If f(x) is an exponential function where f(3.5)=10 and f(9.5)=30, then find the value of f(12), to the nearest hundredth

Answer:

Step-by-step explanation:
Let's represent the missing number with "---" -- so we have so far:

--- --- --- 30 --- --- 128 --- ---  ?
Now, let's say 5th position number is x and 6th position number is y
So, we have 30 + x = y and x+ y = 128
Combining these 2 equation, we get: x + 30 + x = 128 or x = 49, so y = 79

thus from 4th position, the series can be written as
30, 49, 79, 128, 207, 335, 542....
Thus, at 10th position we will have 542 !!!

Answer:

v = 113.04 [tex]units^{3}[/tex]

Step-by-step explanation:

v = 4/3[tex]\pi r^{3}[/tex]

v = 4/3[tex]\pi 3^{3}[/tex]

v = 113.04 [tex]units^{3}[/tex]

1. 80 people attended only the FSU-Butler game.

2. 165. Since it's not possible to have negative number of people, the answer is 0.

3. 210 people attended at least two of these games.

4. 340 people attended the Marist and Butler games, but not the North Carolina State game.

5. 365 people attended the North Carolina State or the Butler game

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The value of the variable x for the given f(x) = 2 by simplifying the antiderivative of  the given function is given by x = 0.4865.

As given in the question,

Given anti derivative of f(x)  :

For the limit 0 to x for the integration of e^4t with respect t

= [tex]\int\limits^x_0 {e^{4t} } \, dt[/tex]

= ( 1/4) e^4x  + ( 1/4 )

Value of the function f (x)  = 2

Now f(x) = 2

Substitute the value of the function f(x) we get,

( 1/4) e^4x  + ( 1/4 ) = 2

⇒ e^4x + 1 = 8

⇒ e^4x = 7

⇒x = log7 / 4

⇒ x= 0.4865

Therefore, the value of the x by simplifying the antiderivative function f(x) for the given f(x) = 2 is equal to 0.4865.

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The volume of the solid is equal to the integral of the area of the semi-circular cross sections multiplied by the length of the interval. The area of the semi-circular cross sections is equal to πr²/2, where r is the diameter running from y. Therefore, the volume is equal to π/2∫0,9r²dy.

Step 1: Substitute the expression for the area of the semi-circular cross section into the equation for the volume of the solid:

V = π/2∫0,9r²dy

Step 2: Integrate the equation to find the volume of the solid:

V = π/2[y³/3]|0,9

Step 3: Evaluate the integral:

V = π/2(9³/3 - 0³/3)

step 4: Solve for the volume of the solid:

V = 7π/2

The volume of the solid is equal to the integral of the area of the semi-circular cross sections multiplied by the length of the interval. The area of the semi-circular cross sections is equal to πr²/2, where r is the diameter running from y. Therefore, the volume is equal to π/2∫0,9r²dy. To calculate the volume, we must first substitute the expression for the area of the semi-circular cross sections into the equation for the volume of the solid: V = π/2∫0,9r²dy. Then, we must integrate the equation to find the volume of the solid: V = π/2[y³/3]|0,9. After that, we must evaluate the integral: V = π/2(9³/3 - 0³/3). Finally, we must solve for the volume of the solid: V = 7π/2. The answer is the volume of the solid is 7π/2.

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Answer:

0

Step-by-step explanation:

I believe this is correct. Since they don't have the same sign then you will just have to subtract them.

Answer: 6

Step-by-step explanation:

When opposite sides of a quadrilateral is equal then the quadrilateral is Parallelogram. (PA = RT and PT = AR)

A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

A quadrilateral is a specific type of polygon known as a parallelogram if it contains two parallel opposed sides. A parallelogram has the following qualities:

Each coordinate of the Parallelogram :

P (-3, 0) , A(3, -1) , R ( 2, -5) and T(-4, -4)

Length of PA = √((3 + 3)² + (-1 - 0)²) = √(36 + 1) = √37

Lenght of TR = √((-4 - 2)² + (-4 + 5)²) = √(36 + 1) = √37

Length of PT = √((-3 + 4)² + (0 + 4)²) = √(16 + 1) = √17

Length of AR = √((3-2)² + (-1 + 5)²) = √(16 + 1) = √17

Here, PA = RT and PT = AR ,

so when opposite sides of a quadrilateral is equal then the quadrilateral is Parallelogram.

