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 hundredth. Using this equation, find the height, to the nearest foot, at a time of 3 seconds.

Answer: 226.19

Step-by-step explanation:

Using the formula for a cyclinder{ V=πr2h} and inputing the values given in the diagram, (the radius and height given) you get 28.27.

Then adding the cone's volume (V=πr2h/3) and inputing that values in the diagram (the radius and height) you get 197.92.

Adding those values you got from the cyclinder and cone together, you get the volume of the composite solid.

Answer:

(7, 8)

Step-by-step explanation:

equation 1:  [tex]6x+6y=90[/tex]

equation 2: [tex]9x+2y=79[/tex]

This system of equations can be solved for using the elimination method.

First, multiply both sides of the first equation by 3/2 to match the number of x's in both equations so that when we subtract the first equation from the second, the x's cancel and we can solve for y.

[tex]\left(\dfrac{3}{2}\right)\left(6x+6y\right)=(90)\left(\dfrac{3}{2}\right)[/tex]

[tex]9x + 9y = 135[/tex]

Next, subtract this from the second equation.

    [tex]9x+2y=79[/tex]       ← eq. 2

[tex]\underline{- (9x+9y=135)}[/tex]    ← modified eq. 1

     [tex]0 - \, 7y \, = -56[/tex]

Then, solve for y by dividing by 7.

[tex]7y = 56\\\overline{\, 7 \ } \ \ \ \ \overline{\ 7 \: }[/tex]

[tex]y=8[/tex]

So, the y-coordinate of the solution pair is 8.

Now that we've solved for the y, all we have to do to get x is plug the solved y-value back into one of the equations. I'll use the first equation.

[tex]6x+6y=90[/tex]

[tex]6x + 6(8) = 90[/tex]

↓ multiplying out 6 and 8

[tex]6x + 48 = 90[/tex]

↓ subtracting 48 from both sides

[tex]6x = 90 - 48[/tex]

[tex]6x = 42\\\overline{\: 6 \: } \ \ \ \ \, \overline{\: 6 \: }[/tex]

[tex]x = 7[/tex]

So, the x-coordinate of the solution pair is 7.

Finally, put the x- and y-coordinates together into an ordered pair in the form [tex](x, y)[/tex].

(7, 8)

Answer:

---------------------------

First, simplify the first equation by dividing all terms by 6:

Then solve it for y:

Now, substitute this into the second equation:

Finally, find the value of y:

The pair of numbers is (7, 8).

For the proportion of all hometowners in the united states that hold a home equity loan, confidence interval is (0.0992, 0.1508).

We have given that in a recent poll of 1000 homeowners in the United states, one in eight homeowners reports havinf a home equity loan that he or she is curently paying off.

If one in eight reports having a home equity loan then for 1000 hometowners = 1000/8 = 125.

Sample proportion p = 125/1000 = 0.125

given that confidence coefficient = 0.99

α = 1 - confidence coefficient = 1 - 0.99

α = 0.01    

z₀.₀₁ / 2 = 2.58

Therefore the interval estimate for the proportion of all homeowners in the United states that hold a home equity

                        = p ± z₀.₀₁/2 √p(1-p)/n

                        = 0.125 ± 2.58 √0.125(0.875)/1000

                        = 0.125 ± 2.58 √0.0001

                        = 0.125 ± 0.0258

                        = (0.125 - 0.0258,0.125 + 0.0258)

                        = (0.0992, 0.1508)

Hence (0.0992, 0.1508) is the confidence interval.

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Answer:

Step-by-step explanation:

Part 1: true

(-4, -1) and (0, 2)

m = 2+1/0+4

m = 3/4

(0, -3) and (4, 0)

m = 0+3/4+0

m = 3/4

Part 2: true

It intercepts at (0, -3)

Part 3:

I can't really see what slope it says but if it says -3/5, then its true, otherwise it's false.

(5, -1) and (0, 2)

m = 2+1/0-5

m = 3/-5

m = -3/5

Part 4: false

Graph A would have 2 and Graph C would have different intersecting points.

Answer:

[tex]\textsf{System of equations: \quad }\begin{cases}x=\dfrac{1}{2}y\\\\2x+2y=360\end{cases}[/tex]

[tex]\begin{aligned} \textsf{Solutions}: \quad x &= 120^{\circ}\\y &= 60^{\circ}\end{aligned}[/tex]

Step-by-step explanation:

An obtuse angle is greater then 90° and less than 180°.

