Using the F’(x) Graph shown, find the Integral from 0 to 1 F’(x)dx if f(5) = -7.8, and f(0) = 3.

Answer:5/8

Step-by-step explanation: you put the numbers in a fraction the smallest goes on top and the more enormous number at the bottom you simply by finding the most significant standard number between the 2 numbers which is in this case 6 divide it by that and that is how you get your answer

Answer:

6.9x10^20

Step-by-step explanation:

688588478685758486759+2345678909876545355=

6.90934158E20

The difference between the investment below and one with the same principal at the same rate compounded yearly is $18123.29.

The Payback Period is the most straightforward metric to use when contrasting investment options. Simply defined, this is the minimal amount required for you to recoup your initial investment.

compound interest, which is referred to as

[tex]A = P(1+r/n)^n×t[/tex]

Where

A = amount at the end of t years

r = interest rate.

n = periodic interval

P = principal amount deposited

Considering  investment compounded annually

P = 7000

r = 3% = 3/100 = 0.03

n = 1

t = 17 years

[tex]A = 7000(1 + 0.03/1)^1× 12A = 7000(1.03)^12[/tex]

A = $9980.32

For the second investment,

n = 6

[tex]A = 7000(1 + 0.08/6)^6 × 12A = 7000(1 + 0.0133)^72A = 7000(1.0133)^72A = $18123.29[/tex]

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If a least square regression line fits the data well, the characteristic should the residual plot exhibit is random scatter

The least squares regression line fits the data well.

The least squares regression is defined as the method that used to find the regression line or best suitable line for the given pattern

So if the data shows a linear relationship between the two given variable so such line will be called least squares regression line

The residual plot is the measure that vertical line how much misses from the data point

Here the least square-square regression lines fits the data well so the characteristics will be random scatter

Therefore, the characteristic that the residual plot exhibit is random scatter

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Answer:

-4

Step-by-step explanation:

Answer:

f(0) = 4

Step-by-step explanation:

[tex]f(x) = {2x}^{2} + 4[/tex]

- When x = 0, then f(x) = f(0)

[tex]f(0) = 2(0) {}^{2} + 4 \\ f(0) = 4[/tex]

Step-by-step explanation:

the answer for -1/4(-8x+12y)

2x-3y

Answer:

2x-3y

Step-by-step explanation:

For this equation we are using distributive property

-1/4(-8x)           -1/4(12y)

     ↓                      ↓

    2x                   -3y

So, 2x-3y is the answer.

Answer:Rewrite the equation in vertex form.

Tap for more steps...

y

=

4

(

x

−

1

)

2

−

9

Use the vertex form,

y

=

a

(

x

−

h

)

2

+

k

, to determine the values of

a

,

h

, and

k

.

a

=

4

h

=

1

k

=

−

9

Since the value of

a

is positive, the parabola opens up.

Opens Up

Find the vertex

(

h

,

k

)

.

(

1

,

−

9

)

Find

p

, the distance from the vertex to the focus.

Tap for more steps...

1

16

Find the focus.

Tap for more steps...

(

1

,

−

143

16

)

Find the axis of symmetry by finding the line that passes through the vertex and the focus.

x

=

1

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Givens:

A (2,3)

B (4,2)

C (3,5)

1. Subtract each x and y value by 4: (x-4,y-4)

A (-2,-1)

B (0,-2)

C (-1,1)

2.  Flip the x and y values: (y,x)

A (3,2)

B (2,4)

C (5,3)

3. Multiply each point by 1.5: (1.5x,1.5y)

A (3,4.5)

B (6,3)

C (4.5,7.5)

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps! :)

━━━━━━━━━━━━━━━━━━━━━━━━━━

Answer:

[tex] \sf \: n = - 3[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of n.

The equation is,

→ 2 - 2n = 3n + 17

Then the value of n will be,

→ 2 - 2n = 3n + 17

→ 2 - 17 = 3n + 2n

→ -15 = 5n

→ 5n = -15

→ n = -15 ÷ 5

→ [ n = -3 ]

Hence, the value of n is -3.

