A rocket is shot off from a launcher. The accompanying table
represents the height of the rocket at given times, where x is time, in
seconds, and y is height, in feet. Write a quadratic regression equation
for this set of data, rounding all coefficients to the nearest tenth. Using
this equation, find the height, to the nearest foot, at a time of 9.7
seconds.
Time in Seconds (x) Height in Feet (y)
1
298
1.8
518
2.4
660
3.8
961
4.8
1137

Answer: 40 degrees

Step-by-step explanation:

m/CBA = m/CED

16 + 6x = 48 - 2x; add 2x on both sides and subtract 16 on both

8x = 32; divide 8 on both sides to isolate the x

x = 4

m/CBA = 16+6(4) = 40

Answer:

5

Step-by-step explanation:

The midpoint of AC is (2,0), and the midpoint of BC is (0,2.5). The third vertex of triangle DEC is E, the midpoint of AB, which can be found using the midpoint formula:

E = ( (A_x + B_x) / 2, (A_y + B_y) / 2 )

= ( (0 + 2) / 2, (0 + 5) / 2 )

= (1, 2.5)

So the vertices of triangle DEC are (0, 2.5), (2, 0), and (1, 2.5). The area of triangle DEC is half the area of triangle ABC, which is (4 * 5) / 2 = 10. So the area of triangle DEC is 10 / 2 = 5.

Pressure at 3000 meters above sea level will be 690.33 millibars.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given, At a height of n meters above sea level, the atmospheric pressure is Pn millibars. At a height of (n + 1000) meters above sea level, the atmospheric pressure is P(n + 1000) millibars.

where,

P(n + 1000) = 0.88Pn

at n = 0

P(1000) = 0.88 P(n = 0)

Since,

P(n = 0) is 1013 milibar

thus,

P(1000) = 0.88 * 1013

At n = 1000

P(1000 + 1000) = 0.88 P(n = 1000)

P( 2000) = 0.88 * 0.88 *1013

at n = 2000

P(2000 + 1000) = 0.88 P(n = 2000)

P( 3000) = 0.88 *0.88* 0.88 *1013

Thus,

P(3000) = 690.33

Therefore, Pressure at 3000 meters above sea level could be 690.33 millibars.

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131 customers would expect to pay with a debit card out of 700 Customers.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

customers paid by cash=35

customers used a debit card = 12

customers used a credit card = 17

If she is expecting 700 customers then number of customers used Debit card will be

= 700 x 12/ (35+12+17)

= 700 x 12/64

= 131.25

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the value of the algebraic equation −8x+6y+6 will be 10.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given,  −8x+6y=4 is a true equation

To find the value of the equation −8x+6y+6

=> −8x+6y+6

Since −8x+6y = 4 given

Thus,

=> 4 + 6

=> 10

Therefore, the value of the algebraic equation −8x+6y+6 will be 10.

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The value of the expression after evaluating it according to the values of c and d is 42.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Since, no expression is given, let us assume that the expression is

c + d / 4

Now we have to evaluate the value of the expression according to the values of c and d,

For that, we will simply put the given values in the expression and solved it accordingly,

Put c = 36 and d = 24 in the expression we assumed,

c + d / 4 = 36 + 24/4

= 36 + 6 = 42

Hence, the value of the expression after evaluating it according to the values of c and d is 42.

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The slope of a straight line that is parallel to the vertical axis is zero.

A slope of zero indicates that the line is flat and has no incline or decline. In a two-variable diagram, this means that there is no relationship between the two variables, as a change in one variable does not affect the value of the other. A line with a slope of zero is a horizontal line, and its equation is of the form y = b, where b is a constant value.

In contrast, a line with an infinite slope (or vertical line) would indicate a perfect correlation between the two variables, such that a change in one variable would result in an infinite change in the other. A line with a finite positive or negative slope would indicate a direct or inverse relationship between the two variables, respectively.

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The graph for the functions is attached.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.

Given

A: graph of y = f(x)

since the graph is in form of a parabola so the function is a quadratic function,

f(x) = ax² + bx + c

the vertex of the graph is at (2, 0)

here in the given curve, the value of the y-axis is 0,

and y = f(x) - 3

in the equation y = f(x) - 3

the shape of the curve will be the same but only change in the vertex of the curve, the new vertex for the curve is (2, -3)

for x = 0 y = -3.

B: given y =g(x)

the graph shows the negative cubic function,

g(x) = -x³

and y = g(x + 4)

= -(x + 4)²

the graph will shift towards 4 units left.

Hence the graph is attached for both equations.