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[tex]44+\cfrac{7}{8}r\implies 44+\cfrac{7}{8}\left( -\cfrac{1}{2} \right)\implies 44-\cfrac{7}{16}\implies \cfrac{(16)44~~ - ~~(1)7}{\underset{\textit{we'll use this LCD}}{16}} \\\\\\ \cfrac{704~~ - ~~7}{16}\implies \cfrac{697}{16}\implies 43\frac{9}{16}[/tex]

Using Trigonometric ratios, the value of missing angle is 60.45°.

There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

If we draw an imaginary line dividing the given triangle in 2 equal parts,

we will get 2 right angled triangles.

So, using trigonometric ratios,

Sin θ = Perpendicular / hypotenuse

⇒ Sin 70 ° = perpendicular / 14

⇒ 0.94 = perpendicular / 14

⇒ perpendicular = 0.94 × 14

⇒ perpendicular = 13.16

Now the other right angled triangle is

Sin θ = Perpendicular / hypotenuse

⇒ Sin θ = perpendicular / 15

⇒  Sin θ = 13.16 / 15

⇒ θ = sin⁻¹(13.16 / 15)

⇒ θ = sin⁻¹(0.87)

⇒ θ = 60.45

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The wheel of the car makes 500.5 revolution per minute

frequency is defined as the number of oscillation or revolution made in one seconds. It measured in Hertz. frequency is denoted as F. And it is expressed as :

F = w/2π

Where w = angular velocity and

2π = 360 which is also a revolution

to calculate w ;

v = wr

r = 35cm = 0.35m

v = 66km/h = 66×1000/60

v= 1100m/mins

therefore from the relation, v = wr

w = v/r

w = 1100/0.35

w = 3142.9rad/mins

therefore F = w/2π

F = 3142.9/ 2×3.14

F = 500.5 revolution per minute

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The inverse demand function is P = 2400 + 5Q

Given that

Q = 480 - 0.2P

We simply make P the subject of the formula

So, we have

0.2P = 480 - Q

Divide by 0.2

P = 2400 + 5Q

To find the marginal revenue function, we can use the inverse demand function P = 2400 + 5Q, and take the derivative of this function with respect to Q.

The derivative of P with respect to Q is dP/dQ = 5. This represents the change in price for a one unit change in the quantity of operations performed.

So the Marginal Revenue function is MR = dP/dQ * Q = 5Q

To maximize profit, the doctor should equate marginal revenue to marginal cost, which is

MC = dAVC/dQ

So, we have

MC = d(2Q² - 15Q + 400)/dQ

Evaluate

MC = 4Q - 15.

So, we have

5Q = 4Q - 15

Q = -15

Take the absolute value

Q = 15

So, the number of operations is 15

We have

P = 2400 + 5Q

This gives

P = 2400 + 5 * 15

Evaluate

P = 2475

To find the profit, we need to subtract the total cost from the total revenue.

The total revenue is found by multiplying the price by the quantity of operations performed: TR = P * Q = 2475 * 15 = 37125

The total variable cost is found by multiplying the average variable cost by the quantity of operations performed: TVC = AVC * Q = (2Q^2 - 15Q + 400) * Q = 2Q^3 - 15Q^2 + 400Q

The total fixed cost is the fixed cost that doesn't change regardless of the level of output : TFC = $8000

The total cost is the sum of the total variable cost and total fixed cost: TC = TVC + TFC = 2Q^3 - 15Q^2 + 400Q + $8000

The profit is the difference between total revenue and total cost:

π = TR - TC = 37125 - (2Q^3 - 15Q^2 + 400Q + $8000)

When Q = 15,

profit is π = 37125 - (2(15)^3 - 15(15)^2 + 400(15) + $8000)

= 19750

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Relative to the mean, there are some school districts where many students are using ipads.

What is called the mean?

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. It is sometimes referred to as the "average" and is the most widely used central tendency metric.

Simply dividing the total number of values in a data set by the sum of all of the values yields it. The calculation can be performed on unprocessed data or data that has been combined into a frequency table.

By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.

Mean: The "average" number; found by adding all data points and dividing by the number of data points. Example: The mean of 4, 1, and 7 is ( 4 + 1 + 7 ) / 3 = 12 / 3 = 4 (4+1+7)/3 = 12/3 = 4 (4+1+7)/3=12/3=4left parenthesis, 4, plus, 1, plus, 7, right parenthesis, slash, 3, equals, 12, slash, 3, equals, 4.

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The total profit of F_1 in the week was $25920 and the total profit of F_2 in the week was $0.

The profit vector can be expressed as p = [35 62 30]. The total profit of F_1 and F_2 can be calculated by multiplying the matrix A by the vector p. The result, Ap, is a vector whose components give the total profits of the two stores in the week.

For example, the total profit of F_1 can be calculated as Ap_1 = [35 62 30] * [400 60 240] = [14000 3720 7200] = 25920.

