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)
Which graph represents the function f(x) = x-2?
Answer:
click in photo
nejdjjd
nxndjdbbdjf
lấy x=0 ta có y= -2 => A(0;-2)
lấy y=0 ta có x=2 => B(2;0)
nối 2 điểm A và B ta có đồ thị:
Family Video stocks 1003 drama movies, 518 science fiction movies and
253 children's movies. How many more drama titles than children's
titles does Family Video have in stock?
Answer:
There are 750 more drama movies that children's movies.
Step-by-step explanation:
There are 1003 drama movies, and 253 children's movies.
1003 - 253 = 750
A bucket contains 4 red balls that are numbered 1, 2, 3, 4. It also contains 6 black balls that are numbered 5, 6, 7, 8, 9, 10. Two balls are drawn from the bucket, one at a time, without replacement. Use this information to answer the following probability questions. Express answers as fractions, or round decimal answers to 4 decimal places. a. What is the probability that the first ball is even and the second ball is odd
The probability is 1/9
We want to find the probability that the first drawn ball is even, and the second is odd.
The probability of randomly drawing an even ball will be equal to the quotient between the number of balls with even numbers and the total number of balls in the bucket.
We have a total of 10 balls (4 red ones and 6 black ones)
and 5 of these have even numbers (2, 4, 6, 8, 10)
Then the probability of drawing a ball with an even number first is:
p = 5/10 = 1/5
now we want to get a ball with an odd number.
notice that we already got a ball with an even number and we did not replace it, so now there are 9 balls left in the bucket, 5 odd ones, and 4 even ones.
The probability of getting an odd ball is computed in the same way thana above, as the quotient between the number of balls with odd numbers (5) and the total number of balls in the bucket (9)
q = 5/9
The joint probability (the probability that these two events happen together) is equal to the product of the individual probabilities, so we will get:
P = p*q = (5/9)*(1/5) = 1/9
The probability is 1/9
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Madison represented the sentence "The product of 3 and the difference of and the quotient of a number and is at most 5" by using the inequality . Which best describes Madison’s error?a) The difference of –4 and the quotient of a number and –2" should be written as . b) The product of 3 and the difference of –4 and the quotient of a number and –2" should be written as . c) The less than symbol should be replaced with the less than or equal to symbol. d) The less than symbol should be replaced with the greater than symbol.
Answer:
c) The less than symbol should be replaced with the less than or equal to symbol.
Step-by-step explanation:
3(-4 - n/-2) < 5
The equation written above could be interpreted as :
The product of 3 and the difference of -4 and the quotient of a number, n and -2 is less than 5
This means that the only error in Maddison's representation is the inequality sign, the inequality sign used by Maddison is wrong.
The equation should be used with a ≤ sign and expressed thus :
3(-4 - n/-2) ≤ 5
This means the left hand side (L. H. S) is less than or equal to 5 ; this means the L. H. S is at most 5
Answer:
C
Step-by-step explanation:
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level.
Step 1 of 2: Suppose a sample of 2845 tenth graders is drawn. Of the students sampled, 2276 read above the eighth grade level. Using the data, estimate the proportion of tenth graders reading at or below the eighth grade level. Enter your answer as a fraction or a decimal number rounded to three decimal places.
Step 2 of 2: Suppose a sample of 2845 tenth graders is drawn. Of the students sampled, 2276 read above the eighth grade level. Using the data, construct the 99% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.
Answer:
Step 1: The estimate the proportion of tenth graders reading at or below the eighth grade level is 0.2.
Step 2: The 99% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.181, 0.219).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Suppose a sample of 2845 tenth graders is drawn. Of the students sampled, 2276 read above the eighth grade level.
So 2845 - 2276 = 569 read below, and the estimate of the proportion of tenth graders reading at or below the eighth grade level is:
[tex]\pi = \frac{569}{2845} = 0.2[/tex], and the answer to step 1 is 0.2.
The sample size is [tex]n = 2845[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2 - 2.575\sqrt{\frac{0.2*0.8}{2845}} = 0.181[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2 + 2.575\sqrt{\frac{0.2*0.8}{2845}} = 0.219[/tex]
The 99% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.181, 0.219).
What is the approximate length of arc s on the circle below? Use 3.14 for Pi. Round your answer to the nearest tenth.
-5.8 ft
-6.3 ft
-27.5 ft
-69.1 ft
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Answer:
69.1 ft
Step-by-step explanation:
The diameter of the circle is 24 ft. The length of the arc is more than twice the diameter, so cannot be less than about 50 ft. The only reasonable choice is ...
69.1 ft
__
The circumference of the circle is ...
