Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number

The average rate of change of the function f(x) is found as  -3.75.

The formula for the average rate of change (A(x)) of f(x) over the interval [a,b] is:

A(x) = f(b) - f(a) / b - a

The function being:

f(x) = 20.(1/4)ˣ

Its average rate of change between x = 1 to x = 2 must be determined.

At x = 1

Then;

f(x) = 20.(1/4)¹

f(1) = 5

At x = 2

Then;

f(x) = 20.(1/4)²

f(2) = 1.25

Add these to the formula above to get;

A(x) = f(2) - f(1) / 2 - 1

A(x) = - 3.75

Consequently, the average rate of change of a function f(x) between x = 1 and x = 2 is -3.75.

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Diego will have 74 pencils remaining after giving 14 pencils to Marcus and 32 pencils to Anna.

The question is about simple Subtraction. First, we know that the total number of colored pencils in the box is 120. Following is the step-by-step explanation for this question.
Let suppose,
Total Colored pencils = x = 120
Pencils given to Marcus = y = 14
Pencils are given to Anna = z = 34.

And, Total Pencil Remaining = R =?

We can show the given information in the equation as given below:
R = x - y - z

By putting the value in the above equation:
R  = 120 - 14 -34
R  = 74.

So, after giving the 14 and 32 pencils to Marcus and Anna, respectively. Marcus would remain with 74 Pencils.

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The radius is increasing fastly at a rate of 2.75 feet per second when it is already 30 feet.

Here, it has been told that the rate of change of the area with respect to the time is = 520 ft²/sec - (i)

This can also be written as = dA/dt (ii)

We need to find the rate of change of radius with respect to the time at 30 feet. This can be written as = dr/dt (iii)

We already know that the area of a circle can be found out using the formula = πr² (iv)

Differentiating equation (ii) with respect to time, we get -

= d(πr² )/dt

= π*(dr²/dt)

= π*(dr²/dr)*(dr/dt)

= π*(2r)*(dr/dt)

= dr/dt = (dA/dt)*(1/ π*2r)

Using the given values, we get -

= (dr/dt) = 520 / π*2*30ft

= (dr/dt) = 2.75 ft/sec

Henceforth, we find that the rate of change of the radius with respect to time at 30 feet is going to be 2.75 ft/sec.

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Jacob's smoking habit may shorten his life expectancy by an average of 10 years and 6 months.

Given,

The age of Jacob when he starts smoking  = 21 years

Jacob's present age = 48 years

In generally if 1 year of smoking reduces 6 months from the life.

Why does smoking cause life to be shorter?

Only a few of the illnesses that are directly linked to smoking and have a significant role in the increased mortality rate among smokers include cancer, lung disease, and cardiovascular disease. The link between smokeless tobacco and cancer is well known.

Here,

Jacob may live 10 years and 6 months less than normal due to his smoking habit.

I have answered the question in general as given question is incomplete.

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Answer:

9 is 8 hours and 10 is 10 hours

Answer:

9.  8 Hours

10. 10 hours

Step-by-step explanation:

48 ÷ 4 = 12  The unit rate is 12 per hour

12x = 96  Divide both sides by 12

x = 8

54 ÷ 6 = 9  The unit rate is 9 per hour

9x = 90  Divide both sides by 9

x = 10

Answer:

i need points

Step-by-step explanation:

229.5 miles separate point A from point C

What is the short definition of cosine law?

According to a trigonometrical rule, the square of a side in a plane triangle is equal to the sum of the squares of the other sides minus twice that amount plus the cosine of the angle between the other two sides.

Given:

Angle AB = 370 miles 24 degrees is A.

Angle BC = 240 miles 37 degrees is B.

Since we have two angles and two sides of a regular triangle, we can apply the cosine law to calculate the distance between points A and C.

Angle B, which is 37 degrees, is the angle opposite side AC.

(AC)^2 =(AB)^2 + (BC)^2 - 2(AB)(BC)cos(B)

solve for AC:

(AC)^2 =(370)^2 + (240)^2 - 2(370)(240)cos(37)

229,48 miles equal AC.

Therefore, 229.5 miles separate point A from point C.

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He should order 10 sandwiches of 6 foot long so, as to make sure that everyone will eat 2 pieces.

