Answers
Related Questions
1. Write the polynomial function that models the given situation.A rectangle has a length of 12 units and a width of 11 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a polynomial function in terms of x.
2. Write the polynomial function that models the given situation. A square has sides of 24 units. Squares x + 1 by x + 1 units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a function in terms of x.
3. Write the polynomial function that models the given situation. A cylinder has a radius of x + 6 units and a height 3 units more than the radius. Express the volume V of the cylinder as a polynomial function in terms of x.
Answers
Answer:
1. (12 - 2x)(11 - 2x)x
2. 4(11 - 2x)²(x + 1)
3. π(x³ + 15x² + 63x + 81)
Step-by-step explanation:
1. Write the polynomial function that models the given situation.
A rectangle has a length of 12 units and a width of 11 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a polynomial function in terms of x.
Since the length of the rectangle is 12 units and its width 11 units and squares of x by x units are cut from its corners, it implies that a length x is cut from each side. So, the length of the open box is L = 12 - 2x and its width is w = 11 - 2x.
Since the cut corners of the rectangle are folded, the side x which is cut represents the height of the open box, h. so, h = x
So, the volume of the open box V = LWh = (12 - 2x)(11 - 2x)x
2. Write the polynomial function that models the given situation. A square has sides of 24 units. Squares x + 1 by x + 1 units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a function in terms of x.
Since the square has sides of 24 units and squares of x + 1 by x + 1 units are cut from its corners, it implies that a length x + 1 is cut from each corner and the length 2(x + 1) is cut from each side. So, the length of side open box is L = 24 - 2(x + 1) = 24 - 2x - 2 = 24 - 2 - 2x = 22 - 2x = 2(11 - x)
Since the cut corners of the square are folded, the side x + 1 which is cut represents the height of the open box, h. so, h = x + 1
Since the area of the base of the pen box is a square, its area is L² = [2(11 - 2x)]²
So, the volume of the open box V = L²h = [2(11 - 2x)]²(x + 1) = 4(11 - 2x)²(x + 1)
3. Write the polynomial function that models the given situation. A cylinder has a radius of x + 6 units and a height 3 units more than the radius. Express the volume V of the cylinder as a polynomial function in terms of x.
The volume of a cylinder is V = πr²h where r = radius and h = height of cylinder.
Given that r = x + 6 and h is 3 units more than r, h = r + 3 = x + 6 + 3 = x + 9
So, V = πr²h
V = π(x + 3)²(x + 9)
V = π(x² + 6x + 9)(x + 9)
V = π(x³ + 6x² + 9x + 9x² + 54x + 81)
V = π(x³ + 15x² + 63x + 81)
Determine the value of X. Please explain the answer
Answers
We have two lines from the same point.
These two lines are also tangents to same circle which implies that they are of the same length.
That is 2x - 1 = 9
2x = 9 +1 = 10
x =10/2
x = 5
I NEED HELP PLEASE!!!!
Answers
Answer:
the answer to that's is B bud
!!I NEED THE ANSWER PLS!!
Which of the following represents the divisor and the dividend for the
synthetic division problem below?
- 3/ 2 4 -4 6
A. -3 and -2x2 - 4x2 + 4x-6
B. x+3 and -2x2 - 4x +47-6
C. X+3 and 2x + 4x2 - 4x+6
D. *-3 and 2x2 + 4x2 - 4x+6
Answers
Answer:
B
Step-by-step explanation:
B . x+3 and -2x2 - 4x +47-6
B . x+3 and -2x2 - 4x +47-6
The divisor and the dividend for the given synthetic division problem are : [tex]x+3[/tex] and [tex]2x^3+4x^2-4x+6[/tex]
What is synthetic division?"It is a way of dividing one polynomial by another polynomial of first degree."
What is dividend?"The value that is divided by another value to get the result. "
What is divisor?"The value that divides another number either completely or with a remainder."
For given question,
We have been given a synthetic division problem.
- 3/ 2 4 -4 6
We need to represent the divisor and the dividend for the given synthetic division problem.
We know that, to perform synthetic division, here are the steps:
- The leading coefficient of the divisor should also be 1.
- Express the dividend in standard form.
- Write the leading coefficient in the dividend.
- Place the product of the number you brought down and the number in the division box in the preceding column.
- Write the result at the bottom of the row.
So, the divisor of the given synthetic division form would be,
x - (-3) = x + 3
And the dividend of the given synthetic division form would be,
There are four leading coefficient.
