The final product of the given algebraic expression is: b⁴ - 64
How to expand algebraic expressions?Algebraic expressions are defined as simply the idea of expression of numbers using letters without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as a, b, c, etc. These letters are referred to as variables. An algebraic expression can be a combination of both the variables and the constants. Any value that is placed before and multiplied by a variable is a coefficient.
The expression is given as:
(b² + 8)(b² - 8)
Expand the expression using (a + b)(a - b) = a² - b²
Thus:
(b² + 8)(b² - 8) = b⁴ - 64
Thus, that is the final product of the given algebraic expression.
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The probability solutions are given as follows;
- P(CS Major and Not Hired) = 43.6% (Marginal)
- P(Other Major) = 31.5% (Marginal)
- P (Hired + CS Major) = 36.3% (Conditional)
- P (Not Hired + Other Major) = 48.5% (Conditional)
How did we arrive at this conclusion?First we need to clarify the meaning of Joint, Marginal, and conditional probability.
Joint probabilities are statistical measures defining how likely two or more distinct occurrences are to happen at once; whereas marginal probabilities represent individual probabilities by isolating each characteristic being measured separate from others around them. Conversely, conditional probabilities measure statistical chances for events conditioned on previously known outcomes.Note that the table of values are attached.
So, the calculation is shows as follows:
P(CS Major and Not Hired) = 102/234 = 43.6% (Marginal)
- P(Other Major) = 74/234 = 31.5% (Marginal)
- P (Hired + CS Major) = 58/160 = 36.3% (Conditional)
- P (Not Hired + Other Major) = 36/74 48.5% (Conditional)
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The cost of book B is $15.00 more than three times the cost of book A. if the cost of books A and B together is $75.00, what is the cost of book A ?
Step-by-step explanation:
we can substitute book B as B
we can substitute book A as A
using the information above we can create an eqaution
we know B is $15.00 more than 3 times the cost of A
B = 3A + 15.00
we know the sum of the books is $75.00
A + B = 75.00
substitute B with eqaution 1 we will get
A + 3A + 15.00 = 75.00
4A + 15.00 = 75.00
- 15.00 -15.00
4A= 60.00
A = 15.00
which means book A is $15.00
2 quantities, a and b, have a proportional relationship, where a is -3 and b is -4. Create an equation to represent this relationship
The equation to represent the relationship is a = [tex]\frac{3}{4}[/tex] b.
What is proportion?
A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.
Here the given two quantities in proportional relationship . Then,
=> a∝ b
=> a=kb
Where k is constant. Then, put a=-3 and b=-4 rhen,
=> -3=-4k
=> k = 3/4
Then the equation is ,
=> a = [tex]\frac{3}{4}[/tex] b.
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21 cm 1.2.1 Calculate the perimeter of the A4 paper. Explain the meaning of the given scale. 1.2.2 1.2.3 What type of scale is shown on the drawing 1+1
ACCOUNTING
Differential Analysis for a Lease-or-sell Decision
Stowe Construction Company is considering selling excess machinery with a book value of $280,200 (original cost of $399,900 less accumulated depreciation of $119,700) for $277,800, less a 5% brokerage commission. Alternatively, the machinery can be leased for a total of $286,800 for 5 years, after which it is expected to have no residual value. During the period of the lease, Stowe Construction Company's costs of repairs, insurance, and property tax expenses are expected to be $24,900.
On the basis of the data presented, it would be advisable to sell the machinery based on the differential analysis.
For selling the machinery,
Revenues = $277,800
Costs = 277,800 × 5% = $13,890
Profit = Revenues - Cost = $277,800 - $13,890 = $263,910
For leasing the machinery,
Revenues = $286,800
Costs = $24,900
Profit = Revenues - Cost = $286,800 - $24,900 = $261,900
Here the profit generated by selling the machinery is greater, which is the better option.
Hence selling the machinery is the better option.
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On the basis of the data presented, it would be advisable to sell the machinery based on the differential analysis.
For selling the machinery,
Revenues = $277,800
Costs = 277,800 × 5% = $13,890
Profit = Revenues - Cost = $277,800 - $13,890 = $263,910
For leasing the machinery,
Revenues = $286,800
Costs = $24,900
Profit = Revenues - Cost = $286,800 - $24,900 = $261,900
Here the profit generated by selling the machinery is greater, which is the better option.
Hence selling the machinery is the better option.
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What is the surface area?
