Answer:
23
110
Step-by-step explanation:
We have a + 1/a = 5
(a + 1/a)² = a² + (1/a²) + 2.a.1/a = a² + (1/a²) + 2
But (a + 1/a)² = 5² = 25
So a² + (1/a²) = 25 - 2 = 23
(a + 1/a)³ = a³ + 3a²(1/a) + 3a(1/a)² + (1/a)2
= a³ + 1/a³ + 3a + 3/a
= a³ + 1/a³ + 3(a + 1/a)
= a³ + 1/a³ + 3(5)
= a³ + 1/a³ + 15
But (a + 1/a)³ = 5³ = 125
So
a³ + 1/a³ + 15 = 125
a³ + 1/a³ = 110
Answer:
23 and 110
Step-by-step explanation:
using the expansion
(a + b)² = a² + 2ab + b² , then
a + [tex]\frac{1}{a}[/tex] = 5 ( square both sides )
(a + [tex]\frac{1}{a}[/tex] )² = 5²
a² + 2(a × [tex]\frac{1}{a}[/tex] ) + [tex]\frac{1}{a^2}[/tex] = 25
a² + 2(1) + [tex]\frac{1}{a^2}[/tex] = 25
a² + 2 + [tex]\frac{1}{a^2}[/tex] = 25 ( subtract 2 from both sides )
a² + [tex]\frac{1}{a^2}[/tex] = 23
---------------------------------------------------------------------
using the expansion
(a + b)³ = a³ + b³ + 3ab(a + b) , then
a + [tex]\frac{1}{a}[/tex] = 5 ( cube both sides )
(a + [tex]\frac{1}{a}[/tex] )³ = 5³
a³ + [tex]\frac{1}{a^3}[/tex] + 3(a × [tex]\frac{1}{a}[/tex] )(a + [tex]\frac{1}{a}[/tex] ) = 125
a³ + [tex]\frac{1}{a^3}[/tex] + 3(1)(5) = 125
a³ + [tex]\frac{1}{a^3}[/tex] + (3 × 5) = 125
a³ + [tex]\frac{1}{a^3}[/tex] + 15 = 125 ( subtract 15 from both sides )
a³ + [tex]\frac{1}{a^3}[/tex] = 110
Evaluate the function.
ƒ(x) = −x² + x + 16
Find ƒ(−7)
Answer:
f(-7) = 58
Write the problem:
f(x) = -x^2 + x + 16
Plug -7 into the equation:
f(-7) = (-7)^2 + (-7) + 16
Solve:
f(-7) = 49 + (-7) + 16
f(-7) = 42 + 16
f(-7) = 58
Hope that helps! Have an amazing rest of your day! Please consider giving me Brainliest! ;)
a potter forms a piece of clay into a right circular cylinder. as she rolls it, the height h of the cylinder increases and the radius r decreases. assume that no clay is lost in the process. suppose the height of the cylinder is increasing by 0.5 centimeters per second. what is the rate at which the radius is changing when the radius is 7 centimeters and the height is 6 centimeters?
The rate at which the radius is changing when the radius is 7 centimeters and the height is 6 centimeters is -0.8571 cm/s
dr/dt = -0.8571 cm/s
A cylinder's volume can be calculated using...
V = πr²h
For a constant volume, by differentiating with respect to t, we obtain...
0 = π(2rh·dr/dt + r²·dh/dt)
Finding for dr/dt, we have ...
dr/dt = dh/dt(-r²/(2rh)) = (dh/dt)(-r/(2h))
Filling in the given numbers gives ...
dr/dt = (0.5 cm/s)(-7 cm)/(2·6 cm)
dr/dt = -0.8571 cm/s
Therefore, the rate at which the radius is changing when the radius is 7 centimeters and the height is 6 centimeters is -0.8571 cm/s
To learn more about volume of cylinder click here:
https://brainly.com/question/16134180
#SPJ4
Name a pair of vertical angles.Vert
The pair of vertically opposite angles are ∠1 and ∠3 and ∠4 and ∠2.
What is vertically opposite angles?Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines and are opposite to each other.
Vertically opposite angles share the same vertex point.
In other words, vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines
Vertically opposite angles are congruent to each other.