We need to convert between the units in order to ensure the accuracy and to prevent measurement misinterpretation. For example, we do not measure the pencil's length in kilometres. In this situation, one must convert from kilometres (km) to centimetres (cm) (cm). In most cases, multiplicative conversion factors are used to convert one unit to another of the same quantity. Let's see how to change the length and mass units.

1 Feet = 12 Inches

So, 6 Foot = 72 inches

The Length of sandwich- piece is 4 inch

So, when we convert 6 foot long sandwich into 4 inch,

Then we get number of piece is = 72/4 = 18

From 6 foot long sandwich we get 18 pieces of 4 inch long sub.

Now, Total people who will attend picnic is 40

and each people will eat 2 pieces.

It means total number of piece required = 2 (90) = 180

Mr. eaton required 180 pieces of sandwiches.

Number of sandwiches = 180 / 1.8 = 10

He should order 10 sandwiches of 6 foot long.

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Answer:

  48 = 2⁴ · 3

Step-by-step explanation:

You want the prime factorization of 48.

You recognize that 48 is an even number, so you can divide by 2 and see what's left. You can keep doing that until you get a number divisible by another prime:

  48/2 = 24

  24/2 = 12

  12/2 = 6

  6/2 = 3

3 is prime.

The prime factorization of 48 is ...

  48 = 2⁴ · 3

Answer:

there will be 3 carrots in each bag and you will have 2 carrots left over

Step-by-step explanation:

hope this helps

The insurance policy's anticipated value is -$81 for the one year life insurance policy.

Consider the various factors and the man's potential benifits.

-$165 because he already paid that sum.

The beneficiary could earn as a potential profit.

140000-165 = $139835

The probability of surviving is 0.9994.

The likelihood of not living is 0.0006.

The expected value is given by;

E(v) = (-165)(0.9994) + (139835)(0.0006)

E(v) = -164.901 + 83.901

E(v) = -81.

Thus, the insurance policy's anticipated value is -$81.

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Answer:

20-foot shadow

Step-by-step explanation:

You need to find what x is equal to for each equation, so you can sub why x is equal to in the place I'd x to eliminate the variable

1. 6x-5y=-4

6x=5y-4

X=5/6y-2/3

2. 4x+2y=28

4x=-2y+28

X=-1/2y+7

Hope this helps!

Answer:

CPCTC

Step-by-step explanation:

BD is perpendicular to AC, forming two right triangles. The hypotenuses are congruent, as is our leg that we will call b. If we use Law of Sines to find our angles a and c (no matter the values), we would find that because b is the same leg in both triangles and the hypotenuses are congruent, angles a and c are congruent, so therefore your missing angle in both triangles is congruent, and using a trig function will find that AD and CD are congruent, making all of both triangles congruent.

∠mkj angle is an adjacent interior angle to ∠jkm

Adjacent interior angles are two angles that share a common vertex and a common side. In the given angle ∠jkm, the common vertex is at point "k" and the common side is the line segment joining points "j" and "m". Therefore, the adjacent interior angle to ∠jkm is ∠mkj.

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The 95% confidence interval for the mean gas mileage for this car model is (26.26, 28.74) mi/gallon.

The confidence interval for a statistical data is written as-

(x+ zr/√n, x- zr/√n)

Here, we are given that-

Mean ⇒ x = 27.5 mi/gallon.

Standard deviation ⇒ r = 4 mi/gallon

Number of samples ⇒ n = 49

and Confidence interval = 95%

z-score at 95% confidence level = 2.17

Substituting the values we have;

= [27.5 - 2.17(4.0) /(√49),  27.5 + 2.17(4.0) /(√49)]

= (27.5 - 8.68 / 7,  27.5 + 8.68 / 7)

= (27.5 - 1.24,  27.5 + 1.24)

= ( 26.26, 28.74)

Therefore, the 95% confidence interval for the mean gas mileage for this car model is (26.26, 28.74) mi/gallon.

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The point estimate of the population standard deviation is 5.91 (Option A)

Standard deviation refers to the spread of a data distribution and measures the distance between each data point and the mean. The sample standard deviation (s) is a point estimate of the population standard deviation σ.