C = 2πr = 2(3.14)(12 ft) = 75.36 ft
The arc length of interest is 330° of the 360° circle, so is 330/360 = 11/12 times the circumference.
s = (11/12)(75.36 ft) = 69.08 ft ≈ 69.1 ft
Answer:D
Step-by-step explanation:
Determine the measure of the interior angle at vertex E.
A. 50
B. 90
C. 30
D. 150
PLS REPLY FAST THIS IS URGENT
The measure of the interior angle at vertex E can be determined by using the properties of triangles. In a triangle, the sum of all interior angles is always 180 degrees.
Therefore, to find the measure of the interior angle at vertex E, we need to subtract the measures of the other two angles at vertices A and B from 180 degrees. Let's assume that the measures of the angles at vertices A and B are a and b degrees, respectively. Then, the measure of the interior angle at vertex E can be calculated as follows: Interior angle at vertex E = 180 degrees - (measure of angle at vertex A + measure of angle at vertex B) Now, let's refer back to the given answer choices: A. 50 B. 90 C. 30 D. 150 Without additional information or a diagram, it is not possible to determine the exact measures of the angles at vertices A and B. Therefore, we cannot directly calculate the measure of the interior angle at vertex E. In order to solve this problem, we need more information about the triangle or a diagram that shows the relative positions of the vertices.
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Help please, but more importantly, I am really trying hard to figure out how, you arrive at the answer. Thanks in advance!
A recent social survey asked respondents whether they like Apple or Microsoft. The responses were recorded in the following table.
Male Female Total
Apple 152 194 346
Microsoft 168 126 294
Total 320 320 640
a. A respondent is randomly selected among those that prefer Apple, what is the probability that the respondent will be female?
b. A respondent is randomly selected among those that are Male, what is the probability that the respondent prefers Apple?
c. What is the relative frequency of a female who prefers Microsoft?ocial survey asked respondents whether they like Apple or Microsoft. The responses were recorded in the following table.
Male Female Total
Apple 152 194 346
Microsoft 168 126 294
Total 320 320 640
a. A respondent is randomly selected among those that prefer Apple, what is the probability that the respondent will be female?
b. A respondent is randomly selected among those that are Male, what is the probability that the respondent prefers Apple?
c. What is the relative frequency of a female who prefers Microsoft?
Answer:
Step-by-step explanation:
#1
A) P(FEMALE|APPLE)
apple total = 346
apple/female = 194
194/346 = .56 = 56 %
B) P(APPLE|MALE)
male total = 320
apple male = 152
152/320 = .475 = 47.5%
C) female prefer Microsoft
152:168 = 76:84 = 38:42 = 19:21
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
What is the volume of the pyramid shown below?
Answer:
B is the answer of this question
Step-by-step explanation:
144 cu. units
Sample information: 24 out of 1000 people who were surveyed had type 2 diabetes. Use the above sample information and construct two confidence intervals (one with confidence level of 90% and the other one with confidence level of 99%) to estimate the proportion of people who have type 2 diabetes. What is the relationship between the confidence level and the size of the confidence interval? Is this significant? Why is it important to understand this concept?
Answer:
it is important because the number of people who are infected by the disease is rising
The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The measurements are given in the table.
Using technology, what is the equation for the least-squares regression line?
y= –34.13 1.98x
y = 1.98 – 34.13x
y = 17.37 0.50x
y = 0.50 17.37x
I think it's (C) y = 17.37 0.50x --> 100%
Answer:
The answer is (C)
17.37 + .50x
ED2021
A spinner contains the numbers 1 through 50. What is the probability that the spinner will land on a number that is not a multiple of 8?
Answer:
22/25
Step-by-step explanation:
Multiples of 8 are 8,16,24,32,40,48
That means there are 6 multiples of 8
50 -6 = 44
There are 44 non multiples of 8
P( non multiples of 8) = non multiples of 8 / total
= 44/50
=22/25
Help for number 2a) b) c)
Thank you!! Make u the brainliest
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Answer:
a) 300 square units
b) 260 square units
c) 264 square units
Step-by-step explanation:
The total surface area of a triangular prism is the sum of the areas of its 5 faces. Two of those are triangles (the bases), and three are rectangles. The area of an individual triangle is A = 1/2bh, but the area of the two of them together will be simply A = bh.
The area of the three rectangular faces is the sum of the products of the height of the prism and the edge length of each face. Then the sum of these products can be computed as the product of the height and the perimeter of the base.
These repetitive calculations are nicely done by a spreadsheet loaded with the appropriate formulas. Areas are all in "square units." (For problem 3, the units are centimeters.)