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The forecast for this year (F(6)) is 18,625. Therefore, the correct answer is 18,625.

Exponential smoothing is a time series forecasting method that uses a weighted average of past observations to make predictions. In this case, the weight assigned to each observation is determined by a smoothing parameter, alpha, which is a value between 0 and 1.

The formula for exponential smoothing with alpha = 0.5 is given by:

F(t) = alpha * Y(t) + (1 - alpha) * F(t-1)

where F(t) is the forecast for time t, Y(t) is the actual observation at time t, and F(t-1) is the forecast for the previous time period.

Starting with the forecast for two years ago, we can use this formula to make a forecast for each year until this academic year.

F(2) = 0.5 * 20,000 + (1 - 0.5) * 16,000 = 18,000

F(3) = 0.5 * 18,000 + (1 - 0.5) * 18,000 = 18,000

F(4) = 0.5 * 16,000 + (1 - 0.5) * 18,000 = 17,000

F(5) = 0.5 * 15,000 + (1 - 0.5) * 17,000 = 16,250

F(6) = 0.5 * 21,000 + (1 - 0.5) * 16,250 = 18,625

So the forecast for this year (F(6)) is 18,625. Therefore, the correct answer is 18,625.

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Complete question:

The president of State University wants to forecast student enrollment for this academic year based on the following historical data: Year Enrollments 5 years ago 15,000 4 years ago 16,000 3 years ago 18,000 2 years ago 20,000 Last year 21,000 What is the forecast for this year using exponential smoothing with alpha = 0.5, if the forecast for two years ago was 16,000?

18,750

19,500

21,000

22,650

None of the above

The lengths that the bolt will be destroyed are given as follows:

The lengths are obtained applying the proportions in the context of this problem.

Considering the mean length of 12 cm, and the standard deviation of 0.1 cm, the length that is 2 standard deviations below the mean is given as follows:

12 - 2 x 0.1 = 11.8 cm.

The length that is 2 standard deviations above the mean is given as follows:

12 + 2 x 0.1 = 12.2 cm.

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The answer to the expression 2b x b is simply 2b^2. Exponentiation is a mathematical operation that raises a number to a power, and in this case, b is raised to the power of 2.

Alternatively, if exponentiation is not allowed, the answer to the expression is simply 2b * b, which can be simplified to 2b^2 as well.

So, the answer to the expression 2b x b is 2b^2, regardless of whether or not exponentiation is used.

The expression 2b x b represents the product of two scalars, 2 and b, multiplied by a scalar b.

The expression could represent a variety of quantities in mathematics and science, including the area of a rectangle, the volume of a cube, or the kinetic energy of an object, among others.

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We need to know how many gallons of gas $23.36 will buy, so we divide the amount by the cost per gallon: $23.36 ÷ $3.25 per gallon = 7.20 gallons.

Once we know how many gallons of gas we are buying, we can then find out how long it will take to pump that amount of gas. To do that, we multiply the number of gallons by the time per gallon: 7.20 gallons × 21 seconds/gallon = 151.2 seconds.

So, the answer to the question is 151.2 seconds, which is the total time it will take to pump $23.36 worth of gas at $3.25 per gallon and 21 seconds per gallon.

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Answer:

6. 4x + 28 + x + 19 + 3x + 13

x = 15

7. x + 123 + 113 + 97 + 90 = 540

x = 117

Step-by-step explanation:

6. 4x + 28 + x + 19 + 3x + 13 = 180

8x + 60 = 180

8x = 120

x = 15

7. x + 123 + 113 + 97 + 90 = 540

x + 423 = 540

x = 117

To solve this problem using a Venn diagram, we need to start by drawing a rectangle to represent the group of 50 students, and then draw two overlapping circles to represent the subjects of Math and Science. Let's label the regions of the Venn diagram as follows:

We know that 20 students like only Math, 15 students like only Science, and the number of students who like both subjects is unknown. We also know that the number of students who like neither subject is double the number of students who like both subjects. Let's use this information to fill in the Venn diagram:

We can set up an equation using this information:

20 + 15 + MS + 2MS = 50

Simplifying this equation, we get:

3MS = 15

MS = 5

Now we can fill in the Venn diagram:

       M    MS

        \  /

         \/

        /  \

       S----MS

We know that MS = 5, so the number of students who like at most one subject is:

20 (like only Math) + 15 (like only Science) + MS (like both subjects) = 20 + 15 + 5 = 40.

Therefore, 40 students in the group of 50 like at most one subject.

Answer:

Step-by-step explanation:

Inverse variation functions have the form y = k / x, where k is a constant.

