A storage bin has the shape of a cylinder with a conical top. What is the volume of the storage bin if its radius is r=5.4 ft, the height of the cylindrical portion is h=7.7 ft, and the overall height is H=16.7 ft?

Answer:

the second quadrant is negative but the reference angle is exactly the same but positive

Step-by-step explanation:

looking at 150 on the unit circle in the second quadrant you will see the cosine is negative square root 3 divided by 2 but the reference angle is 30 degrees and when we look at the cosine of that which is the x value of what we see it is positive square root of 3 divided by 2

Answer: 36.00%

60% can be written as 0.60 and/or 6/10, which simplifies to 3/5 for easier operations. The probability of 2 students both drink coffee with breakfast can be shown as 0.60 • 0.60 = 0.36. This means there is a 36% chance of both students drinking coffee with breakfast in the morning.

Step-by-step explanation:

1. 3x - 4 = 23

add 4 to both sides

3x - 4 + 4 = 23 + 4

3x = 27

Divide both sides by 3

3x/3 = 27/3

x = 9

2. 9 -4x = 17

subtract 9 from both sides

9 -9 -4x = 17 - 9

-4x = 8

Divide both sides by -4

-4x/-4 = 8/-4

x = -2

3. 6(x-7) = 36

Divide both sides by 6

x -7 = 6

add 7 to both sides

x - 7 + 7 = 6 + 7

x = 13

4. 2(x-5) -8 = 34

Expand

2x -10 -8 = 32

2x - 18 = 32

2x = 32 + 18

2x = 50

Divide both sides by 2

x =25

If the area of a trapezoid is A = [tex]\frac{1}{2} (b_{1}+ b_{2})h[/tex], then the equation represents the value of [tex]b_{1}[/tex] is [tex]b_{1}=\frac{2A}{h}-b_{2}[/tex]

The trapezoid is a quadrilateral with at least one pair of parallel sides is called trapezoid. There are four vertices and four edges in the trapezoid.

The area of the trapezoid  A = [tex]\frac{1}{2} (b_{1}+ b_{2})h[/tex]

Where [tex]b_{1}[/tex] and [tex]b_{2}[/tex] are the length of the parallel sides of  the trapezoid

h is the height of the trapezoid

A = [tex]\frac{1}{2} (b_{1}+ b_{2})h[/tex]

Move 1/2  to other side

[tex](b_{1}+ b_{2})h[/tex] = 2A

Move h to other side

[tex](b_{1}+ b_{2})[/tex]  = [tex]\frac{2A}{h}[/tex]

Move [tex]b_{2}[/tex]  to other side

[tex]b_{1}=\frac{2A}{h}-b_{2}[/tex]

Hence, if the area of a trapezoid is A = [tex]\frac{1}{2} (b_{1}+ b_{2})h[/tex], then the equation represents the value of [tex]b_{1}[/tex] is [tex]b_{1}=\frac{2A}{h}-b_{2}[/tex]

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In the table, we can see that the highest number corresponds to the cats who failed. Then, if a comparative bar chart represents the data, the bar representing the number of cats that failed will be the tallest.

A. Cats who failed

The time that David left the money in the account would be = 4 years

An earned interest is the amount of money that is regularly paid to an individual who invested a specific amount of money for a stipulated period of time.

The principal amount(p)= $300

The time (T)= X

The rate of interest yield (R)= 5 %

Simple interest( SI)= $ 60

Using the formula;

SI = P×T×R/100

Make T the subject of formula;

T = SI×100/P*R

T= 60×100/300×5

T= 6000/1500

T = 4 years.

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The value of x in the expression 42/100 of x over 35% is 0.147.

It should be noted that an expression is simply used to show the relationship between the variables or number given.

Therefore, the information will be expressed as:

42/100 × x/35%

= 42/100 × x/0.35

Cross multiply

100 × x = 0.35 × 42

100x = 14.7

Divide.

x = 14.7 / 100

x = 0.147

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The number of red marbles in the bag is 114 .

in the question ,

it is given that ,

total number of marbles in the bag = 120 marbles

let the number of red marbles [tex]=[/tex] r

let the  number of black marbles [tex]=[/tex] b

so , According to the question

b + r = 120   ...eqn(1)

also given that for every black marble there is 19 red marbles

which is represented by , r = 19b

Substituting  r = 19b in eqn (1) , we get

b + 19b = 120

simplifying further , we get  

20b = 120

b = 6

and r = 19(6) = 114

Therefore , The number of red marbles in the bag is 114 .

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When one-third of a number is at least four less than the number, the inequality to represent the information is C. n ≥ 6.

It should be noted that an inequality is simply used to illustrate the expressions that aren't equal.

