The values of[tex]a^3 + 8b^3[/tex]are 280 when b = 3 and 125 when b = 5/2.
To find the value of [tex]a^3 + 8b^3[/tex], we can use the given information about a and b. Let's proceed step by step:
1. We are given that a + 2b = 10. We can rearrange this equation to express a in terms of b: a = 10 - 2b.
2. We are also given that ab = 15. Substituting the expression for a from the previous step into this equation, we get (10 - 2b)b = 15.
3. Expanding the equation, we have [tex]10b - 2b^2 = 15.[/tex]
4. Rearranging the equation, we get[tex]2b^2 - 10b + 15 = 0.[/tex]
5. This is a quadratic equation in terms of b. We can solve it using factoring, completing the square, or the quadratic formula. In this case, we can factor the equation as (b - 3)(2b - 5) = 0.
6. From the factored equation, we find two possible values for b: b = 3 or b = 5/2.
7. To find the corresponding values of a, we substitute these values of b into the expression a = 10 - 2b. We find a = 4 when b = 3, and a = 0 when b = 5/2.
8. Now, we can calculate the value of [tex]a^3 + 8b^3[/tex] using the values of a and b we found. For the case when b = 3, we have [tex]a^3 + 8b^3 = 4^3 + 8(3)^3[/tex] = 64 + 216 = 280. For the case when b = 5/2, we have[tex]a^3 + 8b^3 = 0^3 + 8(5/2)^3 = 0 + 8(125/8) = 125.[/tex]
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A recipe requires 1/3 cup of milk for each 1/4 cup of water. How many cups of water
are needed for each cup of milk?
A. 1/12
B. 3/4
C. 11/12
D. 1 1/3
Answer:
The answer is D 11/3
Step-by-step explanation:
what is the external net force exerted on a 3.5 kg papaya, which is being pushed across a table and has an acceleration of 2.2 m /s² to the left
Answer:
Given -
Mass (m) = 3.5 kgAcceleration (a) = 2.2 m/s²To find -
External net force exerted on papaya.Solution -
From the second law of motion i.e., F = MA
→ F = 3.5 × 2.2
→ 7.7 kg ms-²
Therefore, the external net force exerted on papaya is 7.7 kg m/s².
We have that the external net force exerted is
F=7.7N
From the question we are told
the external net force exerted on a 3.5 kg papaya, which is being pushed across a table and has an acceleration of 2.2 m /s² to the left
Generally the equation for the Force is mathematically given as
[tex]F=ma\\\\Therefore\\\\\F=3.5*2.2\\\\F=7.7N[/tex]
Therefore
The external net force exerted is
F=7.7N
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find an equation for the line below
i’ll give brainliest to whoever gets it right first
Find the slope of the line that passes through the points (2, 4) and (6, 12)
Answer:
The slope is 2.
Step-by-step explanation:
Question is on a picture
Answer:
second option: x is greater than or equal to 8 or x is less than -1
Step-by-step explanation:
If a dozen cupcakes cost $14, how much
does one-fourth of a dozen cupcakes
cost?
Answer:
The answer is A 3.50 if you divide 14 by 4 it would be 3.50
Which triangle side lengths form a right triangle? Choose all that apply.
5, 6, 7
6, 8, 14
8, 15, 17
10, 12, 15
15, 20, 25
16, 18, 20
Answer:
C and D
Step-by-step explanation:
Took the quiz
Many of a bank's customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Each customer spends an average of 90 seconds completing his or her transactions. Transaction time is exponentially distributed. Answer the following questions: Compute the probability that a customer will not have to wait upon arriving at the automatic teller machine (2 decimal points)
The probability that a customer will not have to wait upon arriving at the automatic teller machine is 0.78 (rounded to 2 decimal points).
To compute the probability that a customer will not have to wait upon arriving at the automatic teller machine, we need to determine the arrival rate and the service rate.
Customers arrive at a rate of one every other minute. This means the arrival rate (λ) is 1 customer per 2 minutes, or λ = 1/2 customers per minute.
Each customer spends an average of 90 seconds completing their transaction. This means the service rate (μ) is 1 customer per 90 seconds, or μ = 1/90 customers per second.
To calculate the probability that a customer will not have to wait, we can use the M/M/1 queueing model, where M represents the exponential distribution for both arrivals and service.
