Factor out the Greatest Common Factor (GCF): 64d³ - 24d²
The factored form of 64d³ - 24d² is 8d²(8d³ - 3).
Define greatest common factorThe greatest common factor (GCF), also known as the greatest common divisor (GCD), is the largest positive integer that divides two or more numbers without leaving a remainder. In other words, it is the largest number that divides evenly into two or more given numbers. For example, the GCF of 12 and 18 is 6, since 6 is the largest number that divides both 12 and 18 without leaving a remainder.
The greatest common factor (GCF) of the given terms is 8d². We can factor it out by dividing each term by 8d²:
64d³/8d² - 24d²/8d²
Simplifying the fractions:
8d³ - 3
Therefore, the factored form of 64d³ - 24d² is 8d²(8d³ - 3).
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18. Name a pair of complementary angles in this figure.
Answer:
Step-by-step explanation:
Angle KEF and JEK
Answer:
∠DEH and ∠HEJ or∠JEK and ∠KEF----------------------------
Complementary angles are the angles that together form a right angle.
In the picture we see two right angles:
∠DEJ and ∠JEFThe first one, ∠DEJ has a pair of complementary angles:
∠DEH and ∠HEJThe second one, ∠JEF has a pair of complementary angles:
∠JEK and ∠KEFOn average, a front desk operator receives 2 calls per 30 seconds.
(1)Find the probability that at most 1 call is received in 10 seconds
The probability that at most 1 call is received in 10 seconds is given as follows:
0.8557 = 85.57%.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are listed and explained as follows:
x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval or range of values of the input parameter.On average, a front desk operator receives 2 calls per 30 seconds, hence the mean for 10 seconds, which is one third of the time, is given as follows:
[tex]\mu = \frac{2}{3}[/tex]
The probability of at most one call is given as follows:
P(X <= 1) = P(X = 0) + P(X = 1)
Hence:
[tex]P(X = 0) = \frac{e^{-\frac{2}{3}}\frac{2}{3}^{0}}{(0)!} = 0.5134[/tex][tex]P(X = 1) = \frac{e^{-\frac{2}{3}}\frac{2}{3}^{1}}{(1)!} = 0.3423[/tex]Hence:
P(X <= 1) = P(X = 0) + P(X = 1) = 0.5134 + 0.3423 = 0.8557 = 85.57%.
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Romero Company has a target capital structure that consists of $3.3 million of debt capital, $3.5 million of preferred stock financing, and $4.3 million of common equity. The corresponding weights of its debt, preferred stock, and common equity financing that should be used to compute its weighted cost of capital (rounded to the nearest wo decimal places) are:
The weights of the debt, preferred stock, and common equity financing are 28.6%, 30.4%, and 41.0%, respectively.
To calculate the weighted cost of capital (WACC), the proportion of each component of capital structure is needed. The weight of each component of the capital structure is determined by dividing the market value of the component by the total market value of all the components of the capital structure.
In this case, the total market value of the company's capital structure is the sum of the market value of debt, preferred stock, and common equity.
The weights for each component are calculated as follows:
Weight of debt = Market value of debt / Total market value of capital structure
= $3.3 million / ($3.3 million + $3.5 million + $4.3 million)
= 0.286 or 28.6%
Weight of preferred stock = Market value of preferred stock / Total market value of capital structure
= $3.5 million / ($3.3 million + $3.5 million + $4.3 million)
= 0.304 or 30.4%
Weight of common equity = Market value of common equity / Total market value of capital structure
= $4.3 million / ($3.3 million + $3.5 million + $4.3 million)
= 0.410 or 41.0%
These weights can be used to calculate the weighted cost of capital for Romero Company.
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The function f(x) = 2-5* can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the multiplicative rate of change of the function? 0 2 05 10 • 32
The given function does not represent the curve passing through the given points. The multiplicative rate of change of the function is 5.
What is Curve Line ?A curve is a continuous, smooth line that gradually alters direction. Rather than being straight line that follows a curve may be referred to as a curve line. A curve line can be made by connecting a number of non-straight-line-lying sites. In mathematics, a curve is a geometrical object that can be described by equations, such as parametric or function equations.