The mean of the population ẋ = sum of all values/ total number of values = 97/6 ≈ 16

The point estimate of the population standard deviation S =√(∑(xi - ẋ)^2/n-1)

∑(xi - µ)^2 = (9 – 16)^2 + (13– 16)^2 + (15– 16)^2 + (15– 16)^2 + (21– 16)^2 + (24– 16)^2 = 79 + 9 + 1 + 1 + 25 + 64 = 179

s = √(179/5) = 5.98

Note: The question is incomplete. The complete question probably is: The following information was collected from a simple random sample of a population. 9 13 15 15 21 24 The point estimate of the population standard deviation is Select one: O a. 5.91. O b. 7.688. O C. 7.018. O d. 4.925.

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Answer:

x = 31

Step-by-step explanation:

Distribute 2 to x which equals 2x, and 2 times 14 which equals 28, which gets you to 2x + 28 = 90, then subtract 28 from 90, which leads you to

2x =62, and the final step is to divide 2 from 62 which gets you 31.

Answer:

Step-by-step explanation:

Siny= 4xy +x²

dy/dx(cos y) =4y+ 4x(dy/dx)+2x

making dy/dx the subject

dy/dx(cos y)-4x(dy/dx)=4y+2x

dy/dx(cos y -4x)=4y+2x

dy/dx=(4y+2x)/(cos y -4x)

5⁻¹² is the expression that is equivalent to the quantity 5 raised to the negative second power times 5 raised to the sixth power end quantity all raised to the negative third power.

An expression is combination of variables, numbers and operators.

Given,

5 raised to the negative second power times 5 raised to the sixth power end quantity all raised to the negative third power.

This sentence can be written in the form below

(5⁻² × 5⁶)⁻³

According to laws of indices, we know that;

(a²)³ = a⁶

Thus;

(5⁻² × 5⁶)⁻³=(5⁻² )⁻³×(5⁶)⁻³

⇒ 5⁶ × 5⁻¹⁸

When bases are same then the powers will be added

⇒ 5⁶ × 5⁻¹⁸

⇒ 5⁻¹²

Hence, 5⁻¹² is the expression that is equivalent to the quantity 5 raised to the negative second power times 5 raised to the sixth power end quantity all raised to the negative third power.

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Answer:

1 divided by 5 raised to the twelfth power

Step-by-step explanation:

both of them equal the same thing

Answer: 4

Step-by-step explanation:

Every number you get is 4 higher than the previous number

The component of the data that a data analyst is most interested in is sample size.

Given,

To prevent results from being skewed or causing incorrect conclusions, we must identify the data element on which the data analyst should concentrate;

The data analyst;

A data analyst looks at data to uncover useful consumer insights and possible applications for the knowledge. They also tell the management of the business as well as other stakeholders of this information.

Although it is advisable for data analysts to have a foundational knowledge of statistics and mathematics, many of their responsibilities can still be carried out without it. However, knowledge in statistics, linear algebra, and calculus is often required for data analysts.

Here,

A data analyst's primary interest in the data is sample size

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Answer:

√12 = 3.46410161514

√50 = 7.07106781187

√84 = 9.16515138991

√200 = 14.1421356237

Step-by-step explanation:

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 9 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

If a person is making a minimum salary for a construction worker, in that case, they will make more than 75% of the teachers.

A salary is a form of periodic fee from a corporation to a worker, which can be laid out in an employment contract. it is contrasted with piece wages, in which every task, hour, or other unit is paid one after the other, in place of on a periodic foundation. From the factor of view of going for walks in a commercial enterprise, revenue can also be considered as the fee of obtaining and keeping human sources for jogging operations and is then termed personnel fee or salary cost. Payroll accounts are used in accounting to record.

Salary is a hard and fast amount of cash or compensation paid to a worker via an enterprise in return for work executed. salary is generally paid in fixed durations, for example, monthly bills of 1-twelfth of the annual salary.

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Using partial derivatives, we know that in order to optimize profit, the company should produce 7,000 type A solar panels and 8,000 type B solar panels annually.

A function of two or more variables can yield partial derivatives.

Writing the derivative with regard to x while treating all other variables as constants allows one to determine the partial derivative of a function with respect to one variable, let's say x.

The partial derivatives for each of the other

So, for a business making two different types of solar panels, the revenue and cost functions are provided by:

[tex]\begin{aligned}&R(x, y)=4 x+2 y \\&C(x, y)=x^2-4 x y+9 y^2+22 x-114 y-5\end{aligned}[/tex]

If revenue and cost are stated in millions of dollars annually, x represents the thousands of type A solar panels produced and sold annually, and y represents the thousands of type B solar panels produced and sold annually.

