Find the Total Surface Area and volume of the prism below. Round to the nearest hundredth, if necessary.
12 yd
10 yd
12 yd
Total Surface Area =
Tyds squared
yds cubed
Volume =

Answer:

The inverse function of the exponential function f(x) = a^x is the logarithmic function with base a.

The inverse function of a function f is a function that "undoes" the original function, meaning that it reverses the transformation applied by the original function. In the case of the exponential function, the inverse function is the logarithmic function, which "undoes" the transformation applied by the exponential function.

For example, suppose we have the exponential function f(x) = 2^x. The inverse function of this function is the logarithmic function with base 2, which is written as y = log_2 x. If we apply the inverse function to 2^x, we get:

y = log_2 (2^x)

Solving for x gives:

x = 2^y

This means that the inverse function of the exponential function f(x) = a^x is the logarithmic function with base a, which is written as y = log_a x.

The other options (a. transcendental, c. rational, d. polynomial, e. algebraic) are not correct, since they do not describe the inverse function of the exponential function.

Answer:

b. logarithmic

Step-by-step explanation:

Given exponential function:

[tex]f(x)=a^x[/tex]

The inverse of the given function is the logarithmic function with base a.  

To find the inverse of a function, replace f(x) with y:

[tex]\implies y=a^x[/tex]

Swap the x and y:

[tex]\implies x=a^y[/tex]

Take logs with base a of both sides of the equation:

[tex]\implies \log_ax=\log_aa^y[/tex]

Apply the log power law:  logₐ xⁿ = n logₐ x

[tex]\implies \log_ax=y\log_aa[/tex]

Apply the log law:  logₐ a = 1

[tex]\implies \log_ax=y[/tex]

[tex]\implies y=\log_ax[/tex]

Replace y with f⁻¹(x):

[tex]\implies f^{-1}(x)=\log_ax[/tex]

Thus proving that the inverse of the exponential function f(x) = aˣ is the logarithmic function with base a.            

Answer:

Step-by-step explanation:

You want the 6 trig functions of the angle -5π/6.

The angle is in the 3rd quadrant, so all trig functions are negative except the tangent and cotangent. The reference angle is -5π/6 +π = π/6.

Since you have memorized the values of the trig functions for multiples of π/6, you know ...

  sin(-5π/6) = -1/2

  cos(-5π/6) = -√3/2

  tan(-5π/6) = sin/cos = √3/3

  csc(-5π/6) = 1/sin = -2

  sec(-5π/6) = 1/cos = -2√3/3

  cot(-5π/6) = 1/tan = √3

Answer/Step-by-step explanation:

Use a Unit Circle, you may have access to (hopefully) or have been asked to memorize.

To find -5pi/6 count clockwise the sixths to 5. Or add:

-5pi/6 + 2pi

= -5pi/6 + 12pi/6

= 7pi/6

-5pi/6 is the same as 7pi/6 on the Unit Circle.

Use the coordinates at that spot

(-root3/2 , -1/2)

to find the six trig ratios.

The Unit Circle is a big, giant, Answer Key. It has all the trig answers on it all in one place. It looks like a scary math pizza, but really its all the answers all in one place.

Once you find your angle, the sine is the y-coordinate.

sin theta = -1/2

The cosine is the x-coordinate.

cos theta = -root3/2

Tangent theta is the sine over the cosine, sin/cos,

= y/x

= (-1/2) / (-rt3/2)

Use Keep-Change-Flip to simplify this.

see image.

= root3/3

Sec is cos flipped over. Csc is sin flipped over. Cot is tan flipped over (the math word is reciprocal)

Yes, just flip over sin to get csc:

sintheta = -1/2

csctheta = - 2/1 = -2

Flip over cos to get sec:

costheta = -rt3/2

sectheta = 2/-rt3

Then rationalize, see image.

= -2rt3/3

Flip over tan to get cot.

tantheta = 1/rt3

Use a form that's easy to flip.

cottheta = rt3/1 = rt3

see image.

Answer:

C).    690

Step-by-step explanation:

When you see the word "sum" that means you add the numbers together

667 + 23 = 690

Answer:

OC. 690

Step-by-step explanation:

To find the sum of 667 and 23, you need to add the two numbers together. When you do this, you get 690 as the result. Therefore, the sum of 667 and 23 is 690.

This can be written as an equation: 667 + 23 = 690. The symbol "+" is used to represent the operation of addition, and the equals sign "=" is used to show that the value on the right side of the equation is the result of the operation on the left side.