The rate of change of a function is the ratio of the change in the output (y) to the change in the input (x). In this case, we can calculate the rate of change between the first two points:
Changing at what rate between (1, 10) and (2, 50)?
Y change = 50 – 10 = 40
Variation in x = 2 - 1 = 1
Rate of change equals change in y/change in x, or 40/1, or 40.
In a similar manner, we can determine how quickly the second and third points will change:
The change between (2, 50) and (3, 250) is as follows:
Changing y by 250 - 50 equals 200
Variation in x = 3 - 2 = 1
Rate of change equals change in y/change in x, which is 200/1, or 200.
Now that we have the second rate of change, we can compute the multiplicative rate of change by dividing it by the first:
Multiplicative rate of change is equal to 200/40, or 5.
The function's multiplicative rate of change is thus 5.
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A pair of dice are tossed twice. Find the probability that the first roll is a total of at least 5 and the second roll is a total of at least 4.
The probability that the first roll is a total of at least 5 and the second roll is a total of at least 4 is 0.764 or 76.4%.
What is the probability?The probability is the chance that an expected event occurs out of many possible events.
For two independent events happening, we use the rule of multiplication of independent events based on dice probabilities.
The event that the first roll is a total of at least 5 = A
In the event that the second roll is a total of at least 4 = B
The number of faces on each die, n = 6
The probability of event A = ³⁰/₆ = ⁵/₆
The probability of event B = ³³/₃₆ = ¹¹/₁₂
Multiplying the two probabilities, P(A) and P(B) = ⁵/₆ × ¹¹/₁₂
= ⁵⁵/₇₂ = 0.764
Thus, there is a ⁵⁵/₇₂ or 0.764 chance that the first roll is at least 5 and the second roll is at least 4.
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what does it mean the name of the numbers
help
Answer:
It is called as triangular numbers
Step-by-step explanation:
these numbers can be represented as a triangle of dots
what is the probability that either event will occur
The probability that either event will occur is 7/25
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 which is equivalent to 100% in percentage.
Probability = sample space /Total outcome
P(A or B) = P(A) +P(B) -P(A and B)
The total element = 25+5+15+5 = 50
therefore total outcome = 50
P(A) = 25/50
P(B) = 15/50
P(A and B) = 5/40
Therefore P(A and B) = 25/50+15/50 - 5/50
= 35/50 = 7/25
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Given this unit circle what is the value of x
Answer:
[tex]x=-\dfrac{\sqrt{51}}{10}[/tex]
Step-by-step explanation:
You want the value of x in the third quadrant of a unit circle where y = -7/10.
Pythagorean theoremThe radius of a unit circle is 1, so the Pythagorean theorem tells you the magnitude of the value of x is ...
1² = x² +(7/10)²
x = -√(1 -49/100) = -√(51/100) . . . . . . x < 0 in the third quadrant
x = (-√51)/10
What's the answer to this problem
The function shows that the chairs and sofas the manufacturer should produce to earn that profit is C. (6, 12) P= 1,260
How to explain the functionThe profit function is P = 50x + 80y.
In order to find the optimal production quantities that will maximize the profit function, we need to determine which vertex yields the highest profit.
From the given vertices, we can see that the profit at (0,0) is 0. The profit at (0,15) is 1,200, and the profit at (6,12) is 1,260.
Therefore, the manufacturer should produce 6 chairs and 12 sofas to earn a profit of 1,260.
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Solve for the missing side using c =
Answer:
c=12.04
Explanation:
You can use the formula given: c=√a^2+b^2
c=√8^2+9^2=√64+81=√145=12.04
The mayor of a town has proposed a plan for the construction of a new bridge. A political study took a sample of 800 voters in the town and found that 53% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 49%. Find the value of the test statistic. Round your answer to two decimal places.
the value of the test statistic is approximately 5.19.we can get the answer by using formula .
what is statistic ?