The formula for the probability that the system is in the empty state (no customers in the system) is given by:
P0 = 1 - (λ/μ)
Substituting the values:
P0 = 1 - (1/2) / (1/90)
P0 = 1 - (45/2)
P0 = 1 - 22.5
P0 = 0.775
Therefore, the probability that a customer will not have to wait upon arriving at the automatic teller machine is 0.78 (rounded to 2 decimal points).
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Using approximations to 1 significant figure,
estimate the value of
0.482 x 61.2^2 / square root 98.01
URGENT!
please help i have 5 mins left of my test
Answer:
200
Step-by-step explanation:
Given:
0.482 x 61.2^2 ÷ √98.01
61.2^2 = 3745.44
√98.01 = 9.9
So,
0.482 × 3745.44 ÷ 9.9
= 1,805.30208 ÷ 9.9
= 182.35374545454
To one significant figure
= 200
One significant figure means only 1 non zero value and others are zero
The approximation to 1 significant figure of the result is 200
Given that:
To express [tex]\dfrac{0.482 \times 61.2^2}{\sqrt{98.01}}\\[/tex] with approximation to 1 significant figure.
The calculations will go like this:
[tex]\dfrac{0.482 \times 3745.44}{\sqrt{98.01}}\\\\=\dfrac{1805.302}{9.9}\\\\\approx 182.35\\[/tex]
Significant figure 1 means only 1 non zero digit should be present and rest places can be having zeros.
Rounding to 1 significant figure:
200
Thus, the result approximated to 1 significant figure is 200.
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1. (15 points =5 ′×3) Draw two indifference curves (IC) for each of the following pairs of goods and indicate which IC provides a higher utility. Put the quantity of the 1st good on the horizontal axis and the quantity of the 2 nd good on the vertical axis. 1.1 Rhonda likes carrots and dislikes broccoli. 1.2 Emily likes hip-hop iTunes downloads and does not care about heavy metal downloads. 1.3 Steven dislikes both potatoes and fish. Each fish he eats decreases his utility by a smaller amount that the previous fish.
1.1 For Rhonda, who likes carrots and dislikes broccoli, the indifference curves would show a higher level of utility as they move away from broccoli and towards more carrots. The indifference curve representing a higher utility would be the one farther away from the origin and closer to the carrots axis.
This indicates that Rhonda prefers more carrots and less broccoli, and each indifference curve represents a different level of utility. 1.2 For Emily, who likes hip-hop iTunes downloads and doesn't care about heavy metal downloads, the indifference curves would be upward sloping. As the quantity of hip-hop iTunes downloads increases, Emily's utility would increase. Since she doesn't care about heavy metal downloads, the specific shape of the indifference curves would depend on the individual preferences within the hip-hop downloads. The indifference curve representing a higher utility would be the one farther away from the origin and representing a larger quantity of hip-hop iTunes downloads.
1.3 For Steven, who dislikes both potatoes and fish, the indifference curves would be downward sloping. As the quantity of potatoes and fish increases, Steven's utility would decrease. However, the statement mentions that the utility decrease for each additional fish is smaller than the previous one. This suggests that the indifference curves would have a diminishing slope as they move away from the origin. The indifference curve representing a higher utility would be the one closer to the origin, indicating a lower quantity of potatoes and fish.
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In each diagram, linek is parallel to line 1, and line t intersects lines k and l.
1139
127°
113°
127°
799
xo
V
Vt
Based on the diagrams, which statement is true?
A The value of x is 79, because the two angles shown in each diagram are congruent.
B The value of x is 101, because the two angles shown in each diagram are supplementary.
C The value of x is greater than 90, because the two angles shown in each diagram are
obtuse angles
The value of x is 11, because the two angles shown in each diagram are complementary.
Answer:
Step-by-step explanation:
A
The value of x is 79° because the two angles shown in each diagram are congruent.
Option A is the correct answer.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
Line k is parallel to line l, and line t intersects lines k and l.
We see that,
79° and x° are alternate exterior angles.
Alternate exterior angles are congruent.
Thus,
x° = 79°
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Please need help with this
The two-column proof shown above should be completed with the following reasons:
GivenGivenDefinition of midpointVertical angles theorem.CPCTCSAS congruence postulate.What is a midpoint?In Mathematics and Geometry, a midpoint is a point that lies exactly at the middle of two other end points that are located on a straight line segment.
