Jamal owns a parking garage and is trying to find the relationship between hour of the day and number of cars in the garage. He finds that between 4 am and 10 am he can model this with a linear relationship. The equation for this model is y = 3. 56x + 2. How many cars were in the garage at 4 am?.

The equation of a vertical line is x = c, where c is a constant. So, in this case, x = -5, since the point (-5, -2) is on the line.

The equation of a vertical line is x = c, where c is a constant. A vertical line is a line with all points having the same x-coordinate. This means that all points on the line will have the same x-value, and the y-value will be different. In this case, the point (-5, -2) has an x-value of -5. This means that all points on the line will have an x-value of -5. This gives us the equation x = -5, which is the equation of the vertical line passing through the point (-5, -2).

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The cost function is C(w) = 300/w + 18w² and the cost of materials for the cheapest such container is $222.0

From the question, we have the following parameters that can be used in our computation:

The length is twice the width;

Volume = 10m³

This means that:

V = 10

l = 2w

The volume of the container is calculated as:

V = lwh

So, we have

v = 2w²h

By substitution, we have

h = v/2w²

So, we have

h = 10/2w²

Divide

h = 5/w²

The surface area of an open rectangular storage is:

A = 2h(l + w) + lw

So, we have

A = 2h(2w + w) + 2w²

A = 2h(3w) + 2w²

Substitute h = 5/w²

A = 2 * 5/w² * (3w) + 2w²

Evaluate

A = 20/w + 2w²

The base costs $15, and the sides cost $9

So, the cost function is:

C(w) = 15 * 20/w + 2w² * 9

Rewrite as:

C(w) = 300/w + 18w²

We have

C(w) = 300/w + 18w²

Differentiate

C'(w) = -300/w² + 36w

Set to 0

-300/w² + 36w = 0

Rewrite as:

-36w = -300/w²

Cancel out the negatives

36w = 300/w²

Multiply through by ²

36w³ = 300

Divide through by 36

w³ = 8.33

Take cube roots of both sides

w = 2.03

Recall that:

C(w) = 300/w + 18w²

So, we have:

C(2.03) = 300/2.03 + 18(2.03)²

Evaluate

C(2.03) = 222.0

Hence, the cost of the materials is $222.0

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Two steps that will complete the list correctly are:

4. The original measurement should be multiplied by the conversion factors.

5. Verify that it makes sense.

A conversion factor can be used to switch from one set of units to another by multiplying or dividing a number. When a conversion is necessary, the appropriate conversion factor to an equivalent value must be applied.

Let's use an example of converting from inches to centimeters to address this query.

10 inches should be converted to cm.

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The correct answer is option A that is sources and methods and this element describes the secondary sources and how we collected our primary data.

The process of gathering and analyzing intelligence is known as "sources and methods." The types of information obtained and the sources of that information differ.

Information collected through espionage, satellite pictures, intercepted communications, and news reports that are available to the public are all examples of intelligence sources.

The sources and procedures used by intelligence services are closely guarded since they include the means by which data is gathered and evaluated, which can be used by adversaries to determine the strengths and objectives of their foes.

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the volume of a region bounded by the curve and the -axis between is 19.47787445 cubic units.

What is volume of cone?

The area or volume that a cone takes up is referred to as its volume. Cones are measured by their volume in cubic units such as cm3, m3, in3, etc. By rotating a triangle at any of its vertices, a cone can be created. A cone is a robust, spherical, three-dimensional geometric figure.. Its surface area is curved. The perpendicular height is measured from base to vertex. Right circular cones and oblique cones are two different types of cones. While the vertex of an oblique cone is not vertically above the center of the base, it is in the right circular cone where it is vertically above the base.

So the

V = (1/3)πr²h.

