Find the 92nd term of the arithmetic sequence -29, -22, -15, ...

The derivative of the function is f' ( x ) = 9 / ( 4 + 3x ) ( ln 2 )

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = log₂ ( 3x + 4 )³

On simplifying , we get

On taking the derivative of the function , we get

f' ( x ) = d/dx ( log₂ ( 3x + 4 )³ )

d/dx ( log₂ ( 3x + 4 )³ ) = 1/ ln ( 2 ) [ d/dx( 3x + 4 )³ ]

On applying chain rule , we get

f' ( x ) = 1/ ln ( 2 ) 1/( 3x + 4 )³ ( 9 ( 3x + 4 )² )

So , cancelling out the similar terms , we get

f' ( x ) = 9 / ( 4 + 3x ) ( ln 2 )

Hence , the derivative is f' ( x ) = 9 / ( 4 + 3x ) ( ln 2 )

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Answer: ∠T=45°

Step-by-step explanation:

If triangle RST is congruent to triangle LMN, then the angles R=L, S=M, and T=N. Knowing that the sum of angles in a triangle= 180 degrees, then:

∠R+∠S+∠T=180°

∠R=65°

∠M=∠S=70°

180°-∠R-∠S=∠T

180°-65°-70°=

∠T=45°

The angles in the circle are as follows:

The central angle of an arc is the central angle subtended by the arc.

The measure of an arc is the measure of its central angle.Therefore,mBC = 107 degrees

The angle subtended by an arc at the center is twice the angle subtended at the circumference.

Therefore, m∠BAC = 107 / 2 = 53.5 degrees

The inscribed angle is half the intercepted arc angle.

Therefore, to find mBC, we solve:

46 = 1 / 2

Next, we cross multiply mBC  = 46 × 2

Therefore, mBC = 92 degrees

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Answer:

Step-by-step explanation:

f(x) = [tex]\frac{3+x}{x-3}[/tex]

f(a+2) = [tex]\frac{3+a+2}{a+2-3}[/tex]

f(a+2) = [tex]\frac{5+a}{a-1}[/tex]

The correct variables which are continuous are,

1. Length of a frog's jump.

2. Monthly TV cable bills.

3. Lottery revenues of states.

4. Number of wheels of a car.

We have to given that;

To find correct variables which are continuous.

Since, The number of wheels of a car is a discrete variable, because it can only take certain integer values (2, 3, 4, etc.), while the other variables can take any real value within a certain range.

Hence, The correct variables which are continuous are,

1. Length of a frog's jump.

2. Monthly TV cable bills.

3. Lottery revenues of states.

4. Number of wheels of a car.

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The vertex is at (1, 4).

The vertex is at (-1, -4).

The axis of symmetry is x = 1.

The axis of symmetry is x = -1.

The x-intercepts are (3, 0) and (-1, 0).

The x-intercepts are approximately (-2.3, 0) and (0.3, 0).

The y-intercept is (0, 3).

The y-intercept is (0, -6).

We have,

To solve the equations using the quadratic formula, we need to rewrite them in the standard form ax² + bx + c = 0.

-x² + 2x + 3 = 0 can be rewritten as -1x² + 2x + 3 = 0

Here, a = -1, b = 2, and c = 3

Using the quadratic formula, we have:

x = (-b ± √(b² - 4ac)) / 2a

x = (-2 ± √(2² - 4(-1)(3))) / 2(-1)

x = (-2 ± √(16)) / -2

x = 1 ± 2

So, x = 3 or x = -1

2x² + 4x - 6 = 0 is already in the standard form with a = 2, b = 4, and c = -6

Using the quadratic formula, we have:

x = (-4 ± √(4² - 4(2)(-6))) / 2(2)

x = (-4 ± √(52)) / 4

x = (-2 ± √(13)) / 2

To find the vertex of each parabola, we can use the formula x = -b / 2a and then substitute the value of x into the equation to find y.

For -x² + 2x + 3 = 0

We have a = -1 and b = 2, so the vertex is at

x = -b / 2a = -2 / (2(-1)) = 1.

