When unknown terms been added, what can we do to isolate them?

The volume of Hannah's suitcase in cubic inches is: C: 7938.

The volume can be determine using this formula

Volume = Length × Width × Depth

Where:

Length = 27 inches

Width = 21 inches

Depth = 14 inches

Let plug in the formula

Volume = 27 inches × 21 inches × 14 inches

Volume = 7,938

Therefore we can conclude that the volume is 7,938.

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Answer:

what table?

Step-by-step explanation:

While it is not very likely that there will be exactly 14 births on any given day, it is still possible, and the probability of it happening is about 8.3%.

Let's start by calculating the mean or average number of births per day. To do this, we divide the total number of births in a year (4126) by the number of days in a year. Since there are 365 days in a year, the mean number of births per day is:

4126 / 365 = 11.3

This means that on average, there are about 11 to 12 births per day in this hospital.

In this case, the average rate of occurrence is 11.3 births per day. Using the Poisson distribution formula, we can calculate the probability of having 14 births in a day as follows:

P(X=14) = (e⁻¹¹°³) x (11.3¹⁴) / 14!

where e is the mathematical constant approximately equal to 2.71828, X is the random variable representing the number of births in a day, and ! represents the factorial function.

Using a calculator or a software tool, we get:

P(X=14) = 0.083

This means that the probability of having exactly 14 births in a day is about 8.3%.

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The First Isomorphism Theorem states that under certain conditions, the image of a homomorphism of rings is an ideal and the quotient ring obtained by modulo the kernel of the homomorphism is isomorphic to the image of the homomorphism.

The proof of this theorem follows a similar approach as the proof for the corresponding theorem in group theory, but the specific details depend on the given homomorphism and rings involved.

The First Isomorphism Theorem, also known as Theorem 8.3.14, states that if f is a homomorphism of a ring R into a ring R', then the image of f, denoted f(R), is an ideal of R' and R modulo the kernel of f, denoted R/Ker(f), is isomorphic to f(R).

The proof of the First Isomorphism Theorem is a direct translation of the proof of the corresponding theorem for groups. However, without the specific details of the given homomorphism f and the rings R and R', it is not possible to provide a specific proof. The proof generally involves establishing the well-definedness of the map, showing that it is a homomorphism, proving the surjectivity and injectivity of the map, and verifying that the kernel of f is indeed the set of elements that map to the identity element of R'.

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The circumference of the circle to the nearest hundredth is 21.98 inches.

The circumference of a circle is the measure of the boundary or the length of the complete arc of a circle.

The circumference of a circle is the perimeter of the circle. It's the wholes boundary of the circle.

The circumference of the circle can be found as follows:

circumference of a circle = 2πr

where

Therefore,

diameter of the circle = 7 inches

radius of the circle = 7 / 2 = 3.5 inches

Hence,

circumference of a circle = 2 × 3.14 × 3.5

circumference of a circle = 21.98 inches

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Answer:  the answer is D, if you just graph it in the Desmos graphing calculator you can solve it easily

There is a 16% probability that the individual actually had the disease given a positive test result.

The probability that the individual had the disease can be calculated as follows:

Let A = Event of testing positive and actually having the disease

Let B = Event of testing positive but not actually having the disease

We are looking for P(A|B), which is the probability of actually having the disease given a positive test result.

Using Bayes' Theorem, we have:

P(A|B) = P(A) * P(B|A) / P(B)

Bayes' theorem is a mathematical formula used in probability theory to calculate the probability of an event based on prior knowledge of conditions that might be related to the event.

It states that the conditional probability of an event A given event B is equal to the product of the probability of event B and the conditional probability of event A given event B, divided by the probability of event B. The formula is represented as P(A|B) = P(B|A) * P(A) / P(B).