In this context, we can prove that triangle MNO is congruent with triangle QPO by completing the two-column proof shown above with the following reasons:
Statements Reasons
1. PQ║MN Given
2. O is the midpoint of Np Given
3. NO ≅ OP Definition of midpoint
4. ∠MON ≅ ∠QOP Vertical angles theorem
5. ∠NMO ≅ ∠PQO CPCTC
6. ΔMNO ≅ ΔQPO SAS congruence postulate
In conclusion, SAS is an abbreviation for side, angle, side while CPCTC is an abbreviation for corresponding parts of congruent triangles are congruent.
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Translate figure 3units right and 7 units down
Answer:
A' is located at -4, -5. B is located at 0, -1. C is located at 1, -5.
Step-by-step explanation:
Indicate whether the statement below is true or false, explain why. Convenience samples are generally not representative of the population
a.False; convenience samples are only representative of small populations.
b. False; convenience samples are usually representative of the population since those readily available are typically the majority. c.True d. False; convenience samples are generally very representative of the populations since they tend to be unbiased.
The statement "Convenience samples are generally not representative of the population" is true.
Convenience samples are a type of non-probability sampling in which the researcher selects participants based on their convenience. This means that the researcher selects participants who are easy to reach or who are available at the time of the study. Convenience samples are often used in research because they are quick and easy to collect.
However, convenience samples are not representative of the population because they do not include all members of the population.
For example, if a researcher is interested in studying the effects of a new medication on people with high blood pressure, they might select participants from a convenience sample of people who are easy to reach, such as people who are already taking medication for high blood pressure. However, this convenience sample would not be representative of the population of people with high blood pressure because it would not include people who are not taking medication for high blood pressure.
Here are the reasons why convenience samples are generally not representative of the population:
Bias: Convenience samples are often biased because the researcher selects participants who are easy to reach or who are available at the time of the study. This can lead to a sample that is not representative of the population because it may include more people from certain groups, such as people who are more educated or people who are more likely to respond to surveys.
Small sample size: Convenience samples are often small in size, which can make it difficult to generalize the results of the study to the population.
Heterogeneity: Convenience samples are often heterogeneous, which means that they include people from different backgrounds and with different experiences. This can make it difficult to identify patterns or trends in the data.
If you are conducting a research study, it is important to use a sampling method that will give you a representative sample of the population. Probability sampling methods, such as simple random sampling and stratified random sampling, are more likely to give you a representative sample than convenience sampling.
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Help is required, I am stuck
Answer:
see explanation
Step-by-step explanation:
Given
x² + 4x - 7 = 0 ( add 7 to both sides )
x² + 4x = 7
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(2)x + 4 = 7 + 4
(x + 2)² = 11 ( take the square root of both sides )
x + 2 = ± [tex]\sqrt{11}[/tex] ( subtract 2 from both sides )
x = - 2 ± [tex]\sqrt{11}[/tex]
Thus
x = - 2 - [tex]\sqrt{11}[/tex] ≈ - 5.32 ( to 2 dec. places )
x = - 2 + [tex]\sqrt{11}[/tex] ≈ 1.32 ( to 2 dec. places )
A painter charges $15.36 per hour, plus an additional amount for the supplies. If he made $187.93 on a job where he worked 7 hours, how much did the supplies cost
Answer:
15.36×7=107.52
187.93-107.52=80.41
supplies cost $80.41
A 38- ounce bottle of juice drink contains 6 percent water. Than computed 6 percent of 38. His work is shown below.
6 percent of 38 = 0.6 x 38-22.8
Which statement explains Than's error? please help
Answer:
see below
Step-by-step explanation:
6 percent changed to decimal form is
6/100 = .06 not .6
6 5 of 38
.06 * 38 = 2.28
38 -2.28 =35.72
answer
38 -2.28 =35.72
Casey is a real estate agent. She earns 8.15% commission on each sale she makes. After working with a potential buyer for 3.5 months, she finally sold a house for $877,000. What did casey earn in commissions for this sale
Answer:
Casey earned $71,475.50 in commissions for this sale
Step-by-step explanation:
Percentages
To find a percentage of a given number, the procedure is multiplying the percentage by the number and divide by 100.