20 cm
16 cm
20 cm
24 cm
32 cm
The calculated value of the surface area of the shape is 192 square cm
What is the surface area?From the question, we have the following parameters that can be used in our computation:
The triangle (see attachment)
The surface area is calculated as
Area = 1/2 * Base * Height
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * 24 * 16
Evaluate
Area = 192
Hence, the surface area is 192 sq cm
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a new crew of painters takes two times as long to paint a small apartment as the experienced crew together both crews can paint the apartment in 6 hours how many hours does it take the experienced crew to paint the apartment
In the equation , it take 2 hours for the experienced crew to paint the apartment.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here let us take x as time taken by new crew of painters apartment and y as time taken by experienced crew of painters apartment .
Now a new crew of painters takes two times as long to paint a small apartment as the experienced crew then,
x = 2y ----> 1
both crews can paint the apartment in 6 hours then,
=> x+y = 6
Now put equation 1 into x+y=6 then,
=> 2y+y=6
=> 3y = 6
=> y = 6/3 = 2 hours.
Hence it take 2 hours for the experienced crew to paint the apartment.
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2
At the end of a baseball game, the players were given the choice of having a bottle of
water or a box of juice. Of all of the players, 12 chose a bottle of water, which was
of the total number of players. Write and solve an equation to determine p.
3
4
the total number of players at the baseball game.
Show your work.
An equation to determine p is 12 = 3p/4.
The total number of players at the baseball game is 16 players.
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would a assign variable to the total number of players at the baseball game, and then translate the word problem into a linear equation as follows:
Let the variable p represent the the total number of players at the baseball game.
Since the players had the choice of having a bottle of water or a box of juice., and of all of the players, only 12 chose a bottle of water, which was of the total number of players, a linear equation that can be used to model this situation is given by;
12 = 3/4 × p
48 = 3p
p = 48/3
p = 16 players.
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The graph shows the square root parent function.
-5
5
5
Which statement best describes the function?
OA. The function is negative when x > 0.
OB. The function is negative when x<0 and also when x > 0.
OC. The function is negative when x < 0.
D. The function is never negative.
The function is never negative.
option D is the correct answer.
What is a negative function?A negative function is a function in which the resulting y value is negative.
Also, a negative function is a function that has y values that are less than zero for any x values. In other words, a negative function has a negative sign in front of its output.
From the given graph, the x and y values started from 0 and increases into the positive direction, so we can conclude that the function can never be negative.
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What is a good estimate for 485% of 20? Explain
Answer:
100
Step-by-step explanation:
We can estimate 485% as 500%. We know that 500% is equal to 5.
Therefore,
20 × 500%
= 20 × 5
= 100
sasha bout a car for 22995; six years later it was worth 12645, if depreciation was linear how much did the value of the car go down each year?
The value of the car went down by an average of $1,725 each year over the six-year period.
What is Depreciation?Depreciation is the loss in value of an asset due to factors such as age, wear and tear, market conditions, and obsolescence. It is usually calculated on a linear basis, meaning that the same amount of depreciation is spread evenly over a period of time.
In this case, the car was purchased for $22,995, and six years later it was worth $12,645.
To calculate the linear depreciation of the car, we need to subtract the value at the end of the period from the value at the beginning, and divide by the number of years:
Depreciation = ($22,995 - $12,645) / 6
Depreciation = $1,725
This means that the car depreciated by an average of $1,725 each year. In other words, the value of the car went down by an average of $1,725 each year over the six-year period.
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110° M NOT DRAWN TO SCALE N In the diagram, O is the centre of the circle MNP. If ZMOP = 110°, find the value of x.
The value of angle x is determined as 55⁰.
What is the measure of angle x?The measure of angle x can be calculated by applying circle theorem which states that the angle at the center of a circle is twice the angle at the circumference of a circle.
This theorem is known as, "Angle at the Center Theorem" or "Central Angle Theorem". It states that the angle formed by two radii (lines segment from the center of the circle to any point on the circumference) of a circle is always twice the size of the angle formed by the same arc (portion of the circumference) when measured at the circumference.
The value of angle x is calculated as follows;
from the given figure;
m ∠MOL = 2 m∠MNL
110⁰ = 2x
x = ¹/₂ x 110⁰
x = 55⁰
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Simplify the expression
The simplified expression is (z -3)/z - 5. Option C
How to simply the expressionFrom the information given, we have to simply the expressions by solving the quadratic equation;
From the information given, we have that;
z² -5zx + 6
Find the pair factors and substitute the values
z² - 2z - 3z + 6
Group in pairs, we have;
z(z - 2) - 3(z - 2)
For the denominator, we have;
z² - 7x + 10
Find the factors
z² - 5z - 2z + 10
Group in pairs, we have;
z(z - 5) - 2(z - 5)
Then, we have the simplified form;
(z -3)/z - 5
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help me hurry up 8th grade math
The standard form of each of the numbers is given as follows:
a) 2.35 x 10^-3 = 0.00235.
b) 2.35 x 10³ = 2350.
