The height of a ball thrown in the air can be described by a parabola. After 3
seconds, the ball reaches the maximum height of 42 feet. If the ball was originally
thrown from a height of 6 feet, find an equation for the height, h(t), of the ball after t
seconds.

After calculating the volume of these two rectangular prisms , we have come to conclude that the total volume of two rectangular prisms is 372 in³.

A rectangular prism is a three-dimensional shape with six faces, all of which are rectangles (top, bottom, and lateral faces) and all pairs of opposite faces are congruent.

A rectangular prism, like all three-dimensional shapes, has volume and surface area. A cuboid is simply another name for a rectangular prism.

A rectangular prism is basically a rectangle,

so the volume = l × b × h

Volume of 1st rectangular prisms = 9 × 6 × 3  

                                                       = 162 in³

Volume of 2nd rectangular prisms = 10 × 7 × 3  

                                                          = 210 in³

Total volume = 162 + 210

                      = 372 in³

Learn more about rectangular prism

https://brainly.com/question/24284033

#SPJ9

Step-by-step explanation:

no calculator at hand ?

f(-3.5) means that we have to replace every x in the function expression by -3.5 and then calculate.

f(-3.5) = (-3.5)² - 5(-3.5) + 6 = 12.25 + 17.5 + 6 = 35.75

The value of integral ₀∫¹ ( eˣ - 2 )² dx is 8 + ( e² - 1) / 2 - 4e.

When infinitesimal data are combined, notions such as displacement, area, and volume can be created. An integral assigns numbers to functions in a way that describes these concepts. Integration is the action of locating integrals.

Consider the integral expression,

₀∫¹ ( eˣ - 2 )² dx

Using ( a + b )² = a² + b² + 2ab

[tex]\int_0^{1}( e^{x} - 2 )^{2} dx = \int_0^{1}(e^{2x}+4-2e^{x})dx[/tex]

[tex]\int_0^{1}( e^{x} - 2 )^{2} dx = \int^0_{1}e^{2x} dx +\int_0^{1}4 dx - \int_0^{1}4e^{x} dx[/tex]

Now, integration of eˣ is eˣ + c where c is constant.

Therefore,

[tex]\int_{0}^{1} ( e^{x} - 2 )^{2} dx = [ \frac{e^{2x}}{2} ]_0^{1} + [ 4x ]_0^{1} - [ 4e^{x}]_0^{1}[/tex]

₀∫¹ ( eˣ - 2 )² dx = ( e² / 2 - e⁰/2 ) + ( 4 - 0 ) - ( 4e¹ - 4e⁰ )

₀∫¹ ( eˣ - 2 )² dx =  e² / 2 - 1/2 + 4 - 4e + 4

₀∫¹ ( eˣ - 2 )² dx = e² / 2 - 4e + 8 - 1/2

₀∫¹ ( eˣ - 2 )² dx =  = 8 + ( e² - 1) / 2 - 4e

Learn more about integrals here:

https://brainly.com/question/27419605

#SPJ9

Answer:x is greater than or equal to 0

Step-by-step explanation:

The condition that will create a biased estimator of a population parameter is D. The expected value of the estimator is not equal to the population parameter.

It should be noted that a parameter is a descriptive measure applied to a whole population. There are numerous population parameters exist. For instance, the population size (N) is one parameter.

For T(x) to be an unbiased estimator of population parameter, it is necessary that the expected value of the estimator is equal to population parameter.

Therefore, the condition that will create a biased estimator of a population parameter is that the expected value of the estimator is not equal to the population parameter.

Learn more about population on:

https://brainly.com/question/25896797

#SPJ1

1. 1/2

2. 3/10

3. 2 and 3/5

4. 1 and 7/12

5. 1 and 1/3

Answer:

Wish i could help

Step-by-step explanation:

The co-ordinates of the y-intercept is (0,-9) .

Y-intercept is the point on the graph where the graph passes over the y-axis.

To calculate the y-intercept we have to graphically represent the curve and pick out the points where the graph crosses over the x-axis.

For a graph with an equation in the form y = f(x) , y intercept can be calculated by substituting the value of x as 0 in the equation.

In the graphical representation we can see that the graph passes through  (- 8, 3) and (- 3, - 4.5).

