Part B
? Question
The volume of the rectangular prism is the product of its length, width, and height.
What is the volume of the rectangular prism in simplest terms?
Type the correct answer in the box. Use numerals instead of words.

Answer:

2.28%

Step-by-step explanation:

P(X > 70) = 1 - Ф((70 - 50)/10) = 0.0228 = 2.28%

Answer:

the volume of the toy house is 66cm3

The next two terms of the first quadratic sequences are 37 and 49.

The next two terms of the second quadratic sequences are 39 and 60.

A quadratic sequence is a sequence in mathematics where the second difference between consecutive terms in the sequence is the same

The first step is to determine the relationship between the terms in the quadratic sequence.

The difference between 9 and 13 = 13 - 9 = 4

The difference between 19 and 13 = 19 - 13 = 6

The difference between 27 and 19 : 27 - 19 = 8

It can be seen that the first difference between the terms in the sequence quadratic sequence increases by 2.

The difference between the fourth term and the fifth term would be 8 + 2 = 10

Fifth term = 27 + 10 = 37

The difference between fifth term and the sixth term would be 10 + 2 = 12

37 + 12 =49

The first step is to determine the relationship between the terms in the quadratic sequence.

The difference between 0 and -5 : 0 - -5 =  5

The difference between 0 and 9 = 9 - 0 = 9

The difference between 9 and 22 = 22 - 9 = 13

Based on the first difference between the consecutive terms in the digit, it can be seen that the first difference increase by a value of 4.

The difference between the fourth term and the fifth term would be : 13 + 4 = 17

Fifth term = 22 + 17 = 39

The difference between fifth term and the sixth term would be 21 ( 17 + 4)

39 + 21 = 60

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Answer:

(x,y) -> (x-12, y+4)

Step-by-step explanation:

(x,y) -> (x-12, y+4)

Answer: 5575 Marbles

Step-by-step explanation:

This can be solved simply by subtracting and adding.

3409-1290=2119

2119+3456=5575

The slope-intercept form equation for a line that contains point (0, 5) and has a slope of 5/4 is y = (5/4)x + 5

In this question, we have been given a point (0, 5) and a slope 5/4

We need to write the slope-intercept form equation for a line that contains point (0, 5) and has a slope of 5/4

Using the formula for the point-slope form equation of a line:

(y - y1) = m(x - x1)

y - 5 = (5/4)(x - 0)

y - 5 = (5/4)x

y = (5/4)x + 5

which is slope-intercept form of line.

here slope = 5/4 and y-intercept = 5

Therefore, the slope-intercept form equation for a line that contains point (0, 5) and has a slope of 5/4 is y = (5/4)x + 5

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Answer:

  SSA is not a valid congruence theorem

Step-by-step explanation:

Given a figure with opposite sides the same length, and their ends joined by a line through the midpoint of the segment joining their other ends, you want to know why the shape is not a parallelogram.

The recognized congruence theorems are ...

  AAS, ASA, SAS, SSS

The "would be" SSA theorem is not included, because the case where the angle is opposite the shortest of the two sides does not uniquely specify the triangle.

In this diagram, the sides marked with 2 and 1 hash marks are sequential with the vertical angle where the diagonals cross. Hence the only basis for claiming the triangles congruent is SSA.

The basis for claiming congruence is not a recognized congruence theorem, so we cannot conclude the triangles are congruent. (CPCTC does not apply.)

__

Additional comment

As we noted, the SSA criterion for congruence fails if the given angle cannot be demonstrated to be opposite the longest side. The attachment shows the case where the single-hash segment is longer than the double-hash segment, so there are two ways to draw the figure. One is a parallelogram, the other is not.

The HL congruence theorem is essentially SSA, where the A is the right angle. If the angle can be demonstrated to be the largest in the triangle, then the SSA theorem can be used (as for right- or obtuse triangles).

As the attachment shows, there is nothing in this geometry that requires the vertical angle(s) opposite the double hash be the largest.

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Part A)

Let x be a number of horses that Sunshine Acre Farm can support. Since each horse needs 1.75 acres of pasture, and the farm has at most 35 acres of pasture available, then we can set the following inequality:

Answer Part A)

ANSWER

| x=0

Step-by-step explanation:

f(x) = 2x²

Rewrite the function by completing the

square

f(x)

= 2x²

Find the symmetry

X = 0

Answer: x = (5√2)/2

The last option

Explanation:

The given triangle is a right triangle. Taking angle 45 as the reference angle,

hypotenuse = 5

opposite side = x

We would find x by applying the sine trigonometric ratio which is expressed as

sin θ = opposite side/hypotenuse

By substituting the given values into the equation,

sin45 = x/5

Recall,

Thus,

x = (5√2)/2

The last option

Ice is colder than water due to its more heat absorbing capacity then water and steam is hotter than water due to high heat transfer rate then water.

What is specific heat capacity ?

In scientific terms, a specific heat capacity is the quantity of heat (J) absorbed by a material every time its temperature goes up 1 K (or 1 °C), given in J/(kg K) or J/(kg °C) per unit mass. formulae for specific heat capacity is given by :

Q = mCΔT

Here the given statement is :

If the temperature of water is between the temperatures of ice and steam, then ice is colder than water and steam is hotter than water.