An acute angle is less than 90°.

Therefore, from inspection of the given diagram:

If the measures of the acute angles are one-half times the measures of the obtuse angles:

[tex]\implies x=\dfrac{1}{2}y[/tex]

Angles in a quadrilateral sum to 360°.

[tex]\implies 2x+2y=360[/tex]

Therefore, the system of equations is:

[tex]\begin{cases}x=\dfrac{1}{2}y\\\\2x+2y=360\end{cases}[/tex]

Substitute the first equation into the second equation and solve for y:

[tex]\implies 2\left(\dfrac{1}{2}y\right)+2y=360[/tex]

[tex]\implies y+2y=360[/tex]

[tex]\implies 3y=360[/tex]

[tex]\implies \dfrac{3y}{3}=\dfrac{360}{3}[/tex]

[tex]\implies y=120[/tex]

Substitute the found value of y into the first equation and solve for x:

[tex]\implies x=\dfrac{1}{2} \cdot 120[/tex]

[tex]\implies x=60[/tex]

T be the set of all points x in [0,1] by a Cantor set type construction is  x=∑∞n=1 qn/4n

for some sequence of qns with each qn∈{1,3}.

What is Cantor set type construction?

The Cantor set is a collection of points situated on a single line segment that possesses a variety of odd characteristics.

By deleting the center third of a line segment and then repeating the process with the remaining shorter segments, the Cantor ternary set, the most popular construction, is created. The ternary construction was only briefly described by Cantor as an illustration of a more basic concept—that of a perfect set that isn't dense anywhere.

According to the given question:

The proportion (i.e., measure) of the unit interval that is left can be determined by subtracting the entire length as the Cantor set is defined as the set of points that are not excluded.

T be the set of all points x in [0,1] by a Cantor set type construction is  x=∑∞n=1 qn/4n

for some sequence of qns with each qn∈{1,3}.

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The graph of the Line Segment BC with the endpoints B(8,9) and C(-4,5) is shown below.

In the question ,

it is given that ,

the end points of the line segment is B(8,9) and C(-4,5) .

we have to graph the line segment BC.

first we mark the point on the coordinate plane , with point B and point C .

after that we join the points .

and the equation of the line segment is

(y - 5) = (9-5/8+4)*(x + 4)

(y - 5) = (1/3)*(x + 4)

3y - 15 = x + 4

x - 3y + 19 = 0

Therefore, the graph of the line segment BC is shown below.

The given question is incomplete , the complete question is

Graph line segment BC with endpoints B(8,9) and C(-4,5) and label the points.

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Answer:

Its the 3rd one

Step-by-step explanation:

If the nail is measured with a ruler and its length is 5.46 cm , then the correct statements are :

(a) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.1 cm ;

(b) The uncertainty is in the final digit of the measurement .

The Uncertainty of a number helps to estimates in comparison of experimental numbers .

it is given that , the reported length of the ruler is = 5.46 cm ;

we know that ,

the uncertainty In any number , is present in last digit only ,

the place value of the last digit in 5.46 is 0.01 .

So , uncertainty can be expressed by reporting measurement as 5.46 ± 0.1 cm

Therefore , the correct statements about the certainty and uncertainty are (a) and (b) .

The given question is incomplete , the complete question is

A nail is measured with a ruler and its length is reports as 5.46 cm.

Select ALL the statements that are correct about the certainty and uncertainty represented in this recorded measurement.

(a) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.1 cm ,

(b) The uncertainty is in the final digit of the measurement ,

(c) All three digits shown in the measurement are known with certainty ,

(d) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.01 cm  .

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Answer:

25456

Step-by-step explanation:

592 over 43

592

x 43

multiply 3 by 2, 9 and 5. 3 by 2 is 6. 3 by 9 is 27. 3 by 5 is 15.

add a zero at the second row then,

multiply 4 by 2, 9, 5. 4 by 2 is 8. 4 by 9 is 36. 4 by 5 is 20.

if you aligned them properly, when you add them you should get 25456

I'll try to include a picture of my work, hopefully you can see it**

The value of x in . (4x-101)° = (2x+3) is 52°.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

The value of x. (4x-101)° = (2x+3)

Collect the like terms

4x - 2x = 3 + 101

2x = 104

Divide

x = 104 / 2

x = 52°

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Complete question

Find the value of x. (4x-101)° = (2x+3)

The answers to both subparts are shown:

(A) The derivative of f'(5) means the pace at which the price per pound changes in relation to the weight of coffee sold at $5 per pound.

