Find the surface area of the figure.Assume the cylinder is closed at both ends. Use 3.14 for π and round to the nearest hundredth, if necessary.

The question requires that you evaluate the product of the given mixed fractions:

Express, the mixed fractions as improper fractions:

Since 3 can divide 57 without remainder, it follows:

Change the improper fraction to mixed fraction:

The product of the mixed fractions is 40 3/8.

The recursive formula is of the form

a1 = first term

an = in terms of the previous term

The first term is 1

a1 =1

Looking at the function the second term is found by adding 2 to the first term

a2 = a1+2

The third term is found by adding 3 to the second term

a3 = a2+3

The fourth term is found by adding 4 to the 3rd term

a4 = a3+4

The an part of the recursive formula can be written as

an = a(n-1) + n

Answer:

Let us first bring the equation given into the slope-intercept form.

We see that the above equation has slope 3/ 5, and therefore, the equation that we want to construct must also have this slope. Hence, we already know that the equation we are seeking must take the form

where b is the y-intercept yet unknown.

Let us plug in (x, y) = (8, -4) in the above equation, this gives

Hence, the equation of the line in slope-intercept form is

The roots of the polynomial function are x=-2, x=5 and x=-6

You can express them as

(x+2)(x-5)(x+6)=0

To reach the cubic function you have to expand this expression.

Apply the distributive propperty of multiplications to solve.

First multiply the first two parentheses:

Next multiply this result to the third parentheses:

The solution is the third option.

The cubic function f(x) =  x³ + 3x² - 28x - 60 has zeroes -2, 5, and -6, hence, the third option is the correct answer.

For any cubic function with zeroes α, β, and γ,

Here we have the zeroes as  2, 5, and -6.

Therefore, the factors are (x - (-2)), (x - 5), and (x - (-6))

= (x + 2), (x - 5), and (x + 6)

Therefore the function will be

(x + 2)(x - 5)(x + 6)

Solving the first 2 brackets gives us

(x² - 5x + 2x - 10)(x + 6)

= (x² - 3x - 10)(x + 6)

Now solving these two gives us

x³ - 3x² - 10x + 6x² - 18x -60

= x³ + 3x² - 28x - 60

f(x) =  x³ + 3x² - 28x - 60

To know more about cubic functions visit

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The given expression is

To find the x-intercept, we make y = 0.

To find the y-intercept, we make x = 0.

First, let's draw a diagram showing how many people purchased each type of book:

Now, let's answer each question:

a)

only science: 12 customers

b)

mysteries and science, but not romance: 11 customers

c)

mysteries or science: 15+11+12+7+3+4 = 52 customers

d)

mysteries or science, but not romance: 15+11+12 = 38 customers

e)

exactly 2 types of books: 7+11+4 = 22 customers

This is a simple question let's take a look at the following picture:

We can see above first we have group one and after we changed the way factors are grouped. For the Assosiative Property of Multiplication, the way factors are grouped does not change the result, so that is the property that justifies the step from Line 1 to Line 2. Now let's take a look ate the next picture:

As we can see from line 2 to line 3 we changed just the order of the numbers. For the Commutative Property of Multiplication, even we change the order of the numbers of the multiplication we do not change the product. So o that is the property that justifies the step from Line 2 to Line 3.

By definition

From the graph

To identify whether it is discrete or continuous.

The weight of children in the first grade is continuous data because the weight varies continuously.

ANSWER:

The vertical distance from the ground to the top of the ladder is 18.85 feet

STEP-BY-STEP EXPLANATION:

The figure would be the following:

You want to calculate the vertical distance BC, we can do this by means of the tangent trigonometric ratio that says the following:

Replacing and solving for x:

see the figure below to better understand the problem

The perimeter of the window is equal to

where

D=3 ft ----> diameter of the semicircle

substitute

The answer is 13.71 ft (rounded to two decimal places)

95% confidence interval is given by

x - 2D , and x+ 2D

For 99% confidence interval is

x - 3D , and x + 3D

x = 100000

D = 2000

Then calculate

100000 - 3•2000= 94000

and

100000 + 3•2000= 106000

Now find √D = 44.72

Then interval is

100000 - 44.72 ,. And. 100000 + 44.72

99,956 lower limit and. 100472 upper limit

Then we see that theres only one interval ,

that is between thes 2 limits

ANSWER Is OPTION C) ) ($99.996.46, $100,003.55)

When we have two parallel lines cut by a transversal, the corresponding angles <2 and <6 are equal (congruent). Since the angle <7 is a vertical angle with respect to < 6, then <7 and <6 are congruent or have the same measure. Therefore, we have:

Then, the answer is option A, (3y - 8) degrees (because of the congruency of the angles).

If Harold isn't included, Harold would be sharing twizzlers with 20 friends.

But if it is including Harold, it would be 19 friends.