Casey earns 8.15% commission as a real estate agent on each sale she makes. When she finally sold a house for $877,000, her commission is calculated as follows:
commission = 8.15*877,000/100 = 71,475.5
Casey earned $71,475.50 in commissions for this sale
Find the monomial if the expression is the square of that monomial. 0.0001a^(8)x^(4)
We've found the monomial if the expression is the square of that monomial, which is [tex]0.0001a^(8)x^(4).[/tex]
A monomial is defined as an expression in which all of the terms are multiplied by constants, variables, or both, with no additions or subtractions.
Let's begin by writing the given expression as the square of a monomial.
[tex]0.0001a^(8)x^(4) = (a^(n/2) * x^(m/2))^2[/tex]
We can extract the square root of the expression to get the original monomial:
[tex]sqrt(0.0001a^(8)x^(4)) = sqrt(a^(8/2) * x^(4/2))0.01ax^2[/tex]
is the required monomial.
The process of finding the square of a monomial is known as squaring a monomial.
It entails taking a monomial and squaring each of its terms.
A monomial is a polynomial with one term.
We can extract the square root of an expression to get the original monomial if the expression is the square of a monomial.
The formula for the square of a monomial is as follows:
[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]
If we square a binomial, we use the FOIL method to get the expansion:
[tex](a + b)^2 = a^2 + ab + ba + b^2\\ = a^2 + 2ab + b^2[/tex]
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Pls help me. Plus, working. Thank you
Answer:
Total surface area=228cm²
Step-by-step explanation:
Area of bottom(parallelogram)=12×12=144cm²
area of 1 triangle=1/2×8×12=48cm²
area of 3triangles=48×3=144cm²
Total surface area=144+144=228cm²
who ever answer all these questions will get brilliantist and 5 stars
Answer:
Step-by-step explanation:
Answer:
A. Because 4:5 and 8:10 are equivalent because
4:5 are already in the lowest term
8 and 10 are can simplify by 2 ensure that you know how to lowest term
8 ÷ 2 = 4 and 10 ÷ 2 = 5 Overall it equals to 4:5
B. Because 18:3 and 6:1 are equivalent because
6:1 are already in the lowest term
18 and 3 are can simplify by 3 ensure that you know how to lowest term
18 ÷ 3 = 6 and 3 ÷ 3 = 1 Overall it equals to 6:1
C. Because 2:7 and 10,000:35,000 are equivalent because
2:7 are already in the lowest term
10,000 and 35,000 are can simplify by 5,000 ensure that you know how to lowest term
10,000 ÷ 5,000 = 2 and 35,000 ÷ 5,000 = 7 Overall it equals to 2:7
Explain why 6:4 and 18:8 are not equal
18 and 8 are can simplify by 2 ensure that you know how to lowest term
18 ÷ 2 = 9 and 8 ÷ 2 = 2 Overall it equals to 9:2 not in 6:4
Explain why 3:6 and 6:3 are not equivalent
3:6 can also represent 6:3 just if you reverse it
3 and 6 are can simplify by 3 ensure that you know how to lowest term
3 ÷ 3 = 1 and 6 ÷ 3 = 2 Overall it equals to 1:2
The diagram represents
9:15 but you can simplify this ratio
9 and 15 are can simplify by 3 ensure that you know how to lowest term
9 ÷ 3 = 3 and 15 ÷ 3 = 5 Overall it equals to 3:5
In fruits
A. For every 4 apples there are 3 oranges
B. The ratio of bananas to oranges is 6:3
C. The ratio of apples to bananas is 4 to 6
D. For every 1 orange there are 2 bananas
Which point on the number line could represent 1.ModifyingAbove 6 with bar?
A number line going from negative 6 to positive 6. Point A is between negative 2 and negative 1, point B is between 0 and 1, point C is 1, point D is between 1 and 2.
A
B
C
D
Answer:
the answer is D
Step-by-step explanation:
im not quite sure how but i know because i checked when i got the final grade on my test
Answer:
D
Step-by-step explanation:
im taking the unit test
What is the area of the cross section of a sphere with a volume of about 5575. 3 m³
The area of the cross-section of the sphere with a volume of approximately 5575.3 m³ is approximately 330.29 m².
To find the area of the cross-section of a sphere, we need the radius of the sphere. However, given only the volume of the sphere (approximately 5575.3 m³), we cannot directly determine the radius.