Let the number be n.

This will be illustrated as:

1/3n ≥ n - 4

Collect like terms

1/3n - n ≥ -4

-2/3n ≥ -4

Multiply through by -3/2

n ≥ -4 × -3/2

n ≥ 6

The value is n ≥ 6.

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The ratio of both men and women 15:22

What is Ratio ?

A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Given,

The ratio of men and children = 5:2

The ratio of women and children = 11:3

To find the ratio of men and women we have to divide both the ratio:

men/children/women/children

or,

men/children x children/women

putting the values

=5/2 x 3/11

=15/22

Hence, the ratio of men:women is 15:22

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According to the picture:

For the first statement

The reason is: Given.

This is because it is given in the information to solve the problem.

The second statement must be:

And the reason is also: Given.

For the third statement:

The reason is the Reflexive property.

The fourth statement must be:

The reason is Side Side Side congruence postulate.

The fifth statement must be:

The reason is congruent triangles definition.

A ski trip requires a lot of planning.You must choose your travel dates, choose the ideal location, identify the best ski resorts for your family in the area, book lodging, purchase lift tickets, schedule lessons, consider your equipment and clothing needs, and possibly book flights or a rental car.

Describe the possible effects that traveling to a ski resort might have on travel time?

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The following problem can be well explained by the diagram shown below:

Hence by the trigonometry of the figure use the trigonometric ratio of cos to get:

Hence the support is 6.8 feet away from the wall.

Option A is correct.

The following that represent the sales price and the regular prices are:

regular price: $55.43, sales price: $45.45

regular price: $29.99,  sales price: $24.59

regular price: $652.30, sales price: $534.89

Percentage is the fraction of a number out of hundred. The sign that is used to represent percentages is %.

When a discount is given on the price of an item, the price of the item would reduce by the given price or by the percent reduction.

Sales price = regular price x (1 - discount)

Sales price = regular price x (1 - 0.18)

Sales price = regular price x 0.82

Sales price when the initial price is $55.43: $55.43 x 0.82 = $45.45

Sales price when the initial price is $29.99: $29.99 x 0.82 = $24.59

Sales price when the initial price is $215.33: $215.33 x 0.82 = $176.57

Sales price when the initial price is $849.50: $849.50 x 0.82 = $696.59

Sales price when the initial price is $652.30: $652.30 x 0.82 = $534.89

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The conversion from yards to miles is given by:

The conversion factor is:

Now, if we want to know how many miles are 39 yards, we multiply 39 yards by the conversion factor:

Answer:

-0.07

Step-by-step explanation:

Find the average

The equation of the line perpendicular to y = - (2 / 3) · x and the point (4, - 8) is y = (3 / 2) · x - 14.

Mathematically speaking, lines are represented by equations of the form y = m · x + b, where m and b are the slope and the intercept of the line. Additionally, two lines are perpendicular to each if the product of their slopes is equal to - 1.

First, we determine the slope of the perpendicular line:

m' = - 1 / m

m' = - 1 / (- 2 / 3)

m' = 3 / 2

Second, the intercept of the perpendicular line is:

b = y - m · x

b = - 8 - (3 / 2) · 4

b = - 8 - 6

b = - 14

Then, the equation of the perpendicular line is y = (3 / 2) · x - 14.

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Initially, Joshua had $155 in his account.

Deposits of $25 and $40

Withdrawals = $15, $35

At the end of the month, he had $170 in his account.

Solution:

Let x be the amount of money he had initially.

Then,

x + 25 + 40 - 15 -35 = 170

x + 65 - 50 = 170

x = 170 + 50 - 65

x = 220 - 65

x = 155

Therefore, initially, he had $155 in his account.

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• The Same roots

• The same axis of symmetry

1) If we compare two parabolas from this family, like:

Note that the difference is in the leading coefficient "a".

2) Both parabolas will have the same roots, the same x-intercepts:

In addition to this, we can state that both will share the same axis of symmetry:

As well as:

Hence, the answer is:

0. Same roots

1. Same axis of symmetry

The inequality is lies between the 5.26 < 5.71

The correct option is (a)

Given,

From the figure,

To see the number line and determine the which of the expression is true.  

What is Inequality?

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.

The number line goes from 5.0 to 6.0 with 9 labeled marks in between.

Each mark increases by point one

There are five labeled points.

A point labeled 5.04 is between 5.0 and 5.1.

A point labeled 5.26 is between 5.2 and 5.3.

A point labeled 5.4 is at the mark labeled 5.4

A point labeled 5.520 is between 5.5 and 5.6.

A point labeled 5.71 is between 5.7 and 5.8.

