A ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 1 foot above the ground. The distance along the ramp to the building is 5 feet. What is the angle of elevation of the ramp to the nearest degree?
A. 11°
B. 0°
C. 12°
D. 1°

The example that would be continuous data is A. The volume of liquid in a pop can.

Continuous data is data that has no fixed value. Continuous data includes height, weight, temperature, and length. Some continuous data, such as a baby's weight in its first year or the temperature in a room throughout the day, will change over time.

Discrete data is a type of numerical data that consists of whole, concrete numbers that have specific and fixed data values determined by counting. Continuous data consists of complex numbers and varying data values measured over a specific time period.

In this case, the volume of the liquid is s continuous data.

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The correct statement that is a combination of both conditional statements is;  X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides.

A triangle is defined as a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees.

We are given the conditional statements as;

X → Y: If the sum of the interior angles of a shape is 180°, then it's a triangle.

Y → Z: If a shape is a triangle, then it has three sides.

Now, transitive property states that “if two quantities are equal to a third quantity, then we can say that all the quantities are equal to each other”.

Thus, applying transitive property to our given statements we can say that;  X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides.

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The piece of information does he need is  ∠F ≅ ∠J.

What is triangle?

A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°. It is a polygon having the least number of sides.

Properties of triangle?

Given,

ΔFGH = ΔJKL

By SAS property of triangle;

[tex]\bar{FH}[/tex] ≅ [tex]\bar{JL}[/tex],     FG ≅ JK

third property ,

                         ∠F = ∠J

By SAS property at least two side their ratio must be equal and one angle.

[tex]\frac{FG}{JK} = \frac{FH}{JL}[/tex]

∠F = ∠J

So, option A is correct.

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The difference of a linear, quadratic reation.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation.

Trigonometric ratios describe these operations. The ide and trigonometric functions In the previous chapters, we discovered that the polynomial equation is the equation that results from equating a polynomial function to zero. A linear equation results from equating a function to zero if it is a linear polynomial. We get a quadratic equation if the function is a quadratic polynomial.

When we graph a linear equation, we get a straight line, however with a quadratic equation, we get a parabola.

Unlike the slope of a linear polynomial, the slope of a quadratic polynomial is constant.

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The factoring is the representation of a polynomial in multiplication term thus the factoring of (1/3)b - 1/3 will be 1/3(b - 1).

An algebraic factor is the multiplication of two algebraic terms.

That term could be in form of summation multiplication or in subtraction.

The root of the quadratic equation formed by the algebraic factor is always real.

As per the given polygon,(1/3)b - 1/3

Take 1/3 as common in the whole polygon,

1/3(b - 1).

Since the terms 1/3 and (b - 1) both are in the multiplication of each other.

Hence "The factoring is the representation of a polynomial in multiplication term thus the factoring of (1/3)b - 1/3 will be 1/3(b - 1)".

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Answer:

It's B. A good way to look at it is the last number. The last number is the y-intercept. Here the y-intercept is -3. That's how I would always figure it out.

The inequality that can be used to determine the maximum number of hours h the frozen yogurt machine can be used if the rental cost for the day will not exceed $300 is 150+25h ≤300.

According to the question,

We have the following information:

The cost to rent a frozen yogurt machine is $150 per day plus $25 per hour of use.

And h represents the number of hours.

So, we have the following expression to find the total cost:

150+25h

Now, it is given that the total rental cost should not exceed $300.

So, we have the following inequality:

150+25h ≤300

Hence, the correct option is C.

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Answer:

Tuition and Fees = $5,992.93

Room = $5,115.92

Board = $4,044.01

Computer Costs = $1,088.15

The contribution margin rate is 40%.

What is contribution margin rate?

A company's contribution margin rate is the total revenue minus variable costs divided by the revenue.

First we need to determine the contribution margin in order to calculate the contribution margin rate. There are two approaches to determine the contribution margin.

Contribution Margin = $15 - $9 = $6

The contribution margin is $6.

