The factor of the expression \(5p(p + 2)^{\frac{2}{3} } + 4(p + 2)^{\frac{1}{3} }\) is\((p + 2)^{\frac{2}{3} } (5p^{3} + 10p^{2} + 20p + 4)\)
To answer the question, we need to know what factorization is
What is factorization?Factorization is the process of breaking down an expressing into a simpler form containing its factors.
Since
\(5p(p + 2)^{\frac{2}{3} } + 4(p + 2)^{\frac{1}{3} }\)
Since \((p + 2)^{\frac{1}{3} }\) is common, we factor it out. So, we have
\((p + 2)^{\frac{2}{3} } (5p(p + 2)^{2} + 4)\)
Expanding the bracket, we have
\((p + 2)^{\frac{2}{3} } (5p(p^{2} + 2p + 4) + 4) = (p + 2)^{\frac{2}{3} } (5p^{3} + 10p^{2} + 20p + 4)\)
So, the factor of the expression \(5p(p + 2)^{\frac{2}{3} } + 4(p + 2)^{\frac{1}{3} }\) is\((p + 2)^{\frac{2}{3} } (5p^{3} + 10p^{2} + 20p + 4)\)
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8. Lesly took a test with 30 questions. The ratio of correct answers to incorrect answers
for Lesly was 7 to 8. How many answers did she get correct?
Lesly got 14 answers correctly.
Let the correct answers be C.Let the incorrect answers be I.Given the following data:
Total number of questions = 30 questions.Ratio of C to I = 7 : 8C to I = 7 + 8 = 15To find the number of answers she got correctly;
\(C = \frac{7}{15}\) × \(30\)
\(C = 7\) × \(2\)
Correct answers, C = 14 answers
Therefore, Lesly got 14 answers correctly.
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What is the value of x in the equation 2.5 minus 0.25 x = negative 3
Answer:
-22
Step-by-step explanation:
Cell phone production engineers have noticed that among a group of 138 customers aged 14-23 who send more text messages tend to use a higher percentage of their phone’s memory.What are the explanatory variable and response variable for this relationship?
Explanatory variable: age of customer
Response variable: percentage of phone memory used
Explanatory variable: percentage of phone memory used
Response variable: age of customer
Explanatory variable: number of text messages sent
Response variable: percentage of phone memory used
Explanatory variable: percentage of phone memory used
Response variable: number
Answer:
it is c my guy
Step-by-step explanation:
on edge2020
The explanatory variable is the number of text messages sent, and the response variable is the percentage of phone memory used. The correct answer is (C)
What is the independent and dependent variable?In mathematics, independent and dependent variables are values that vary in relation to one another. The dependent variable is dependent on the independent variable, which means that if the value of the independent variable changes, so will the dependent variable.
In this situation, the explanatory variable is the number of text messages sent, because it is believed to influence or "explain" the variation in the response variable, which is the percentage of phone memory used.
The explanatory variable is also sometimes called the independent variable, because it is the variable that is being manipulated or controlled in an experiment. The response variable is also sometimes called the dependent variable, because it is the variable that is believed to depend on the explanatory variable.
Therefore, in this problem, the explanatory variable is the number of text messages sent, and the response variable is the percentage of phone memory used.
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You can make 6 centerpieces in 100 minutes. How many can you make in 250 minutes?
Answer:
15
Step-by-step explanation:
Answer:
15 centerpieces
Step-by-step explanation:
You have 6 centerpieces in 100 minutes (the easiest way is to apply proportion).
6/100=x/250
solve for x
x=(6/100)*250
x = 15 centerpieces
line v has a slope of - 5/2. line w has a slope of - 2/5. are line v and line q parallell, perpendicular, or neither?
Answer:
neither
Step-by-step explanation:
Parallel lines need to have the same slope.
Perpendicular lines have opposite reciprocal slopes.