By deducting costs from revenues, the profit function is obtained as follows:

[tex]\begin{aligned}&P(x, y)=R(x, y)-C(x, y) \\&P(x, y)=4 x+2 y-\left(x^2-4 x y+9 y^2+22 x-114 y-5\right) \\&P(x, y)=-x^2-9 y^2-18 x+116 y+4 x y+5\end{aligned}[/tex]

The profit function's partial derivatives with regard to x and y are as follows:

[tex]\begin{aligned}&\frac{\partial P}{\partial x}=-2 x+4 y-18 \\&\frac{\partial P}{\partial y}=4 x-18 y+116\end{aligned}[/tex]

When both of these partial derivatives are equal to zero, the profit is maximized:

[tex]\begin{aligned}&0=-2 x+4 y-18 \\&0=4 x-18 y+116\end{aligned}[/tex]

The first equation above is multiplied by two, and the two equations are then added to yield:

[tex]\begin{aligned}&0=-10 y+80 \\&y=8\end{aligned}[/tex]

Inputting into the first equation results in:

[tex]\begin{aligned}&0=-2 x+4(8)-18 \\&2 x=14 \\&x=7\end{aligned}[/tex]

Therefore, using partial derivatives, we know that in order to optimize profit, the company should produce 7,000 type A solar panels and 8,000 type B solar panels annually.

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Answer: 40.24

Step-by-step explanation: Use the Pythagorean Theorem

a^2 + b^2 = [tex]\sqrt[2]{c}[/tex]

36^2 + 18^2 = [tex]\sqrt[2]{1620}[/tex]

1296 + 324 = 1620

[tex]\sqrt[2]{1620}[/tex] = 40.24

Using percentage formula, Malik can afford the board with the discount only if he has $120 with him

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

To know if Malik can afford the hoverboard, we have to calculate 20% of 150

20% of 150 = 20/100 = x /150

0.2 = x / 150

x = 150 * 0.2

x = 30

Subtracting the discount, the amount will be 150 - 30 = 120

Malik can afford the hoverboard if he has $120 with him.

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Answer:

1300=X

Step-by-step explanation:

Answer:

1,300

Step-by-step explanation:

You would first start off with adding 100 + 100= 200. Then you would add another 100 to 200 which is 300. Then comes the final step which is adding 1000 to 300 which = 1300

X= 1,300

The predicted quantity of balls in the first bin is (1/n)n.

Considering that,

There are the same number of balls and containers.

If so, then each container must always contain one ball. The probability of each ball landing in the first bin is (1/n)n.

For instance -

Three balls and three bins should be present. Next to each ball, place an A, B, and C. There are numbers 1, 2, and 3 on the containers. Ball A has a 1/3 chance of landing in bin 1. Although there is a 1/3 probability that ball B will drop in bin 1 and a 1/3 chance that ball C will do the same, both outcomes are possible. Therefore, bin 1 should be equal to 1/3 + 1/3 + 1/3. The rationale behind the projected values of bins 2 and 3 is identical.

According to the same logic, bins 2 and 3 should also have expected values of 1.

How probable is it that the first bin will receive all three balls?

In general, (1/n)n, which equals (1/3)3, or 1/3 x 1/3 x 1/3, equals 1/27.

Therefore, (1/n)n would be the expected number of balls in the first bin.

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When the null hypothesis is rejected

The  conclusion is that there is enough evidence to support the claim of the researcher

When a type I error occurs. The consequences is that the conclusion that there is enough evidence to support the claim of the researcher is actually incorrect

When a type II error occurs. The consequences is  that the conclusion that there is enough evidence  to support the claim of the researcher is actually correct      

From the question we are told that,

Generally if the null hypothesis is rejected then the conclusion would be that there is enough evidence to support the claim of the researcher

Generally a Type I error is a an error that occurs when the null hypothesis is incorrectly rejected

So in the case of this question the consequence of making this type of error is that the conclusion that there is enough evidence to support the claim of the researcher is actually incorrect

Generally a Type II  error is an error that occurs when the null hypothesis is incorrectly not rejected

So in the case of this question the consequence of making this type of  

error is that the conclusion that there is enough evidence to support the claim of the researcher is actually correct.

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