The volume of a sphere is calculated using the formula:
V = (4/3) * π * r³,
where V is the volume and r is the radius of the sphere.
To find the radius, we can rearrange the formula:
r = ((3 * V) / (4 * π))^(1/3).
Substituting the given volume into the formula, we have:
r = ((3 * 5575.3) / (4 * π))^(1/3).
Using the value of π as approximately 3.14159, we can calculate the radius:
r ≈ ((3 * 5575.3) / (4 * 3.14159))^(1/3) ≈ 10.25 m.
Now that we have the radius (approximately 10.25 m), we can calculate the area of the cross-section of the sphere.
The formula for the area of a cross-section of a sphere is:
A = π * r².
Substituting the radius we found, we have:
A = π * (10.25)² ≈ 330.29 m².
The area of the cross-section of the sphere with a volume of approximately 5575.3 m³ is approximately 330.29 m².
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The radius of a sphere is increasing at a constant rate of 2 inches per minute. At the instant when the radius of the sphere is 9 9 inches, what is the rate of change of the volume?
Given: The radius of a sphere is increasing at a constant rate of 2 inches per minute. At the instant when the radius of the sphere is 9 inches,
We need to find the rate of change of volume.
Using the formula of the volume of the sphere:
V = (4/3)πr³Where V is the volume and r is the radius.
Now differentiate it with respect to time t on both sides to find the rate of change of volume.
dV/dt = d/dt[(4/3)πr³]
dV/dt = 4πr²(dr/dt)Put the given values in the above formula and solve for dV/dt.
r = 9 inches, dr/dt = 2 inches/minute
So, dV/dt = 4πr²(dr/dt)dV/dt
= 4π(9²)(2)
cubic inches/minute
Therefore, the rate of change of the volume of the sphere is 1017.87 cubic inches/minute (approx.).
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4. ( 6x²y + 3ab)(6x²y -3ab) = ( _____ ) - 9a²b²
Answer:
The answer is;
36x^4y^2 - 9a^2b^2
Step-by-step explanation:
Here, we simply want to write the right hand side in the form of the left hand side.
The best route to use here is the route of the difference of two squares.
Say we have the value a^2-b^2
We can simply write this as (a-b)(a + b)
This looks similar to what we have in the question above. What is left is just to
multiply the term 6x^y together and place it before the subtraction sign.
Mathematically;
6x^2y * 6x^2y = 36x^4y^2
For what valuels of x is the equation |4x + 2| = x + 8 TRUE?
Answer:
[tex]x=-2\quad \mathrm{or}\quad \:x=2[/tex]
Step-by-step explanation:
[tex]|4x + 2| = x + 8 \\\\\mathrm{For\:each\:absolute\:find\:positive\:and\:negative\:intervals}\\\\\mathrm{Solve\:the\:inequality\:for\:each\:interval:}\\\\\mathrm{For\:}x<-\frac{1}{2}:\quad x=-2\\\\\mathrm{For\:}x\ge \:-\frac{1}{2}:\quad x=2\\\\\mathrm{Combine\:Solutions:}\\\\x=-2\quad \mathrm{or}\quad \:x=2[/tex]
what is 1/4 less than -3/4
Answer:
-1
Step-by-step explanation:
less than means it comes after
-3/4 - 1/4
-4/4
-1
Which of the following numbers is divisible by 11?
Answer:
I dont see any numbers?
HELP ME PLZZ I NEED HELP WITH THIS
Answer:
5 cups
The Commutative Property of Addition
Step-by-step explanation:
They have a common denominator of 12
21/12+6/12+20/12+4/12+3/12+6/12=60/12=5 cups
or you could group ingredients with the same denominators
7/4+1/4+1/2+1/2+5/3+1/3=
8/4+2/2+6/3=
2+1+2=5
The Commutative Property of Addition says the order of the numbers doesn’t change the outcome.
Financial Decision Making
The daily cost of public transportation to get you to and from your current job is $5. You regularly work 8 hours a day Monday through Friday and 4 hours on Saturday. You have been offered a new job close to home where you could walk to and from work each day. The new job pays $0.75 less an hour than your current job. You will work an average of 44 hours a week. Will you make or lose money by taking the new job?
Answer:
Lose money. you lose $3 a week
Step-by-step explanation:
5*6 = 30
0.75*44=33