Therefore, the pair of vertical angles are as follows:
∠1 and ∠3 ∠4 and ∠2learn more on vertically opposite angles here: https://brainly.com/question/12017933
#SPJ1
I need the answers to this assignment it’s one questions but multiple steps
Solution;
[tex]\begin{gathered} D=305-50P \\ \end{gathered}[/tex][tex]\begin{gathered} Solving\text{ for P;} \\ 50P=305-D \\ P=\frac{305}{50}-\frac{D}{50} \\ P=\frac{61}{10}-\frac{D}{50} \end{gathered}[/tex][tex]\begin{gathered} When\text{ D=240 pints;} \\ P=6.1-\frac{240}{50} \\ P=\text{ \$}1.3 \end{gathered}[/tex]What is 2/1250 as a percentage
Answer: 0.16 (can I get a brainest point plssssss :)
Step-by-step explanation:
2 of 1250 can be written as:
2
1250
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
2
1250
×
100
100
= (
2 × 100
1250
) ×
1
100
=
0.16
100
Therefore, the answer is 0.16%
If you are using a calculator, simply enter 2÷1250×100 which will give you 0.16 as the answer.
Answer:
6.25%
Step-by-step explanation:
Which are clearly sources of intentional bias? Select all that apply.
A blood pressure measuring device is later found to be inaccurate.
A test is taken using a computer. Students from households without a computer are at a disadvantage.
A math teacher is testing a new method of factoring trinomials. The teacher offers students in the class using the new method help sessions outside of class time. The class using the traditional method are not offered help sessions.
A study compares the cholesterol level of subjects eating a high-fat diet to subjects eating a low-fat diet. The blood test was later found to be inaccurate.
Two labs were asked to compare the effectiveness of a new medicine to treat kidney infections to the currently used drug. The researcher at one lab chose only healthy subjects for the new drug group, and gave less healthy patients the traditional drug.
The researcher at another lab included both healthy and sick subjects in order to better represent the population.
The options that are clearly sources of intentional bias include:
A test is taken using a computer. Students from households without a computer are at a disadvantage.A math teacher is testing a new method of factoring trinomials. The teacher offers students in the class using the new method help sessions outside of class time. The class using the traditional method are not offered help sessions.Two labs were asked to compare the effectiveness of a new medicine to treat kidney infections to the currently used drug. The researcher at one lab chose only healthy subjects for the new drug group, and gave less healthy patients the traditional drug.What is bias?It should be noted that bias in sampling simply gives an inaccurate information about the population.
It should be noted that using news devices for some people and using old devices is a bias that's intentional.
Also, when the test is taken using a computer, those that don't have computers will be affected. This is bias.
Learn more about bias on:
https://brainly.com/question/4540984
#SPJ1
What is an equation of the line that passes through the points ( -4, 5) and
(-4, -2)?
The equation is x = -4.
How to find the equation?
Use slope and slope intercept form y = mx + b,
Slope = y2 - y1/x2 - x1
Slope = 5 - (-2 )/-4 - (-4) = 7/0 = undefined
Equation of point-slope form,
(y-(-2)) = 7/0(x-(-4))
y+2 = 7/0(x+4)
7(x+4) = 0
x = -4
To learn more about slope intercept form sums, refer
https://brainly.com/question/19440459
#SPJ13
Rewrite the expression as the sum of two numbers.
2(16 + 23)
Write y=-2x in standard form. Then graph the function.
The equation y = -2x in the standard form is 2x + y = 0 and the graph of the function is shown below .
In the question ,
it is given that
the equation is y = -2x
The equation in standard form is represented as ax + by = c
to write the equation y = -2x in the standard form
taking all the terms to LHS , we get
2x + y = 0
hence y = -2x in standard form is 2x + y = 0 .
the graph is shown below .
Therefore , The equation y = -2x in the standard form is 2x + y = 0 and the graph of the function is shown below .
Learn more about Equations here
https://brainly.com/question/23854108
#SPJ1
suppose there are two candidates for elected office. explain how the facts that a) voting might not be compulsory and b) resources are needed to finance reelection campaigns affect the conclusions of the median voter model.
The fact that voting might not be compulsory will make the voter ranks the candidate as their proximity, and the median voter wins the vote
The fact that resources are needed to finance reelection campaigns will make the probability of the median voter be in danger
According to median voter model theorem, at-least there must be two candidates
Being that we have two candidates for elected office, let's see how the following may affect the conclusions of the median voter model:
Part a
Voting might not be compulsory:
Here, voter ranks the candidates as per as their proximity, and the median voter will win the vote.
Part b
Resources are needed to finance re-election campaign :
When resources are needed to finance reelection campaign, none can cast their votes and it will distort this strategy. So the probability of median voter is in danger.