Example: (2a)
Base area = 5×12 = 60 . . . . combined area of both bases
Lateral area = (5 +12 +13)(8) = 30×8 = 240
Total surface area = 60 + 240 = 300 . . . . square units
Answer:
2. a. 300 units²
b. 260 units²
c. 264 units²
Step-by-step explanation:
2. a. Surface area of triangular prism = bh + (s1 + s2 + s3)*H
Where,
b = 12
h = 5
s1 = 13
s2 = 12
s3 = 5
H = 8
Plug in the values into the formula
Surface area of triangular prism = 12*5 + (13 + 12 + 5)*8
= 60 + (30)*8
= 60 + 240
Surface area = 300 units²
b. Surface area of triangular prism = bh + (s1 + s2 + s3)*H
Where,
b = 11
h = 3
s1 = 11
s2 = 5
s3 = 6.7
H = 10
Plug in the values into the formula
Surface area of triangular prism = 11*3 + (11 + 5 + 6.7)*10
= 33 + (22.7)*10
= 33 + 227
Surface area = 260 units²
c. Surface area of triangular prism = bh + (s1 + s2 + s3)*H
Where,
b = 6
h = 8
s1 = 10
s2 = 6
s3 = 8
H = 9
Plug in the values into the formula
Surface area of triangular prism = 6*8 + (10 + 6 + 8)*9
= 48 + (24)*9
= 48 + 216
Surface area = 264 units²
The price of a item has reduced by 85% the original price was $60
Answer:
The price now would be 9 dollars
Step-by-step explanation:
60 x 85% is 51 and you subtract that from 60
The scatterplot shows the number of bedrooms in a house and the selling price for that house.
Calculate the residual for the house with 6 bedrooms, to the nearest thousand.
The residual for the house with 6 bedrooms is ___
-30k
-26k
26k
30k
Answer:
-26k, -26,000 ; (B)
ED2021
The residual for the house with 6 bedrooms is -26k.
What is Scatterplots?Scatterplots are the plotting of set of points on a vertical axis and an horizontal axis. The shows the correlation extent between the numbers of the observed quantities.
Given is a scatterplot showing the selling price of houses with the number of bedrooms.
Equation of the line of best fit is given as,
y = 6.3x + 4.8
Residual = Actual value - Predicted value
From the scatterplot,
Actual selling price of house with 6 bedrooms = 40 × 10,000 = 400,000
Predicted selling price for 6 bedrooms = (6.3 × 6) + 4.8
= 42.6 × 10,000
= 426,000
Residual = 400,000 - 426,000
= -26,000
Hence the residual is -26k.
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If 4 men working 4 hours for 4 days complete 4 units of work, then how many units of work will be completed by 2 men working for 2 hours per day in 2 days.
Answer:
16 days
Step-by-step explanation:
Here,
By the question,
4 men takes 4 days working each day 4 hours to complete 4 units of work..
then..
if 1 man works 1 hour each day then i would take ( 4×4×4 ) days
= 64days
then..
if 2 men work for 2 hours per day then.
it would take
4×4×4 / 2×2 days
= 16 days
Charlotte has to read a book for school. There are 513 pages in the book. She read 113 pages on
Saturday, she read 78 pages on Sunday, and 101 pages on Monday. How many pages does Charlotte
have left to read?
A.221 pages
B.513 pages
C.292 pages
D.400 pages
which of the following statements is true? -6 < -8 -6> -8 or -6=-8
Answer:
-6>-8
Step-by-step explanation:
-6 is more than -8.
The value of f(x)= 5x -4x²+3 when x= -1, is
Answer:
F(x) =5(-1)-4(-1)^2+3,
=-5-4+3
=-6
A patient is supposed to have 800 mL every 24 hours. You kmow that the patiemt has three fourths of the fluid between breakfast 8am and dinmer 6pm. How much should be injested between 8am and 6pm?
Answer: 600 ml
Step-by-step explanation:
The patient has 3/4 out of 800 milliliters of fluid. To find how much they take in, multiply 3/4 * 800.
3/4 *800= 2400/4
simplify 2400/4
= 600
An exponential function f(x) = ab^xpasses through the points (0, 2) and (3, 54). What are the values of a and
b?
a=
b =
Answers:
a = 2
b = 3
=======================================================
Explanation:
Plug in x = 0 and y = 2 to find that
y = a*b^x
2 = a*b^0
2 = a*1
2 = a
a = 2
Then plug in x = 3 and y = 54 to determine the value of b
y = a*b^x
y = 2*b^x
54 = 2*b^3
2b^3 = 54
b^3 = 54/2
b^3 = 27
b = (27)^(1/3)
b = 3
So we have y = a*b^x update to y = 2*3^x
is jannelle correct ?
Answer:
yes
Step-by-step explanation:
o
Two identical lines are graphed below. How many solutions are there to the system of equations?
A. Two
B. One
C. Zero
D. Infinitely many
Answer:
the answer is D. infinitely many
The number of solutions there are to the system of equations is Infinitely many, the correct option is D.