In general, when you add two or more numbers together, you find their sum by combining their values and counting the total. For example, to find the sum of the numbers 3 and 4, you would add them together to get 7. To find the sum of the numbers 5, 6, and 7, you would add them together to get 18.

I hope this helps to clarify the concept of addition and the meaning of the term "sum." Let me know if you have any further questions.

Correct interpretation of this result is together, income and friend count account for 45% of the variation in happiness.

Variation refers to this relationship between the change in a variable's value when the values of the linked variables change. An example of a straightforward equation, y = mx, in which m is a constant, can be used to show this. The equation becomes y = 5x if we suppose that the value of m is 5. A function in which the variables are related by how they alter in relation to one another is known as a variation function. In this function, for instance, if x rises or falls, D follows suit. Direct and inverse variation functions are the two different categories of variation functions.

Given

A researcher is examining the effects of income (X1) and number of friends (X2) on personal happiness (Y) and finds an R2 of 0.45.

Here, the independent variables of income (X₁) and friend count account (X₂) for 45% of the variation in happiness.

Correct interpretation of this result is:

D) Together, income and friend count account for 45% of the variation in happiness.

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Two members of the maths competition team solve 13 problems in 1 hour.

Person=13

Time=1 hour

Then.

Rate=13/1 (person/time)

With the help of question,

Let us consider,

x team members are needed to solve in 1 hour 39 problems,

2M×1/13=1×xM/39

2M/13=x M/39

2M=x M/13

M=26

26 team members are needed to solve in 1 hour 39 problems,

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The inequality that represents the line in the figure will be y > - (2/3) x + 3.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

From the figure, the points of the line are (0, 3) and (3, 1). And the region above the line is a consideration. Then the equation of the line is given as,

(y - 3) > [(3 - 1) / (0 - 3)](x - 0)

Simplify the equation, then we have

(y - 3) > [(3 - 1) / (0 - 3)](x - 0)

(y - 3) > - (2/3)x

y > - (2/3) x + 3

The disparity that addresses the line in the figure will be y > - (2/3) x + 3.

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Answer:

a = 8

b = 2

c = 48

Step-by-step explanation:

3 cups of flour is needed to make 24 servings.

3:24

Simplify. First, divide 3 from both sides of the ratio.

(3)/3 : (24)/3

1:8

Next, solve for b. You multiply 2 to 8 to get 16. Next, multiply 2 to 1

1 x 2 = b = 2

Finally, multiply 8 to 6 to get c.

8 x 6 = c = 48

~

Based on the information provided, a linear model is not appropriate for summarizing the relationship between home size and sale price because of the random scatter of points in the residual plot. In a linear model, the residuals should be randomly distributed around a mean of zero, without any discernible pattern. However, the residual plot shown in the question indicates that the residuals are randomly scattered throughout the graph, which suggests that a linear model may not be the best way to summarize the relationship between the variables. Therefore, a linear model is not appropriate for this data.

Answer:

Not Appropriate

Step-by-step explanation:

Based on the information provided in the problem, it appears that a linear model is not appropriate for summarizing the relationship between home size and sale price. This is because the residual plot shows a random scatter of points, which suggests that there is not a strong linear relationship between these variables. Furthermore, the scatterplot of home price versus home size shows a line with a positive slope, which indicates that there is some relationship between these variables, but it is not necessarily a linear relationship. In this situation, it would be more appropriate to use a non-linear model to summarize the relationship between home size and sale price.

The expression to the scenario it's represent is as follows:

The price of a USB memory stick selling at 21% discount off it marked price(m) → 0.21m

The price of Cd that sells for 21%  more than the amount (m) needed to manufacture the CD → 1.21m.

The final value of painting after the initial value, m increases by 2 / 5 → 7 / 5 m.

The total number of markers Nancy have if she gives away 2 / 5 of her m markers to Amy → 3 / 5 m

An algebraic expression is made up of variables and constants, along with algebraic operations like subtraction, addition, multiplication and division.

Therefore, let's match the algebraic expression with the scenario.

The price of a USB memory stick selling at 21% discount off it marked price(m).

Hence, the expression is 21% of m = 21 / 100 m = 0.21m

The price of Cd that sells for 21%  more than the amount (m) needed to manufacture the CD.

Hence, the expression is 21%m + m  = 0.21m + m = 1.21m.

The final value of painting after the initial value, m increases by 2 / 5.

