successful outcomes / Total number of outcomes

For purple and blue, the number of successful outcomes is the same (2 and 3, respectively) and the total number of outcomes is 8, so the probability of landing on either color is equal.

Probability of landing on purple or blue = 2 / 8 = 3 / 8 = 0.25

The solution set of the inequality is (-7.5, 1), and the correct graph is the one in option A.

Here we want to solve the inequality below:

-10 < 2x + 5 < 7

To solve this, we need to isolate the variable x, then we will get:

-10 < 2x + 5 < 7

-10 - 5 < 2x < 7 - 5

-15 < 2x < 2

-15/2 < x < 2/2

-7.5 < x < 1

So the solution set is (-7.5, 1)

So the graph of this will be a number line that starts at -7.5 and ends at 1, that would be the one in option a.

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Answer:

50 degrees. Complementary angles are any two angles that add up to 90 degrees. In this case, if the complement is 30 less than its bigger angle, and the bigger angle is twice the size of its complementary angle, then that would mean you take the unknown angle as x.(WORK SHOWN BELOW)

Step-by-step explanation:

[tex]x=2\times (\left90-x)\right-30\\[/tex]

Then regroup

[tex]x= 180-2x-30[/tex]

Work with like terms. For example, a whole's like term is another whole.

[tex]x+2x=(\left180-30)\right\\180-30=150\\x+2x=1+2\\x+2x=3x\\3x=150[/tex]

If 3x is the same as 150, then 150 divided by 3 is also x. We know this because almost any correct equation with some form of a constant or variable can be flipped into the opposite of itself.

[tex]x=\frac{150}{3}[/tex]

And lastly, 150 divided by 3 is 50.

Hope this helps!

The glide reflection maps triangle ABC to triangle A'B'C' is (x, y) -> (x + 8, -y)

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The rule for the glide reflection is to first reflect the point across the y-axis and then translate the point 8 units to the right. Mathematically, this can be written as:

(x, y) -> (x + 8, -y)

So, to apply this rule to the vertices of triangle ABC, we would do the following:

A(-4, -2) -> (A(-4, -2) + 8, -(-2)) = A'(4, 2)

B(-2, 6) -> (B(-2, 6) + 8, -(6)) = B'(6, -6)

C(4, 4) -> (C(4, 4) + 8, -(4)) = C'(12, -4)

And so, the glide reflection maps triangle ABC to triangle A'B'C'.

Hence,  the glide reflection maps triangle ABC to triangle A'B'C' is (x, y) -> (x + 8, -y)

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The concentration of 1 mg/mL can be described as: 103 ug/mL and [tex]10^{9}[/tex] ppm.

The concentration of a solution can be expressed as the amount of solute in a given volume of the solution. The expression for concentration can be in terms of mass per volume, such as milligrams per milliliter (mg/mL) or grams per liter (g/L), or in terms of moles per volume, such as moles per liter (mol/L).

A concentration of 1 mg/mL means that there is 1 milligram of solute in every milliliter of the solution. This can be converted to micrograms per milliliter (ug/mL) by multiplying by 1000, giving us

[tex]1mg/mL=1000ug/mL=10^{6} ug/mL[/tex].

Parts per million (ppm) is another expression of concentration. To convert mg/mL to ppm, we need to know the density of the solution, which is given as 1.00 g/mL. We can use this density to convert the mass of solute to volume and then find the ratio of solute to solution volume.

[tex]1mg/mL=1mg/1mL=1g/1000mL=1/1000 g/mL= 10^{-3}g/mL\\[/tex]

So, [tex]1mg/mL=10^{-3}g/mL=10^{-3} *10^{6} mg/mL=10^{9} ppm[/tex].

Therefore, the concentration of 1 mg/mL can be expressed as: 103 ug/mL and [tex]10^{9}[/tex] ppm.

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Answer:

57 degrees

Step-by-step explanation:

Answer:

No the answer is

[tex]14 - 7y[/tex]

There is no maximum and minimum values.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is f(x)=∛(x+1)

Find where the first derivative is equal to 0 to find the local maxima and minima.

By differentiating the given function we get

[tex]f(x)=(x+1)^{\frac{1}{3} }[/tex]

[tex]f'(x)=\frac{1}{3(x+1)^{\frac{2}{3} }}[/tex]

For maxima f'(x)=0

0= [tex]\frac{1}{3(x+1)^{\frac{2}{3} }}[/tex]

No local maxima or minima

Therefore, there is no maximum and minimum values.

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The figures that will be formed are isosceles triangle and right angle.

option B and D.

A triangular pyramid is a geometric shape that has a triangular base and three triangular faces.

If all three sides of the base are congruent, then a verticals slice perpendicular to the base of the triangular pyramid will form the following figures;

Thus, the isosceles triangle will be formed because all three sides of the base are congruent, and third side will be from the vertical slice to the base creating a third unequal side.

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Answer:

The vertical tank is basically a cylinder that is sometimes referred to as a V-120 cylinder. Both 120-gallon tanks can hold up to 96 gallons of propane when full (not 120 gallons). That’s due to the 80% rule; all propane tanks can be filled up to 80% of their maximum capacity.

Answer:

75%

Step-by-step explanation:

Box plot is the use of a rectangle to represent data where the vertical sides of the rectangle represents the lower and upper quartile.

From the box plot,

The minimum is 153 cm

The first quartile is 168.4 cm

The second quartile is 174.2 cm

The third quartile is 183.9

The maximum is 195 cm

See attachment for the missing box plot.

There are 5 vertical lines in a box plot

The first represents the minimum value

The second represents the first quartile

The third represents the second quartile i.e. the median

The fourth represents the third quartile

The last represents the maximum quartile

From the attached box plot.

The first vertical line is 153 cm

The second vertical line is 168.4 cm

The third vertical line is 174.2 cm

The fourth vertical line is 183.9 cm

The firth vertical line is 195 cm

Hence:

The minimum is 153 cm

The first quartile is 168.4 cm

The second quartile is 174.2 cm

The third quartile is 183.9

The maximum is 195 cm

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Answer: Yes.

Step-by-step explanation:

Proportional relationships are relationships between two variables where their ratios are equivalent. In other words, a proportional relationship is one side is always multiplied/divided by the same value. In this case, the value is 2.

Hope this helps!

Step 1: To construct

The box plot for the given data.

Step 2 : Explanation

Box plots are a graphical tool used in statistics to show the concentration of data. They also demonstrate how far the extreme numbers differ from the majority of the data. The smallest value, the first quartile, the median, the third quartile, and the maximum value are used to create a box plot.

Use a horizontal or vertical number line and a rectangular box to make a box plot. The axis's ends are labelled by the smallest and largest data values. One end of the box is marked by the first quartile, while the other end is marked by the third quartile. Approximately half of the data is included within the box. From the box's ends to the smallest and greatest data values, the "whiskers" extend. The median or second quartile can be in the middle of the first and third quartiles, or it can be either one or the other.

The box plot's five numerical summaries are as follows:

# of movies Frequency Cumulative frequency

0 5 5

1 9 14

2 6 20

3 4 24

4 1 25

N=25

Answer:$920

Step-by-step explanation:

Step-by-step explanation:

The interest earned is $920.