What is scientific notation?A number in scientific notation is given by the notation presented as follows:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1, justifying the open interval at 10.
For item a, to obtain the standard form of the number, we must move the decimal points three places to the left, hence:
2.35 x 10^-3 = 0.00235.
For item b, to obtain the standard form of the number, we must move the decimal points three places to the right, hence:
2.35 x 10³ = 2350.
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Mr. Pearson drives a bus for the city of Greenwood. Last month, he kept track of the number of bus riders each day. 50 60 Bus riders 70 What was the least number of bus riders? 80 90 100
In a case wherebyMr. Pearson drives a bus for the city of Greenwood and Last month, he kept track of the number of bus riders each day the least number of bus riders is 50.
How can the least number be known?The least number can be described as the number that serves as the smallest among the given number.
Based on the record that was kept, t can be deduced that the highestnumber is 100 whereby the least of the number is 50 which implies that option A is correct because it is considered to be smallest number hence te least number.
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compete question;
Mr. Pearson drives a bus for the city of Greenwood. Last month, he kept track of the number of bus riders each day.
Bus riders
50
60
70
80
90
100
What was the least number of bus riders?
4
Please help
Question in image
The value of x is given as follows:
B. 6.
How to obtain the value of x?The value of x is obtained applying the two secant segment theorem, which means that the following equation will hold true:
4(x + 4) = 5(5 + 3)
(we add the two parts), with the outer part being the multipler.
Expanding the operations, the value of x is obtained as follows:
4x + 16 = 40
4x = 24
x = 6.
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If Thursday seen 400 customers and Friday had a 1/5 increase from Thursday what is the number of people on Friday?
Answer:
There were 480 customers on Friday.
To calculate the increase from Thursday to Friday, we can use the following formula:
```
Increase = (percent increase / 100) * starting value
```
In this case, the percent increase is 1/5, and the starting value is 400 customers. So, the increase is:
```
Increase = (1/5 / 100) * 400 = 8
```
This means that there were 8 more customers on Friday than there were on Thursday. So, the total number of customers on Friday is:
```
Total = Starting value + Increase
= 400 + 8
= 480
```
Step-by-step explanation:
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4x+5/x+7
Answer:
x = 2.4
Step-by-step explanation:
4x + 5 / x + 7
combine like terms
X + 4x = 5x
5 + 7= 12
12/ 5x
Divide
12 /5= 2.4
X= 2.4
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Answer:
-1/2
Step-by-step explanation:
The information provided about the line is that the line passes through the points (2, 2) and (6, 0)
Therefore, the first step consists in computing the slope. The formula for the slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Now, by plugging the corresponding numbers is , we get that the slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-2}{6-2} =-\frac{1}{2}[/tex]
So then, we find that the slope is [tex]m=-\frac{1}{2}[/tex] and that the line passes through the point [tex](2,2)[/tex].
Conclusion: Based on the data provided, we conclude that the slope of the line is [tex]m=-\frac{1}{2}[/tex].
a small coffee shop owner wants to know which brand of coffee her customers prefer
population or sample explain?
If the small "coffee-shop" owner is trying to determine the preference of her customers by conducting a survey among a group of customers who visit the shop during a specific time frame, then this group would be a sample rather than a population.
A "Sample" is defined as a subset of the population that is selected to represent the entire population. In this case, the owner is trying to determine the preference of her customers by surveying a specific group of customers.
So, this group of customers is a sample of the population of all customers who visit the coffee shop.
To obtain meaningful results from the survey, the sample should be selected randomly and should be representative of the population. The results obtained from the sample could then be used to make inferences about the preferences of the entire population of customers who visit the coffee shop.
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The given question is incomplete, the complete question is
A small coffee shop owner wants to know which brand of coffee her customers prefer.
Is the data considered a "population" or "sample", Explain?
Find the equation (in terms of x) of the line through the points (-4,-1) and (3,-3)
Y=
The equation of the line through the points is 7y = -2x - 15.
What is the equation through the points?