A statistic is a numerical value or measure that is calculated from a sample of data, and is used to describe or make inferences about a population. Statistics are used in various fields, including business, economics, social sciences, and natural sciences, to analyze data
In the given question,
To test the claim that the percentage of residents who favor construction is more than 49%, we can use a one-sample z-test. The test statistic can be calculated as:
z = (p - P) / √(P * (1 - P) / n)
where:
p = the sample proportion (0.53)
P = the hypothesized population proportion under the null hypothesis (0.49)
n = the sample size (800)
Substituting the given values into the formula, we get:
z = (0.53 - 0.49) / √(0.49 * 0.51 / 800) ≈ 5.19
Rounding the test statistic to two decimal places, we get:
z ≈ 5.19
Therefore, the value of the test statistic is approximately 5.19.
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The sales of a certain product after an initial release can be found by the equation s=12 sqrt (4t) + 10 , where s represents the total sales (in thousands) and t represents the time in weeks after release. Make a table of values, graph the function and use the graph to estimate the sales 12 weeks after release.
about $586,000
about $586
about $93
about $93,000
The sales 12 weeks after release is $586,000 . Option A is the correct answer.
To create a table of values, we can plug in different values of t and find the corresponding values of s:
t s
0 10
1 19.882
2 26.248
3 31.177
4 35.064
5 38.185
6 40.731
7 42.837
8 44.6
9 46.095
10 47.384
11 48.508
12 49.498
To graph the function, we can plot the values from the table on a coordinate plane. The horizontal axis represents time in weeks, and the vertical axis represents sales in thousands of units. The resulting graph is a curve that starts at (0,10) and increases as t increases.
To estimate the sales 12 weeks after release, we can look at the graph and see that the corresponding value of s is around 49.5 thousand units. Therefore, the answer is about $586,000 (49.5 x 1000 x 12). Option A is the correct answer.
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please help me
What degree of rotation about the origin will cause the triangle below to map
onto itself?
Find the length of the missing side
Step-by-step explanation:
This is a right triangle , so the Pythagorean theorem applies
c^2 = a ^2 + b^2 c is the hypotenuse a and b are the legs
15^2 = 9^2 + x^2
15^2 - 9^2 = X^2
x = 12 ft
$5850 is invested at 6.5% compounded continuously. How long will it take for the balance to reach $11700? Round your answer to two decimal places.
Answer:10.66 years. Punch again to double check
Step-by-step explanation:
A=Pe^(rt)
11700=5850e^(.065t)
isolate the variable expression
2=e^(.065t) divide by 5850
ln2=lne^(.065t) take the natural log of both sides
ln2=.065t. Bring down the power, lne equals
t is about 10.66 years. Divide ln2 by .065
A manager of Furniture store has compiled a list of written complaints during the past three months. The complaints were categorized as follows. Type and Frequency Error in billing, Rudeness by store personnel, Late delivery, Questions not answered during telephone inquiry,and Other 42 14 8 6 5 Total 75 Present the above data using pie-chart(put the relative frequencyand the central angle measure toeach categoryon a table)
We can conclude that there is significant evidence that the number of complaints received by Lara music store is different from number of complaints received by music stores in general.
Here, we have,
H0 : μ ≥ 6
H1 : μ < 6
Test statistic :
n = 20
Sample Mean, x = 3
σ = 1.5
Test statistic = (x - μ) ÷ σ/sqrt(n)
Test statistic = (3 - 6) ÷ 1.5/sqrt(20)
Test statistic = - 3 / 0.3354101
Test statistic = −8.944271
Since, sample size is < 30 ;
Obtaining the Critical value using the from T;
Tcritical at 0.05, df = 19 = - 1.729
Tstatistic < Tcritical
−8.944271 < - 1.729
Hence, we reject the Null:
We can conclude that there is significant evidence that the number of complaints received by Lara music store is different from number of complaints received by music stores in general.
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1. Ashenge Private Limited Company is about to start production of new products. Before the start of the new production, it cost the company $200,000 to construct the factory building. Once the construction is over, the cost per unit of production is estimated to be Birr 20. Upon selling, the company will incur a 20% commission expense. Moreover, the price per unit of products is decided to be Birr 50.
Required:
a) Construct the total cost equation in terms of quantity.
b) Determine the break-even quantity and break-even revenue.