Hence, the expression is 2 / 5 m + m = 7 / 5 m.

The total number of markers Nancy have if she gives away 2 / 5 of her m markers to Amy.

Hence, the expression is m - 2 / 5 m = 3 / 5 m.

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Answer:

-----------------------------------

Given:

Distribute and simplify it to get  equivalent expression:

This is matching the last option.

The length of the birth in centimeters will be 58.42 centimeters.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

James was also measured 23 inches long.

We know that, in one inch, there are 2.54 centimeters.

The length of the birth in centimeters is calculated as,

⇒ 23 inches

⇒ 23 x 2.54 centimeters

⇒ 58.42 centimeters

The number of birth in centimeters will be 58.42 centimeters.

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Taking two count variables, say count3 and count5, to store the count of numbers divisible by 3 and 5 respectively.

Iterate over the range [1, N] using a variable, say i, and perform the following steps:

If the value of count3 and count5, print “FizzBuzz”.

If the value of count3 is equal to 3, print “Fizz”.

If the value of count5 is equal to 5, print “Buzz”.

If none of the above conditions match, then print i.

In a typical coding challenge during an interview, candidates are asked to create a solution that prints integers from 1 to N, designating any integers that are divisible by 3 as "Fizz," any integers that are divisible by 5 as "Buzz," and any integers that are both divisible by 3 and 5 as "FizzBuzz." Good coding practises can be reinforced by knowing how to solve it.

// C++ program for the above approach

#include <bits/stdc++.h>

using namespace std;

// Function to generate FizzBuzz sequence

void fizzBuzz(int N)

{

// Stores count of multiples

// of 3 and 5 respectively

int count3 = 0;

int count5 = 0;

// Iterate from 1 to N

for (int i = 1; i <= N; i++) {

// Increment count3 by 1

count3++;

// Increment count5 by 1

count5++;

// Initialize a boolean variable

// to check if none of the

// condition matches

bool flag = false;

// Check if the value of count3

// is equal to 3

if (count3 == 3) {

cout << "Fizz";

// Reset count3 to 0, and

// set flag as True

count3 = 0;

flag = true;

}

// Check if the value of count5

// is equal to 5

if (count5 == 5) {

cout << "Buzz";

// Reset count5 to 0, and

// set flag as True

count5 = 0;

flag = true;

}

// If none of the condition matches

if (!flag) {

cout << i;

}

cout << " ";

}

}

// Driver Code

int main()

{

int N = 15;

fizzBuzz(N);

return 0;

}

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Answer:

3.8

Step-by-step explanation:

4 x 0.95 = 3.8

The possible value for the side length of the plot of land is 46 meters.

Area is a measurement of the size of a two-dimensional space or shape. It can be measured in square feet, square meters, and other units of measurement. Area is often used to measure the size of a room, a garden, a piece of land, and many other objects. In mathematics, area is a concept used to calculate the size of a shape or figure. It is calculated by multiplying the length of a shape by its width. Area can also refer to the total amount of space a shape takes up, such as the area of a circle or triangle.
The area of a square is calculated by multiplying the length of one of its sides by itself. Therefore, the side length of Abby's plot of land can be calculated by taking the square root of the area. The square root of 2200 is 46.89, and of 2400 is 48.98. Therefore, the possible side lengths of Abby's plot of land are 46 meters and 48 meters.
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Step-by-step explanation:

the slope-intercept form is in general

y = ax + b

a being the slope, b being the y-intercept (the y-value when x = 0).

the slope is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.

we got 2 points identified, so, let's use them.

(2, 44) and (5, 80)

x changes by +3 (from 2 to 5).

y changes by +36 (from 44 to 80).

the slope is +36/+3 = 12.

so, we got "a" for our equation. to get "b" we need to use the coordinates of one of the given points as x and y.

I usually use the one with the smaller numbers.

here : (2, 44).

44 = 12×2 + b = 24 + b

b = 44 - 24 = 20

our equation is

y = 12x + 20

The solution to the equation 125x³ - 27 = 0 is (5x−3)(25x ^2 +15x+9)

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculationsolving the equation 125x³ - 27 = 0 by grouping

Rewriting 125x^ 3 −27 as (5x) ^3 −3³

The difference of cubes can be factored using the rule:: a ^3 −b^ 3 =(a−b)(a^ 2 +ab+b^ 2 )

Polynomial 25x^ 2 +15x+9 is not factored since it does not have any rational roots.