-5/2 and -2/5 are opposite reciprocals nor are they equal.
consider the following system of equations. does this system has a unique solution? if yes, find the solution 2x−y=4 px−y=q 1. has a unique solution if p=2 2. has infinitely many solutions if p=2,q=4 a)1 correct b) 2correct c)1dan2 correct d)1 dan 2 are false
The given system of equations has a unique solution if p is not equal to 2. If p is equal to 2 and q is equal to 4, the system has infinitely many solutions.Therefore, the correct answer is (a) 1 correct.
The given system of equations is:
2x - y = 4
px - y = q
To determine if the system has a unique solution, we need to analyze the coefficients of x and y.In the first equation, the coefficient of y is -1. In the second equation, the coefficient of y is also -1.If the coefficients of y are equal in both equations, the system may have infinitely many solutions. However, if the coefficients of y are different, the system will have a unique solution.
Now, we consider the options:
a) 1 correct: This statement is correct. If p is not equal to 2, the coefficients of y in both equations will be different (-1 in the first equation and -1 in the second equation), and thus the system will have a unique solution.b) 2 correct: This statement is correct. If p is equal to 2 and q is equal to 4, the coefficients of y in both equations will be the same (-1 in both equations), and therefore the system will have infinitely many solutions.
c) 1 and 2 correct: This statement is incorrect because option 1 is true but option 2 is only true under specific conditions (p = 2 and q = 4).d) 1 and 2 are false: This statement is incorrect because option 1 is true and option 2 is also true under specific conditions (p = 2 and q = 4).
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a. 51 b.102 c.112 d.258
Jenny bought notebooks at the store for $1.35 each. She spent $8.10 on the notebooks. Let x represent the number of notebooks Jenny bought. Use the equation 1.35x = 8.10 to find the number of notebooks she bought
Answer:
She bought 6 notebooks
Step-by-step explanation:
Here, we want to find the number of notebooks bought
This is represented by the number x
To find the value of x, we simply divide both sides of the equation by 1.35
Thus, we have
x = 8.1/1.35
x = 6
Suppose your friend's parents invest $25,000 in an account paying 7% compounded annually. What will the balance be after 8 years?
Answer:
42954.65.
Step-by-step explanation:
Answer: uhhh sorry if it's wrong but i think its 14000
Step-by-step explanation:
If 35 cycles were produced in 5 days by a company then how many cycles will be produced in 21 days.
Answer:
126
Step-by-step explanation:
35/5 = 6.
6 is the number in 1 day
6x21=126
126 is the number in 21 days
Hope that helps
how many sequences of length 10 can be formed from the digits 1,2 and 3 if repetition is not allowed?
The number of sequences of length 10 that can be formed from the digits 1, 2, and 3 without repetition is 59,049.
The number of sequences of length 10 that can be formed from the digits 1, 2, and 3 without repetition is 3^10, or 59,049.
This is because for each of the 10 positions in the sequence, you have 3 choices: 1, 2, or 3, and since repetition is not allowed, the choices for each position are mutually exclusive.
Two occurrences are mutually exclusive or disjoint in logic and probability theory if they cannot occur at the same time. The set of outcomes of a single coin toss, which can result in either heads or tails but not both, is a good example.
Mutually exclusive is a statistical word that describes two or more occurrences that cannot occur at the same time. It is typically used to describe a circumstance in which the occurrence of one result takes precedence over the occurrence of the other. War and peace, for example, cannot exist together.
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PLS HELPPP THXXXX dudnrudnd
Answer:
15.5kg and 13.25kg
Step-by-step explanation:
8x+4y=177
3x+2y=73 (changes to -----> 6x+4y=146)
subtract
2x=31
x=15.5 (large)
plug back in
3(15.5)+2y=73
46.5+2y=73
26.5=2y
13.25=y
A package of 4 red,white and blue hats costs $8. What is the unit rate
Answer:
$2/ hat
Step-by-step explanation:
Find the unit rate:
$ to hats
8 to 4
Divide by four to get the unit rate; over 1
2 to 1
So, $2 per hat
Hope this helps!