This means the dividend polynomial must be of degree 3.
From the leading coefficients 2 4 -4 6
[tex]2x^3+4x^2-4x+6[/tex]
Therefore, the divisor and the dividend for the given synthetic division problem are : [tex]x+3[/tex] and [tex]2x^3+4x^2-4x+6[/tex]
Learn more about the synthetic division here:
https://brainly.com/question/11850611
#SPJ2
Solve 2x^2+5x+5=0 round solutions to the nearest hundredth.
Answers
Answer:
-0.56
Step-by-step explanation:
Find the length of the segment indicated. circles 4
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I need more information, comment on my "answer".
Please Answer This!!! I NEEEDDD TOOO KNOWWWWW ANSWER!!!
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Answer:
77.5
Step-by-step explanation:
Its rising at a constant rate between +10-15 each hour, so we if we were to add 25 or so to the 50, it would be close to 77.5, so I would assume the answer was B
Need help pleaseeee!!!
Answers
Answer:
C is wrong!
Step-by-step explanation:
The explanation is in the picture!
I need to know the answer ASAP
Answers
Answer:
Step-by-step explanation:
Simplify: −4(b+6)−2b(1−4b
Answers
Step-by-step explanation:
-4b-24-2b+8b2
8b2-6b-24=0
A study was conducted in order to estimate ?, the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be ? = 3.6 hours.
A similar study conducted a year earlier estimated that ?, the mean number of weekly hours that U.S. adults use computers at home, was 8 hours. We would like to test (at the usual significance level of 5%) whether the current study provides significant evidence that this mean has changed since the previous year.
Using a 95% confidence interval of (7.7, 9.3), our conclusion is that:
a. the current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval.
b. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval.
c. the current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.
d. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.
e. None of the above. The only way to reach a conclusion is by finding the p-value of the test.
Answers
Answer:
d. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.
Step-by-step explanation:
Mean was of 8 hours, test if it has changed:
At the null hypothesis, we test if it has not changed, that is, the mean is still of 8, so:
[tex]H_0: \mu = 8[/tex]
At the alternative hypothesis, we test if it has changed, that is, the mean is different of 8, so:
[tex]H_1: \mu \neq 8[/tex]
Using a 95% confidence interval of (7.7, 9.3), our conclusion is that:
8 is part of the confidence interval, which means that the study does not provide evidence that the mean has changed, and the correct answer is given by option d.
Help on 3,5,7,9,11,13.15,17, please thank you
Answers
Answer:
3. 6a+60
5. 25+5w
7. 90-10t
11. 4.5-12c
13. f-2
15. 12z+1.5
Step-by-step explanation:
3.
6(a+10)
Multiply 6 by both factors in the parentheses, in this case, a and 10.
6*a = 6a
6*10 = 60
6(a+10) = 6a + 60
I only put the step- by- step explanation for #3, but you should be able to figure the rest out with that.
Please help I need this done ASAP
10 points + crown for whoever has the most accurate answer
Answers
Part a)
Time:distance
1:3
Part b)
6 hours
Part C)
81km
Answered by Gauthmath must click thanks and mark brainliest
Question 3 of 28
What is the length of IN in the right triangle below?
M
19
N
O A. 442
B. 442
O c. 1200
D. 280
Answers
Answer:
Option C. √280
Step-by-step explanation:
From the question given above, the following data were obtained
MN = 19
ML = 9
LN =?
We can obtain the value of LN by using the pythagoras theory as illustrated:
M ² = ML² + LN²
19² = 9² + LN²
361 = 81 + LN²
Collect like terms
361 – 81 = LN²
280 = LN²
Take the square root of both side
LN = √280
Therefore, the length of LN is √280
One book is 4cm thick, find out how many such books can be placed in a space of 53cm.
Answers
Then getting the answer 13.25. Since we can’t have (.25 cm) of a book we can fit 13 whole books
In June 2005, a CBS News/NY Times poll asked a random sample of 1,111 U.S. adults the following question: "What do you think is the most important problem facing this country today?" Roughly 19% of those sampled answered "the war in Iraq" (while the rest answered economy/jobs, terrorism, healthcare, etc.).
Exactly a year prior to this poll, in June of 2004, it was estimated that roughly 1 out of every 4 U.S. adults believed (at that time) that the war in Iraq was the most important problem facing the country. We would like to test whether the 2005 poll provides significant evidence that the proportion of U.S. adults who believe that the war in Iraq is the most important problem facing the U.S. has decreased since the prior poll.
