Artrigerator contains 5 cans of diet soda and 8 cans of regular soda. If three cans of soda are randomly selected without replacement, determine the probability that all can selected are diet soda. Use combinations to determine theprobabilityThe probability that all can selected are diet soda is(Type an integer or a simplified fraction)

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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Let's use the following inequation as an example:

First let's simplify it dividing the inequation by 2:

Now, let's draw a number line, and include the point 3 in it:

We want the values of y that are greater than 3, that is, the numbers to the right of the number 3 in the number line. So we mark the area that corresponds to the values of y that satisfies the inequation:

The number 3 is not part of the answer, because 3 is not greater than 3, so we draw a small empty circle on the number 3. If the number 3 was part of the answer, the circle would be filled.

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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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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Given the expression:

a - 5 - b

we want to evaluate it when a = 10 and b = 4. To do it, we have to replace these values into the equation as follows:

10 - 5 - 4 = 1

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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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:

43

Step-by-step explanation:

So, the key to solving this is PEMDAS, or parenthesis, exponents, multiplication/division from left to right, and addition/subtraction from left to right. So, you start off with 14x3, which is 42. So, you have 42-2+3. Next, you have to do 42-2, which is 40. Finally, you do 40+3, which is 43.

Answer:

43

Step-by-step explanation:

14 x 3 - 2 + 3

PEMDAS says multiply before adding or subtracting

42 - 2 + 3

Then subtract

40 +3

Then add

43

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

The expression is √3/2 (sin x) - (cos x)/2

Here we have

sin( x + 11π/6)

We have to express it in terms of sin(x) and cos(x)

sin ( 2π - π/6 + x)

sin ( 2π + ( x - π/6))

sin(2π + Ф ) = sin Ф

So

sin( x - π/ 6)

Formula :

sin(A -B) = sin A cos B - cos A sin B

sin( x - π/ 6)

sin x cos π/6 - cos x sin π/6

con π/6 = √3/2  and sin π/6 = 1/2

√3/2 sin x - 1/2 cos x

Therefore the expression is √3/2 sin x - 1/2 cos x.

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total number of sides = 6

sides that are 2 or 5 = 2

Divide the sides thata re 2 or 5 (2) by the total sides:

2 /6 = 1/3

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.

Answer: -4.5,-3,165,227

Step-by-step explanation:

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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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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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.

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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Answer:

a=1/3, b=-6, c=7

Explanation:

Given the polynomial:

We reorder it to rewrite the polynomial in the form ax²+bx+c:

Next, by comparing:

• a is the coefficient of x²: a=1/3

• b is the coefficient of x: b=-6

• c is the constant: c=7

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 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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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

Answer:

y = x-13

Step-by-step explanation:

So this question asks for two numbers. Let's call them x and y.

Since we know that x is larger than y, and the difference between them is 13, x must be greater than y by 13. So, x = y + 13
x = y + 13 isn't what the question is asking for though, so we have to isolate y to make one side contain only x and numbers. To do that, subtract both sides by 13 to get:
x - 13 = y

rearrange:

y = x - 13

Based on the conversion rate between kilometers and miles, the data to complete the table is:

For every given mile, there will be 1.61 kilometers. To convert miles to kilometers therefore, you have to multiply the number of miles by the number of kilometers in a mile.

If given 8 miles, the number of kilometers is:

= 8 x 1.61

= 12.88 kilometers

If given 3.1 miles, the number of kilometers is:

= 3.1 x 1.61

= 4.991 kilometers

If given 1.5 kilometers, then the number in miles is:

= 1.5 x 0.62

= 0.93 miles

If given 9 kilometers, then the number in miles is:

= 9 x 0.62

= 5.58 miles

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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:

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

Given,

The equation of table is

Here,

Hence, the output of the table is F, F, F, and T

ANSWER:

35 miles

STEP-BY-STEP EXPLANATION:

We can make a proportion, since we know the number of miles per 18 gallons, so for 2 3/10 gallons we can calculate the number of miles proportionally

solving for x:

Therefore you can travel a total of 35 miles.

An object's capacity is expressed in terms of volume.

The container's volume is 56 in3.

The capacity of an object is expressed in terms of volume.

A cup's capacity is said to be 100 ml, for instance, if it can hold 100 ml of water in its brim.

The quantity of space a three-dimensional item takes up can also be referred to as volume.

The figure's volume is equal to Bh.

V = Bh

where

B is the base's region.

h is the figure's height.

h = 4 in

The area of the base B is

B = (4*4) - (1*2) = 14 in

V = 14*4 = 56 inch cube.

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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.