Therefore the slope of the line passing through these points is given by:

[tex]m=\frac{-4.5-3}{-3-(-8)} \\\\m=\frac{-7.5}{5} \\\\m=-\frac{3}{2}[/tex]

Now the equation of the line is given by :

[tex]y-3 =- \frac{3}{2} (x-(-8))[/tex]

[tex]y-3 =- \frac{3}{2} x - 12[/tex]

[tex]y=- \frac{3}{2} x - 9[/tex]

Therefore at x = 0 , the value of y is -9.

So the y-intercept is given by the point (0,-9) .

to learn more about the y-intercept visit:

https://brainly.com/question/14180189

#SPJ1

The coordinates of the y-intercept are ( 0 , 9 / 5 ) .

Finding equation of line :

( y - 3 ) / ( x + 8 ) = ( 3 + 4.5 ) / ( - 8 + 3 )

( y - 3 ) / ( x + 8 ) = ( 7.5 ) / ( - 5 )

- 5 y + 15 = 7.5 x + 6

- 5 y - 7.5 x + 9 = 0

Equation of line : 5 y + 7.5 x - 9 = 0

Writing equation in Slope - Intercept form

y = m x + c

y = [ ( - 7.5 x ) / ( 5 ) ] + [ 9 / 5 ]

Hence , y - intercept = 9 / 5 .

To learn more on y - intercept follow link :

https://brainly.com/question/10700419

#SPJ1

Answer:

Step-by-step explanation:

-6+2y=10

2y=10+6

2y=16

2y/2=16/2

y=8

so the final answer of first question is y=8

The next one is

6x-2y=-10

as we got from the first question y=8 so

6x-2(8)=-10

6x-16=-10

6x=-10+16

6x/6=6/6

so the final answer is 1

Answer:

x = 0

Step-by-step explanation:

Let's solve the problem,

→ (x/9) + 8 = 8

→ x/9 = 8 - 8

→ x = 0 × 9

→ [ x = 0 ]

Thus, the value of x is 0.

Answer:

Step-by-step explanation:

21 divided by 7 is 3 so 3 minus 10 is negative 7

The solution is : 7 when subtract the quotient of 21 and 7 from 10.

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

given that,

the quotient of 21 and 7

i.e. we have to divide 21 by 7

i.e. 21/7 = 3

so, we get,

the quotient of 21 and 7 is 3

now, we have to Subtract 3 from 10

i.e. 10 - 3

= 7

so, we get,

21 divided by 7 is 3 so 10 minus 3 is  7.

Hence, The solution is : 7 when subtract the quotient of 21 and 7 from 10.

To learn more on subtraction click:

brainly.com/question/2346316

#SPJ2

Answer:

5/8 of pizza left

Step-by-step explanation:

The error led to the incorrect difference is-

meghan and hopsida do their math homework together

To find,

           5 - (-8)

meghan's answer was incorrect.

meghan put the neagative sign before 13 that's why there was difference in the answer.

Definition for difference in Math

distinction in math is the result of one of the essential mathematical operations, that is obtained by using subtracting  numbers. It tells us by means of how lots a range of differs from the other.

How do you find difference in math?

a way to locate the difference among two Numbers. To discover the difference among  numbers, subtract the number with the smallest value from the wide variety with the biggest cost. The fabricated from this sum is the distinction between the 2 numbers. consequently the distinction between forty five and one hundred is fifty five.

To learn more about difference https://brainly.com/question/17057903

#SPJ9

The amount of bacteria after 12 hours would be 8 grams

Rate can be defined as  the ratio between two quantities that are related in size but may be in different units.

It is also known as the ratio of comparison between quantities of different units.

From the information given, we have that;

To determine the amount of bacteria after 12 hours, we have;

= 12 × 15/ 100

multiply and find quotient

= 1. 8

In 12 hours, the amount of bacteria is ;

= 6 + 1. 8

= 7. 8 grams

= 8 grams

Thus, the amount of bacteria after 12 hours would be 8 grams

Learn more about rate here:

https://brainly.com/question/19493296

#SPJ1

Answer: 105 degrees

Step-by-step explanation:

two sides of a trapezoid add up to 180 degrees

180 - 75 = 105

The value of y' according to the given equation in the task content is; 1.