The above statement is justified below :

The steam exhibit more energy than water at the same temperature that is 100° C. The steam uses the latent heat of vaporization so as to get vaporized and water do not exhibit energy and also, The arrangement of molecules in substances is widely influenced by the state of the matter of the substance. In this way, in solids the molecules have a fix organization and are closely packed due to this, solids have both a defined shape and volume; in liquids the molecules are still close to each other but there is no a defined structure and therefore liquids have a defined volume but not a defined shape; finally, in gases molecules do not follow an orderly arrangement and there is more space between them which makes them not have a define volume or shape.

According to this, we can say that Ice is colder than water due to its more heat absorbing capacity then water and steam is hotter than water due to high heat transfer rate then water.

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Answer:

9

Step-by-step explanation:

the absolute value function always delivers only the positive value of anything inside the absolute function.

therefore, x is 9 and only 9.

The following statement "A supply shock is a sudden shortage of a good" is true.

A supply shock is an unexpected incident that abruptly affects the supply of a product or commodity, resulting in an unanticipated change in price. Supply shocks can be negative, resulting in a fall in supply, or positive, resulting in an increase in supply.

Assuming that aggregate demand remains constant, a negative (or unfavorable) supply shock causes a product's price to rise, whereas a positive supply shock causes the price to fall.

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The value of the division of the expression will be;  19.52 x 10^{25}.

The number is written in the form  [tex]a \times 10^b[/tex] where we have  [tex]1 \leq a < 10[/tex]

The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10.

Scientific notations have some of the profits; Better readability due to compact representation that value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.

Given the expression as 6.1 x [tex]10^{20}[/tex] by 3.2 x 10⁵

We have to divide the expression

( 6.1 x [tex]10^{20}[/tex] ) / (3.2 x 10⁵)

= 19.52 x [tex]10^{20 + 5}[/tex]

=  19.52 x [tex]10^{25}[/tex]

Therefore, the value of the division of the expression will be;  19.52 x [tex]10^{25}[/tex].

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Considering the normally distributed variable, the proportion/percentage are given as follows:

a) Proportion of serves faster than 121 mph: 0.16.

b) Percentage of serves between 109 and 133 mph: 84%.

The z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the following equation:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

As stated in the problem, the mean and the standard deviation of the serve speeds are given as follows:

[tex]\mu = 115, \sigma = 6[/tex]

The proportion of serves faster than 121 mph is one subtracted by the p-value of Z when X = 121, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (121 - 115)/6

Z = 1

Z = 1 has a p-value of 0.8413.

1 - 0.8413 = 0.1587, which is the desired proportion.

The proportion of serve speeds between 109 and 133 mph is the p-value of Z when X = 133 subtracted by the p-value of Z when X = 109, hence:

X = 133:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (133 - 115)/6

Z = 3

Z = 3 has a p-value of 0.9987.

X = 109:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (109 - 115)/6

Z = -1

Z = -1 has a p-value of 0.1587.

0.9987 - 0.1587 = 0.84, hence the percentage is of 84%.

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Coterminal angles are angles with the same terminal sides.

For the given angle, the coterminal angles are;

From the given answer choices, the coterminal angle is;

The sum of the length around a square is known as the perimeter thus the possible length of each side of the chicken pen assuming it to be square is 12.5 feet.

Perimeter is the addition of an external measure of sides it will always positive.

A perimeter is a length and has a degree of the unit as one.

Perimeter of square = side + side + side + side

Let's assume the chicken pen to the square in order to find the length of each side.

Now since fencing is fitted around the sides so it will be the same as the perimeter of the square.

Perimeter of square = 4 × side

4 × side = 50

Side = 50/4 = 12.5 feet.

Hence "The sum of the length around a square is known as the perimeter thus the possible length of each side of the chicken pen assuming it to be square is 12.5 feet".

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SOLUTION:

Step 1:

In this question, we are meant to solve the following:

Step 2:

The perimeter of the largest figure is:

On the other hand, the area of the largest figure is:

The width of the plantation is 110. 7 kilometers

It is important to note that the formula for calculating the area of a rectangle is expressed as;

Area, A = lw

Where;

Given that;

The value of the area of the large plantation is eleven and seven hundredths kilometers.

This is expressed as;

Area = 11. 07 kilometers

The value of the length is one tenth kilometers.

This is expressed as;

Length = 1/10 kilometers = 0. 1 kilometers

Now, substitute the values into the formula to determine the width

11. 07 = 0. 1w

Divide both sides by the coefficient of w, w have;

11.07/0.1 = 0.1w/0.1

Find the quotient

w = 110. 7 kilometers

Hence, the value is 110. 7 kilometers

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The representation of the composite functions f(x) and g(x) are f(x) =√x and g(x) = 4x + 8

From the question, we have the following parameters

(fg)(x) = h(x)

Such that

h(x) = √4x + 8

The given parameter implies that

(fg)(x) =√4x + 8

Let g(x) = 4x + 8

Substitute g(x) for 4x + 8 in the above equation (fg)(x) =√4x + 8

So, we have

(fg)(x) =√g(x)

Substitute g(x) for x in the above equation (fg)(x) =√g(x)

f(x) =√x

This means that

f(x) =√x and g(x) = 4x + 8

Hence, the possible equations are f(x) =√x and g(x) = 4x + 8

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ANSWER:

1. b = 5

2. h = 6

3. b = 30

STEP-BY-STEP EXPLANATION:

We know the ratio between height and base.