Learn more about median voter model here:
https://brainly.com/question/15579425
#SPJ4
imagine that a researcher is interested in whether residents in his local area have higher levels of well-being than the national average. what would be an appropriate alternate hypothesis for a one-tailed or directional z-test for this test? group of answer choices
The alternate hypothesis for the directional z-test is:
Local resident's average > National average
A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge.
One of the ideas put out in the hypothesis test is the alternate hypothesis.
A researcher wants to know if people in his neighborhood have a better well-being than people nationwide.
The appropriate hypothesis for a one-tailed or directional z test for the test will be that the average local residents are higher than the national average.
Learn more about hypothesis here:
brainly.com/question/606806
#SPJ4
remember that the practitioner got the correct answer 44% (0.44) of the time. according to emily's model, on average, what proportion of times do we expect the practitioner to guess the correct hand? make sure your answer is a number between 0 and 1.
Using the probability concept, the proportion of times do we expect the practitioner to guess the correct hand is of 0.44.
What is a probability?The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
The probability can be interpreted as the proportion of times that we expect a trial to happen.
In the context of this problem, this probability is of 44%, as stated for Emily's model, that is, out of 100 trials, the correct answer was obtained in 44 of them, hence the proportion of times do we expect the practitioner to guess the correct hand is of 0.44.
More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ1
Which system of inequalities is represented by the graph?
Answer:
C ( third choice )
Step-by-step explanation:
It has two equations with the operator ' > ' ( due to the dashed lines )
and one equation with the operator ' ≤ ' ( due to the solid line)
So that narrows the choices to B or C
C fits the line on the Left of the graph
when x = - 4 y = -3 (-4) - 6 = 12 -6 = 6
order the following mumbers from least to greatest 1 8/251.35/4
Answer
(5/4) < 1.3 < 1 (8/25)
Explanation
We are told to order the given numbers from the least to the greatest number.
To do that, we will need to express the numbers in decimal form, so it is evident which one is bigger.
1 (8/25)
= 1 + (0.32)
= 1.32
1.3
= 1.30
(5/4)
= 1.25
We can easily see that
1.25 < 1.30 < 1.32
In the form of the numbers given, we have
(5/4) < 1.3 < 1 (8/25)
Hope this Helps!!!
14x(4+17)+38-11
A) 89
B) 99
C) 109
D) 321
Answer:
321
Step-by-step explanation:
14x(4+17)+38-11
(we solve what's in the brackets first)
=14x(21)+38-11
(we solve the multiplication)
=294 + 38 -11
=321
Fatima uses 3 cups of flour to bake 33 healthy muffins. Describe the relationship between the cups of flour and the amount of healthy muffins baked.
The relationship between the cups of flour and the number of healthy muffins baked is C = 11M.
What is an equation?An equation is a representation variable and constants on both sides of the equality showing that terms of both sides of the equality sign are equal.
According to the given Fatima uses 3 cups of flour to bake 33 healthy muffins.
Assuming no. of cups to be C and no. of Muffins to be M.
If we divide M/C we get a scale factor of 11.
∴ The relationship between the cups of flour and the number of healthy muffins baked is C = 11M Or M = C/11.
We can put values of C and M to confirm that our equation is correct.
learn more about equations here :
https://brainly.com/question/10413253
#SPJ1
Lola’s pumpkin patch is selling 4 pumpkins for $10.00. At this rate, how many pumpkins can you buy for $37.50?
help please
Answer:
15 pumpkins.
Step-by-step explanation:
Lola is selling 4 pumpkins for $10 which means 1 pumpkin for $2.50, divide $37.50 by $2.50 & you get 15 pumpkins total.
Select the correct answer. Which statement correctly compares functions f and g? function f function g An exponential function passes through (minus 1, 5), and (2, minus 1.5) intercepts axis at (1, 0), and (0, 2) Function g is a decreasing exponential function with a y-intercept of 5 and no x-intercept. A. They have different end behavior as x approaches -∞ and different end behavior as x approaches ∞. B. They have the same end behavior as x approaches -∞ and the same end behavior as x approaches ∞. C. They have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞. D. They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞.
Ans just ad it to your profile
Step-by-step explanation:
in a class there are 6 girls and 4 boys. (a) two students are chosen at random from the class. in how many ways can this be done? (b) if it is necessary for there to be one girl and one boy, how many ways are possible?