Now we will calculate the contribution margin rate using this formula,

Contribution Margin Rate = Contribution Margin [tex]/[/tex] Sales Revenue

Contribution Margin Rate = $6 / $15

                                             = 0.4 * 100

                                             = 40%.

Hence the contribution margin rate is 40%.

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Step-by-step explanation:

[tex]250n^2+20n^8[/tex]

common factor is [tex]10n^2[/tex]:

[tex]10n^2(25 +2n^6)[/tex]

rearrange:

[tex]10n^2(2n^6+25)[/tex]

Answer:

The distance between two points on a 2D coordinate plane can be found using the following distance formula. d = √ (x2 - x1)2 + (y2 - y1)2. where (x 1, y 1) and (x 2, y 2) are the coordinates

Step-by-step explanation:

Answer:

the answer is 6

Step-by-step explanation:

I hope I helped, if you have questions let me know. I'll try to answer.

According to the following frequency table, the mean of the number points deducted from each student on an economics is 5.1

Frequency table:

Frequency table means the method of organizing raw data in a compact form by displaying a series of scores in ascending or descending order, together with their frequencies—the number of times each score occurs in the respective data set.

Given,

Here we need to determine the mean of the number of points deducted from each student on an economics test given in the follow grouped frequency table.

For the given table of data, the frequency table of the data is attached below.

In order to find the mean of the frequency table we have to use the following values,

The total frequency is 204

And the number of frequency is 40.

So, the mean is

=> 204/40

=> 5.1

Therefore, the mean of the data is 5.1

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(a) The shape of the distribution of donations is rectangular.

(b) The proportion of donations are at least 75 cents id 0.24

(a)The density curve is rectangular in shape.

This indicates that donations are distributed uniformly.

(b) From the question, we have

The probability of donations at least 75 cents as follows:

[tex]P(X\geq 75) =\int\limits^a_b {\frac{1}{99-0} } \, dx \\[/tex]

Substituting the limits,  we get

[tex]P(X\geq 75) =\frac{99-75}{99} \\=\frac{24}{99} \\=0.24[/tex]

Probability:

Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

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Answer:

False

Step-by-step explanation:

using the rule of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]

given

[tex]\frac{9x^7}{3x^2}[/tex]

= [tex]\frac{9}{3}[/tex] × [tex]\frac{x^7}{x^2}[/tex]

= 3 × [tex]x^{(7-2)}[/tex]

= 3[tex]x^{5}[/tex]

The true bearing at which Jasenio should aim his bow and arrow is; b) 11.31°

We have different trigonometric ratios such as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

We are told the track is 50 meters away from Jasenio and that by the time the arrow reaches it, the paper rabbit will be at a point about 10 meters to the right of what would be directly in front of him.

This means that there will be a right angle triangle formed with the height as 50 m and the base length as 10m. Thus, by trigonometric ratios, we have;

tan θ = 10/50

where θ is the true bearing angle. Thus;

tan θ = 0.2

θ = tan⁻¹0.2

θ = 11.31°

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Answer: [tex]x=\pm \sqrt{22}[/tex]

Step-by-step explanation:

[tex]\log(x-1)+\log(x+1)=\log 21\\\\\log((x-1)(x+1))=\log 21\\\\\log(x^2-1)=\log 21\\\\x^2-1=21\\\\x^2=22\\\\x=\pm \sqrt{22}[/tex]

Answer:

sqrt(22) = [tex]\sqrt{22}[/tex]

Step-by-step explanation:

we can use the logarithm rule, "log x + log y = log(xy)" to solve this problem

log(x-1) + log(x+1) =  = [tex]log((x-1)(x+1))[/tex] = log(21)

this means that x^2 - 1 equals 21

xx-1 = 21

xx=22

x=sqrt(22)

Answer:

[tex] = \frac{10}{0.2} = \frac{100}{2} = 50 \\ = \frac{10}{0.02} = \frac{1000}{2} = 500 \\ = \frac{10}{0.002} = \frac{10000}{2} = 5000 \\ \\ [/tex]

hopefully that will help u

The critical number are 0, 7 , -7.

