explain why 15 + 1/2n is an algebraic expression ​

Answer:

[tex]x \approx 3.195[/tex] satisfies the conclusion of the Mean Value Theorem for [tex]f(x) = \ln x^{3}[/tex] over the interval [tex][1,e^{2}][/tex].

Step-by-step explanation:

According to the Mean Value Theorem, for all function that is differentiable over the interval [tex][a, b][/tex], there is at a value [tex]c[/tex] within the interval such that:

[tex]f'(c) = \frac{f(b)-f(a)}{b-a}[/tex] (1)

Where:

[tex]a[/tex], [tex]b[/tex] - Lower and upper bounds.

[tex]f(a)[/tex], [tex]f(b)[/tex] - Function evaluated at lower and upper bounds.

[tex]f'(c)[/tex] - First derivative of the function evaluated at [tex]c[/tex].

If we know that [tex]f(x) = \ln x^{3} = 3\cdot \ln x[/tex], [tex]f'(x) = \frac{3}{x}[/tex], [tex]a = 1[/tex] and [tex]b = e^{2}[/tex], then we find that:

[tex]\frac{3}{c} = \frac{3\cdot \ln e^{2}-3\cdot \ln 1}{e^{2}-1}[/tex]

[tex]\frac{3}{c} = \frac{6\cdot \ln e-3\cdot \ln 1 }{e^{2}-1 }[/tex]

[tex]\frac{3}{c} = \frac{6}{e^{2}-1}[/tex]

[tex]c = \frac{1}{2}\cdot (e^{2}-1)[/tex]

[tex]c \approx 3.195[/tex]

[tex]x \approx 3.195[/tex] satisfies the conclusion of the Mean Value Theorem for [tex]f(x) = \ln x^{3}[/tex] over the interval [tex][1,e^{2}][/tex].

Answer:

C. 1/2(e^2-1)

Step-by-step explanation:

Edge AP Cal 2022

Answer:

The cylindrical tank can hold 9.7 cubic meter  more water than the rectangular prism shape tank .

Step-by-step explanation:

We are given that

Diameter of cylinderical water tank, d=4 m

Radius of  cylinderical water tank,r=d/2=4/2=2 m

Height of  cylinderical water tank,h=3 m

Length of rectangular prism, l=7 m

Width of rectangular prism ,w=2 m

Height of rectangular prism, h=2m

Volume of cylinder=[tex]\pi r^2 h[/tex]

Where [tex]\pi=3.14[/tex]

Using the formula

Volume of cylinderical tank=[tex]3.14(2)^2\times 3=37.7m^3[/tex]

Volume of rectangular prism=[tex]lwh[/tex]

Using the formula

Volume of rectangular prism=[tex]7\times 2\times =28m^3[/tex]

Difference between volumes=37.7-28=9.7 cubic meters

Hence, the cylindrical tank can hold 9.7 cubic meter  more water than the rectangular prism shape tank .

Answer:

4(x-3) = 8

Step-by-step explanation:

4 times the difference would be 4(x-y), and we already know what y is, which is 3. Finally, the "is 8" means "equals 8" giving us our equation: 4(x-3) = 8.

Answer:

4(x-3) = 8

Step-by-step explanation:

Answer:

The new jar would be smaller than the original.

Step-by-step explanation:

First you would have to find one 1/5 of the original size. This gives you the increased size.

Then, you'd find 1/5 of the new size and subtract it from the increased size of the jar.

1/5 of the increased size is larger than 1/5 of the original size, so no matter what number it is, you'll always end up with a smaller-sized jar of coffee at the end.

The new jar would be smaller than the original.

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.

First, you would have to find one 1/5 of the original size. This gives you the increased size.

Then, you'd find 1/5 of the new size and subtract it from the increased size of the jar.

1/5 of the increased size is larger than 1/5 of the original size, so no matter what number it is, you'll always end up with a smaller-sized jar of coffee at the end.