(B) The unit of f'(5) is pounds/dollar.

The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument.

Calculus's core tool is the derivative.

We may find the slope of a function at any point by using its derivative. We can find numerous derivatives by adhering to certain rules.

For instance: A constant value, such as 3, always has a slope of 0.

(A) Meaning of derivative of: f'(5)

We have: Q = f(p) ...(1)

Differentiating Q in relation to p results in:

qQ/dp = f'(p) ...(2)

The rate of change of the price per pound in relation to the volume of coffee sold is implied by equation (2).

If p = 5, we get:

qQ/dp = f'(5) ...(3)

The rate at which the price per pound changes in relation to the amount of coffee sold at $5 per pound is implied by equation (3).

(B) Unit of f'(5):

Equation (3)'s result that qQ/dp = f'(5) suggests that f'(5) units are pounds/dollar.

Therefore, the answers to both subparts are shown:

(A) The derivative of f'(5) means the pace at which the price per pound changes in relation to the weight of coffee sold at $5 per pound.

(B) The unit of f'(5) is pounds/dollar.

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Correct question:
The quantity (in pounds) of gourmet ground coffee that is sold by a coffee company at a price of p dollars per pound is Q = f(p). (a) What is the meaning of the derivative f '(5)? The rate of change of the price per pound with respect to the quantity of coffee sold. The supply of coffee needed to be sold to charge $5 per pound. The rate of change of the quantity of coffee sold with respect to the price per pound when the price is $5 per pound. The rate of change of the price per pound with respect to the quantity of coffee sold when the price is $5 per pound. The price of the coffee as a function of the supply. What are the units of f '(5)? dollars dollars/pound pounds/(dollars/pound) pounds dollars/(pound/pound) pounds/dollar

Answer:

x = 7/3.

Step-by-step explanation:

DE is parallel to BC and AD= DB and AD = EC.

So, AD/DB = (x+1)/(4x-6)

(x + 1)/(4x - 6) = 1

x + 1 = 4x - 6

1 + 6 = 4x - x

3x = 7

x = 7/3.

The value of x is 80

The measure of angle FOW, m ∠FOW, is 80°

The measure of angle FLW, m ∠FLW, is 112°

The measure of angle OLW, m ∠OLW, is = 68°

From the question, we are to determine the measure of the missing angles

From the given diagram, we can write that

(2x - 48)° = x° + 32°

Solve for x

(2x - 48)° = x° + 32°

2x° - 48° = x° + 32°

Subtract x° from both sides of the equation

2x° - x° - 48° = x° - x° + 32°

x°  - 48° = 32°

Add 48° to both sides of the equation

x° - 48° + 48° = 32° + 48°

x° = 32° + 48°

x° = 80°

Therefore,

x = 80

Calculating the m ∠FOW

m ∠FOW = x°

m ∠FOW = 80°

Calculating the m ∠FLW

m ∠FLW = (2x - 48)°

m ∠FLW = (2(80) - 48)°

m ∠FLW = (160 - 48)°

m ∠FLW = 112°

Calculating the m ∠OLW

m ∠OLW + m ∠FOW + m ∠OWL = 180° (Sum of angles in a triangle)

m ∠OLW + 80° + 32° = 180°

m ∠OLW + 112° = 180°

m ∠OLW = 180° - 112°

m ∠OLW = 68°

Hence, the measure of m ∠OLW is 68°

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When t = 3869, the rate of change of p is proportional to p.

A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions.

Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three. Due to the prevalence of these relationships, differential equations are widely used in many fields, including engineering, physics, economics, and biology.

The primary focus of studying differential equations is on the solutions—the collection of functions that satisfy each equation—as well as the characteristics of those solutions.

Only the most basic differential equations can be solved using explicit formulas, but many features of a particular differential equation's solutions can be deduced without doing an exact calculation.

When a closed-form expression is used, it is common for.

According to our question-

The revised equation is then

P=5000exp(-0.0513t)

Find P at t=5 now.

P=5000 exp(-0.0513×5)

P=5000 ×exp(-0.25647) (-0.25647)

P=5000 × 0.77378

P=3868.89.