The total cost equation is 200,000 + 40n and the break-even revenue is 20,000.
Given that a company is starting a new production, it cost the company $200,000 to construct the factory building.
The cost per unit of production is estimated to be Birr 20.
The company will incur a 20% commission expense.
The price per unit of products is decided to be Birr 50.
We need to find the total cost equation in terms of quantity and determine the break-even quantity.
a) The fixed cost of the company is $200,000, and 40 per unit sell,
Therefore for n units the total cost =
200,000 + 40n
b) BEQ = FC / P−VC
= 200,000 / 50-40
= 20,000
Hence the total cost equation is 200,000 + 40n and the break-even revenue is 20,000.
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Between 7 am and 11 am the temperature in Antartica increased by 8.4 C. If the temperature at 11 am was -28.3 degrees, what was the temperature at 7 am?
Answer:
the temperature at 7 am was -36.7 degrees.
Step-by-step explanation:
Let's denote the temperature at 7 am by "x". Since the temperature increased by 8.4 C between 7 am and 11 am, we can set up the equation:
x + 8.4 = -28.3
Subtracting 8.4 from both sides, we get:
x = -36.7
Therefore, the temperature at 7 am was -36.7 degrees.
Brynen is driving to a new job five days this week. He drives 27 miles each way. His car gets 35 miles per gallon of gas. How many gallons of gas will he use driving to and from work this week? Round to the nearest tenth.
The number of gallons of gas Brynen will use in driving to and from work, during the week, obtained using arithmetic operations is 7 5/7 gallons
What are arithmetic operations?Arithmetic operations are operations involving addition, subtraction, multiplication, and division.
The distance Brynen travels each way to his new job = 27 miles
The distance his car gets per gallon of gas = 35 miles
The number of gallons he will use in a week (five days of driving in the week), can therefore, be found by arithmetic operations follows;
The distance Brynen travels = 27 × 2 × 5 = 270 miles
The number of gallons = 270 miles/(35 miles/gallon) = 270/35 = 7 25/35
7 25/35 = 7 5/7
The volume of gas he will use to and from work this week is; 7 5/7 gallons
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Fixed expenses are defined as those that do not very with changed in volume. Examples include:
A( direct staffing costs
B( lease costs and taxes
C( utilities and supplies utilized in production of service or product
D( utilities, rent, lease, depreciation
Answer:
B (lease costs and taxes) and D (utilities, rent, lease, depreciation) are examples of fixed expenses as they typically do not vary with changes in volume.
Direct staffing costs (A) and utilities and supplies utilized in the production of service or product (C) are generally considered variable expenses as they tend to vary based on the volume of production or sales. For example, if a business produces more goods or provides more services, it will typically need to hire more staff and use more supplies, leading to an increase in expenses.
Step-by-step explanation:
100 POINTS!!!!!! please answer will give brainliest If the length of each side of the right triangle shown on the grid is measured in cm; find the area of the triangle: 25 cm2 50 cm2 100 cm? 225 cm?'
Answer:
B) 50cm^2
Step-by-step explanation:
A total of 480 black and red jerseys were produced in a factory. Each black Don jersey was sold at $56. Each red jersey was sold at $75. After all the jerseys were sold, the amount of money collected from the sale of the black jerseys was $18315 less than that of the red jerseys. (a) How many black jerseys were sold? (b) How much money was collected from the sale of the red jerseys?
Answer:
Step-by-step explanation:
Need help! I HAVE 30 MIN! will pay for all work shown (ZELLE ONLY) Do all 3 please!
Answer: i gotchu
Step-by-step explanation:
1) Since the base of this function is greater than 1, this means its increasing exponentially (increases from left to right). So as x approaches positive infinity, y approaches positive infinity as well.
Domain (-∞,∞) Range (0,∞)
2) If the base changes to 1/9 the function would decrease. So as x approaches positive infinity, y approaches 0 (Check attached screenshot)
3) The "+5" raises the horizontal asymptote up 5 units. So the new equation for the horizontal asymptote is y=5.
The "x-2" shifts the x values to the right by 2 units.
u dont have to pay me, i literally just learned this like a month ago :)
25 POINTS
Which is the BEST definition of dilation?
