Find the surface area and volume of the solid. Round each measure to the nearest tenth, if necessary.

Answer: 220

Step-by-step explanation: quick maths ;)

Answer:

lets denote x as 6

so,

(x-2)÷2

(6-2)÷2

4÷2

2(proved)

The length of each side of the octagon would be 8.23 inches.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

We are aware that one side of the square is 20 inches long and that one side is made up of the length of the octagon added. We also know that two sides of a right triangle have smaller angles inside that are 45 degrees, making those two sides equal to one another. Therefore, we add the two sides of the right angle triangle to the side of the octagon, which equals 20 inches, to determine the value of x, which is designated as the side of the octagon.

Since a side of the square is 20 inches

Here, y is the two equal sides of the right-angle triangle

So y + x + y = 20

Using Pythagoras's theorem for the right angle triangle

y² + y² = x²

2y² = x²

y² = (x²)/2

y = x /√2

So substitute the value of y = x /√2 in the equation

x /√2 + x + x /√2 = 20

2x /√2 + x = 20

2x /√2 + x√2 /√2 = 20

x[2/√2 + √2 /√2] = 20

x[(2 + √2) /√2] = 20

x(2 + √2) = 20√2

x = 20√2/(2 + √2)

x = 28.2843/3.4142 = 8.2343

Round to the nearest hundredth of an inch

x = 8.23

Therefore, the length of each side of the octagon would be 8.23 inches.

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Based on the equation, the value of x in 8x^2 + 9 = 313 is 6.2

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The quadratic equation is given as

8x^2 + 9 = 313

Subtract 9 from both sides of the quadratic equation

So, we have

8x^2 + 9 - 9 = 313 - 9

Evaluate the difference in the above equation

So, we have

8x^2 = 304

Divide both sides of the quadratic equation by 8

So, we have

8x^2/8 = 304/8

Evaluate the quotient in the above equation

So, we have

x^2 = 38

Take the square root of both sides

x = 6.2

Hence, the value of x in the quadratic equation given as 8x^2 + 9 = 313 is 6.2

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Answer:

7⁻²=[tex]\frac{1}{49}[/tex]

3⁻⁴ [tex]=\frac{1}{81}[/tex]

9⁰=1

11⁻¹=[tex]\frac{1}{11}[/tex]

Answer:

13

Step-by-step explanation:

d) = √(-1 - -6)2 + (-4 - 8)2

= √(5)2 + (-12)2

= √169

= 13

Answer:

13

Step-by-step explanation:

We use the distance formula to find the distance between two points

d = sqrt ( (x2-x1)^2 + y2-y1) ^2)

Where ( x1,y1) and ( x2,y2) are the two points

d = sqrt( ( -1 - -6) ^2 + ( -4 - 8) ^2)

   = sqrt ( ( -1+6) ^2 + ( -12) ^2)

  = sqrt( 5^2 + 144)

 = sqrt ( 25+ 144)

 = sqrt ( 169)

 = 13

use real numbers for the proof

3^3 times 3^2 =

27 times 9 =

243 which is

3^5

The probability that a group consisting of 2 Democrats and 2 Republicans will be chosen for early release will be 5/11.

It should be noted that probability simply means the likelihood that a particular event will happen.

In this case, there are there are 5 Democrats and 6 Republicans and rour of these people will be randomly chosen for early release.

The probability that a group consisting of 2 Democrats and 2 Republicans will be chosen for early release will be:

Number of Democrats = 5

Number of Republicans = 6

Total number = 5 + 6 = 11

This will be illustrated through the combination formula:

= (5C2 × 6C2) / 11C4

= (10 × 15) / 330

= 150/330

= 5/11

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For function f(x) = (x − 1)³ and g(x) = 1-6x ,value of following function is:

a. (f ∘ g)(x)=-216x³

b. (g ∘ f)(x)=-6x³+18x²-18x+7

c. f(f(x))=(x³ -3x² +3x -2)³

d. f²(x)=(x-1)⁶

As given,

Given function :

f(x)=(x − 1)³

g(x)=1-6x

The value of following functions are:

a.(f ∘ g)(x)

=f(g(x))

=f(1-6x)

=(1-6x -1)³

=(-6x)³

=-216x³

b.  (g ∘ f)(x)

= g(f(x))

=g(x − 1)³

=1 -6(x − 1)³

=1 -6(x³ -3x² +3x -1)

=-6x³+18x² -18x+7

c. f(f(x))

=f(x-1)³

=((x-1)³ -1)³

=(x³ -3x² +3x -1-1)³

=(x³ -3x² +3x -2)³

d. f²(x)= (f · f)(x)

=f(x) × f(x)