Where:

P(A) = 1/500 (probability of having the disease)

P(B|A) = 0.95 (probability of a correct positive result given that the individual has the disease)

P(B) = P(B|A) * P(A) + P(B|A') * P(A') (probability of a positive test result)

= 0.95 * 1/500 + 0.01 * 499/500 (probability of a false positive result given that the individual does not have the disease)

Plugging in the values, we have:

P(A|B) = (1/500) * 0.95 / [0.95 * 1/500 + 0.01 * 499/500] = 0.16 or 16%

Therefore, there is a 16% probability that the individual actually had the disease given a positive test result.

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The areas under the standard normal curve are approximately 0.9099, 0.4292, and 0.4894 for the given ranges.

(a) The area that lies between Z=-1.73 and Z=1.73 is being calculated. (b) The area that lies between Z=-0.18 and Z=0 is being determined. (c) The area that lies between Z=-2.27 and Z=0.28 is being calculated.

To determine the area under the standard normal curve, we can use a standard normal distribution table or statistical software.

(a) For Z=-1.73 and Z=1.73, we look up the corresponding areas in the table or calculate using software. The area between these two Z-scores is approximately 0.9099.

(b) For Z=-0.18 and Z=0, we find the area in the table or using software. The area between these two Z-scores is approximately 0.4292.

(c) For Z=-2.27 and Z=0.28, we refer to the table or use software to find the area. The area between these Z-scores is approximately 0.4894.

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The length of the rectangular  playground is 241.86 foot.

Given that area of rectangle is 19,500 sq.ft and length of rectangle is three times its width.The area for rectangle is given by formula: A=LW.

Now according to the given condition, L= 3W. Further we'll solve by putting L= 3W in the formula for rectangle.

A=LW

As given A= 19,500 sq.ft and considering L=3W,

19,500 = 3W*W

19,500 = 3W^2

∴ W^2 = 6500

∴ W = \(\sqrt{6500}\)

∴ W = 80.6225 ft. ≈ 80.62 ft.

Now putting the value W = 80.62 in equation L =3W,

L = 3* 80.62

L = 241.86 ft.

The length of the rectangular playground is 241.86 foot.

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As per the unitary method, there would be approximately 84 deer in a 560 square mile region, based on the assumption that the deer population density is uniform throughout the region.

In this case, we want to find the number of deer in a 560 square mile region, given that there are 15 deer in a circular region with a radius of 10 miles.

The first step is to find the area of the circular region with a radius of 10 miles. We can use the formula for the area of a circle, which is A = πr², where A is the area and r is the radius. Substituting the values, we get:

A = π(10)² = 100π

The area of the circular region is 100π square miles.

Next, we can use a unitary method to find the number of deer in one square mile. We know that there are 15 deer in 100π square miles. To find the number of deer in one square mile, we can divide both sides by 100π:

15 deer ÷ 100π square miles = x deer ÷ 1 square mile

Simplifying this equation, we get:

x = (15 ÷ 100π) deer per square mile

Now, we can use this value of x to find the number of deer in a 560 square mile region. We can multiply x by 560 to get:

x deer per square mile × 560 square miles = 560x deer

Substituting the value of x, we get:

560(15 ÷ 100π) deer = 84 deer (rounded to the nearest whole number)

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Answer:

Step-by-step explanation

$12x17.5=210

$11x12.5=137.5

210+137.5=$347.5

Elizabeth worked for 17.5 Hours

Her sister worked 12.5 hours

The minimum volume of the box is 48 feet³.

The volume of the empty space that needs to be filled with packing peanuts to protect the model is 32 feet³.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume.

Given:

Pyramid base= 4 cm, height= 4 cm

So, Volume of pyramid

= a²h/3

= 16 x 3 /3

= 16 feet³

and, Volume of Cuboidal box

= lbh

= 4 x 4 x 3

= 16 x 3

= 48 feet³

So, Volume of empty space in box

= 48- 16

= 32 feet³

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The diameter of the circle is approximately 60 inches.

To explain further, we can use the formula relating the central angle of a sector to the length of its intercepted arc. The formula states that the length of the intercepted arc (A) is equal to the radius (r) multiplied by the central angle (θ) in radians.