V = π ∫ (x^2)^2 dx - π ∫ 0 dx = π ∫ (x^4) dx - 0 = π (x^5 / 5)

Evaluating from 2 to 1 yield the following:

π (2^5 / 5 - 1^5 / 5) = π (32/5 - 1/5) = 31π/5 cubic units, approximately equal to 19.47787445 cubic units

Hence, the volume of a region bounded by the curve and the -axis between is 19.47787445 cubic units

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The solution to the problem are 8 × 3 = 24, –7 × 5 = -35, –6 × (–9) = 54, 8 ÷ (–2) = -4, –24 ÷ (–3) = 8, –36 ÷ 6 = -6.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Solve as shown below,

(a) 8 × 3 = 24

(b) –7 × 5 = -35

(c) –6 × (–9) = -(-54) = 54

(d) 8 ÷ (–2) = 8 × 1 / (-2) = - 4

(e) –24 ÷ (–3) = -24 ×  1 / (-3) = 8

(f) –36 ÷ 6 = -36 × 1 \ 6 = -6

Therefore, the solution to the problem are 8 × 3 = 24, –7 × 5 = -35, –6 × (–9) = 54, 8 ÷ (–2) = -4, –24 ÷ (–3) = 8, –36 ÷ 6 = -6.

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When taking the square root of both sides of this equation, the square roots may depend upon equation.

Let, the equation be:

x² = 4

May be the Equation has two solutions:

x = ±√4 = ±2

Equations involving distances, such as those obtained when using the Pythagorean theorem, have solutions. Negative solutions are irrelevant because there are no negative distances.

    c² = a² + b²

⇒ c = √(a² + b²) .

Generally these are considered irrelevant as they are useless. Mathematically, negative time values ​​work in the equation, but have no real interpretation.

Expressions such as:

x⁶ = 4

This, has 2 real and 4 complex solutions.

Again,

x³ = ±2 . after rooting both sides

The two real solutions are :

x = ±∛2

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Answer:

808.72 ft

Step-by-step explanation:

We can create a right triangle with the following points:

- the top of the lighthouse

- the base of the lighthouse

- the rock jutting out of the water

I will label the distance from the base of the lighthouse to the rock d.

See the attached image for a detailed model.

Then, solve for the two acute angles of the triangle.

The larger acute angle (∠1) is complementary to 6°, so we can solve by setting their sum to 90°:

6° + m∠1 = 90°

m∠1 = 84°

Because this is a right triangle, the smaller acute angle (∠2) is complementary to the larger acute angle, so we can solve once again by setting their sum to 90°:

m∠1 + m∠2 = 90°

84° + m∠2 = 90°

m∠2 = 6°

We can use either of these angles in combination with the trigonometric ratio tangent to solve for the distance d. I will use tangent of ∠1.

[tex]\tan(84\textdegree) = \dfrac{d}{85 \, \textrm{ft}}[/tex]

[tex]d = 85\tan(84\textdegree)[/tex]

[tex]d \approx 808.72 \, \textrm{ft}[/tex]

Answer:

If the model is made using a 1:25 scale, then every inch on the model corresponds to 25 inches on the actual house. Therefore, if a part of the model measures 7 inches, the corresponding measurement on the actual house would be 7 * 25 = <<7*25=175>>175 inches.

Step-by-step explanation:

Percent 20.5% of 78 is 16 rounded to the nearest tenth.

How to calculate percentage?

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Let x% of 78 is 16

⇒ [tex]\frac{x}{100}\times 78=16[/tex]

⇒ x = [tex]\frac{16\times 100}{78 }=\frac{1600}{78}=20.5[/tex]

Therefore, 20.5% of 78 is 16.

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Answer:

Step-by-step explanation:

4m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/8

Answer And step-by-step explanation: The sum of x and y is 58. In other words, x plus y equals 58 and can be written as equation A:

x + y = 58

The difference between x and y is 18. In other words, x minus y equals 18 and can be written as equation B:

x - y = 18

Now solve equation B for x to get the revised equation B:

x - y = 18

x = 18 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 58

18 + y + y = 58

18 + 2y = 58

2y = 40

y = 20

Now we know y is 20. Which means that we can substitute y for 20 in equation A and solve for x:

x + y = 58

x + 20 = 58

X = 38

Summary: The sum of two numbers is 58 and their difference is 18. What are the two numbers? Answer: 38 and 20 as proven here:

Sum: 38 + 20 = 58

Difference: 38 - 20 = 18

Hope this is helpful if it is can I be marked With Crown?

Answer:    

x=38 y=20

Step-by-step explanation:

x+y=58

x-y=18

combine

2x=76

x=38

38+y=58

-38    -38

y=20

Answer: $5.50

Step-by-step explanation:

$275 x 2% = 550

550/100 = 5.5

The salesperson makes $5.50 in commission.