Hence, (5x−3)(25x ^2 +15x+9)

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Answer:

7x+7y siuuuuuuuuuuuuuuuuu

Step-by-step explanation:

i hope this helps u get an idea how to solve the problems, sorry for the bad handwriting though

Good luck!!

The interval of convergence of the power series is (-10/7, 10/7).

What does Interval of convergence tell you?

A group of x-values on which a power series converges is known as the interval of convergence. In order to create a convergent series, you can plug in this interval of x-values.

The interval of convergence of a power series is the set of values of x for which the series converges. To find the interval of convergence of the given power series, we can use the ratio test.

The ratio test states that if the series [tex]∑ a_nx^n[/tex] has a positive radius of convergence R, then the series converges for |x| < R and diverges for |x| > R. The radius of convergence is given by the formula

                     [tex]R = 1/limsup|a_n+1/a_n|.[/tex]

In the given power series, the coefficient [tex]a_n[/tex] is given by  [tex]a_n = (7x)^n/(10n)!.[/tex]

We can rewrite this as [tex]a_n = x^n(7/10)^n/n!.[/tex]

Taking the limit of the ratio [tex]a_n+1/a_n[/tex] as n goes to infinity, we get:

             [tex]limsup|a_n+1/a_n| \\\\= limsup|x^(n+1)(7/10)^(n+1)/(n+1)!/(x^n(7/10)^n/n!)|\\\\= limsup|x(7/10)/(n+1)|\\\\= |x(7/10)|[/tex]

Therefore, the radius of convergence R is [tex]1/|x(7/10)|[/tex].

This means that the interval of convergence is  [tex]|x| < 1/|7x/10| = 10/7.[/tex]

We can check the endpoints of the interval to see if the series converges at these points. At x = 10/7, the series becomes [tex](7(10/7))^n/(10n)! = 1^n/(10n)!.[/tex]

This series is a geometric series with first term 1 and common ratio 1/10, and it converges because [tex]|1/10| < 1.[/tex]

At x = -10/7, the series becomes[tex](7(-10/7))^n/(10n)! = (-1)^n/(10n)![/tex]. This series is an alternating series with first term 1 and common ratio (-1/10), and it also converges because [tex]|-1/10| < 1.[/tex]

Therefore, The interval of convergence of the power series is (-10/7, 10/7).

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Answer:

Exact  answer 12 +  6[tex]\sqrt{2}[/tex]

Answer rounded to the nearest whole number 20

Step-by-step explanation:

B. Because the standard deviation is unaffected by a change in a single data value, it will remain unchanged.

A change in a single data value has no impact on the standard deviation, which measures the spread of a data collection. As a result, even if the single data value changes, the standard deviation won't.

The variability of a data set is measured by the standard deviation. It is calculated by taking the square root of the average of the sum of the squares of the differences between each value in a data set and the mean. When a single value in a data set is changed, the mean of the data set will change, but the standard deviation will not be affected. This is because the standard deviation is not calculated based on individual data points, but on the overall variability of the data set. Therefore, when a single data value is changed, the standard deviation of the data set will remain the same.

Let x be one of the students in the class

Mean = (76.9 + 82)/2 = 79.4

Standard Deviation = sqrt(((76.9 - 79.4)^2 + (82 - 79.4)^2)/2) = 3.2

The complete question is : There are 40 students in a college statistics class. After the first exam, their instructor told them that the class scores were normally distributed with a 10 points mean of 76.9 and a standard deviation of 3.2. However, one of the students pointed out that the instructor recorded 28 for his score when he actually earned 82. The class recalculates the mean and standard deviation The mean is now 78.1. Which of the following is true about the standard deviation? A. The standard deviation will increase because the value of an exam score increased. B. The standard deviation will stay the same because it is not affected by a change in a single data value C. The standard deviation will decrease because the change moved an exam score closer to the mean D. The standard deviation will increase because the change moved an exam score further from the mean

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(i) The triple integral that gives the volume of the right circular cylinder enclosed by the surfaces x^2 + y^2 = 4 , z=-10 and z=0 is:

where the limits of the integration are:

0 ≤ x ≤ 2*sqrt(2), -2*sqrt(2) ≤ y ≤ 2*sqrt(2), 0 ≤ z ≤ -10.

This triple integral gives the volume of the right circular cylinder which is enclosed by the given surfaces and extends from z = 0 to z = -10.