Similarly, the total profit of F_2 can be calculated as Ap_2 = [35 62 30] * [0 0 0] = [0 0 0] = 0.

Therefore, the total profit of F_1 in the week was $25920 and the total profit of F_2 in the week was $0.

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The length of the air strip is 451feet

Perimeter is the sum of length of the sides used to made the given figure. A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthed n sides).

Given;

Perimeter= 8876feet

Let the length be x

and the width be y

Then, length will be x= 10+35y

Perimeter of rectangle= 2l+2b

8876=2(10+35y)+y

8876=20+700y+y

y=12.6

x=10+35y

x=451

Therefore, the length by the given perimeter will be 451feet

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To calculate the dollar amount billed to the insurance plan:

What's the math rate?

A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. Cents and ounces are the two dissimilar units in this ratio.

$340.00 (total charge for office visit) x 75% (insurance reimbursement rate) = $255.00

To calculate the amount the patient must pay:

$340.00 (total charge for office visit) x 25% (patient responsibility rate) = $85.00

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The value of the expression → p(q(-1)) will be → 5.

        [tex]${\displaystyle \forall x\in X,\forall y\in Y,\forall z\in Y,\quad ((x,y)\in R\land (x,z)\in R)\implies y=z.}[/tex]

        [tex]${\displaystyle \forall x\in X,\exists y\in Y,\quad (x,y)\in R.}[/tex]

Given are the graphs of two function as shown in the image.

We have to find -

p(q(-1))

Now, we can see from the graph that -

q(-1) = -2

Then, p(q(-1)) will be -

p(-2) = 5

Therefore, the value of the expression → p(q(-1)) will be → 5.

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The chef needed a) 3¾ cups of lemon juice and b) 20 pints olive oil for the larger batch.

A mixed fraction is one that has both its quotient and remainder represented. A mixed fraction like 2 1/3 is one where the remainder is 1 and the quotient is 2. Therefore, a mixed fraction is made up of both a whole number and a correct fraction.

The recipe was for 4 person, but now here are 40

The scale multiple is = 40/4

                                   = 10

a) As 1 cup = 16 tablespoon

The number of tablespoon of lemon required for 40 men = 6 × 10

                                                                                                 = 60

Converting to cup = 60/16

                              = 3¾ cups

b) As 1 cup = 0.5 pints

The number of cups of olive oil required for 40 men = 1 × 10

                                                                                        = 10

Converting to pints = 10/0.5

                              = 20 pints

Thus, The chef needed 3¾ cups of lemon juice and 20 pints olive oil for the larger batch.

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Answer:

  (3n +8) -3n = 8

Step-by-step explanation:

You have the difference (3n+15) -7, and you want its value when it is decreased by the triple of the original number (n).

The phrase "triple the original number" will be translated to 3n. This is the value you want to subtract.

  (3n +15) -7 = 3n +8 . . . . . "the difference"

  (3n +8) -3n = 8 . . . . . . . . "decreased by triple the original number"

This simplifies to 8, which is the point of the exercise: showing the sequence of steps always gives a value of 8.

T = si is an expression that can be used to represent the party's projected cost.

T = si is an expression that can be used to represent the party's projected cost.

It should be remembered that expressions depict how variables relate to one another.

We can use the following phrase to obtain an estimated party cost:

T = s×i

where:

T is the ice cream party's overall budget.

s is the number of ninth-graders.

I = the ice cream unit price.

discover more on expressions;

All ninth graders are invited to an ice cream celebration as a prize for accomplishing their goals.

1) Write an expression that could represent an estimated cost for the party. Use at least one letter. State what each part of the expression represents.

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Answer: 50

Step-by-step explanation:

You can plug in 4 for any of the equations given.

y = 10 + 10(4)

y = 10 + 40

y = 50

OR

y = 30 + 5(4)

y = 30 + 20

y = 50

Answer:

y = 50

Step-by-step explanation:

Since x = 4, plug the value into either equation.

[tex]y =10+10x\\y = 10 + 10(4)\\y=10+40\\y=50[/tex]

Therefore, y equals 50.

When working with word problems, students should first read the problem and decide if it is a one-step or two-step problem.

A one-step problem involves solving for a single unknown quantity, such as finding the total cost of 10 pencils at $0.50 each. The formula for this would be C = Pn, where C is the cost, P is the price, and n is the number of items. To solve this problem, the student would multiply the price and number of items, so C = 0.50 x 10 = $5.00. A two-step problem involves solving for two unknowns, such as finding the total cost of 10 pencils at a 10% discount. The formula for this would be C = Pn (1 - r), where r is the discount rate. To solve this problem, the student would first calculate the discount by multiplying the price and number of items by the discount rate, so C = 0.50 x 10 x 0.10 = $0.50. Then the student would subtract the discount from the total cost, so C = 0.50 x 10 - 0.50 = $4.50.