P = 3869. Roughly

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The volume of the gas becomes 4L. Option B is correct.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,

From the ideal gas equation, we know that,

Volume is directly proportional to the temperature,

So,

V₁ / V₂ = T₁ / T₂

Where,

V₁ and T₁ are the initial pressure and temperature,

V₂ and T₂ are the final pressure and temperature.

Substitute the values,

8 / V₂ = 400 / 200

V₂  = 4

Thus, the volume of the gas becomes 4L. Option B is correct.

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The exact amounts for each category are given as follows:

The exact amounts for each category are obtained applying the proportion  relative to the percentage of each category, that is, multiplying the decimal equivalent of the percentage by the total amount of $800.

Hence the amounts are given as follows:

The pie chart with the categories and their percentages is given by the image shown at the end of the answer.

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the Discriminant will always be greater than or equal to zero. This means that the polynomial has at least one real root.

Let f(x) = a0 + a1x + a2x2 + a3x3 be a polynomial function of odd degree 3.

We know that the degree of a polynomial is the highest power of the variable in the equation. Since the degree of f(x) is 3, then a3 ≠ 0.

Now, consider the Discriminant of the polynomial, which is defined as the expression below:

Discriminant = b2 - 4ac

In this case, b2 = a2^2, c = a0 and a = a3, thus the Discriminant is:

Discriminant = a2^2 - 4a0a3

Since a3 ≠ 0 (as mentioned before), the Discriminant will always be greater than or equal to zero. This means that the polynomial has at least one real root.

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Answer:

2

Step-by-step explanation:

First, we must add 14 to both sides to put the variable and coefficient alone.

4s - 14 = -6

   +14     +14

4s = 8

s = 2

The number of sticks in pattern 6 is; 26

The nth term of the sequence formed is; aₙ = 4n + 2

From the attached image, we see that;

Number of sticks in pattern 1 is 6

Number of sticks in pattern 2 is 10

Number of sticks in pattern 3 is 14

Thus, the sequence will be;

6, 10, 14, ...

This is an AP because the difference is 4.

The formula for the nth term of an AP is;

aₙ = a + (n - 1)d

where;

a is first term

n is position of term

d is common difference

In our sequence, first term; a = 6

Common difference; d = 10 - 6 = 4

Thus, the equation for the nth term is;

aₙ = a + (n - 1)d

aₙ = 6 + (n - 1)4

aₙ = 6 + 4n - 4

aₙ = 4n + 2

Now, substitute n = 6 in the above equation to find the number of sticks in pattern 6. This gives;

a₆ = 4(6) + 2

a₆ = 26

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Answer: b. radius of the cone = 5; height of the cone = 12

Step-by-step explanation:

The volume of the cylinder is [tex]\pi (5^2)(4)=100\pi[/tex].

The only option that makes the same volume is option b. In this case, the volume is [tex]\frac{\pi}{3}(5^2)(12)=100\pi[/tex].

The correct expression to model the cost of manufacturing b basketballs in 1 day is:

O $5.25b-$1,400.00

The fixed costs of manufacturing the basketballs are $1,400.00 per day, and the variable costs are $5.25 per basketball. To find the total cost of manufacturing b basketballs in 1 day, you need to add the fixed costs and the variable costs for each basketball.

The variable costs for b basketballs would be $5.25 * b. To find the total cost, you need to subtract the fixed costs of $1,400.00 from this amount. This can be represented by the expression $5.25b - $1,400.00.

The other expressions do not correctly represent the cost of manufacturing b basketballs in 1 day because they do not correctly account for both the fixed costs and the variable costs.

The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the degrees of freedom.

How are the degrees of freedom determined?

Hence, the t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the degrees of freedom.

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Let f(t) be 51000+ (2100)t which represent Chelsea's salary at Company A and g(t) be 45000(1.041)t which Chelsea salary at Company B.

Chelsea's offer from company A includes a raise of $2100 annually and a starting salary of $45,000.

Since the increase is constant, the salary of Chelsea from Company A is a linear function, as can be seen here.

f(t) is salary of chelsea from company A after t years.

f(t) = 45000+ (2100)t

The offer made to Chelsea by company B includes a starting salary of $45,000 and an annual raise of 4.1%.

we can see here that raise is exponential, so raise is:

(1+4.1/100) = (1+0.041) = (1.041) per year.