To know more about scale factors follow

https://brainly.com/question/25722260

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Answer:

120+22+x=180

x=38

120+22+38=180

Step-by-step explanation:

Hope it helps

Mark me as brainiest

Answer:

Step-by-step explanation:

-2+y=14

-5x-7y=10

y=14+2

y=16

-5x-7(16)=10

-5x-112=10

    +112  +112

-5x=122

x=-24.4

Answer:

148

Step-by-step explanation:

Answer:

If you divide both top and bottom of [tex]\frac{2}{10}[/tex] by 2, you get [tex]\frac{1}{5}[/tex]

Answer:

because you have to find common denominators

2/10= 1/5

2/10= 1x2/5x2

Whatever you do to the bottom, you do to the top so that is why i also multiplied the numerator by 2.

2/10=2/10

Hope it helped!! Pls mark brainliest :)) Have a good day

Step-by-step explanation:

Answer:

1.5 km/hour

Step-by-step explanation:

d is the David's speed in still water

c is the speed of the current

Going with the current, he travels d+c km per hour.

Going against the current, he travels d-c km per hour.

d+c = (20 km)/(2.5 hours) = 8 km/hour

d-c = (20 km)/(4 hours) = 5 km/hour

Add the equations to eliminate the c terms

d+c = 8

d-c = 5

----------

2d = 13

d = 6.5 km/hour

c = 8-d = 1.5 km/hour

Answer:

36 degrees

Step-by-step explanation:

Angles in a triangle add up to 180.

180-62-62=36

36 degrees

Step-by-step explanation:

Answer:

2x-15=65

Step-by-step explanation:

You have to subtract 15 dollars from 65 because it is extra money that Griffin had earned. Now you are left with 40 so now you would divided 2 since its both Griffin and Andrew. At the end, Griffin earned 35 dollars and Andrew earned 20 dollars.

Answer:

[tex]64a^{3} b^{6}[/tex]

Step-by-step explanation:

[tex](4ab^2)^3[/tex]

=> [tex]4^{3} a^{3} b^{6}[/tex]

=> [tex](4 \times 4 \times 4) a^{3} b^{6}[/tex]

=> [tex]64a^{3} b^{6}[/tex]

Answer:

Wow your on apec to?

Step-by-step explanation:

Wait could you show the whole question and the other answers please. I was going to say C.

I noticed a few others answers missing so I can't properly answer your question.

Answer:

15/22

Step-by-step explanation:

Answer:

If the total price of an object is A, and we have a tax of X%, then the new price of the object is:

Price = A + A*(X%/100%) = A*(1 + X%/100%)

In this case, the initial price of the car is:

A = $16,368

a) the tax is 6.6%

In this case, the price will be:

Price = $16.368*(1 + 6.6%/100%) = $17,448.288

b) the tax is 8.25%

In this case, the price will be:

Price = $16.368*(1 + 8.25%/100%) = $17,718.36

c) the tax is r.

we only replace X% by r.

Price = $16.368*(1 + r/100%)

d) We want to solve for r the above equation, we just need to isolate r.

Price/( $16.368) = (1 + r/100%)

Price/($16.368) - 1 = r/100%

(Price/($16.368) - 1)*100% = r

Answer:

36°, 42°, 72°, 102°, 108°

Step-by-step explanation:

Angles at a point = 360°

Therefore:

(3x - 6) + x + 3x + 2x + (x + 6) = 360°

Open parthenogenesis

3x - 6 + x + 3x + 2x + x + 6 = 360

Add like terms

10x = 360

Divide both sides by 10

x = 36

✔️Value of each angle:

Plug in the value of x in each expression

x = 36°

3x - 6 = 3(36) - 6 = 102°

3x = 3(36) = 108°

x + 6 = 36 + 6 = 42°

2x = 2(36) = 72°

Answer:

11/24

Step-by-step explanation:

change it to :

20/24-9/24

then solve

Answer:

11/24

Step-by-step explanation:

10/12 - 3/8

10/12 + -3/8

5/6 + -3/8

20/24 + -9/24

20 + -9 / 24

= 11/24

Answer:

y=1/2t+1

Step-by-step explanation:

To get a perpendicular line, the slopes have to be reciprocals.