What are the appropriate hypotheses in this case?
Answers
Answer:
The appropriate null hypothesis is [tex]H_0: p = 0.25[/tex]
The appropriate alternative hypothesis is [tex]H_1: p < 0.25[/tex]
Step-by-step explanation:
Exactly a year prior to this poll, in June of 2004, it was estimated that roughly 1 out of every 4 U.S. adults believed (at that time) that the war in Iraq was the most important problem facing the country.
At the null hypothesis, we test if the proportion is still the same, that is, of [tex]\frac{1}{4} = 0.25[/tex]. So
[tex]H_0: p = 0.25[/tex]
We would like to test whether the 2005 poll provides significant evidence that the proportion of U.S. adults who believe that the war in Iraq is the most important problem facing the U.S. has decreased since the prior poll.
Decreased, so at the alternative hypothesis, it is tested if the proportion is less than 0.25, that is:
[tex]H_1: p < 0.25[/tex]
Which of the following graphs is described by the function given below?
y = x2 - 6x-7
Answers
Answer:
A
Step-by-step explanation:
We are given the function:
[tex]\displaystyle y = x^2 - 6x - 7[/tex]
And we want to determine its graph.
One of the most important features of a quadratic is its vertex. So, we can start by finding the vertex using the formulas:
[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 1, b = -6, and c = -7.
Find the x-coordinate of the vertex:
[tex]\displaystyle x = -\frac{(-6)}{2(1)} = 3[/tex]
Substitute this back into the equation to find the y-coordinate:
[tex]\displaystyle y(3) = -16[/tex]
Therefore, our vertex is at (3, -16).
The only graph whose quadratic's vertex is at (3, -16) is Graph A. Thus, our answer is A.
It takes 12 people 15 hours to complete and certain job.how many hours would it take 18 people, working at the same rate to complete 2/5 of the same job?
Answers
Answer:
9 hours
Step-by-step explanation:
12 people take 15 hours to complete one job. First let's ask how long it would take 18 people working at the same rate to complete the same job? We can use proportions to answer this
[tex]\frac{12 people}{15 hours} = \frac{18 people}{x hours}\\x = \frac{18\times15}{12} = 22.5[/tex]
Now we know that one job takes 18 people 22.5 hours, so 2/5 of the job would take
[tex]\frac{18\times15}{12} \times \frac{2}{5} = 9[/tex]
Explain how the given graph is deceptive.
Complete the statements based on the bar graph.
By not starting the horizontal axis at 0, the
bar appears to be about one-fourth the height of the Pecan bar. The
bar appears to be about one-half the height of the Pecan bar. The
bar appears to be less than one-half the height of the Pecan bar. This misleads the viewer to
the number of each type of nut used
Ans:
Pine Nut
Walnut
Almond
Understimate
Answers
Answer:
In the picture below.
Step-by-step explanation:
From the commenter and answer above, confirmed on edge 2022.
State if the scenario involves a permutation or a combination. Then find the number of possibilities.
A team of 15 basketball players needs to choose two players to refill the water cooler.
Permutation/Combination:
Answer:
Answers
Answer:
Permutation ; 210 ways
Step-by-step explanation:
Permutation and combination methods refers to mathematical solution to finding the number of ways of making selection for a group of objects.
Usually, selection process whereby the order of selection does not matter are being treated using permutation, while those which takes the order of selection into cognizance are calculated using combination.
Here, selecting 2 players from 15 ; since order does not matter, we use permutation ;
Recall :
nPr = n! ÷ (n - r)!
Hence,
15P2 = 15! ÷ (15 - 2)!
15P2 = 15! ÷ 13!
15P2 = (15 * 14) = 210 ways
Find the length of the arc. Round your answer to the nearest tenth
Answers
Answer:
12.6 mi
Step-by-step explanation:
Arc length = 2πr (Θ/360)
2π(12) (60/360)
= 12.6 mi
Answered by g a u t h m a t h
Which function has lowest rate of change?
5x – 2y = 15 (or) Cost of 5 pencils is 15 dollars
O Algebraic Function
O Verbal Description
Both the functions
O None of the choices
Answers
Answer:
A: Algebraic Function
Step-by-step explanation:
Algebraic function is given as;
5x – 2y = 15
Since we are dealing with rate of change, let's make y the subject first and find dy/dx.