The graph that best models the situation of the home value increasing every year is Graph A

To find the graph, use the percentage increase to find the value of the house in two different time periods and then check which graph coincides with this prediction.

After 5 years, the value of the house should be:

= 200, 000 x ( 1 + 6 % ) ⁵

= $ 267, 645

After 10 years :

= 200, 000 x ( 1 + 6 % ) ¹⁰

= $ 358, 170

The best graph for the situation is therefore Graph A which starts from $ 200, 000 and passes through the above points.

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The weighted mean cost of a haircut for Malachi is $15.67, divided by the total number of haircuts, which comes to 6, to yield a total cost of $94.00.

We must compute the total cost of all haircuts and divide it by the total number of haircuts in order to determine the weighted mean price of a haircut for Malachi. The expense of each haircut must be weighed according to the frequency with which it occurred, though, because they varied in price.

To begin, let's figure out how much each haircut will cost overall:

2 haircuts at $12.00 each = $24.00

3 haircuts at $15.00 each = $45.00

1 haircut at $25.00 = $25.00

Total cost = $24.00 + $45.00 + $25.00 = $94.00

Next, We must determine the total number of cuts:

2 haircuts + 3 haircuts + 1 haircut = 6 haircuts

Finally, The weighted mean cost of a haircut can be determined by dividing the total cost by the total number of haircuts:

The weighted mean cost of a haircut = Total cost / Total number of haircuts

= $94.00 / 6 haircuts

= $15.67 per haircut (rounded to the nearest cent)

Therefore, Malachi's weighted mean haircut expense is $ 15.67 , divided by the total number of haircuts, which comes to 6, to yield a total cost of $94.00.

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The percentage of decrease in the amount of land that Simon owns is 20.1%.

1,510 - 1,208 = 302

302 / 1,510 = 0.201

0.201 x 100 = 20.1%

Simon recently sold his old farmland, which was 1,510 acres in size, and purchased a new plot of land that is 1,208 acres in size. To calculate the percent of decrease in the amount of land that Simon owns, we subtract the new land size from the old land size and divide the result by the old land size. This number is then multiplied by 100 to get the percent of decrease. In this case, we subtract 1,208 from 1,510 to get 302. We then divide 302 by 1,510 to get 0.201. When we multiply 0.201 by 100, we get 20.1%, which is the percent of decrease in the amount of land that Simon owns now.

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The correct interpretation of the 90% confidence interval is given as follows:

There is a 90% chance that the true proportion of teenagers who drive their own car to school will be (0.5907, 0.9093).

It means that it is x% likely that the true population parameter(mean/proportion/standard deviation) is between a and b, which are the bounds of the confidence interval.

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Answer:

(- 12x ^ 2 + 8x + 27y)/(3x * y ^ 2)

Step-by-step explanation:

The required number of markers does Gerald has 56 markers.

Let's represent the number of markers that Gerald has with the variable "m", and the number of pens he has with the variable "p". We can set up two equations based on the information given:

m + p = 78 (equation 1)

(m + 11) + (p + 11) = 78 (equation 2)

In equation 2, we add 11 to both the number of markers and the number of pens, since Gerald has 11 more of each. We can simplify equation 2 by combining like terms:

m + p + 22 = 78

m + p = 56 (equation 3)

Now we have two equations with two variables. We can use either substitution or elimination to solve for one of the variables. Let's use substitution and solve for "m" in terms of "p" using equation 1:

m + p = 78

m = 78 - p

Now we can substitute this expression for "m" into equation 3:

m + p = 56

(78 - p) + p = 56

Simplifying the equation, we get:

78 - p + p = 56

78 = 56 + p

p = 22

Therefore, Gerald has 22 pens. To find the number of markers he has, we can substitute this value of "p" into equation 1:

m + 22 = 78

m = 56

So, Gerald has 56 markers.

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To solve the equation cos²x + sin x = 1, we can use the trigonometric identity cos²x = 1 - sin²x. By substituting this identity into the equation, we get:

1 - sin²x + sin x = 1

Combining like terms, we get:

1 - sin²x = 0

Solving for sin x, we get:

sin x = 1

However, the sine function has a range of [-1, 1], so the only solution in the interval [0, 2π] is sin x = 1, which corresponds to x = π/2. So the solution to the equation cos²x + sin x = 1 in the interval [0, 2π] is x = π/2.