When k > 0, the graph of the inverse variation function is a hyperbola that opens upwards or downwards, depending on the sign of k. When k > 0, the hyperbola opens upwards and the two branches of the hyperbola move away from the x-axis as x increases. This means that as x increases, the value of y decreases. When x approaches 0 from the right, y approaches positive infinity, and when x approaches 0 from the left, y approaches negative infinity.

On the other hand, when k < 0, the graph of the inverse variation function is a hyperbola that opens upwards or downwards, depending on the sign of k. When k < 0, the hyperbola opens downwards and the two branches of the hyperbola move toward the x-axis as x increases. This means that as x increases, the value of y increases. When x approaches 0 from the right or left, y approaches negative infinity.

In both cases, the inverse variation function is undefined for x = 0, as division by zero is undefined.

Answer:

A.) 16

B.) 18

Step-by-step explanation:

Mode is the number that shows up the most. For A.) they are saying the mode is 1. We see that for 1, the corresponding number is 17. Since no number can go larger than 17, that means x must be 16.

For B.) they are saying the mode is 2. the corresponding number is X. they want the smallest value possible, so what we do if find the largest number, which is 17, and simply add one

The amount of money they had in total is $25

One bestfriend went to the store with $5

The other best friend went to the store with $20

The amount of money they had in total can be calculated as follows

= 20 + 5

= 25

Hence the amount of money the best friends had in total is $25

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Answer: 25$

Step-by-step explanation: 20 plus 5 equals 25.

Answer:

A. $6.50 + $7.25x ≤ $35.50

B.  4 games  

Step-by-step explanation:

x = number of games played

$6.50 + $7.25x ≤ $35.50

7.25x ≤ 35.5 - 6.50

7.25x ≤ 29

x ≤ 29/7.25

x ≤ 4

The remaining amount of money in Denise's account is $250 - (2x).

Therefore, if Denise buys x bottles of water, she will have $250 - (2x) remaining in her account.

Denise has $250 in her checking account.

Each time she buys a bottle of water, she spends $2.

If Denise buys x bottles of water, the total amount of money spent is 2x.

To calculate the remaining amount in Denise's account, we need to subtract the total amount of money spent (2x) from the original amount of money in her account (250).

Therefore, the formula to calculate the remaining amount is $250 - (2x).

Substituting the value of x in the formula, we get the remaining amount of money in Denise's account.

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For every bottle of water Denise buys her balance decreases by $2. So If Denise buys x bottles of water, her balance decreases by $2 * x.

Let's call the amount of money remaining in Denise's account after buying x bottles of water M.

The equation to find M is:

M = 250 - 2x

This equation says that the money remaining in Denise's account is equal to her initial $250 balance minus the amount she spent on buying x bottles of water, which is $2 per bottle.

In other words, for every bottle of water Denise buys, her balance decreases by $2. So, if she buys x bottles of water, her balance decreases by $2 * x.

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Answer:

-2 leis.

Step-by-step explanation:

212 * 14 = 2,968 leis

2,968/30 = 99 boxes

99*30=2970

2968-2970=-2

There is a problem with the wording of this question. There isn't a total so it's really confusing...

Answer:

∠ A = 138° , ∠ C = 75°

Step-by-step explanation:

ABCD has parallel bases and is a trapezium

each lower base angle is supplementary to the upper base angle on the same side.

∠ A + 42° = 180° ( subtract 42° from both sides )

∠ A = 138°

∠ B + ∠ C = 180 , that is

12x - 3 + 9x - 6 = 180

21x - 9 = 180 ( add 9 to both sides )

21x = 189 ( divide both sides by 21 )

x = 9

Then

∠ C = 9x - 6 = 9(9) - 6 = 81 - 6 = 75°

Answer:

21 & 12

Step-by-step explanation:

let the sum of x and y be 33.. so,

x + y = 33

x - y = 9

x = 9 + y

x + y = 33

9 + y + y = 33

9 + 2y = 33

2y = 24

y = 24/2

y = 12

similarly,

x + y = 33

x + 12 = 33

x = 21

hence, sum: 21 + 12 = 33

      difference : 21 - 12 = 9

Answer:

16.826

Step-by-step explanation:

I think you divide 875 by 52 which is 16.826 correct me if im wrong.

Answer:

16.8 miles in each track meet

Step-by-step explanation:

You divide 875 by 52 to see how many miles Mark ran in each track meet

875/52 = 16.8

The letters in the word MIAMI are rearranged at random so that every possible anagram is equally likely. The probability that it still spells MIAMI is 1/5.