Thus;
2y = 5x - 15
y = (5x/2) - 15/2
dy/dx = 5/2
dy/dx = 2.5
The verbal function is given as;
Cost of 5 pencils is 15 dollars
Thus, rate of 1 pencil = 15/5 = 3 pencils per dollar
We can see that the lowest rate of change is 2.5 and it is the algebraic function.
What's the value of n if 13+19= n+25
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.
.
..
.
.............
Answer:
[tex]13+19=n+25[/tex]
[tex]n+25=13+19[/tex]
Add 13+19= 32
[tex]n+25=32[/tex]
Now Subtract 25 from both sides
[tex]n+25-25=32-25[/tex]
[tex]n=7[/tex]
OAmalOHopeO
Factor.
64x^12 + 27y^3
Answers
Answer:
answer is (4x^4+3y)(16x^8-12x^4y+9y^2)
Step-by-step explanation:
Find the difference: -18 - (-18)
Answers
Answer:
0
Step-by-step explanation:
-18-(-18)
= -18+18 [(+) + (+)=(+)]
=0 [(-) + (-)=(-)]
A factory makes twenty-three million, five hundred fifty candies each month. This number in standard form is
Answers
Answer:
23,000,550
Step-by-step explanation:
A million has six zeroes, so twenty three million is
23,000,000
Since five hundred fifty is not in the thousands, it replaces the last trio of zeroes.
We have the number in standard form as
23,000,550
Answer:
23000550
Step-by-step explanation:
HELP keep saying im getting wrong
instruction find the perimeter of the polygon
Answers
Answer:
perimeter = 50
Step-by-step explanation:
Tangents to a circle from an external point are congruent , then
perimeter = (8 + 8) + (10 + 10) + (7 + 7) = 16 + 20 + 14 = 50
Which functions represent a vertical stretch of the parent function, f(x) = 1/x? Check all that apply.
g(x) = 3/x
g(x) = -2/x
g(x) = 1/4x
g(x) = 5/2x
g(x) = 1/2x
Answers
Answer:
[tex]g(x) = \frac{3}{x}[/tex]
[tex]g(x) =-\frac{2}{x}[/tex]
[tex]g(x) =\frac{5}{2x}[/tex]
Step-by-step explanation:
Given
[tex]f(x)=\frac{1}{x}[/tex]
Required
Which represents vertical stretch of f(x)
The transformation is represented as:
[tex]g(x) = a* f(x)[/tex]
Where:
[tex]|a| > 1[/tex]
So, the functions are:
[tex]g(x) = \frac{3}{x}[/tex] ---- [tex]|3| > 1[/tex]
[tex]g(x) =-\frac{2}{x}[/tex] --- [tex]|-2|>1[/tex]
[tex]g(x) =\frac{5}{2x}[/tex] --- [tex]|\frac{5}{2}| > 1[/tex]
Answer:
the other person is correct if you need them quick it is a b and d
Step-by-step explanation:
Trong một lớp học có $35$ sinh viên nói được tiếng Anh, $25$ sinh viên nói được tiếng Nhật trong đó có $10$ sinh viên nói được cả tiếng Anh và tiếng Nhật. Mỗi sinh viên trong lớp nói được ít nhất một trong hai: tiếng Anh hoặc tiếng Nhật. Hỏi sỹ số của lớp là bao nhiêu
Answers
Answer:
please write this question in English then I give answer
The American Management Association is studying the income of store managers in the retail industry. A random sample of 49 managers reveals a sample mean of $45,420. The standard deviation of the population is known to be $2,050.
a). Compute a 95% confidence interval, as well as the margin of error.
b). Interpret the confidence interval you have computed.
Answers
Answer:
a) The 95% confidence interval for the income of store managers in the retail industry is ($44,846, $45,994), having a margin of error of $574.
b) The interval mean that we are 95% sure that the true mean income of all store managers in the retail industry is between $44,846 and $45,994.
Step-by-step explanation:
Question a:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{2050}{\sqrt{49}} = 574[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 45420 - 574 = $44,846.
The upper end of the interval is the sample mean added to M. So it is 45420 + 574 = $45,994.
The 95% confidence interval for the income of store managers in the retail industry is ($44,846, $45,994), having a margin of error of $574.
Question b:
The interval mean that we are 95% sure that the true mean income of all store managers in the retail industry is between $44,846 and $45,994.