Two students are selected at random from the class this can be done in 45 ways.
It is necessary for there to be one girl and one boy this is done in 24 ways.
In a given class there are six( 6 ) girls and four( 4 ) boys.
In this case, there are given two cases that two students are selected at random from the class, In how many ways can this be done
And the other case is it necessary for there to be one girl and one boy, how many ways are possible
To solve the two cases we use Combinations;
Total number of students in a class = 6 + 4 = 10
For case ( 1 ):
Two students are selected at random from the class this can be done by;
A = ¹⁰C₂
A = [tex]\frac{10!}{2!*(10-2)!}[/tex]
A = 45
For case ( 2 ):
It is necessary for there to be one girl and one boy thus is done by;
B = ⁶C₁ ˣ ⁴C₁
B = [tex]\frac{6!}{1!*(6-1)!} \\[/tex] ×[tex]\frac{4!}{1!*(4-1)!}[/tex]
B = 6 × 4
B = 24
Two students are selected at random from the class this can be done in 45 ways.
It is necessary for there to be one girl and one boy this is done in 24 ways.
To learn more about random click here:
brainly.com/question/17238189
#SPJ4
4−32⋅(−0.25)−12÷1/3 help
Answer:
Your answer is 8.
Answer:
Step-by-step explanation:
-24
What are both answers
The most appropriate choice for percentage will be given by-
a)Percentage of people arrive at their office before 7 am = 10%
b)Percentage of people arrive at their office after 7:59 am = 64 %
What is percentage?
Suppose, there is ratio of two numbers and it has to be expressed as a fraction of 100, percentage is that ratio.
So percentage is the ratio of two numbers expressed as a fraction of 100.
Here,
a) Number of people arrive at their office before 7 am = 15
Total number of people = 15 + 39 + 75 + 21
= 150
Percentage of people arrive at their office before 7 am = [tex]\frac{15}{150}\times 100[/tex]
= 10%
b)Number of people arrive at their office after 7:59 am = 75 + 21
= 96
Percentage of people arrive at their office after 7:59 am = [tex]\frac{96}{150}\times 100[/tex]
= 64 %
To learn more about percentage, refer to the link
https://brainly.com/question/24304697
#SPJ9
Mike Lasueze is a salesperson in the appliance department at Wicklow Appliance Inc. He is guaranteed a minimum salary of $220 per week or 5.5% of his total sales, whichever is greater. What is his gross pay for a week in which his total sales were $8,400?
For a sale of $8400 made his gross pay is $373.21
In this question, we have been given Mike Lasueze is guaranteed a minimum salary of $220 per week or 5.5 percent of his total sales, whichever is greater.
We need to find his gross pay for a week in which his total sales were $8,400
weekly pay = $220
commission = 5.5% of sales
= 0.055 of sales
Let m be the total sale and his gross pay be represented by y.
So, we get an equation for the total/gross pay:
y = 0.055x + 220
Required is the gross pay y for x = 8400
y = 0.055(8400) + 220
y = 682
Therefore, for a sale of $8400 made his gross pay is $373.21
Learn more about an equation here:
brainly.com/question/649785
#SPJ1
-91=6p + 9 - 4p solve for p
Answer:
p= - 50
Step-by-step explanation:
Move the p variables to one side and the constant numbers (intergers) to the other
-91=6p + 9 - 4p
-91 - 9 = 6p- 4p
-100 = 2p
[tex]\frac{-100}{2}[/tex] = [tex]\frac{2p}{2}[/tex]
-50 = p
p= -50
ANSWER: p=50
-91=6p + 9 - 4p solve for p
1. 6p - 4p = 2p
2. -91= 2p + 9
-91-9= 100
3. 100 = 2p
p= 100/2
p= 50
HELP ASAP
Use the matrices to show that matrix multiplication is associative.
Drag a matrix to each box to correctly complete the equations.
Since the multiplication of the matrices (A x B) x C and A x (B x C) are equal, the multiplication of matrices is associative.
How to multiply matrices?Matrices are multiplied multiplying the lines of the first matrix by the columns of the second matrix.
The multiplication of the matrices being associative means that:
(A x B) x C = A x (B x C).
Hence, applying the rules, of the multiplication of the lines by the columns, we have to solve for the two cases, and find the results.