=(x-1)³ × (x -1)³

=(x -1)⁶

Therefore, for function f(x) = (x − 1)³ and g(x) = 1-6x ,the value of following function is:

a. (f ∘ g)(x)=-216x³

b. (g ∘ f)(x)=-6x³+18x²-18x+7

c. f(f(x))=(x³ -3x² +3x -2)³

d. f²(x)=(x-1)⁶

The complete question is:

For function f(x) = (x − 1)³ and g(x) = 1-6x find the value of the following.

a. (f ∘ g)(x)

b. (g ∘ f)(x)

c. f(f(x))

d. f²(x)= (f · f)(x)

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We use the following formula for integration:

We have the following integral:

Separate into two integrals:

Calculate the first integral. Take the coefficient out of the integral:

Apply the integration formula:

Calculate the second integral. Take the coefficient out of the integral:

Express the radical as a fractional exponent:

Apply the integration formula:

The total integral is:

Answer:

349.42499999998

Step-by-step explanation:

$232.95 divided by 22 hours of work = amount per hour = 10.588636363636

If you get paid 10.588636363636 per hour then multiply this by 33 hours to get the answer of : $349 and 42499999998 cents

The probability of getting 12 p events is 0.0139

The expected value, or mean, of a binomial distribution is calculated by multiplying the number of trials (n) by the probability of successes (p), or n x p.

The binomial distribution formula is calculated as:

[tex]P(x:n,p) = ^nC_x * p^x*(1-p)^ {n-x}[/tex]

where:

n is the number of trials (occurrences)

X is the number of successful trials

p is probability of success in a single trial

is the combination of n and x. A combination is the number of ways to choose a sample of x elements from a set of n distinct objects where order does not matter and replacements are not allowed.

So, we have given that N = 15, P = 0.50 , and x = 12

So,

[tex]^{15}C_1_2 * (0.50)^{12}*(1-0.50)^ {15-12}\\^{15}C_1_2 * 0.50^{12}*(0.50)^ {3}\\[/tex]

=0.0139

Therefore, the probability of getting exactly 12 P events is 0.0139

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The polynomial for the total electricity generated by both geothermal and wind power during 2002-2007 is given by adding the two other ones, we will get:

862x^2 + 93x + 24,621

Here we have two polynomials:

Both of these are in gigawatts, so are in the same units, which means that we can directly add the two polynomials to get a polynomial for the total electricity.

-17x^2 + 165x + 14,481 + 879x^2 - 72x + 10,140

Now we group like terms:

(-17x^2 + 879x^2) + (165x - 72x) + (14,481 + 10,140)

862x^2 + 93x + 24,621

This polynomial represents the total electricity generated during 2002-2007

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3y - y= -5

2y= -5

y= -5/2

y= -2.5

rounded of answer is 3

Only D satisfies both of the inequalities in the system represented by the graph. (Please check the graph attached)

Equations are not necessarily about having a "equal to" sign balanced evenly on both sides. It can occasionally refer to a "not equal to" connection, where one object is more than the other or less than. A connection that compares two numbers or other mathematical expressions in an unequal way is referred to as an inequality in mathematics. These mathematical statements are classified as inequalities in the algebraic language.

To test point in that system satisfies both of the inequalities

The system of inequalities is shown by the graph.

While x + 2y is more than or equal to 3, 2x + 3y is less than or equal to 4.

Both of the system's inequalities represented by the graph are satisfied at the test point (4, -1).

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Step 1 of the solution:

Let the parent function of the absolute value function is f(x) = |x|

Step 2 of the solution:

This function passes through (0, 0) and slope = 1 or -1.

Step 3 of the solution:

After transformation vertex (0, 0) becomes (-2, 3) and a point through which this function passes through is (-1, 0)

Step 4, let's find the slope of the absolute value funtion, this way:

Step 5: Interpretation

Since slope of the absolute value function is less than the parent function: -3 < -1

Therefore, the parent function will be dilated by a scale factor other than 1.

Answer:

aaaaaaaaaa

Step-by-step explanation:

aaaaaaaa

Answer:

m=-4/3

Explanation:

Given the points: (13,-4) and (1, 12)

To determine the slope of the line that joins the point, use the formula below;

Substitute the given points:

The slope is -4/3.

P is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P if P(x) is a polynomial with integer coefficients and if is a zero of P(x) (P() = 0). (x).

The Reasonable Zeros Theorem can be used to locate every rational zero in a polynomial.

According to the Rational Zeros Theorem, if P(x) is an integer-coefficient polynomial and is its zero (P() = 0), then p is a factor of P(xconstant )'s term and q is a factor of P's leading coefficient (x).

Finding the rational solutions to a polynomial equation is done using the rational root theorem, as its name suggests (or zeros or roots of a polynomial function). The answers obtained from any polynomial equation are referred to as the roots or zeros of polynomials. It's not necessary for a polynomial to have rational zeros.