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The total number of seats in the auditorium is 3500.

What is the arithmetic series?

An arithmetic series is a sequence of numbers in which the difference between any two consecutive terms is always the same. It can also be defined as a sum of a finite number of terms of an arithmetic progression.

The seating capacity of the auditorium can be found by using the formula for the sum of an arithmetic series.

The formula for the sum of an arithmetic series is:

S = n/2 (2a + (n-1)d)

Where:

S is the sum of the series (total number of seats)

n is the number of terms in the series (number of rows of seats)

a is the first term in the series (number of seats in the first row)

d is the common difference between terms in the series (increase in number of seats per row)

In this case,

a = 20 (number of seats in the first row)

d = 25 - 20 = 5 (increase in number of seats per row)

n = 35 (number of rows of seats)

So,

S = 35/2 (2(20) + (35-1)(5))

S = 35/2 (40 + 160)

S = 35/2 (200)

S = 35*100

S = 3500

Hence, the total number of seats in the auditorium is 3500.

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Answer:

10%

Step-by-step explanation:

if the volume of the water increase by 10 when turns to

ice so it must be decrease by 10 if it changes to water again

The correct answer is This study demonstrates clearly that seat belts save children from injury.

Given that,

According to an analysis of the 27,000 child passenger vehicle incidents in Michigan with records currently available, around 10% of children who were wearing seatbelts (group SB) and 15% of children who were not (group NSB) sustained injuries. Which of the following statements is NOT appropriate for a report summarizing this study?

Options are :

(A)Driver conduct could be a complicating variable.

(B) The location of the youngster in the vehicle could be a complicating variable.

(C) Since this study was not an experiment, drawing conclusions about causes and effects is not appropriate.

(D) This study amply demonstrates how seat belts protect kids from harm.

(E) It is dangerous to draw the conclusion that seatbelts protect kids from harm, at least until the study is independently reproduced.

So,The correct answer is This study demonstrates clearly that seat belts save children from injury.

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A Gallup poll conducted in April found that 55% of Americans believe driverless cars will be common in the next 10 years, as presented in a histogram showing the percentage of responses in different time intervals.

A Gallup Poll was conducted in April that surveyed adults aged 18 or older to gauge their perceptions on when fully automated "driverless cars" will be commonly used in the United States.

The question asked was "how soon do you think driverless cars will be commonly used in the United States?" The survey indicated that 55% of Americans believe that driverless cars will be common in the next 10 years.

The results of the survey were presented in a histogram, showing the percentage of responses in different time intervals, which means it shows how many people responded within a certain time frame (e.g. within 5 years, within 10 years, etc.) when they think driverless cars will be commonly used.

This poll gives an insight into how people perceive the future of driverless cars and how soon they think it will become a common sight on the roads.

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The question is -

A Gallup Poll utilizing a random sample of adults ages or older was conducted in April. The survey indicated a majority of Americans () say driverless cars will be common in the next years (). The question asked was: Thinking about fully automated, "driverless cars," cars that use technology to drive and do not need a human driver, based on what you have heard or read, how soon do you think driverless cars will be commonly used in the [United States]? The figure below shows a summary of the results of the survey in a histogram indicating the percentage of the total responses in different time intervals.

The grams of sugar that is in Stefanie's syrup = 3.60g

The grams of sugar that is in John's syrup = 7.50g

The quantity of sugar syrup that Stefanie has = 18grams

The percentage of sugar syrup that is sugar = 20%

That is, 20/100 × 18

= 360/100

= 3.60g

The quantity of sugar syrup that John has = 30 g

The percentage of sugar syrup that is sugar = 25%

That is;

= 25/100 × 30

= 750/100

= 7.50g

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The P-value of the test is the probability of observing a sample proportion of 80/100 or less, given that the null hypothesis is true.

This can be calculated using the formula P(X <= x) = Σ (n x) p^(x) q^(n-x), where n = 100, x = 80, p = 0.75 and q = 1-0.75. Following this formula, the P-value of the test is calculated to be 0.0009. This means that there is a 0.0009 probability of observing a sample proportion of 80/100 or less, given that the null hypothesis is true. Therefore, the data provide convincing evidence that the proportion of people who lose their balance while standing on one foot and closing their eyes is less than 75%.The P-value of the test is the probability of observing a sample proportion of 80/100 or less, given that the null hypothesis is true.

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