The equation of a line that passes through two given points is calculated as follows;
y - y1 = m(x - x1)
Where;
m is the slope of lineThe slope is calculated as;
m = (y2 - y1) / (x2 - x1)
m = (-3 + 1) / (3 + 4)
m = -2/7
The equation of the line is calculated as;
y - y1 = m(x - x1)
y - (-1) = (-2/7)(x - (-4))
y + 1 = (-2/7)(x + 4)
y + 1 = (-2/7)x - (8/7)
y = (-2/7)x - (15/7)
7y = -2x - 15
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Help me please I need help
Answer:
(2,5] or (7,∞)
Step-by-step explanation:
I need help understanding how to solve this.
Answer:
The common ratio of this geometric sequence is -1/2, so we have
a(7) = 16 × -1/2 = -8, a(8) = -8 × -1/2 = 4.
Dividing by -1/2 is the same as multiplying by -2. Working backwards, we have:
a(5) = -2 × 16 = -32
a(4) = -2 × -32 = 64
a(3) = -2 × 64 = -128
a(2) = -2 × -128 = 256
a(1) = -2 × 256 = -512
Karla drove her vehicle 12,000 miles last year. How many gallons of gasoline would she have saved last year had she driven a fuel-efficient hybrid car averaging 48 miles per gallon rather than an SVU averaging 15 miles per gallon?
Step-by-step explanation:
so, she drove the 12,000 miles with an SUV that gave her 15 miles per gallon.
that means she used
12000 / 15 = 800 gallons of gasoline.
if she would have used a car that gave her 48 miles per gallon, she wound have needed
12000 / 48 = 250 gallons of gasoline.
so, she would have saved
800 - 250 = 550 gallons of gasoline.
In the conversion of fractions to decimals, the fraction should be thought of as (n) ___ problem
In the conversion of fractions to decimals, the fraction should be thought of as a division problem.
A fraction represents the division of the numerator (n) by the denominator (d). So, when you have a fraction like n/d, you can convert it to a decimal by dividing n by d.
A trucker had a load of grain containing 2 tons. She unloaded 1 ton and 500 pounds at the warehouse. How much grain does she still have left on the truck?
Answer:
1500 pounds Or 0.75 tons
Step-by-step explanation:
To solve this problem, we need to convert all units to the same unit, either tons or pounds. Let's convert 1 ton and 500 pounds to pounds:
1 ton = 2000 pounds
1 ton and 500 pounds = 2000 + 500 = 2500 pounds
Now we can subtract the amount of grain that was unloaded from the total amount:
2 tons = 2 * 2000 = 4000 pounds
4000 pounds - 2500 pounds = 1500 pounds
Therefore, the trucker still has 1 ton and 500 pounds, or 1500 pounds, of grain left on the truck.
To convert 1500 pounds to tons, we can use the conversion factor:
1 ton = 2000 pounds
Dividing both sides by 2000, we get:
1 pound = 1/2000 tons
Multiplying both sides by 1500, we get:
1500 pounds = 1500/2000 tons
Simplifying the fraction, we get:
1500 pounds = 0.75 tons
Therefore, 1500 pounds is equivalent to 0.75 tons.
f(x)=x^2. What is g(x)?
Answer:
A. g(x) = -x^2 - 2
Step-by-step explanation:
Okay so it has the same slope as f(x) which means it's x^2, however, it's negative and going the other way so it's -x^2
Since the y-intercept is -2,
g(x) = -x^2 - 2
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A "flush" in poker is having all the same suit of cards in your poker hand. Remember that a standard deck of cards has 52 cards of four suits: clubs, diamonds, hearts, and spades. Each suit has 13 cards in it.
What is the probability that a player is dealt five cards resulting in a flush that is not the suit of hearts or clubs?
sin2x=
please help!!
Answer:
A
Step-by-step explanation:
It is a double angle identity.
sin2x = 2sinxcosx
Answer: 2sinxcosx
Step-by-step explanation:
What formula could you use to help find the area of the given triangle?
Angle Addition Postulate
Pythagorean Theorem
Midpoint Formula
The formula that will be useful in finding the area of the triangle is: Pythagoras theorem
How to find the area of a triangle?The formula to find the area of the triangle is expressed by the formula:
A = ¹/₂bh
Where:
b is base
h is height
Now, we have the base but we don't have the height.
Pythagoras Theorem is defined as the way in which we find the missing length of a right angled triangle.
The triangle has three sides, namely the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
where c is the hypotenuse
Thus, to find the height of the triangle, we will use Pythagoras theorem to get:
h = √(6² - 4²)
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