The total number of Twittzlers = 80

let the number of friends he wants to share them with = y

Each friend gets = 4 twizzlers

The total number of Twittzlers/the number of friends = amount each friend gets

Solve for y to get number of friends:

The number of twizzlers Harold would have wasn't stated. If Harold isn't included, Harold would be sharing twizzlers with 20 friends.

But if it is including Harold, it would be 19 friends.

t ≤ 8

Reservation fee = $35

Additonal fee = $8.80

let the number of hours = t

Amount to be spent is atmost $105.40

atmost $105.40 written as ≤ $105.40

solve for t:

They can rent the room for up to 8 hours

Possible amount of time ≤ 8 hours

1) Let's apply the distributive property, factor 3 is going to be equally distributed as the GCD of that expression. Let's do it:

3(2x+4y+5z)

6x +12y +15z

2) So that's equivalent to that factored expression. Note that 3 is the GCD of 6,12,15. And the factored form allows us to deal with smaller coefficients.

True because point B is the interior

To determine the measure of arc VU, given that we know the measure of ∠STU and arc SV, the first step is to determine the measure of arc SVU.

The relationship between the measure of an angle that has a vertex on the circle and its intercepted arc is that the measure of the said arc is twice the measure of the angle. Then the measure of arc SVU is twice the measure of ∠STU

Now, arc SVU is formed by arcs SV and VU, so to determine the measure of VU you have to subtract SV from SVU:

Arc VU measures 44º

The roots of a polynomial are the values of x that make the polynomial zero, so they are where the graph crosses the x-axis. Therefore,

y = 0 in

Then, answer is:

C. A root of -4 with a multiplicity of 2 & a root of 1 with a multiplicity of 1

In the given figure of ractangular prism :

Length = 13 in, height = 12 in, width = 11 in

The expression for the surface area of rectangular prism is = 2 (LW +LH + HW)

As the prism is open with top, thue reduce the area of top part : Height x Length

The expression for the surface aea of the prism = 2(LW + LH + HW) - HL

Substitute the value :

Surface area of rectangular prism is 706 in square.

8.24%

Explanation:

The original number of deaths due to heart disease = 255

The new number of death due to heart disease = 234

Therefore, the percent decrease in deaths due to heart disease this represents is 8.24% (2 decimal place)

In plotting a pair of coordinates, the first number will be the x-value while the second number is the y-value.

In other words, the first number will be the column number, while the second number is the row number.

Let's plot the given pairs in the graph.

For Part C, we have:

The rule for Pattern 2 should be adding 4 however, Anna said it's multiplied by 4. Anna made the mistake of using the relationship between Patterns 1 and 2.

To find the rule for Pattern 2, Anna should compare each term in Pattern 2 to the term that comes before it in Pattern 2. The rule for Pattern 2 is adding 4.

However, rounded to the nearest whole numbers would be 91.

The equation of a line with slope m that passes thorugh the point (x1,y1) is given as:

Plugging the values we know we have:

Therefore the equation of the line is:

To find the graph we need another point. If x=0, then:

Then we have the point (0,3). Plotting the points (0,3) and (6,0) and join them with a straign

Let's go!

So, it's

Because the interval is closed on the -1, meaning it is a part of it and opened in 3, meaning it is not.

x greater or equal to -1 and less than 3 (the way you read it)

The given formula is

First, we multiply the equation by 3.

Then, we divide the equation by H

Using the Factor Theorem, the polynomial function that could be represented by the graph is:

f(x) = 3x² - 18x + 24.

The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the rule presented as follows.

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative).

From the graphed polynomial, the roots are given as follows:

x' = 2, x' = 4.

(roots are the values of x where the function crosses the x-axis).

Hence it is written as follows:

f(x) = a(x - 2)(x - 4)

f(x) = a(x² - 6x + 8)

When x = 3, y = -3, hence the leading coefficient is given as follows:

-3 = a(1)(-1)

a = 3.

Hence:

f(x) = 3x² - 18x + 24.

(maybe your graph is different as the one I gave here, however the procedure is the same, you identify the roots and then build the equation).

The problem is given by the image at the end of the answer.

More can be learned about the Factor Theorem at https://brainly.com/question/24380382

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Answer:

(a)3,003 ways.

(b)360,360 ways.

Explanation:

• The number of colors = 15

• The number of colors to be chosen = 5

(a)If the order of choices is not relevant we use the combination formula:

In this problem: n=15, x=5

This can be done in 3,003 ways.

(b)If the order of choices is relevant we use the permutation formula:

In this problem: n=15, x=5

This can be done in 360,360 ways.

Certain functions, such as exponential functions, always have a horizontal asymptote. A function of the form f(x) = a (bx) + c always has a horizontal asymptote at y = c.

Exponential functions have asymptotes because the denominator equals zero for a particular value of x or because the denominator increases faster than the numerator as x increases.

I hope this clarifies.

the second degree trinomial is

we must find the factorization as

where

hence,