Then:
[tex](AB)C = \left[\begin{array}{ccc}11&-8&37\\21&28&15\end{array}\right] \times \left[\begin{array}{c}1\\-2\\0\end{array}\right][/tex]
As the multiplication of a 2 x 2 matrix by a 2 x 3 matrix results in a 2 x 3 matrix, and then we multiply by C as follows:
[tex]\left[\begin{array}{ccc}11&-8&37\\21&28&15\end{array}\right] \times \left[\begin{array}{c}1\\-2\\0\end{array}\right] = \left[\begin{array}{c}27\\-35\\\end{array}\right][/tex]
Multiplying the lines by the columns, we have that the first line is, for example:
11 x 1 - 8 x (-2) + 37 x 0 = 27.
In the second case, the multiplication of B and C is given by:
[tex]BC = \left[\begin{array}{c}5\\-8\end{array}\right][/tex]
Multiplying by A, we get the same result as above, hence the multiplication of matrices is associative.
More can be learned about multiplication of matrices at https://brainly.com/question/28815379
#SPJ1
………………………………………………..
Answer:
A coma is placed where there is a pause in a sentence, or a list of things. Therefor the commas will be placed as shown.
I pledge allegiance to the red, white, and blue flag.
My brother slowly picked up the spooky, wooden box with gold, silver, and copper inlay.
Step-by-step explanation:
Hope it helps! =D
-38 = -3 + 5v solve for v simplify your answer as much as possible
Answer:
v = -7
Step-by-step explanation:
-38 = -3 + 5v
add 3 to both sides:
-38 + 3 = -3 + 5v + 3
-35 = 5v
divide both sides by 5:
-35/5 = 5v/5
v = -7
12. At first, the ratio of Julian's money to Max's money was 11: 8. After each of them bought a calculator for $13.60, the ratio of Julian's money to Max's money became 3:2. How much money did Julian have at first?
Answer:
ry shortening your search to focus on the most important keywords or phrases.
Step-by-step explanation:
Please help me it would make my whole month please!!! ILY
Answer:
David: $50.00
Pam: $47.50
Step-by-step explanation:
David:
first 10 lb $2 per lb
Additional lbs are $1
When buying 40 pounds:
first 10 lbs: $2 × 10 = $20
other 30 lbs: $1 × 30 = $30
total cost: $20 + $30 = $50.00
_______________
Pam:
$10 entrance fee
first 10 lb $1.5 per lb
Additional lbs are $0.75
When buying 40 pounds:
Entrance: $10
first 10 lbs: $1.5 × 10 = $15
other 30 lbs: $0.75 × 30 = $22.5
total cost: $10 + $15 + $22.50 = $47.50
Which of the following is equal to 1
(a) 2 + 3 +4 (b) 2 (c) (3( d) (3
PLEAZE HELP
The value that will be equal to 1 is D. 3^0.
How to calculate the value?It should be noted that this is a straightforward question. In this case, it's important to find the values and get the answer that is equal to 1.
In this case, it should be noted that:
2 + 3 + 4 = 9
It should be noted that:
2 × 1 = 2
It should be noted that:
3¹ = 3
It should be noted that:
3^0 = 1
Therefore, the correct option is D.
Here is the complete question attached below.
Learn more about numbers on:
brainly.com/question/24644930
#SPJ1
Which of the following is equal to 1
(a) 2 + 3 +4 (b) 2 × 1 (c) (3¹ d) 3^0
PLEAZE HELP
the like term of 9x^3
The most appropriate choice for algebraic expressions and like terms will be given by the like terms of [tex]9x^3, 16x^2y, -8x^3,12xy^2,6x^3[/tex] are [tex]9x^3, -8x^3, 6x^3[/tex]
What are algebraic expressions and like terms?
Algebraic expressions are the expressions consisting of numbers, variables and arithmetic operations.
[tex]2x + 3y + z[/tex] is an example of algebraic expression. An algebraic expression consists of one or more terms.
The terms having the same variable are known as like terms.
Here,
The terms of [tex]9x^3, 16x^2y, -8x^3,12xy^2,6x^3[/tex] having the same variables are
[tex]9x^3, -8x^3, 6x^3[/tex].
So the like terms of [tex]9x^3, 16x^2y, -8x^3,12xy^2,6x^3[/tex] are [tex]9x^3, -8x^3, 6x^3[/tex].
To learn more about algebraic expression and like terms, refer to the link:
https://brainly.com/question/16731338
#SPJ10
Complete Question
Find the like terms in [tex]9x^3, 16x^2y, -8x^3,12xy^2,6x^3[/tex].