You are using a local moving company to help move you from your parent’s house to your new place. To move locally (within Indiana) they estimate you will need 3 movers for 2 hours to load and unload the truck for a total of $480. If you move long distance, (outside of Indiana) they estimate you will need 5 movers for 2 hours to load and unload the truck for a total of $680. How much does the moving company charge per mover and per hour?
Thus, the long-distance moving company charges $68 per mover-hour.
To determine the charge per mover and per hour for a local and long-distance move, let us first find the hourly rate for each of the moves.
If for a local move 3 movers were hired for 2 hours, the total time the movers would have worked would be:3 movers * 2 hours = 6 mover-hour sIf the charge for the move was $480, the hourly rate for this move would be:$480/6 mover-hours = $80 per mover-hour
Thus, the local moving company charges $80 per mover-hour. Similarly, if for a long-distance move 5 movers were hired for 2 hours, the total time the movers would have worked would be:5 movers * 2 hours = 10 mover-hoursIf the charge for the move was $680,
the hourly rate for this move would be: $680/10 mover-hours = $68 per mover-hour Thus, the long-distance moving company charges $68 per mover-hour.
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A car uses 15 gallons of gasoline to travel 450 miles.
How far can the car travel on 18 gallons of gasoline?
Answer:
540 miles
Step-by-step explanation:
450/15 = 30
so the car can travel 30 miles per gallon
18*30 = 540
Answer:
540 miles
Step-by-step explanation:
Gallons: 15 18
Miles: 450 x
450 divided by 15 = 30
18 times 30 = 540
-2.6f + 0.7f - 15 - 9
Answer is
-2.6f + 0.7f - 15 - 9= -1.9f-24
I need help on algebra
Answer:
LOOK
Step-by-step explanation:
7- 0.10X+0.25Y=0.80
8- 2 QUATERS ARE 50 CENTS.80 CENTS-50 CENTS IS 30 CENTS
Is it true that If B is produced by interchanging two rows of A, then detB = detA.
No. It is not true that if B is produced by interchanging two rows of A, then detB = detA.
det(B) = -det(A) is the correct formula for calculating the determinant of a matrix obtained by interchanging two rows of another matrix.
Two rows of a matrix are interchanged, the determinant of the resulting matrix is equal to the determinant of the original matrix multiplied by -1.
Therefore, we have det(B) = -det(A).
This can be seen from the formula for calculating the determinant of a matrix.
When two rows are interchanged, the determinant of the resulting matrix is equal to the determinant of the original matrix multiplied by -1 raised to the power of the number of row interchanges.
Since we have interchanged two rows, the power is 2, so the determinant of the resulting matrix is equal to the determinant of the original matrix multiplied by (-1)² = 1.
det(B) = -det(A) is the correct formula for calculating the determinant of a matrix obtained by interchanging two rows of another matrix.
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Consider the following vector field.
F(x, y, z) =
9ex sin(y), 2ey sin(z), 8ez
sin(x)
(a)
Find the curl of the vector field.
curl(F) =
(b)
Find the divergence of the vector field.
div(F) =
The curl of the vector field
curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k
The divergence of the vector field
div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z
To find the curl of the vector field F(x, y, z) = 9ex sin(y), 2ey sin(z), 8ez sin(x), we need to compute the determinant of the curl matrix.