Then the ascending order of the number line will be :

5.04 < 5.26 < 5.4 < 5.52 < 5.71

Hence, The correct option is (a)i.e., 5.26 < 5.71

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a)The smaller break even quantity is 10

b)The quantity that must be sold to maximize the profit= 14.25

c)The maximum profit = $36.13

STEP - BY - STEP EXPLANATION

What to find?

• The smaller break even quantity is

• The quantity that must be sold to maximize the profit

• The maximum profit.

Given:

C(x)= 13x + 370

R(x)=70x - 2x²

a) At the break even quantity, the revenue = cost, that is no profit and no loss.

R(x) = C(x)

So that we have;

70x - 2x² = 13x + 370

Re-arrange.

-2x² + 70x - 13x - 370 =0

-2x² +57x - 370 =0

2x² - 57x + 370 = 0

We can now solve the quadratic equation above.

Using the qudaratic formula

a=2 b=-57 c=370

Substitute the values into the formula and evaluate.

Or

x = 37/2 or x=10

We take the smaller value.

Hence, x=10

Therefore, the smaller break even quantity is 10.

b)To find the quantity that will maximize the profit, find the profit function.

p(x) = R(x) - C(x)

P(x) = 70x - 2x² - (13x +370)

= 70x - 2x² - 13x - 370

P(x) =-2x² + 57x - 370

Equate to zero

-2x² + 57x - 370 = 0

2x² - 57x + 370 =0

The maximum is at x = -b/2a

b= -57 and a=2

Substitute the values

x= - (-57) /2(2)

x= 57 /4

x= 14.25

c) To find the maximum profit, simply substitute x=14.25 into the profit function and simplify.

That is;

P(x) =-2x² + 57x - 370

P(14.25) =-2(14.25)² + 57(14.25) - 370

= -406.125 + 812.25 - 370

= 36.125

≈ 36.13

Hence, the maximum profit is $36.13

One factory that obtained 90 kg of total beef from overseas. The company needs 390 oz of meat filler to make meatballs out of this shipment of beef.

In processed meat products, starches are frequently employed as fillers to bind water that would otherwise leak out of the product, increasing its texture and sensory qualities.

As cheap fillers or inferior fiber sources, items including corncobs, feathers, soy, cottonseed hulls, peanut hulls, citrus pulp, screening, weeds, straw, and cereal by-products are frequently used.

One factory that has obtained 135 kg of beef from overseas.

They want to add a total of 1.3oz of filler for each pound of beef.

Given is:

0.45 kg = 1 pound

So, 135 kg = 300 pounds

The company that wants to add a total of 1.3 oz of filler for each pound of beef.

So, for 300 pounds they will need = 390 oz of filler.

Therefore, the company needs 390 oz of filler.

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Answer: his total bill is 7.24

Step-by-step explanation:

Callan hikes at the rate of 3 miles per hour, that means, the table of values of values would be completed as follows;

Hours, x Miles, y

1 3

3 9

5 15

The ordered pair above is derived by multiplying every hour by 3 to arrive at the number of miles.

The graph is now shown as;

This statement is justified by the angle addition postulate.

From the picture, we have the graph of the linear parent function f(x) = x.

We have the following statements as descriptions of the function:

A. The function is negative when x < 0.

From the graph, we see that the function takes negative values for x < 0. This statement is true.

B. The function is negative when x < 0 and also when x > 0.

The first part of this statement is true, but the second is not because that we see that the function takes positives values for x > 0. So this statement is false.

C. The function is never negative.

If we see the graph, the function is negative when x < 0. So this statement is false.

D. The function is negative when x > 0.

Again, seeing the graph we note that the function takes positive values for x > 0. So this statement is false.

So the only statement that it is true, is option A.

h(g(x)) is equivalent to the expression 1/2|x|-10

Given g(x) = 1/2|x|-6 and h(x) = x-4

h(g(x)) = h(1/2|x|-6)              

Put the value of g(x) in the expression

Now, evaluate the expression using the  definition of h(x) by replacing x in x-4 with 1/2|x|-6:

h(g(x)) = 1/2|x|-6 - 4 = 1/2|x|-10

Since  h(g(x)) = 1/2|x|-10. Therefore, 1/2|x|-10 is the expression equivalent to h(g(x)) so the third option is the answer.

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Use the next property:

Answer:

8

Step-by-step explanation:

Find the prime factorization of 40

40 = 2 × 2 × 2 × 5

Find the prime factorization of 96

96 = 2 × 2 × 2 × 2 × 2 × 3

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, GCF = 2 × 2 × 2

GCF = 8

Answer:

8

Step-by-step explanation:

8 is the greatest number that 40 and 96 divides into