Answer:

answer is A

Step-by-step explanation:

because area of a rectangle is L × B

or length × width

since the length is expanded by x

10.5 (12x)

Answer:

Option C

Step-by-step explanation:

The original length of the room = 12 feet

After expansion, the new length = [tex](12 + x)[/tex] feet

Width of the room = 10[tex]\frac{1}{2}[/tex] feet = 10.5 feet

Area of a rectangle = Length × Width

The shape of the living room is a rectangle.

∴Area of living room = [tex](12 + x)[/tex] feet × [tex](10.5)[/tex] feet  
                                     [tex]= 10.5(12 + x)[/tex] square feet

Expand the brackets or parenthesis by applying the Distributive Law:

                                  [tex]= (12)(10.5) + (10.5)(x)[/tex] square feet

                                  = [tex](125 + 10x)[/tex] square feet

∴Option C

Answer:

3/8

Step-by-step explanation:

1. If there are three parts green and 5 parts yellow, you can add them to find the total parts

2. 5+3 is 8

3. Then to find the green, which is three, we can divide it

4. 3 green parts/ total which is 8

5. 3/8

Un-simplified rate of dollars-gallons = 22.5/9  $ and and gallons to dollars 9/22.5 $ .  and simplified rate of dollars-gallons = 22.5/9  $ = 2.5 and and gallons to dollars 9/22.5  = 0.4 .

Here first we have to calculate the rate of gallons of gas as per gallons so for that we will find the rate of 1 gallons for that we will divide the  22.4$ to 9 gallons so ans is 22.5$/9 is the rate for 1 gallons

and 2nd we have to calculate the amount of gas as per $ like we have to calculate the the amount if we spend 1 $  so for that we will divide 9 gallons / 22.5$ = 9/22.5

And here in 1st part we  are not calculate the ans in decimal as we have to calculate this on un-simplified  ans .

and in 2nd part we calculate it .

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Answer:

[tex]-22.8[/tex]

Step-by-step explanation:

[tex]\int^{1}_{0} f'(x) \text{ } dx=f(1)-f(0)=f(1)-3 \\ \\ \\ B=\int^{5}_{1} f'(x) \text{ } dx=12 \implies f(5)-f(1)=12 \\ \\ -7.8-f(1)=12 \implies f(1)=-19.8 \\ \\ \therefore f(1)-3=-19.8-3=-22.8[/tex]

By algebra properties and trigonometric formulas, the trigonometric expression (1 + cos x) / (1 - cos x) - (1 - cos x) / (1 + cos x) is equivalent to trigonometric expression 4 · cos x · csc² x.

In this problem we need to prove the equivalence between two trigonometric expressions, this can be done by using algebra properties and trigonometric formulas. First, write one side of the expression:

(1 + cos x) / (1 - cos x) - (1 - cos x) / (1 + cos x)

Second, use algebra properties to simplify the expression:

[(1 + cos x)² - (1 - cos x)²] / (1 - cos² x)

Third, expand the resulting expression:

(1 + 2 · cos x + cos² x - 1 + 2 · cos x - cos² x) / (1 - cos² x)

4 · cos x / (1 - cos² x)

Fourth, use trigonometric formulas to simplify the expression:

4 · cos x / sin² x

4 · cos x · csc² x

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Answer:

see explanation

Step-by-step explanation:

given sinΘ = - [tex]\frac{3}{5}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]

the negative sign indicates sinΘ is in the third quadrant where sinΘ < 0

this is a 3- 4- 5 right triangle with opposite = 3 and hypotenuse = 5

then the adjacent side = 4

cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = - [tex]\frac{4}{5}[/tex] ( since cosΘ < 0 in third quadrant )

secΘ = [tex]\frac{1}{cos0}[/tex] = [tex]\frac{1}{-\frac{4}{5} }[/tex] = - [tex]\frac{5}{4}[/tex]

tanΘ

= [tex]\frac{sin0}{cos0}[/tex]