Range of the Function is {1, 2, 3, 4, 5}

What is Range of a Function?

In mathematics, the range of a function can refer to one of two closely related concepts: the function's codomain. A function's range is the collection of potential output values.

Solution:

f(x) = |x + 3|

Domain = {-2, -1, 0, 1, 2}

The range will be

At x = -2; f(x) = 1

At x = -1; f(x) = 2

At x = 0; f(x) = 3

At x = 1; f(x) = 4

At x = 2; f(x) = 5

Range of the Function is {1, 2, 3, 4, 5}

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A  1 angle of the square Class 1 is a type of four-sided polygon. It is a regular polygon, meaning that all of its sides have the same length and all of its angles are equal.

There are only right angles in a square. Having the opposing sides parallel defines a square as a quadrilateral. Only one dimension, the side length, may be used to describe a square. Each angle is 90° in length and has an equal number of sides. To help you comprehend the topic better, let's talk more about square angles and work through a few instances. A square Class 1 is a type of four-sided polygon. It is a regular polygon, meaning that all of its sides have equal length and all of its angles are equal. The sides of a square Class 1 are all of the same length, and the angles between them are all 90 degrees. This type of polygon is also known as a regular square.

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Answer:

Roughly 7,500.

Step-by-step explanation:

15% of 50,000 is 7,500. That would make their salary about 42,500 after income taxes.

Answer:

$7,500

Step-by-step explanation:

50,000 / 12 = 4,166.67

4,166.67 * 0.15 = 625

625 * 12= 7,500

Answer:

It would cost her either $233.25 or $231.65 if she needed 21 books.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, The total cost of five books is $61.25, and 15 books cost$159.75.

So, The cost of 20 books is (61.25 + 159.75) = $221.

If she needs one more book it could cost her $(61.25/5) Or $(159.75/15).

Which is either $12.25 Or $ $10.65.

So, for 21 books it could cost (221 + 12.25) = $233.25 Or (221 + 10.65) = $231.65.

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Answer:

b. Write the equation/inequality:

I think I'm not sure

The equation of a line passes through the given point and the slope is y -3 = 1/2(x +2).

Here we have to find the equation of the line that passes through (-2, 3).

Data given:

Line passes through the point = (-2,3)

Slope of the line = 1/3

The formula for the equation of the line:

y - y1 = m(x -x1)

m = slope of the line

(x1, y1) = point on the line

Now put the values in the formula, we have:

y -3 = 1/3(x -(-2))

y - 3 = 1/3( x +2)

Therefore the equation of the line is y -3 = 1/3(x +2).

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The interpretation of the straight line graph of the gallons of gas to distance in miles are as follows;

(a) After 100 miles, the equation for the graph and the graph indicates that Linda's car will have more gas

Linda's car will have 1 gallon more gas than Shen's car.

(b) Linda and Shen will have the same amount of gas in their cars after 150 miles

The graph indicates that Shen's car will have less gas than Linda's car before reaching 150 miles

A straight line graph is a graph of a linear equation.

The points on the graphs are;

Linda; (0, 14), (150, 8)

Shen; (0, 11), (150, 8)

The equation for the amount of gas remaining in Linda's car can be found as follows;

Slope of the line = (8 - 14)/(150 - 0) = -6/150 = -1/25 = -0.004

Equation of the line is therefore;

y - 14 = (-1/25)(x - 0)

The slope of the graph of the equation of Shen's car = (8 - 11)/(150 - 0) = -0.02

The equation of the line is; y - 11 = -0.02·x

After 100 miles we get;

Gas left in Linda's car = -0.04 × 100 + 14 = 10

Gas left in Shen's car = -0.02 × 100 + 11 = 9

Therefore, Linda's car will have more gas after 100 miles

Her car will have 10 gallons of gas

(b) From the graph, at the point x = 150, the tanks of Linda and Shen will contain the same amount of gas

If the miles driven is less than 150 miles, the graph indicates that Shen's car will have less gas than Linda's car

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With the help of ratio, we know that when the length will be 1cm then the width of the rectangle will be 2cm.

In mathematics, a ratio shows how frequently one number appears in another.

For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.