A: a transformation that either reduces or enlarges an object in the coordinate plane
B: a transformation that spins an object in the coordinate plane
C: a transformation that either slides or shifts an object in the coordinate plane
D: a transformation that flips an object in the coordinate plane
Answer: A
Step-by-step explanation:
A dilation is not a rigid transformation, which means it has to scale the object into a different measure. So, enlarging or reducing the size of an object is a dilation.
Find a polynomial f(x) of degree 5 that has the following zeros.
0, 1 (multiplicity 2), -6, -3
Leave your answer in factored form.
This polynomial has zeros at 0, 1 (with multiplicity 2), -6, and -3, as required, and is of degree 5.
How to solveA polynomial f(x) of degree 5 with the given zeros can be represented in factored form as:
f(x) = [tex]A(x - 0)(x - 1)^2(x + 6)(x + 3)[/tex]
Since the leading coefficient is not specified, we can leave A as a constant factor. Simplifying the expression, we have:
f(x) = [tex]A(x)(x - 1)^2(x + 6)(x + 3)[/tex]
This polynomial has zeros at 0, 1 (with multiplicity 2), -6, and -3, as required, and is of degree 5.
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Find the length of the third side. If necessary, round to the nearest tenth.
6 and 10
The length of the third side is 8units
What is Pythagoras theorem?Pythagoras theorem states that : the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
If a and b are the legs of the triangle and c is the hypotenuse,then
c² = a²+b²
For example , if a = 3 and b = 4 , then
c = √3²+4²
c = √ 9+16
c = √25
c = 5units.
Similarly, c = 10, a= 6, and b is unknown
therefore
10²= 6²+b²
b² = 10²-6²
b² = 100-36
b² = 64
b = √64
b = 8units
therefore the length of the third leg is 8units.
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3. A room is 17 feet by 16 feet. Carpet for the room costs
$101 per square yard.
How much will it cost to carpet the room?
Question 1
Answer: First, let's convert the room's dimensions from feet to yards, since the carpet cost is given per square yard:
17 feet = 5.67 yards (rounded to two decimal places)
16 feet = 5.33 yards (rounded to two decimal places)
Next, we can calculate the area of the room in square yards by multiplying these values:
Area = 5.67 yards × 5.33 yards = 30.23 square yards (rounded to two decimal places)
Finally, we can multiply the area by the cost per square yard to get the total cost:
Total cost = 30.23 square yards × $101/square yard = $3,056.23 (rounded to two decimal places)
Therefore, it will cost $3,056.23 to carpet the room.
Can you help me answer this question?
Step-by-step explanation:
The constant of proportionality is just the slope of the line
using 0,0 and 3,2 points
slope = (y1-y2 ) / ( x1-x2) = (0-3) / ( 0-2) = 3/2 = constant of proportionality
on any day ,the probability that marcus will get a seat on the schoo bus is 0.93 . what is the probability that he does not get a seat on the school bus?
Marcus not getting a seat on the school bus is therefore 0.07 or 7% likely as 0.07 percent of people will not receive a seat .
what is probability ?The prospect of an event happening is assessed by probability. It is a number between zero and 1, where 0 denotes an improbable occurrence and 1 denotes a certain occurrence. For instance, if we flip a fair coin, the odds of obtaining heads are 0.5, or 50%, and the odds of receiving tails are also 0.5, or 50%. In each case, there are various ways to compute probability. In general, if an event has n equally possible results and k of them are favourable, the likelihood that the event will occur is: Event P = k/n . All possible outcomes are thought to be equally likely under what is referred to as the classical probability.
given
Simply put, the likelihood that Marcus won't obtain a seat on the school bus is the complement of the likelihood that he will.
By deducting the probability from 1, one can determine the complement of a probability. So:
Chance of not being seated equals one less than the likelihood of being seated.
The likelihood of not getting a seat is equal to 1 - 0.93.
0.07 percent of people will not receive a seat.
Marcus not getting a seat on the school bus is therefore 0.07 or 7% likely as 0.07 percent of people will not receive a seat .
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