Let us count the total number of ways MIAMI can be arranged regardless of condition.

There are 2 M’s 2 I’s 1 A in word.

Total ways of arrangement will be = 5!/2!2!

​Total ways of arrangement will be = (5 × 4 × 3 × 2!)/2! × 2 × 1

Total ways of arrangement will be = 5 × 2 × 3

Total ways of arrangement will be = 30 ways

Now, ways in which all similar words are together, thus we have to consider 2M's as one unit, similarly 2 I's as a unit, so number of ways will be 3!.

Thus, the probability will be = 3!/30

The probability will be = (3 × 2 × 1)/30

The probability will be = 6/30

The probability will be = 1/5

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Answer:

$49.59

Step-by-step explanation:

$20.75+$10.59+$18.25=$49.59

Answer:

3/2

Step-by-step explanation:

You can divide the numerator and denominator by its GCF(Greatest common factor) which in this case is 20.

60/ 20 = 3

40/20 = 2

3/2

A kilometer (km) is a unit of length in the metric system, which is based on the meter as the basic unit of length.

It is equal to one thousand meters, or one million centimeters, and is used in many contexts around the world when referring to the measurement of distances between two points.

Kilometers are commonly used in the context of travel, as they are often used to measure the distance between two cities or countries, or to measure the length of a journey or route. In addition, kilometers are often used to measure the depth of bodies of water, and to measure the size of land features such as mountains and valleys.

In mathematics, the kilometer is used to measure the magnitude of certain quantities, such as the speed of an object or the acceleration of a body. It is also used to measure the size of certain objects, such as the radius of a circle or the length of a line.

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A kilometer is a unit of length in the metric system. In mathematics, a kilometer is a unit of length used to measure distance.

It is part of the metric system, which is the most widely used system of measurement in the world. A kilometer is defined as 1000 meters. This makes it a convenient unit of measurement for large distances, such as those between cities, or for measuring the length of roads and highways.

In mathematical calculations involving distances, kilometers can be used to express the length of a segment or the distance between two points. They can also be converted to other units of length, such as meters, centimeters, or miles, by using appropriate conversion factors.

In conclusion, a kilometer is a unit of length in the metric system that is used to measure large distances in mathematics and in everyday life.

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Circle: a cross-section that goes through the center of the sphere and creates a circular shape.

Point: a cross-section that goes through the center of the sphere and creates a single point.

(-6,-5), (-2,3), (2,-5), (6,3) are the ordered pairs given on the graph.

In mathematics, a transformation is a process that changes the position, size, or orientation of a geometric shape or figure. The term is used in various branches of mathematics, including geometry, algebra, and calculus.

In geometry, transformations include translations, rotations, reflections, and dilations. A translation involves moving a shape a certain distance in a certain direction, while a rotation involves rotating a shape around a fixed point. A reflection involves flipping a shape over a line, and a dilation involves stretching or shrinking a shape by a given scale factor.

In algebra, transformations can involve changing the form of an equation, such as solving for a variable, transforming an equation into a different coordinate system, or solving a system of equations.

In calculus, transformations can involve changing the form of a function, such as finding its derivative or integral, or transforming a function from one coordinate system to another.

To find the ordered pairs that are on the transformations of the function, we can apply the transformations to the original point (-2, -1) to obtain the points on each transformation.

y = f(x-4) - 4: If we apply the x-4 transformation to the x-coordinate of the original point, we get -2-4 = -6. So, the point is (-6, f(-6) - 4).

y = f(x-4) + 4: The x-coordinate of the point is -6, so the point is (-6, f(-6) + 4).

y = f(x+4) - 4: If we apply the x+4 transformation to the x-coordinate of the original point, we get -2+4 = 2. So, the point is (2, f(2) - 4).

y = f(x+4) + 4: The x-coordinate of the point is 2, so the point is (2, f(2) + 4).

So, the ordered pairs that must be on each of the transformations of f(x) are:

y = f(x-4) - 4: (-6, f(-6) - 4)

y = f(x-4) + 4: (-6, f(-6) + 4)

y = f(x+4) - 4: (2, f(2) - 4)

y = f(x+4) + 4: (2, f(2) + 4)

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To evaluate [tex]8^{\frac{2}{3} }[/tex] first find the square of 8 and then take the cube root.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Depending on the powers they possess, many rules of exponents are given.

Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.

Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.

Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.

The given value can be written as:

[tex]8^{\frac{2}{3} } = \sqrt[3]{8^{2} }[/tex]

Hence, to evaluate [tex]8^{\frac{2}{3} }[/tex] first find the square of 8 and then take the cube root.

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