What is the Point-slope form?
The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
We are given that;
The two identical lines
Now,
We can find the equations of the two lines by using the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
For line 1, we have two points (0,2) and (1,0), so we can find the slope as:
m1 = (0 - 2) / (1 - 0) = -2
Using point-slope form, we can write the equation of line 1 as:
y - 2 = -2(x - 0)
y = -2x + 2
For line 2, we have two points (-1,4) and (2,-2), so we can find the slope as:
m2 = (-2 - 4) / (2 - (-1)) = -2
Using point-slope form, we can write the equation of line 2 as:
y - 4 = -2(x - (-1))
y = -2x + 2
We can see that the two lines have the same slope and the same y-intercept.
Therefore, by the given slope of the line the answer will be infinitely many.
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represent (-12)+(-8)+14 on a number line
Answer:
-6
Step-by-step explanation:
(-12)+(-8)= -20
-20+14= -6
A certain positive integer has exactly 20 positive divisors.
What is the largest number of primes that could divide the integer?
thx for the help in advance
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Answer:
3
Step-by-step explanation:
20 has at most 3 proper factors greater than 1: 2×2×5. Each of these can represent a prime factor of the number of interest, and is 1 more than that prime's power. That is, the number of interest (n) will have at most 3 prime factors p, q, r, and will be ...
n = p·q·r^4
_____
For some prime factorization ...
[tex]\displaystyle n=\prod_{k=1}^m{p_k^{q_k}}[/tex]
The total number of divisors of n is ...
[tex]\displaystyle\prod_{k=1}^m{(q_k+1)}[/tex]
A particle is moving such that its height h at time t is given by h(t) = 2 + 8t - 3t^2 + 1/5t^3. The average velocity of the particle on the period [0,3] is
[tex]\\ \Large\sf\longmapsto h(t)[/tex]
[tex]\\ \Large\sf\longmapsto 2+8t-3t^2+\dfrac{1}{5}t^3[/tex]
[tex]\\ \Large\sf\longmapsto 2+8(3)-3(3)^2+\dfrac{1}{5}(3)^3[/tex]
[tex]\\ \Large\sf\longmapsto 2+24-3(9)+\dfrac{27}{5}[/tex]
[tex]\\ \Large\sf\longmapsto 26-27+5.4[/tex]
[tex]\\ \Large\sf\longmapsto -2+5.4[/tex]
[tex]\\ \Large\sf\longmapsto h(t)=3.4m[/tex]
25(0.3x-4)-5(1.5x-6)+100(13/4) simplify the following expression and evaluate for x=0.345
Answer:
255
Step-by-step explanation:
Given :
Simplify the expression :
25(0.3x-4)-5(1.5x-6)+100(13/4)
Open each Bracket:
7.5x - 100 - 7.5x + 30 + 325
7.5x - 7.5x - 100 + 30 + 325
= 255
The simplified equation = 255
Please help me out with how to solve this
In a math class, one of your 4 test scores is dropped. On the first three tests, you have the following scores: 79, 34, and 95. What score do you need on the next test for your average to be 75 (assuming you drop the lowest test score)?
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Answer:
51
Step-by-step explanation:
Your score total must be 3×75 = 225. Subtracting the two high scores gives ...
225 -95 -79 = 51
__
The score of 34 is below that value, so it is the one that will be dropped.
You need a test score of 51 on the next test for your average to be 75.
which of the following expressions are equivalent to 36x + 24y? choose all that apply
6x (6+4y) 6(6x + 4y) 12(36x + 24y) 12(3x + 2y) 4y(9x + 6) 4(9x + 6y)
The following expressions are equivalent to 36x + 24y is 6(6x+4y).
6x(6+4y)
6(6x+4y)
12(3x+2y)
4(9x+6y)
We have,
What is the expression?The expression consists of numbers and arithmetic operators. It does not contain equality or inequality symbols. The expression consists of unknown variables
36x + 24y
=6(6x)+6(4y)
=6(6x+4y)
Therefore, The following expressions are equivalent to 36x + 24y is 6(6x+4y).
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Which of the following rational functions is graphed below?
o
A. F(x) = 1/2x
B. AX) = 1/x-2
C. F(x) = 1/x+2
Answer:
Option B.
Step-by-step explanation:
We can see that we have an asymptote at x = 2
Remember that in a rational function, the asymptote is at the x-value such that the denominator is equal to zero.
So, the denominator is something like:
(x + a)
we have that the denominator is zero when x = 2
Then:
(2 + a) = 0
solving that for a, we get:
a = -2
Then the denominator of the rational function is:
(x - 2)
For the given options, the only one with this denominator is option B, then the correct option is B.
Answer:
B. f(x) = 1/x-2
Step-by-step explanation:
Math is ez bro.