(a) Curl of F:
The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:
curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k
In this case, we have:
P(x, y, z) = 9ex sin(y)
Q(x, y, z) = 2ey sin(z)
R(x, y, z) = 8ez sin(x)
Taking the partial derivatives, we get:
∂P/∂y = 9ex cos(y)
∂Q/∂z = 2ey cos(z)
∂R/∂x = 8ez cos(x)
∂R/∂y = 0 (no y-dependence in R)
∂Q/∂x = 0 (no x-dependence in Q)
∂P/∂z = 0 (no z-dependence in P)
Substituting these values into the curl formula, we have:
curl(F) = (0 - 2ey cos(z))i + (8ez cos(x) - 0)j + (0 - 9ex cos(y))k
= -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k
Therefore, the curl of the vector field F is given by:
curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k
(b) Divergence of F:
The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:
div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z
In this case, we have:
∂P/∂x = 9e^x sin(y)
∂Q/∂y = 2e^y sin(z)
∂R/∂z = 8e^z
Substituting these values into the divergence formula, we have:
div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z
Therefore, the divergence of the vector field F is given by:
div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z
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A turbine manufacturer conducts reliability testing of its products for a duration of 5000 hrs. Six failures occur, whose corrective maintenance times are as follows (in hrs.) 6 12 8 7 9 8 The sum of preventive maintenance times during the test duration is 50 hrs. What is the failure rate? What is the probability that the product will survive an operating duration of 45 hrs.? What is the probability that the product will fail during an operating duration of 45 hrs.? What is Mct? What is the unit of measurement for Inherent Availability? What is the Inherent Availability of the product? Show your work for each step. Note that all questions above require you to compute the results except the question on the "unit of measurement".
The failure rate of the turbine product is 0.0012 failures per hour. The probability of survival for an operating duration of 45 hours is approximately 0.7767, while the probability of failure during the same duration is approximately 0.2233. The MCT (Mean Corrective Time) for the failures is 8.3333 hours.
To calculate the failure rate, we divide the total number of failures (6) by the total operating time (5000 hours). Hence, the failure rate is 6/5000 = 0.0012 failures per hour.
To calculate the probability of survival for 45 hours, we use the formula \(P(survive) = e^{-failure\ rate * duration}\). Substituting the values, we get \(P(survive)=e^{-0.0012 * 45}= 0.7767.\)
The probability of failure during 45 hours can be calculated as 1 - P(survive). Hence, the probability of failure is approximately 0.2233.
MCT (Mean Corrective Time) is calculated by summing up the corrective maintenance times and dividing it by the total number of failures. In this case, the sum of corrective maintenance times is 6 + 12 + 8 + 7 + 9 + 8 = 50 hours. Therefore, Mct = 50/6 = 8.3333 hours.
The unit of measurement for Inherent Availability is typically a ratio or percentage, representing the proportion of time that the system is available for use. It does not have a specific physical unit.
To calculate the Inherent Availability, we use the formula Inherent Availability = 1 - (failure rate * Mct). Substituting the values, we get Inherent Availability = 1 - (0.0012 * 8.3333) = 97.765%.
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2) Janelle is making crumb cake. The recipe makes three cakes, but she
only wants one, so she will only use one-third of the ingredients. If the
recipe calls for 1 cups of sugar, how much sugar will Jancolle need to
make one-third of the recipe?
Answer:
1.5 cups per cup. cups/cake
6 cups/ 4 cakes
= 1.5 cups per cake
Step-by-step explanation:
hope I help I ma a noob so can I have brainliest pls
Answer:
Janelle will need 1/3 cups of sugar to make 1 cake.Step-by-step explanation:
To answer this question, I am going to multiply the total cups of sugar said in recipe by 1/3. This will tell me how much sugar is required for 1/3 of recipe.
=> 1 x 1/3 => 1/3 cups of sugarHence, Janelle will need 1/3 cups of sugar to make 1 cake.
Hoped this helped.
\(BrainiacUser1357\)
Rationalize the denominator:
Please give step by step solution
Answer:
1 + i
Step-by-step explanation:
To rationalize multiply numerator and denominator by (2 + i )
\(\frac{3+i}{2-i}= \frac{3+i}{2-i} \times \frac{2+i}{2+i} = \frac{(3+i)(2+i)}{(2-i)(2+i)} = \frac{6+3i+2i-1}{4-(-1)} = \frac{5+5i}{5} = 1 + i\)
Solve using substitution and show your work:
-3x-3y=3
y=-5x-17
Answer:
Step-by-step explanation:
Isolate any variable, x or y, but since y has already been isolated, use y to solve for x.