According to the task content, it follows that the equation given is; 2x³y - 3x² = 4y'.

On this note, the value of y' can be determined by substituting the given values of x and y as follows;

2(2)³×1 - 3(2)² = 4y'

16 - 12 = 4y'

y' = 4/4

y' = 1.

Read more on solving equations;

https://brainly.com/question/25678139

#SPJ1

the slope is represented by m

the x coordinate of the ordered pair is x1

the y coordinate of the preferred pair is y1

y-y1=m(x-x1)

Answer:

x = -36

Step-by-step explanation:

Subtract 9 from 3.2(x−6)=14⋅−6

Multiply 14 by −6.2(x−6)=−84

Divide each term

Simplify the left side.

Move all terms not containing x to the right side of the equation.

x = -42 + 6

Add -42 & 6

x = -36

The value of x in the equation x = [a^2 + a^2]/[ab + 1] is [2a^2]/[ab + 1]

Equations are mathematical expressions that are represented by the equal to or equality sign i.e =

Examples of equations are:

a + b = c

y = mx + c

Ax + By = C

y = ax^2 + bx + c

y =  x

The equation is given as

x = [a^2 + a^2]/[ab + 1]

To start with, we evaluate the like terms i.e. we add a^2 and a^2

This is represented as

a^2 + a^2 = 2a^2

Substitute 2a^2 for a^2 + a^2 in the given equation

So, we have

x = [2a^2]/[ab + 1]

The above equation cannot be further simplified

Hence, the value of x in the equation x = [a^2 + a^2]/[ab + 1] is [2a^2]/[ab + 1]

Read more about equations at

https://brainly.com/question/13763238

#SPJ1

[tex]y = x {}^{2} - 8x + 12 \\ y = x {}^{2} - 8x + 12 + 4 - 4 \\ y = (x {}^{2} - 8x + 16) - 4 \\ y = ( x - 4)^{2} - 4[/tex]

The number of minutes of each medium should be used to minimize costs if television costs $900/minute and radio costs $200/minute is 45 minutes and 3.33 minutes respectively.

x ≥ 0

y ≥ 0

x + y ≤ 80

0.09x + 0.006y ≤ 2.16

From (1)

x ≤ 80 - y

0.09x + 0.006y ≤ 2.16

0.09(80 - y) + 0.006y ≤ 2.16

7.2 - 0.09y + 0.006y ≤ 2.16

7.2 - 0.084y ≤ 2.16

-0.084y ≤ 2.16 - 7.2

-0.084y ≤ -5.04

y ≤ -5.04 / -0.084

y ≤ 60

x + y ≤ 80

x + 60 ≤ 80

x ≤ 80 - 60

x ≤ 20

The number of minutes of each medium should be used to minimize costs if television costs $900/minute and radio costs $200/minute is

Television = $900 / 20

= 45 minutes

Radio = $200/60

= 3.33 minutes

Learn more about inequality:

https://brainly.com/question/25275758

#SPJ1

The equations which have no solution are choices A, B, C and D.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. It will be regarded as a phrase.

To learn more about equations, visit :

brainly.com/question/2972832

#SPJ9

Answer:

[tex]7x + 5y \leqslant 30[/tex]

Answer:

3 heartbeats per sec.

Step-by-step explanation:

Number of heartbeats / Total time will give the rate or number of heartbeats per sec.

According to the solving the amount should be invested in each account should be :$500.

A borrower as well as deposit-taking financial organization paying interest to a lender or depositor on an amount in excess of the original payment at a specified rate. It is not the same as a fee paid by the borrower to the lender or a third party.

Debit your Interest Expense account and credit our Accrued Interest Payable account to record the accrued interest for an accounting period. This increases the value of your expenditure as well as payable accounts.

Let the amount invested at 5 be x.

Let the amount invested at 6% be 2000 - x.

Interest on 5% will be 0.05

Interest on 6% will be 6%(2000 - x) = 120 - 0.06x

This will be:

0.05x + 120 - 0.06x = 105

- 0.01x = -15

x = 1500

The amount invested at 6% will be:

= 2000 - 1500

= 500

To know more about interest visit:

https://brainly.com/question/13324776

#SPJ9