(ii) The triple integral that gives the volume of the right circular cylinder with a hemisphere sitting atop the cylinder is:

where the limits of the integration are:

0 ≤ x ≤ 2*sqrt(2), -2*sqrt(2) ≤ y ≤ 2*sqrt(2), 0 ≤ z ≤ -10, and 0 ≤ r ≤ sqrt(x^2 + y^2).

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Answer:

740

Step-by-step explanation:

R = 200

Blue = 200-20 = 180

Green = 2(200-20) = 2( 180) = 360

200 + 180 + 360

740

Answer:

Red section (full)=200 people

Blue section (full)=200-20=180 people

Green section (full)=2×blue section ( full)=2×180=360 people

Stadium (full)=(200+180+360) people=740 people

The median is 43 g. By using median formula and by simple observation method we can find median of the given data.Hence median is 43 g.

The middle number ,by ordering all data points and picking out the one in the middle.Arrange the all values from lowest to highest.Then we can find easily.Median is also type of average which is used to find centre value.

There are the following formula we use to find median.

Median= (n+1)th/2  terms (if n is odd)

Where n is the number of observations.

So,if n is even then we use

Median= (n/2)th  terms

if number of term is even,then the median is the simple average of the middle two numbers.  

So we can find median by two methods

median= n/2 -th term

median =6/2 -th term

median = 3-th term

Hence our third term is 43 g so our median will be 43 g.

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There will be enough leftover yarn to knit a scarf for her younger brother If the child scarf takes 125 yards of yarn.

What is Unit conversion ?

Unit conversion is a necessary step in many mathematical problems. Calculations must be performed using mathematical conversions.

Tessa has bought 9 balls of yarn which are each 185 yards long.

So, She has total 1665 (185 × 9) yards of yarn.

She needs 1450 yards of yarn to knit a blanket.

So, The leftover yarn = 1665 - 1450

                                   = 215.

She needs 125 yards of yarn to knit a scarf for her brother.

So, She has enough yarn to knit the scarf for her brother because the leftover yarn is greater than the yarn needed for scarf.

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The distance between these two points is given as follows:

[tex]d = 2\sqrt{1 - a}[/tex]

The equation of the parabola is given as follows:

y - k = a(x - h)².

Hence:

y = a(x - h)² + k.

The horizontal line one unit above the vertex has the equation given as follows:

y = k + 1.

(as k is the y-coordinate of the vertex).

Then the intersection of this line with the graph is obtained as follows:

k + 1 = a(x - h)² + k.

a(x - h)² = 1

(x - h)² = 1 - a

[tex]x - h = \pm \sqrt{1 - a}[/tex]

[tex]x = \pm \sqrt{1 - a} + h[/tex]

Then the points are given as follows:

The distance between these two points is of:

[tex]d = \sqrt{1 - a} + h - (-\sqrt{1 - a} + h)[/tex]

[tex]d = 2\sqrt{1 - a}[/tex]

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Answer: 9/2

Step-by-step explanation:

To express 0.27 and 0.06 as fractions, we first need to convert them to fractions with denominators that are powers of 10. We can do this by multiplying 0.27 by 100 to get 27/100, and multiplying 0.06 by 100 to get 6/100. The ratio of 0.27 to 0.06 is then equal to the ratio of 27/100 to 6/100, which simplifies to 27/6. To express this ratio in simplest form, we can divide both the numerator and denominator by the greatest common factor of 27 and 6, which is 3. This gives us a simplified fraction of 27/6 = 9/2.

Answer:

Below

Step-by-step explanation:

2x-y = 20

2x + y = 48       add the two equations to get

4x = 68

x = 17    <==== use this value in either equation to calculate y = 14

Mark can travel a distance of 110 km on 1000 worth of gas.

The operations that we use in daily life are problems like adding, subtracting adding multiple times, and dividing things are called Mathematical operations.  

The four basic mathematical operations are

1. Adding, 2. Subtracting, 3. Multiplication, and 4. Division.

Here in this problem, we use Multiplication and Division to solve the

Here we have

Mark car can travel 22 km per liter of gas costs 200 per liter  

Here we need to find how many kilometers can mark travel on 1000 worth of gas

Given the cost of 1 liter of gas = 200 Rs

=> Amount gas that can be worth 1000 = 1000/200 = 5 liter  

Given Mark can travel 22 km with 1 liter

The distance can be travel with 5 liters = 5 × 22 = 110 km

Therefore,

Mark can travel a distance of 110 km on 1000 worth of gas.

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