Substitute x = 1 into the equation to find y:

y = -1(1)² + 2(1) + 3 = 4.

So the vertex is at (1, 4).

For 2x² + 4x - 6 = 0,

We have a = 2 and b = 4, so the vertex is at x = -b / 2a = -4 / (2(2)) = -1. Substitute x = -1 into the equation to find y: y = 2(-1)² + 4(-1) - 6 = -4.

So the vertex is at (-1, -4).

The axis of symmetry is a vertical line that passes through the vertex.

For -x² + 2x + 3 = 0, the axis of symmetry is x = 1.

For 2x² + 4x - 6 = 0, the axis of symmetry is x = -1.

To find the x-intercepts, we can set y = 0 in each equation and solve for x using the quadratic formula.

For -x² + 2x + 3 = 0, we have:

x = (-2 ± √(2² - 4(-1)(3))) / 2(-1)

x = (-2 ± √(16)) / -2

x = 1 ± 2

So the x-intercepts are (3, 0) and (-1, 0).

For 2x² + 4x - 6 = 0, we have:

x = (-4 ± √(4² - 4(2)(-6))) / 2(2)

x = (-4 ± √(52)) / 4

x = (-2 ± √(13)) / 2

So the x-intercepts are approximately (-2.3, 0) and (0.3, 0).

To find the y-intercept, we need to set x = 0 and solve for y.

Setting x = 0 in -x² + 2x + 3 = 0.

-0 + 0 + 3 = 3

Therefore, the y-intercept is (0, 3).

Setting x=0 in 2x² + 4x - 6.

2(0)² + 4(0) - 6 = -6

Therefore, the y-intercept is (0, -6).

Thus,

The vertex is at (1, 4).

The vertex is at (-1, -4).

The axis of symmetry is x = 1.

The axis of symmetry is x = -1.

The x-intercepts are (3, 0) and (-1, 0).

The x-intercepts are approximately (-2.3, 0) and (0.3, 0).

The y-intercept is (0, 3).

The y-intercept is (0, -6).

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Answer:

x<-12 or x>16

Step-by-step explanation:

Answer:

|x - 2| + 3 > 17

|x - 2| > 14

x - 2 < -14 or x - 2 > 14

x < -12 or x > 16

Since the average rates of change of f and g cannot be determined from the given information provided.

We can find the average rate of change of function f over the interval [-6, -3) as:

The average rate of change of f;

= (f (6) - f (3)) / (6 - 3)

= (71 - 59) / 2 = 6

We have the two given points to set up equations:

-53 = a(3)^b - 41

-53 = a(5)^b - 41

0 = a(3^b - 5^b)

Since 3^b ≠ 5^b, we must have a = 0, that means g is not a valid exponential function passing through the given points.

Therefore,

We can conclude, that the average rates of change of f and g cannot be determined.

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the volume of a prism is

length × width × height

so, for the small prism we have

5 × 4 × height = 100 in

height = 100/20 = 5 i

for the large prism we have

5 × 4 × height = 200 in³

height = 200/20 = 10 in

the larger prism is 10/5=2 times taller than the small prism.

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Answer: To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the initial principal (the amount borrowed)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time period in years

In this case, we have:

P = $21,000

r = 8.75% = 0.0875

n = 1 (interest is compounded annually)

t = 13 years

So, plugging these values into the formula, we get:

A = 21,000(1 + 0.0875/1)^(1*13)

A = 21,000(1.0875)^13

A = $58,150.51

Therefore, if the loan is paid in full at the end of the 13-year period, $58,150.51 must be paid back, which includes the original principal plus the interest accrued over the 13-year period.

Step-by-step explanation:

The correct statement is:

"Divide out a common factor of x - 7." The limit of the given expression is 1/6.

Multiply by (√(x + 2) + 3)/(√(x + 2) + 3):

This statement is not correct.

We generally multiply by the conjugate of the expression to eliminate square roots, but in this case, multiplying by (√(x + 2) + 3)/(√(x + 2) + 3) does not help simplify the expression.