Oranges make up 8:14 of the total fruit, whereas lemons make up 6:8 of the total fruit.

So, 1st we have a rectangle which:

length 7cm

width 14cm

Just get the ratio of length:width:

7:14

7/14

1/2

1:2

When height becomes 1cm, then according to the ratio the width will be:

1/2 * 1/1 = 1/2cm

Where 2cm is the width when height becomes 1cm

Therefore, with the help of ratio, we know that when the length will be 1cm then the width of the rectangle will be 2cm.

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The inverse of a conditional statement is when both the hypothesis and conclusion are negated.

What is hypothesis and conclusion?

A conditional statement's first clause, or "if," contains the hypothesis.

A conditional statement's second, or "then," component is the conclusion. A hypothesis produced the conclusion.

You can enroll in a reputable college if you earn good grades.

You will get into a good college if you get good grades, and the part that comes after the "if" is known as a hypothesis.

The part that comes after the "then" is known as a conclusion. An "If-then" or "conditional statement" is a series of hypotheses followed by a conclusion.

The opposite of a conditional statement is when the hypothesis and conclusion are both negated.

This is done by negating both the "If" part (p) and the "then" part (q).

The conditional statement is known as p q in geometry. The inverse is written as pq, where q stands for the negation of the statement or not.

Hence, the inverse of a conditional statement is when both the hypothesis and conclusion are negated.

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Answer: Inverse

Step-by-step explanation: Inverse Statements: The inverse of a conditional statement is found by negating the hypothesis and the conclusion. That means you will write the opposite for both parts of the conditional statement.

Example: statement: If two angles are vertical angles, then they are congruent.

Inverse: If two angles are not vertical angles, then they are not congruent. This is not valid.

The given sequence is a arithmetic sequence with the common difference is -6.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is an=a+(n-1)d

The given sequence is 22, 16, 10.

Here,

Common difference = Second term - First term

16-22=-6 and 10-16=-6

Since the common difference between the terms is same, the given sequence is arithmetic sequence.

Hence, 22, 16, 10 is a arithmetic sequence with the common difference is -6.

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the vallue of k is 25,  positive integers 6^6 and 8^8.

What is LCM?

In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple. The smallest number among all the common multiples of the provided numbers is the least common multiple of two or more numbers. Consider the integers 2 and 5. There will be different multiples for each. Least Common Multiple is the meaning of the abbreviation LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers.

Only the primes 2 or/and 3 are present in LCM, hence k cannot have any other primes.

In light of the fact that the power of 3 in LCM is greater than the powers of either the first or second number, k must have 312 as its multiple (otherwise, how would 312 appear in LCM?).

Because at least one of the numbers must have the words (224) and (312) as its factors in order for (224) * (312) to be a common multiple, b must now equal 12. (maybe other numbers).

As can be seen, the 224 component is already taken care of by 88.

As a result, k must handle the LCM's 312 component.

Since a can take on any value between 0 and 24 (inclusive) without modifying the LCM's value, the value of k is therefore (2a) * (312).

Hence the vallue of k is 25.

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Answer: 8

Step-by-step explanation:

fifty-two divided by six rounded down is eight.

The required sentences can be completed as follows:

68% of the scores are between 68 and 84.

95% of the scores are between 60 and 92.

99.7% of the scores are between 52 and 100.

To complete the first sentence, we need to find the range of scores that includes 68% of the values.

We know that 68% of the scores fall within 8 points of the mean, so the range of scores that includes 68% of the values is 76 - 8 to 76 + 8, or 68 to 84.

Therefore, the first sentence can be completed as follows:

68% of the scores are between 68 and 84.

To complete the second sentence, we need to find the range of scores that includes 95% of the values.

We know that 95% of the scores fall within 16 points of the mean, so the range of scores that includes 95% of the values is 76 - 16 to 76 + 16, or 60 to 92.

Therefore, the second sentence can be completed as follows:

95% of the scores are between 60 and 92.

To complete the third sentence, we need to find the range of scores that includes 99.7% of the values.

We know that 99.7% of the scores fall within 24 points of the mean, so the range of scores that includes 99.7% of the values is 76 - 24 to 76 + 24, or 52 to 100.

Therefore, the third sentence can be completed as follows:

99.7% of the scores are between 52 and 100.

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