Answer:

The factored expression is: [tex]2x(x + 3)[/tex]

Step-by-step explanation:

We are given the following expression:

[tex]2x^2 + 6x[/tex]

To factorize it as fully as possible, we first find the GCF between the numeric values, and the coefficients:

Numeric:

GCF between 2 and 6 is 2, because:

2 - 6| 2

1 - 3|

1 and 3 are not divisible by the same number, so 2.

Coefficient:

Between x² and x, x.

Factorizing:

Simplifying by 2x.

[tex]2x(\frac{2x^2}{2x}+\frac{6x}{2x}) = 2x(x + 3)[/tex]

The factored expression is: [tex]2x(x + 3)[/tex]

Answer:

The population had a 400% increase

Answer:

dont know

Step-by-step explanation:

Answer:

Sam is 24 years old and his mother is 48 years old.

Step-by-step explanation:

Equations

Let's call

x   = Sam's current age

Since Sam's mother is twice as old as Sam:

2x = Sam's mother current age

x + 12 = Sam's age in 12 years

2x - 12 = Sam's mother age 12 years ago

These two last expressions are equal:

x + 12 = 2x - 12

Subtracting x and adding 12:

x = 24

2x = 48

Sam is 24 years old and his mother is 48 years old.

Answer:

Sam is 24 and his mom is 48

Step-by-step explanation:

Answer:

The table shows locations on a map.

Place

Location

Which places on the map are 4 units apart?

O the park and the farmer's market

O the farmers market and the bus stop

✓ the post office and the park

O the post office and the bus stop

Step-by-step explanation:

Distance :---

[tex]→ \sqrt{ {(2 - ( -2 ))}^{2} + {(2 - 2)}^{2} } \\ = \sqrt{ {4}^{2} + {0}^{2} } = \sqrt{ {4}^{2} } = \boxed{4 \: units}[/tex]

Answer:

y=x+2.

Step-by-step explanation:

1. if the point A has coordinates (-3;1) and B - (1;3), then it is possible to make up the equation:

[tex]\frac{x-X_A}{X_B-X_A}= \frac{y-Y_A}{Y_B-Y_A}; \ => \frac{x+3}{4} =\frac{y+1}{4};[/tex]

2. if to evaluate the equation, then

x+3=y+1; ⇔ y=x+2 (slope-interseption form).

Answer:

0.4

Step-by-step explanation:

40 divided by 100= 0.4

Answer:

24 ; Tstat > Tcritical ; 0.052 ; Fail to eject the Null

Step-by-step explanation:

Claiborne model:

$4.7 $3.8 $6.7 $3.8 $3.9 $4.2 $4.0 $4.0 $4.8 $3.1 $3.1 $5.5 $3.4 $6.1 $4.9

Sample size, n1 = 15

Using calculator :

Mean, m1 = 4.4

Standard deviation, s1 = 1.056

Klein model:

$4.0 $3.8 $3.6 $2.5 $4.9 $5.2 $5.9 $4.9 $4.4 $3.6 $5.1 $4.7

Sample size, n = 12

Mean, m2 = 4.38

Standard deviation (s) = 0.923

To obtain the degree of freedom for unequal variances test, use the Relation :

Degree of freedom (DF) = (s1²/n1 + s2²/n2)² / { [ (s1² / n1)² / (n1 - 1) ] + [ (s2² / n2)² / (n2 - 1) ] }

(1.056^2/15 + 0.923^2/12)^2 / {[(1.056^2/15)^2 / (15 - 1)] + [(0.923^2/12)^2 / (12 - 1)]}

0.0211226 / (0.0003947 + 0.0004581)

= 24.768527

df = 24 rounded down to the nearest whole number.

Decision region :

α = 1-0.95 = 0.05

Tdf, 0.05 = 1.711

Tcritical = 1.711

Reject Null, if Tstat > Tcritical

The t - test statistic :

(m1 - m2) / (s1²/n1 + s2²/n2)

(4.4 - 4.38) / sqrt(1.056^2 / 15 + 0.923^2 / 12)

0.02 / 0.3812301

= 0.0524617

= 0.052

Since, Tstat < Tcritical, we fail to reject the Null. It is not reasonable to conclude that Claiborne model earns more.