Consequently, the salary of Chelsea from Company B is a function that is exponential.

g(t) is salary of chelsea from company B after t years.

g(t) = 45000(1.041)t

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For each of the values of GPD, use the regression equation to predict the carbon dioxide emission amount is 1300.715.

What is carbon dioxide ?

Our atmosphere contains carbon dioxide, an odorless and colorless gas. According to its chemical composition, CO2, it is made up of one carbon atom joined to two oxygen atoms. It is a waste product created both by burning fossil fuels and by human bodies.

Given regression eq.

[tex]$$\hat{y}=166.92+115.725$$[/tex]

* Given [tex]$x=2.6$[/tex]

[tex]$$\begin{aligned}& \hat{y}=166.9(2.6)+115.725 \\& \hat{y}=549.665\end{aligned}$$[/tex]

* Given [tex]$x=4.0$[/tex]

[tex]$$\begin{aligned}& \hat{y}=166.9(4.0)+115.725 \\& \hat{y}=783.325\end{aligned}$$[/tex]

* Given [tex]$x=7.1$[/tex]

[tex]$$\hat{y}=166.9(7.1)+115.725$$[/tex]

[tex]\hat{y}=1300.715[/tex]

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The lower estimate and upper estimate of the erupted materials of total q(6) quantity after 6 seconds is equal to 160 metric tons and 218 metric tons respectively.

As given in the question,

Reading of the rate is represented by r(t) in metric tons

Time interval in seconds:

t :       0     1     2       3      4       5       6

r(t) :  2     10    18     32    44     54     60

Lower estimate for the q(6) quantity of the erupted material after 6 seconds.

= r(0)(1) + r(1)(1) + r(2)(1) + r(3)(1)+ r(4)(1) + r(5)(1)

= 2 + 10 + 18 + 32 + 44 + 54

= 160

Upper estimate for the q(6) quantity of the erupted material after 6 seconds.

=  r(1)(1) + r(2)(1) + r(3)(1)+ r(4)(1) + r(5)(1) + r(6)(1)

=  10 + 18 + 32 + 44 + 54 + 60

= 218

Therefore, the lower estimate and upper estimate of the total q(6) quantity after 6 seconds is equal to 160 metric tons and 218 metric tons respectively.

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The area bounded by f(x)=3x³-3x²-x+8, g(x) = 2x³- 10x² + 29x+8

over the interval [1, 5] is 164 square units.

Exactly one element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The domain and codomain of the function are, respectively, the sets X and Y as a whole.

The first presentation of the idea of function that is known about was developed by two Persian mathematicians, Al-Biruni and Sharaf al-Din al-Tusi. Originally, functions were used to depict the desired relationship between two varying values. For example, time affects the position of a planet. Up to the 19th century, the functions that were taken into consideration were differentiable.

Given,

f(x)=3x³-3x²-x+8

g(x) = 2x³- 10x² + 29x + 8

And the interval is  [1, 5].

By using area formula,

A=[tex]\int\limits^a_b {f(x)-g(x)} \, dx[/tex]

A=[tex]\int\limits^a_b[/tex](Upper function-Lower function)dx

A=[tex]\int\limits^3_1[/tex][g(x)-f(x)]dx+[tex]\int\limits^5_3[/tex][f(x)-g(x)]dx

A=[tex]\int\limits^3_1[/tex](-x³-7x²+30x)dx+[tex]\int\limits^5_3[/tex](x³+7x²-30x)dx

A= (118/3)+(374/3)

A=164 square units.

Therefore, the area bounded by f(x)=3x³-3x²-x+8, g(x) = 2x³- 10x² + 29x+8

over the interval [1, 5] is 164 square units.

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Answer:

92 apples remaining

Step-by-step explanation:

2 * 69 = 138 apples

138 * (3/9) =

138 * (1/3) =

138 * 1/3 =

138/3 = 46 apples

138 - 46 = 92 apples remaining

Answer:

you have 2 apples

then you got it 69 times= 2×69 = 138

then you give 3 ninths to a friend

138/9 = 15.33

you gave it 3 one-ninths = 3× 15.33 = 46

so must be left with 138-46 = 92

Answer:

-7 - 4/4

= -7 - 1

= -8

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

-7 - 4/4= -7 - 1= -8