The nth term of a different sequence is 10n^2+5 work out the 5th term of this sequence

The Volume of the given composite shape is: 432 ft³

The formula for the volume of a triangular prism is:

Volume = base area * height

The volume of a cuboid is:

Volume = Length * Width * Height

Thus:

Volume of composite shape = (6 * 12 * 4) + (6 * 6 * 4)

= 432 ft³

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(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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Answer:

10 and 12

Step-by-step explanation:

let the consecutive even integers be n and n + 2 , then

n² - 64 = 3(n + 2) ← distribute parenthesis

n² - 64 = 3n + 6 ( subtract 3n + 6 from both sides )

n² - 3n - 70 = 0 ← in standard form

(n - 10)(n + 7) = 0 ← in factored form

Equate each factor to zero and solve for n

n - 10 = 0 ⇒ n = 10

n + 7 = 0 ⇒ n = - 7

Since n must be a positive even integer then n = 10 and n + 2 = 10 + 2 = 12

The 2 numbers are 10 and 12

Answer:

A) One Solution

Step-by-step explanation:

3x + 4 = -x

4 = -4x

x = -1

y = 3(-1)+4

y = 1

One Solution

Answer:

B

Step-by-step explanation:

x is greater than or equal to 2 and x is less than or equal to 5

The algebraic expression that can be represented by the statement is -5x/2 = 10

From the question, we have the following statement that can be used in our computation:

The negation of the product of five times a number divided by two is ten

Represent the variable with y

So, we have the following representation

The negation of the product of five times x divided by two is ten

Express the product as an actual product

So, we have the following representation

The negation of 5x divided by two is ten

Express the quotient as an actual quotient

So, we have the following representation

The negation of the 5x/2 is ten

Lastly, we have

-5x/2 = 10

Hence, the expression is -5x/2 = 10

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Answer:

1

Step-by-step explanation:

there are 3 people and 1 boat holds three people

Answer:

2

Step-by-step explanation:

First off, the slope of f(x) is -4.  It is in the form y=mx+b and m=-4.

For g(x), the slope can be calculated from any two points given.  I willuse (1,9) and (3,21) because I like positive numbers.  So, slope is rise over run and it is calculated from (y1-y0)/(x1-x0)  This gives me (21-9)/(3-1) which is equal to 6.  So adding the two slopes: 6+ (-4)=2

Answer:

Step-by-step explanation:

Answer:(-9,6)

Step-by-step explanation:

I got it right on the e2020 course

Hope it helps:)

Answer: Approximately 7.4162

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

\(\sqrt\\ 55\) = 7.416198487095663, rounded to the nearest integer is 7.

The compound event probability of spinning an even number and flipping heads is P ( A ) = 1/4

Given data ,

Let the total number of outcomes in spinning a spinner be = 6

The number of even outcomes = 3

Let the number of outcomes in flipping a coin = 2

So , the probability of landing an even number = 3/6 = 1/2

The probability of landing a heads = 1/2

And , probability of spinning an even number and flipping heads is given by P ( A ) = probability of landing a heads x probability of landing an even number

On simplifying , we get

P ( A ) = 1/2 ( 1/2 )

P ( A ) = 1/4

Hence , the probability is 1/4 or 25 %

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Answer:

y ≈ 11,97 ft

Step-by-step explanation:

Use trigonometry:

\( \tan(26.5°) = \frac{y}{24} \)

Cross-multiply to find y:

\(y = \tan(26.5°) \times 24 ≈11.97 \: ft\)

Answer:

let length be b+5 and breadth be b

given,

perimeter of rectangle=150

or, 2(l+b) =150

or, 2(b+5+b)=150

or, 2b+5=150/2

or, 2b+5=75

or, 2b=70

therefore, b=35m

l=b+5

=35+5

=40m

The correct statement is Most of the songs were between 3 minutes and 3.8 minutes long.

Based on the given information from the graph, we can determine the following:

The graph shows an upward trend from 2.8 to 3.4 on the horizontal axis.

Then, there is a downward trend from 3.4 to 4 on the horizontal axis.

From this, we can conclude that most of the songs played during the one-hour interval were between 3 minutes and 3.8 minutes long. This is because the upward trend indicates an increase in length from 2.8 to 3.4, and the subsequent downward trend suggests a decrease in length from 3.4 to 4.

Therefore, the correct statement is:

Most of the songs were between 3 minutes and 3.8 minutes long.

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Answer:

A

Step-by-step explanation:

Answer:

Q= 126°

Step-by-step explanation:

Using the picture given, because these are parallel lines broken by a transversal, we can say the following

M=A=Q=F

B=C=D=G

Since, for example, M and C are the same line, we can say that M+C=180 and so on.

M=Q

Q= 126°

the first student did better in terms of their performance relative to their respective class averages and standard deviations.

To determine which student did better on their respective tests, we need to compare their scores relative to their class averages and standard deviations.

Let's calculate the z-scores for each student, which will allow us to compare their scores in terms of standard deviations from their class averages.

For the first student:

Z-score = (Student's Score - Class Average) / Standard Deviation

Z-score = (80 - 85) / 5

Z-score = -1

For the second student:

Z-score = (Student's Score - Class Average) / Standard Deviation

Z-score = (65 - 50) / 10

Z-score = 1.5

The z-score represents the number of standard deviations a score is above or below the mean. A positive z-score indicates a score above the mean, while a negative z-score indicates a score below the mean.