Given function:

g(x) = [tex]\sqrt{49-x^{2} }[/tex]

first derivative is,

= -x/([tex]\sqrt{49-x^{2} }[/tex] )

-x = 0 or x = 0

[tex]\sqrt{49-x^{2} }[/tex] = 0

49 - [tex]x^{2} =0[/tex]

49 = [tex]x^{2}[/tex]

x = 7 , -7.

Therefore the critical number are 0, 7 , -7.

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The proportion of selling times is 0.35

From the question, we have

Selling Time___ Frequency

0 10____________3

10 20__________ 4

20 30__________ 6

30 40__________ 4

40 50__________ 3

Proportion of selling times in sample above that are less than 20 days :

total frequency = (3 + 4 + 6 + 4 + 3) = 20

Selling time which is less Than 20 days :

(0 - 10) = 3

(10 - 20) = 4

Total = (3 + 4) = 7

Proportion = selling time less Than 20 days / total frequency

= 7 / 20

= 0.35

Addition:

The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.

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The mean of the data is 3.85 using the stem-and-leaf plot.

It means the average feet that the heavy ball was thrown is 3.85 feet, which is the typical number.

To find the mean of a data set that is represented by a stem-and-leaf plot, first, list out all the data values that are represented on the stem-and-leaf plot, add all the values, and divide by the number of values that were represented on the stem-and-leaf plot.

Given the stem-and-leaf plot, using the key, the data points represented are:

2.0, 2.1, 2.4, 3.1, 3.2, 3.6, 4.1, 4.3, 4.7, 5.1, 5.1, 6.5

Mean = [2.0 + 2.1 + 2.4 + 3.1 + 3.2 + 3.6 + 4.1 + 4.3 + 4.7 + 5.1 + 5.1 + 6.5]/12

Mean = 46.2/12

Mean = 3.85 feet

The mean of 3.85 feet means that the average distance that the heavy ball was thrown in feet is 3.85.

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The image point of the point (-3, -2) after the transformation r x-axis R 270° is; (3, -2).

It follows from the task content that the image point of the pair of coordinates given is to be determined.

Given point is; (-3, -2).

Hence, after a reflection over the x-axis; we have; (-3, 2).

Also, after a rotation of 270°, it follows that we have; (x, y) ==> (-x, -y).

Therefore, the image point is; (-(-3), -(2)).

The image point is therefore; (3, -2).

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Option A. The statement that can be said to be true for h is h(2) = 16

If we look at the domain and range, we can rule out some straight away.

For h - 3 = -1

this is outside of the range of the such that -1 ∉ 1 ≤ hx ≤ 25

When h is 13 = 18

This is also outside of the domain such that 13 ∉ -3 ≤ x ≤ 11

When h is 8 = 21

there is going to be a contradiction with what the question has stated earlier. This is because we are told that h(8) = 19

Therefore on h(2) = 16

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Answer: -14

Step-by-step explanation:

−110+96

Add −110 and 96 to get −14.

−14

Answer: -14

Step-by-step explanation:

In this case, it's best you bring out the negative

- (110 - 96)

- (14)

= -14

Answer:

I believe... f(x)=1400+4x

The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B  t = ln(3) / 0.05

Given,

The population of a city can be modeled using the formula P=100,000e^(0.05t)

t is the number of years after 2012

P is the population of the city

We have to find the equation that can be used to find the number of years after 2012 that the population will triple to 300,000.

Here,

Substitute 300000 in for P and solve for t

300000=100000e^0.05t

Divide both sides by 100000:

We get,

3 = e^0.05t

Multiply both sides by the natural log (ln)

Then,

ln(3) = 0.05t

Now, divide 0.05 on both sides to get t by its self

t = ln(3) / 0.05

Therefore,

The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B  t = ln(3) / 0.05

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