In this case, we are given the central angle (225 degrees) and the length of the intercepted arc (30π inches).

To find the diameter (d) of the circle, we need to find the radius (r) first. Since the length of the intercepted arc is equal to the radius multiplied by the central angle, we can set up the equation 30π = r * (225π/180). Simplifying this equation gives us r = 20 inches.

The diameter of the circle is twice the radius, so the diameter is equal to 2 * 20 inches, which is 40 inches. Therefore, the diameter of the circle is approximately 60 inches.

In summary, by using the formula for the relationship between central angle and intercepted arc length, we can determine the radius of the circle. Doubling the radius gives us the diameter, which is approximately 60 inches.

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To solve this inequality, we must first isolate the absolute value on one side of the equation.

Step 1: Add 5 to both sides of the equation.

−2x−5 + 5 ≤ 5 + 5

Step 2: Simplify the left side.

−2x ≤ 10

Step 3: Divide both sides by -2.

x ≥ -5

Step 4: Graph the solution on a number line.

The solution set is {x | x ≥ -5}

Answer: 7 pies

Unit price: $3.50

Step-by-step explanation:

1. To find the unit price, you must divide the cost by the amount of pies

11 divided by 3 is 3.70

24.50 divided by 7 is 3.50

2. You now have the unit price. To find the better buy, you need to determine which price is lower.

3.50 < 3.70

3. The better buy is the 7 pies.

Answer:

Answer: 27:8

Step-by-step explanation:

There are 24 + 16 + 14 = 24+16+14= 54

54 marbles in total.

The ratio of total marbles to red marbles is 54 : 16, which simplifies to 27 : 8.

Answer: 27:8

Answer:

4

Step-by-step explanation:

took the test and got it right!

Answer:

57

Step-by-step explanation:

-7+2*36-8

-7+72-8

65-8

57

No,  5/8 cannot make the equation \(\frac{8}{15}-x=\frac{3}{7}\) to be true

The given fractional equation is:

\(\frac{8}{15}-x=\frac{3}{7}\)

To calculate the fraction that will make the equation \(\frac{8}{15}-x=\frac{3}{7}\), solve for x in the given equation:

\(\frac{8}{15}-x=\frac{3}{7}\)

Collect like terms

\(x=\frac{8}{15}-\frac{3}{7}\)

Simplify the resulting fraction as follows:

\(x=\frac{56-45}{105} \\\\x=\frac{11}{105}\)

Therefore, the missing fraction that will make the equation \(\frac{8}{15}-x=\frac{3}{7}\) true is 11/05

We can conclude that 5/8 cannot make the equation \(\frac{8}{15}-x=\frac{3}{7}\) to be true

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Since \(\frac{5}{8} \neq\frac{11}{105}\), hence \(\frac{5}{8}\) will not make the equation true.

Given the equation

a is the fraction that will make the equation to be equal

Subtract \(\frac{8}{15}\) from both sides;

\(\frac{8}{15}-a-\frac{8}{15} =\frac{3}{7}-\frac{8}{15}\\-a= \frac{3}{7}-\frac{8}{15}\\-a=\frac{3(15)-7(8)}{105} \\-a=\frac{45-56}{105}\\-a=\frac{-11}{105}\)

Multiply both sides by a negative sign to have:

\(-(-a)=-(-\frac{11}{105} )\\a=\frac{11}{105}\)

Since \(\frac{5}{8} \neq\frac{11}{105}\), hence \(\frac{5}{8}\) will not make the equation true.

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Answer:

y = 10.5x - 37

General Formulas and Concepts:

Pre-Algebra

Algebra I

Equality Properties

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

Point (-4, 47)

Point (2, -16)

Step 2: Find slope m

Step 3: Find y-intercept b

Step 4: Write linear equation

Combine all parts.

y = 21/2x - 37

y = 10.5x - 37

And we have our final answer!

Answer: 16

Step-by-step explanation: Solve for x

by simplifying both sides of the equation, then isolating the variable.