Get x - 1 in the numerator:

This statement is not correct. The expression does not involve x - 1 in the numerator.

Get (x - 7)(√(x + 2) - 3) in the denominator:

This statement is not correct. We want to simplify the expression, not introduce a more complex denominator.

Divide out a common factor of x - 7:

This statement is correct. By factoring out (x - 7) from both the numerator and denominator, we can cancel out the common factor.

Calculate the limit as 1/6:

This statement is not correct. We need to perform further simplification to determine the limit.

After canceling out the common factor of x - 7, the simplified expression becomes:

lim x -> 7 (√(x + 2) - 3)/(x - 7) = lim x -> 7 1/(√(x + 2) + 3)

To find the limit, we substitute the value x = 7 into the simplified expression:

lim x -> 7 1/(√(7 + 2) + 3) = 1/(√(9) + 3) = 1/(3 + 3) = 1/6

Therefore, the correct statement is: "Divide out a common factor of x - 7." The limit of the given expression is 1/6.

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There are 58 Adventure Scouts slept outside on the camping trip.

Let's denote the number of scouts who slept in a cabin, tent, and outside as c, t, and o, respectively. We know that the total number of scouts is 115, so:

c + t + o = 115

We also know that twice as many scouts slept in a cabin as slept in a tent, so:

c = 2t

And we know that the same number of scouts slept outside as slept in a cabin, so:

o = c

We can use these equations to solve for the number of scouts who slept outside:

c + t + o = 115

2t + t + t = 115 (substituting c = 2t and o = c)

4t = 115

t ≈ 28.75

Since we can't have a fractional number of scouts, we need to round this up or down. However, we also know that the number of scouts who slept outside is the same as the number who slept in a cabin, which means that either c or o must be even (since c is twice t). Therefore, we'll round t up to 29 and use that to solve for c and o:

c = 2t ≈ 58

o = c ≈ 58

So, we can conclude that 58 Adventure Scouts slept outside on the camping trip.

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Answer:

46

Step-by-step explanation:

You need to find how many Adventure Scouts slept outside. Start with the information in the problem.

A total of 115 scouts went camping.

Twice as many slept in a cabin as slept in a tent.

The same number slept outside as slept in a cabin.

You can use a diagram to model the problem. Fewer scouts slept in a tent than the other choices. So, start with the scouts who slept in a tent.

Twice as many scouts slept in a cabin as slept in a tent. So, draw 1 box to represent the number who slept in a tent and 2 boxes to represent the number who slept in a cabin.

tent

cabin

outside

The same number of scouts slept outside as slept in a cabin. There are 2 boxes for scouts who slept in a cabin. So, draw 2 boxes to represent the number who slept outside.

tent

cabin

outside

There are 5 boxes in the diagram in all. There were 115 scouts on the trip altogether. So, each box represents 115÷5 scouts. Divide.

2 3

5

1 1 5

– 1 0

1 5

– 1 5

0

Each box represents 23 scouts. There are 2 boxes for the scouts who slept outside. Multiply to find the number of scouts who slept outside.

2 3

×  2

4 6

46 Adventure Scouts slept outside.

The type of test used in this problem is given as follows:

1 proportion z test.

At the null hypothesis, we consider if there is not enough evidence to conclude that the mean is different of 0.55, hence:

[tex]H_0: p = 0.55[/tex]

At the alternative hypothesis, we test if there is enough evidence to conclude that the mean is different of 0.55, hence:

[tex]H_a: p \neq 0.55[/tex]

We are testing a proportion, hence the z-distribution is used, thus the correct option is given as follows:

1 proportion z test.

(in the case of a proportion, a z test is used, for sample means that we can use either z test or t test depending on the problem).

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Based on the information, the required result of the expansion for the expression is 8.

In mathematics, an expression is a combination of numbers, variables, operators, and/or functions that can be evaluated to obtain a numerical or symbolic result. Expressions can take many forms, but typically involve some combination of mathematical symbols such as +, -, ×, ÷, =, and parentheses.