Based on the z-scores, we can conclude that the first student performed better relative to their class average compared to the second student. The first student's score of 80 was 1 standard deviation below the class average, while the second student's score of 65 was 1.5 standard deviations above the class average.

Therefore, the first student did better in terms of their performance relative to their respective class averages and standard deviations.

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Answer:

6.32455532034

Rounded: 6.32

Hope this helps! :)

Yes, his pulse rate is in the normal range for children. His pulse rate was calculated to be 120 beats per minute, which falls within the range of 60-100 beats per minute.

The student took his resting pulse rate by counting the number of beats in 20 seconds. He then multiplied his result by three to calculate his pulse rate for a minute. To determine if his pulse rate was within the normal range for children, he compared his result to the data shown in the table. His pulse rate of 120 beats per minute was within the range of 60-100 beats per minute, so it was considered to be normal for children. To ensure accuracy, the student could have taken his pulse rate for a longer period of time, such as 30 or 60 seconds, before calculating his pulse rate for a minute. This would have given him a more accurate result.

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To write a quadratic function from its vertex and another point, we can use the vertex form of a quadratic function, which is f(x) = a(x-h)^2 + k. Substitute the coordinates of the vertex and the other point into the vertex form to find the value of a. Then, substitute the value of a back into the vertex form to get the quadratic function.

To write a quadratic function from its vertex and another point, we can use the vertex form of a quadratic function, which is f(x) = a(x-h)^2 + k. In this form, (h, k) represents the coordinates of the vertex of the parabola.

Let's say the vertex of the quadratic function is (h, k) and the other point is (x1, y1). We can substitute these values into the vertex form to find the value of a.

Substituting the vertex coordinates, we get:

f(h) = a(h-h)^2 + k

f(h) = k

Substituting the coordinates of the other point, we get:

f(x1) = a(x1-h)^2 + k

Now, we have two equations:

k = a(0)^2 + k

y1 = a(x1-h)^2 + k

From the first equation, we can see that k = k, which is always true. Therefore, we can ignore this equation.

From the second equation, we can solve for a:

y1 - k = a(x1-h)^2

a = (y1 - k) / (x1-h)^2

Now that we have the value of a, we can substitute it back into the vertex form to get the quadratic function:

f(x) = a(x-h)^2 + k

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The percentage of the sheets with no air bubbles is given as follows:

13.53%.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are listed and explained as follows:

The mean for this problem is given as follows:

\(\mu = 2\)

The proportion of these sheets with no air bubbles is P(X = 0), hence it is given as follows:

P(X = 0) = e^-2 = 0.1353 = 13.53%.

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Answer:

The two will retain its unit place value

Step-by-step explanation:

We are given the number 506,092

Which is stated in words as

"Five hundred and six thousand and ninety two"

2 represents 2 units in the number

When we shift 2 by two places to the right, the number becomes

50,609,002

We can still see that "two" still retains it unit place value and the whole number now reads fifty million six hundred and nine thousand and 2

Answer:

7/18 i think

Step-by-step explanation:

Answer:

Area=57.75 m squared

Step-by-step explanation:

Area= L x W

Area= 11 x 5.25

Area=57.75 or 57 3/4

The total number of possible 7-place license plates are 67600000.

Given: A 7-plate license plate. 2 places are for letters and 5 places are for numbers. To find how many different 7-plate license plates are possible

Let's solve the given problem:

The license plate has 7 places. 2 places are for letters and the remaining 5 places are for numbers.

Therefore, the total number of ways in which the 7-place license plate can fill are: Total possible ways in which the two letters can be filled × Total possible ways in which the 5 number places can be filled

= 676 × 100000

= 67600000 ways

Hence the total number of possible 7-place license plates are 67600000.

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The value are give below:

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Using Pythagoras theorem in FPO

FO²= FP²+ OP²

FO²=12.5²+19²

FO²=39.75

FO= 22.74

Now In OQR

OR²=OQ²+QR²

517.25= x² +14²

x²= 321.25sx

x=17.9

31. Now, given triangle

    H² = 5²+10²

    H²=125

    H=11.18

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The value of x in the figure is 17.9

Considering the triangle FOP, where:

From the question, we have:

OP = 19

FG = 25

Where:

FP = 0.5 * FG

FP = 0.5 * 25 = 12.5

Using Pythagoras theorem, we have:

FO² = FP² + OP²

Substitute known values

FO² = 12.5² + 19²

Evaluate the sum of squares

FO² = 517.25

Considering the triangle ROQ, where:

From the question, we have:

OQ = x

RS = 28

Where:

RQ = 0.5 * RS

RQ = 0.5 * 28 = 14

Using Pythagoras theorem, we have:

OR² = OQ² + RQ²

Recall that

OR = FO

Square both sides

OR² = FO²

This means that:

FO² = OQ² + RQ²

Substitute known values

517.25 = x² + 14²

Collect like terms

x² = 517.25 - 14²

Evaluate

x² = 321.25

Take the square root of both sides

x = 17.9

Hence, the value of x is 17.9

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