Substitute y into the first equation -3x-3y=3
This equals -3x - 3 (-5x - 17) = 3
Distribute to get -3x + 15x + 51 = 3
Then bring like terms together. -3x + 15x = 3 - 51
12x = -48
Solve for x
x = -4
Substitute -4 for x in the equation: y = -5x - 17
y = − 5x − 17
y = (−5) (−4) − 17
y = 20 - 17
y = 3 ( Simplify both sides of the equation)
Answer:
x = − 4 and y = 3
your company is producing special battery packs for the most popular toy during the holiday season. the life span of the battery pack is known to be normally distributed with a mean of 250 hours and a standard deviation of 20 hours. what would typically be a better distribution than the normal distribution to model the life span of these battery packs?
In order to determine whether the Weibull distribution or another distribution might be a better fit for the lifespan of these battery packs, it would be important to analyze the data and compare the goodness-of-fit statistics for different distributions.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
The normal distribution is a very common and useful distribution for modeling many real-world phenomena, including the lifespan of battery packs. However, there are certain situations where other distributions may be more appropriate.
One example of a distribution that could potentially be a better fit for the lifespan of these battery packs is the Weibull distribution. The Weibull distribution is often used to model the failure rates of components, including batteries. It has a flexible shape that can be adjusted to fit different types of failure patterns, and it can handle both increasing and decreasing failure rates.
In order to determine whether the Weibull distribution or another distribution might be a better fit for the lifespan of these battery packs, it would be important to analyze the data and compare the goodness-of-fit statistics for different distributions. This could involve using statistical software to fit various distributions to the data and comparing the resulting fit statistics, such as the Akaike information criterion (AIC) or the Bayesian information criterion (BIC), to determine which distribution provides the best fit.
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please only help me with number 7.
which value is less than 1?
a (1/6)^-8
b (5^-4)^-9
c 2^-3
d 6^-4/6^-5
Answer:
c
Step-by-step explanation:
\(a) (1/6)^{-8}=6^8>1 \\ \\ b) (5^{-4})^{-9}=5^{36}>0 \\ \\ c) 2^{-3}=1/8<1 \\ \\ (d) \frac{6^{-4}}{6^{-5}}=6>1\)
What is the coefficient of y in the expression 2x4+3y
Answer:
3
Step-by-step explanation:
What is the next item in the pattern -1, 2, -4, 9
Find the domain, range, and intercepts of the function f(x)=7x+11
x£ℝ
multiply X f equals 7x
Step-by-step explanation:
let 7x+ll=o
x=-ll/7
domain= {x/x=-ll/7}
range=xER
maria bought 160 mangoes at sh 10 each. she paid sh 200 for transport to the market .she sold the mangoes and made a 60% profit. what was selling price of each mango?
The selling price of each mango is sh 18
What is selling price?
Selling price can b described as the amount at which a particular product is sold at the market
Write out the parameters
160 mangoes are sold at Sh 10
The calculation can be done as follows
cost price= 160 × 10
= 1600
Sh 200 was paid for transportation
The total cost price is 1600 + 200
= 1800
Formula
selling price= cost price (1+r/100)
= 1800(1 + 60/100)
= 1800( 1+ 0.6)
= 1800(1.6)
= 2880
Therefore the selling price of each mango can be calculated as follows
= 2880/160
= 18
Hence the selling price of each Mango is Sh 18
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for brainly and points thank you
Answer: A
Step-by-step explanation:
Subtract 2 from both sides of the equation ,
Simplify , Subtract the numbers , 9x from both sides of the equation, Combine like terms, Divide both sides of the equation by the same term, then you get your solution! I hope this helps.