So, to find rational zero theorem states:

If  P(x) is a polynomial with integers coefficients and if is a zero of P(x)(P()=0), then

P is a factor of the constant term of P(x) and q is a factor of of the leading coefficient

Of P(x).

To find all the rational zero of a polynomial we can use the rational zeros theorem

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The the minimum and maximum possible measures of 31 centimeters is {30.5. 31.5}

To find it, one need to add the biggest possible inaccuracy to each measurement, then multiply to get the biggest volume you can. Also Subtract the largest potential mistake from each measurement, then multiply, to to know the smallest volume that can be produced.

Note that the smallest value in the data set is the minimum. The highest value in the data collection is called the maximum.

Since only one data set is given, the  possible measures can only be around it hence the largest and the smallest value close to it.

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Answer: 6.67

Step-by-step explanation: first you divide 4 and 3 to then get 1.3 and times that by 5

The points at which a graph changes direction (from increasing to decreasing or decreasing to increasing) are called turning point.

A turning point is when the derivative's sign changes. A relative maximum or relative minimum might mark a turning point (also known as local minimum and maximum). A turning point is a stationary point if the function is differentiable, however not all stationary points are turning points.

A turning point is a location on a graph where the trend shifts from rising to dropping or from decreasing to increasing (falling to rising). To determine the point, identify the leading term of the polynomial function if the function were enlarged. A polynomial of degree n will have at most n1 turning points. Next, determine the polynomial function's degree.

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Using speed, distance and time relation, Mr. Vigrass  will travel 48 miles  in an hours.

If we know how far something travels and how long it takes, we can determine how fast something is moving in a straight line. This equation illustrates the link between journey time, distance, and speed:

Distance divided by travel time equals speed.

Distance equals Time * Speed

Time = Speed / Distance

Distance x Time equals Speed

Given,

distance = 168 miles

time = 3 1/2 hours

speed = distance / time

speed = 168 × 2/7

speed = 48 miles/hour

At same speed,

distance travelled in 1 hour will be

distance = speed × time

distance = 48 × 1

distance = 48 miles.

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The distance between two points is 15.

The length of the line segment bridging two points on a plane is known as the distance between the points. Counting each number in between them is a quick and easy approach to determine how far apart two numbers are on a number line. Finding the distance by taking the absolute value of the values' difference is a quicker method. For instance, |4| and |-4| have the same absolute value of 4, which is 4.

Given Data

Points (-8,7) and (5,7)

Formula of distance between two points

d = [tex]\sqrt{(x_{2} - x_{1})^{2}+(y_{2} - y_{1})^{2} }[/tex]

x₂= 7 x₁= -8

y₂ = 7 y₁ = 7

d = [tex]\sqrt{(7-(-8))^{2}+(7-7)^{2} }[/tex]

d = [tex]\sqrt{(7+8)^{2}(0) }[/tex]

d = [tex]\sqrt{15^{2} }[/tex]

d = 15

The distance between two points is 15.

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If Seema tend to make used of compatible numbers to estimate the product of (–25.31)(9.61). her estimate is -$250.

Given data  or information :

Product  = ( – 25. 31 ) (9. 61)

Now let estimate the product by first  approximating the product to the nearest tenth.

Approximation :

So,

-25.31 = - 25 ( Approximately )

9.61 =10 ( Approximately )

Hence , her estimate can be calculated as :

Estimate :

Estimate =  (-25) (10)

Estimate =-250

Therefore based on the information or data  given if  Seema  tend to make used of  compatible numbers to estimate the product of (–25.31)(9.61). her estimate is -$250.

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Based on your original grades in your exams and the scores after you retake your exams, the percentage points you improved your average score by is 3.83%

To find the percentage that you improved by, the first thing to do is to find your average score in the first exam:
= (75 + 85 + 90 + 90 + 100 + 75 + 80 + 100 + 90) / 9

= 785 / 9

= 87.22

The average score after the exam was retaken was:

= (85 + 85 + 100 + 90 + 100 + 85 + 80 + 100 + 90) / 9

= 815 / 9

= 90.56

The percentage increase is:

= (90.56 - 87.22) / 87.22 x 100%

= 0.0382939692731024994267369869296 x 100%

= 3.83%

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$8,125 is the compound interest.

What is compound interest?

P = $6500

R = 25%

T = 1

compound Interest A = P( 1 + r/100)ⁿ

                                   = 6500( 1 + 25/100)¹

                                   = 6500( 5/4)

                                   = 6500 * 5/4

                                   = $8,125

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Given:

Depreciation rate = 75% per year.

Let's find the value of the car in 2 years.

Given:

Cost = $16,500

Depreciation rate = 75%

From the equation we have:

Present value, a = 16500

x is the number of years = 2

Thus, we have:

Therefore, the value of the car in 2 years is $1,031

ANSWER:

$1,031