Answer:

x= 1/3

Step-by-step explanation:

1. Combine multiplied terms into a single fraction

2. Multiply all terms by the same value to eliminate fraction denominators

3. Cancel multiplied terms that are in the denominator

4. Divide both sides by the same factor

5. Simplify

(A) If Two independent events, A and B, are such that P(A) = 0. 2 P(A U B) = 0. 8, then probability P(B) =  5/8.

The possibility of the result of any random event is referred to as probability. This term refers to determining how likely an event is to occur. What are the chances of getting a head when we toss a coin in the air, for instance? The quantity of outcomes depends on the response to this question. Here, the outcome could be either head or tail. Thus, there is a 50% chance that the result will be a head.

The probability serves as a gauge for the likelihood that an event will occur. It gauges how likely an event is to occur. The probability equation is given by;

P(E) = Number of Favourable Outcomes/Number of total outcomes

We know that

P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = P(A) + P(B) - P(A).P(B)

0.8 = 0.2 + P(B) - 0.2.P(B)

0.5 = P(B)  - 0.2.P(B)

0.5 = 0.8.P(B)

P(B) = 0.5/0.8

P(B) = 5/8

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Answer:

110011001 is the binary equivalent of the number 409

Answer:

let s regroup the terms

2ax - 15 = 3(x + 5) + 5(x - 1) *** add 15 to both sides ***

<=> 2ax = 15 + 3x + 15 + 5x - 5 *** develop to remove the parentheses***

<=> 2ax = 8x + 25 *** simplify ***

<=> (2a-8)x = 25 *** subtract 8x from both sides ***

<=> (a-4)x=25/2 *** divide by 2 both sides ***

There is no solution is a-4 = 0 ,

because it would mean 0 = 25/2 and this is not possible

So it gives a = 4

Step-by-step explanation:

I hope this helps

Answer:

Create your own real-world example of a relation that is a function.

Domain: The set of: 0

Range: The set of: 16

The domain of a function is the set of all possible inputs for the function while the range of a function is the set of all possible outputs for the function.

A function is an expression that shows the relationship between two or more variables and numbers.

The domain of a function is the set of all possible inputs for the function while the range of a function is the set of all possible outputs for the function.

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The values of x and y are x=6.75 and y=-0.6875.

Value is a concept that denotes the worth of something or the importance it has to an individual or group. It is often used in terms of ethics, morality, economics, and social sciences. Value is a subjective concept and depends on the context and perspective of the individual or group. It can be measured in terms of money, time, effort, or other resources. Value can also be seen as something that adds meaning to life and can be a source of motivation when pursuing goals.

To solve for x and y using elimination, we must manipulate both equations to have the same coefficient for x. To do this, we first multiply the first equation by -3. This gives us:

(-18x+12y=30)
2x+14y=4

Now, we can add the equations together, which gives us:

-16x+26y=34

Next, we can divide both sides of the equation by -16, which gives us:

x+7y=-2.125

Now, we can substitute this value into either equation and solve for the other variable. Let's substitute it into the first equation:

-6x+4y=10
-6(-2.125)+4y=10
12.75+4y=10
4y= -2.75
y= -0.6875

Now, to find x, we can substitute -0.6875 into either equation, and solve for x:

2x+14(-0.6875)=4
2x-9.5=4
2x=13.5
x=6.75

Therefore, the values of x and y are x=6.75 and y=-0.6875.

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A typical water bed weighs around 1797.6 pounds. It depends upon the volume of water bed and the unit conversion of the weight and volume units.

A typical water bed holds 28 cubic feet of water.

The volume of the typical water bed and its weight can be calculated with the help of the quantities:

Identify the volume of water held by the water bed, which is 28 cubic feet.
Multiply the volume by the weight of 1 cubic foot of water, which is 64.2 pounds.
Perform the calculation: 28 cubic feet × 64.2 pounds per cubic foot = 1797.6 pounds.

Therefore, a typical water bed weighs approximately 1797.6 pounds when filled with water.

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