By means of the following proportions we can determine the missing dimensions in each case:

The first quartile (Q1) is defined as the middle number between the smallest number (minimum) and the median of the data set. The first quartile is the median of the first half of a data set.

First QuartileQ1 =11

The third quartile (Q3) is the middle value between the median and the highest value (maximum) of the data set. The third quartile is the median of the second half of a data set.

Third QuartileQ3 = 24

The interquartile range (IQR), is equal to the difference between 75th and 25th percentiles. IQR = Q3 − Q1

IQR = 13

Place the data points in descending order of size to find the center number. The median is as shown. The median is the average of the two numbers if there are two of them. The number that appears the most frequently in a piece of data is the mode.

The middle value in a list that is arranged from smallest to greatest is called the median. The value that appears the most frequently on the list is the mode. Organize the numbers in a set in whatever order—from lowest to highest or highest to lowest—and then tally the frequency with which each number appears in the group. The mode is the one that shows up most frequency

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The total capacity of her tank would be; 21 gallons.

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

Given that Leslie makes a stop at a gas station. she put 14 gallons into her tank. if the tank is now 2/3 full.

Let c be the total capacity of the tank.

Then, we can find the capacity of her tank;

c x 2/3 = 14

Cross multiplication;

c = 14 x 3/2

c = 7 x 3

c =21

Hence, the total capacity of her tank would be; 21 gallons.

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Using proportions, the trails that you can hike are given as follows:

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication or division.

Two examples of proportions are used in this problem:

The time you want to complete a trail is:

1 and 1/2 hours with an absolute deviation of at most 15 minutes.

1 and 1/2 hours = 1.5 hours, as 1 + 1/2 = 1 + 0.5 = 1.5 hours.

1.5 hours = one hour and 30 minutes with a deviation of 15 minutes, the time lengths are:

Considering the rate of 3 miles, the distances are between:

The times for each trail, converting the mixed numbers to decimals, and the decimals to hours and minutes, are given as follows:

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Answer:

What are the outstanding traditional Chinese culture?

1. Drama is a general term for stage performing arts that achieve narrative purposes in the form of language, movement, dance, music and puppets.

2. Chinese painting, originated in the Han Dynasty, mainly refers to the scroll painting painted on silk, rice paper and silk and mounted.

3, Calligraphy, calligraphy is a unique form of artistic expression of the beauty of Chinese characters in China and the surrounding countries and regions that have been deeply influenced by Chinese culture.

4, Shadow Puppets, also known as "Shadow Puppets" or "lantern Puppets", is a kind of folk drama made of animal skins or cardboard silhouettes to perform stories.

5. Pingju, which is popular in northern China, is one of the traditional operas of the Han nationality and one of the most popular operas among the people. It ranks among the five kinds of operas in China.

Answer: [tex]m\angle 2=75^{\circ}, m\angle 1=105^{\circ}[/tex]

Step-by-step explanation:

By the alternate interior angles theorem, [tex]m\angle 2=75^{\circ}[/tex].

Using linear pairs, [tex]m\angle 1=105^{\circ}[/tex].

A cosine function is said to have an amplitude of 3, a midline of 5, and a period of 3/4.

It is required to write the cosine function.

Recall that the standard form of a cosine function is:

Where a is the amplitude, 2π/b is the period, c is the horizontal shift, and d is the midline or vertical shift.

Equate the given period to 2π/b and solve for b:

Hence, substitute a=3, b=8π/3, and d=5 into the standard form of the cosine function:

Since it is not given that the cosine function has a horizontal shift, substitute c=0 to get the required function:

The function is y=3cos((8π/3) x)+5.

The given line equation is y=1.

The general form of the line equation is

Comparing this equation with y=1, we get

Compare coefficient of x and constant term, we get

Here m=0 is the slope of the line y=1.

Hence the slope of the line y = 1 is zero.

This statement is true.

The expressions which can be used to find m∠ABC and from the task content are;

It follows from the task content that the expressions which can be used to find m∠ABC are to be identified among the answer choices.

Since, it follows from trigonometric ratios that;

Sin theta = opposite/hypothenuse

Cos theta = adjacent/hypothenuse

It therefore follows that;

Therefore, the measure of angle ABC can be determined using any of the formulas above;

Therefore the two expressions which can be used to find m∠ABC are;

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Answer: the answer is B [tex]cos^{-1}(\frac{6.3}{9.8}) sin^{-1}(\frac{7.5}{9.8})[/tex]

Step-by-step explanation: it will be show below.