= [tex]\frac{-\frac{3}{5} }{-\frac{4}{5} }[/tex]

= - [tex]\frac{3}{5}[/tex] × - [tex]\frac{5}{4}[/tex]

= [tex]\frac{3}{4}[/tex]

The area and perimeters of the shapes are: (1) Area = 702 ft², perimeter = 96 ft (2): Area = 20 in² Perimeter = 21 in

Perimeter is the distance round the object while the area is the floor space the object occupies

1) Area =  (l*w) + (L*W)

Area = (6*9)  + (24*27)

Area = 54 + 648

Area = 702 ft²

ii) perimeter = 24+27+30+9+6= 96 ft

2)  Area =  (l*w) + (L*W)

Area = (2*3) +( 7*2)

Area = 6+14 = 20 in²

ii) perimeter =2+7+2+2+3+2+3 = 21 in

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If randomly throw two darts at the board and break two balloons, then [tex]\frac{2}{35}[/tex] is the probability that both of the balloons you break are purple.

Considering what is meant by probability,

However, you must be aware that probability refers to the likelihood—greater or lesser—of a given event occurring.

In other words, probability creates a connection between the total number of conceivable events and the number of favorable events.

Then, the ratio between the number of favorable circumstances (cases in which event A may or may not occur) and the total number of possible cases is used to define the likelihood of any event A. Laplace's Law is what governs this.

[tex]P(A)=\frac{number of favorable cases}{number of possible cases}[/tex]

If the occurrence of one of them has an impact on the occurrence of the other, then two occurrences A and B are dependent. The likelihood for events that are dependent is:

P(A and B)= P(A)× P(B|A)

The phrase "the probability of B, provided that A has occurred" is denoted by the symbol P(B|A).

In this instance:

[tex]P(A)=\frac{4 balloons}{15 balloons} =\frac{4}{15}[/tex]

If the first balloon is purple, there are still 3 purple balloons available out of the total of 14. P(B|A) then equals [tex]\frac{3}{14}[/tex].

[tex]P(A and B)=\frac{4}{15} *\frac{3}{14}[/tex]

[tex]P(A and B)=\frac{2}{35}[/tex]

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Answer: A

Step-by-step explanation:

To solve for x, we can set the expression equal to 24√47 and solve for x.

24√47 = x√47

24 = x

Therefore, the value of x that makes the expression equivalent to 24√47 is x = 24, which corresponds to the answer choice A.

The measure of m∠A is 27.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

m∠A = (2x + 5) and m∠B = (4x + 19)

∠A and ∠ B are complementary angles.

So,

Solve for x.

(2x + 5) + (4x + 19) = 90

2x + 5 + 4x + 19 = 90

6x + 24 = 90

6x = 90 - 24

6x = 66

x = 11

Now,

m∠A.

= (2x + 5)

= 2 x 11 + 5

= 22 + 5

= 27

Thus,

m∠A = 27

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0 |-1| , 1.3 , 2, |2.7|

Step-by-step explanation:

it's right because |-1| is an absolute value and the absolute value is 1

Answer:

0,  |- 1| , 1.3,  2,  |2.7|

Step-by-step explanation:

The absolute value of any number, x,  denoted by |x| is the positive of that number

So | 2.7 | = 2.7

| - 1 | =  1

Therefore the order of the absolute values is
0,  1, 1.3, 2, 2.7 which is the same as 0,  |- 1| , 1.3,  2,  |2.7|

Answer:

48 residents

Step-by-step explanation:

Let's assume that there are 100 residents in the neighboring house. 64% of the residents subscribe to "Our Football" magazine, so there are 64 residents who subscribe to it. 84% of the residents subscribe to "Top Gear" magazine, so there are 84 residents who subscribe to it. The number of residents who subscribe to both magazines can be calculated by finding the intersection of the two sets, which is equal to the number of residents who belong to both sets. This can be found using the formula:

Number of residents subscribing to both magazines = 100 - (100 - 64) - (100 - 84)

= 100 - 36 - 16

= 48

Therefore, 48 residents of the neighboring house subscribe to both magazines.