The given expression is 2x-3 .

when x =1, we will get 2(1)-3 = 2-3 =-1

When x=2, we will get, 2(2) -3 = 4-3 =1

When x=3, we will get 2(3)-3 = 6-3=3

When x=4, we will get 2(4)-3 = 8-3=5

The required result of the expansion is -1+1+3+5=8

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Answer:90

Step-by-step explanation:

Answer:

54300 ml is greater than 54 L. This is because 54300 ml is equivalent to 54.3 L, which is larger than 54 L.

Answer: The correct answer is 42

Step-by-step explanation:

Answer:

8/21

Step-by-step explanation:

4 2/3=8/3, times 1/7 (or divide by 7) equals 8/21.

The amount that the jeweler would charge Mrs. Luisa, given the prices of the successive jewelry would be $ 19, 680

The charge for repairing the jewelry pieces is calculated in a geometric progression:

= 6, 63, 63 ², 63 ³, ..., 63 ⁷

The sum of the first n terms in such a progression is:

S = a x (r ⁿ - 1) / ( r - 1 )

Seeing as there are 8 pieces of jewelry, the total cost to Mrs. Luisa would be:

S = 6 x ( 3 ⁸  - 1) / ( 3 - 1 )

S = 6 x ( 6561 - 1 ) / 2

S = 6 x 6560 / 2

S = 3 x 6560

S = $ 19, 680

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The probability that the student was female and got grade C is P ( A ) = 0.12833

Given data ,

Let the table represent the group of students with their gender and the grades in school

Now , the probability that the student was female = total number of females / total number of students

So , probability that the student was female = 22/60

Now , the probability that the student got grade C = 21/60

So , the compound probability P ( A ) = probability that the student was female and got grade C

On simplifying , we get

P ( A ) = ( 22/60 ) ( 21/60 )

P ( A ) = 462/3600

P ( A ) = 0.12833

Hence , the probability is P ( A ) = 0.12833

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Answer:

1 1/5 = 6/5

1 1/3 = 4/3

Step-by-step explanation:

hope this helps, if you’re looking for 1 1/5 + 1 1/3 please tell me and I will solve that for you

Answer:

63

Step-by-step explanation:

b x h = A

9 x 7 = 63

Answer:

She spends 70 minutes in total or 1h 10min

PLEASE MARK IT THE BRAINLIEST!!!!!

Answer:

0.66

Step-by-step explanation:

please read attachments

The whole number for "forty-two thousand, fifteen" is 42,015.

We have, "forty-two thousand, fifteen".

To write a sentence as a whole number using digits, you would typically replace the words with their numerical representations. Here's an example:

Sentence: "I have three apples and four bananas."

Whole number: "I have 3 apples and 4 bananas."

Here the numeric terms are forty- thousand and fifteen then the numerical digit will be

= 42, 015.

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The number of tiles that would be grey tiles out of the total tiles given would be = 28 tiles.

To calculate the number of grey tiles, the total number of tiles given should be divided into two since the path is made up of only white and grey tiles.

The total number of tiles = 56 tiles.

Therefore the grey and the white tiles have the same number of tiles = 56/2 = 28 grey tiles

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Answer:

La suma de los cuatro ángulos de un cuadrilátero es igual a 360 grados. Entonces, si dos ángulos miden 60° y 80°, la suma de esos ángulos es de 140 grados.

Los otros dos ángulos están en una proporción de 2:9, lo que significa que la suma de sus medidas es de 11 partes. Si representamos las medidas de estos ángulos como 2x y 9x, respectivamente, entonces podemos escribir la ecuación:

2x + 9x = 11 partes

11x = 11 partes

x = 1 parte

Por lo tanto, el ángulo más pequeño mide 2x = 2 partes o 2 × 1 = 2 grados, y el ángulo más grande mide 9x = 9 partes o 9 × 1 = 9 grados.

En resumen, los dos ángulos faltantes miden 2° y 9°.

Step-by-step explanation: