Answer:
x^4 + 8x^2 + 8x^3 - 32x - 48
Step-by-step explanation:
You have to group the terms so the only terms that are similar are -4x^2 and +12x^2. -4x^2+12x^2 =+8x^2
There aren't any other similar terms so you can leave it as x^4 + 8x^2 + 8x^3 - 32x - 48
Answer:
x^4 + 8 x^3 + 8 x^2 - 32 x - 48
Hope This Helps!!!
500 children ages 5-11 were asked the following question:
"Do you read books for fun every day?"
Results are shown in the two-way table below.
Boy Girl Total
Yes 48 75
No 182 195
Total 500
a. In this sample, what proportion of children are boys? (Round your answer to the nearest hundredth)
b. What proportion of boys read books for fun every day? (Round your answer to the nearest hundredth)
c. What proportion of girls read books for fun every day? (Round your answer to the nearest hundredth)
d. Based on the findings, does the likelihood of reading books for fun depend on the gender of a child? Explain.
e. If a child is selected at random, find the probability that the child reads book for fun. (Round your answer to the nearest hundredth)
f. If a child is selected at random, find the probability that the child is a girl AND reads book for fun. (Round your answer to the nearest hundredth)
g. If a child is selected at random, find the probability that the child is a girl OR reads book for fun. (Round your answer to the nearest hundredth)
h. If a child is selected at random, find the probability that the child reads book for fun GIVEN that the child is a girl. (Round your answer to the nearest hundredth)
500 children ages 5-11 were asked the following question:
"Do you read books for fun every day?"
Results are shown in the two-way table below.
Boy Girl Total
Yes 48 75 123
No 182 195 377
Total 230 270 500
What are proportions?A proportion is the number of desired outcomes divided by the number of total outcomes.
a. Proportion of children that are boys.There are 500 children and 230 are boys.
230/500 = 0.46
b. Proportion of boys who read books for fun every day.There are 230 boys and 48 read books for fun every day.
48/230 = 0.21
c. Proportion of girls who read books for fun every day.There are 270 girls and 75 read books for fun every day.
75/270 = 0.28
d. Does the likelihood of reading books for fun depend on the gender of a child?Based on the results from b and c, it would seem more likely for a girl to read books for fun than for a boy.
e. For a child selected at random, what is the probability that the child reads books for fun?There are 500 children and 123 read books for fun.
P = 123/500 = 0.25
f. For a child selected at random, what is the probability that the child is a girl and reads books for fun?There are 500 children and 75 are girls who read books for fun.
P = 75/500 = 0.15
g. For a child selected at random, what is the probability that the child is a girl or reads books for fun?There are 500 children. The favorable cases are the girls (270) plus the children who read books for fun (123) minus the girls who read books for fun (75).
P = (270 + 123 - 75)/500 = 0.64
h. For a child selected at random, what is the probability that the child reads books for fun given that the child is a girl.There are 270 girls and 75 of them read books for fun.
P = 75/270 = 0.28
a. The proportion of children who are boys is 0.46.b. The proportion of boys who read books for fun every day is 0.21.c. The proportion of girls who read books for fun every day is 0.28.d. It would seem more likely for a girl to read books for fun than for a boy.e. For a child selected at random, the probability that the child reads books for fun is 0.25.f. For a child selected at random, the probability that the child is a girl and reads books for fun is 0.15.g. For a child selected at random, the probability that the child is a girl or reads books for fun is 0.64.h. For a child selected at random, the probability that the child reads books for fun given that the child is a girl is 0.28.Learn more about proportions here: https://brainly.com/question/25259185
Find the absolute maximum and minimum values of the following function on the given region R. f(x,y)=5x2+5y2−10x+21; R=(x,y): x2+y2≤4, y≥0
We first compute the partial derivatives of f(x, y):
f(x, y) = 5x² + 5y² - 10x + 21
∂f/∂x = 10x - 10
∂f/∂y = 10y
The critical points of f occur where both ∂f/∂x and ∂f/∂y are equal to zero. This only happens at the point (x, y) = (1, 0). (And this point does lie inside R.)
Next, compute the Hessian matrix H(x, y) for f :
[tex]H(x, y) = \begin{bmatrix}\frac{\partial^2f}{\partial x^2} & \frac{\partial^2f}{\partial x\partial y} \\ \frac{\partial^2 f}{\partial y\partial x} & \frac{\partial^2f}{\partial y^2}\end{bmatrix} = \begin{bmatrix}10&0\\0&10\end{bmatrix}[/tex]
Since det(H(x,y)) = 100 is positive for all x and y, this means the critical point (1, 0) is a local minimum, and we have f(1, 0) = 16.
Next, we check for extrema along the boundary of R, which is comprised of a semicircle with radius 2 and the line segment connecting (-2, 0) and (2, 0).
• Parameterize the semicircular portion by
x(t) = 2 cos(t)
y(t) = 2 sin(t)
with 0 ≤ t ≤ π. Then
f(x(t), y(t)) = 20 sin²(t) + 20 cos²(t) - 20 cos(t) + 21
which is simplifies to a function of one variable t,
g(t) = 41 - 20 cos(t)
Find the extrema of g over the interval [0, π] : we have critical points when
g'(t) = 20 sin(t) = 0
which happens at t = 0 and t = π. At these points, we get local extreme values of
•• t = 0 => x = 2 and y = 0 => f(2, 0) = 21
•• t = π => x = -2 and y = 0 => f(-2, 0) = 61
• Over the line-segment portion, we take y = 0, so f(x, y) again reduces to a function of one variable:
f(x, 0) = 5x² - 10x + 21
Completing the square, we have
5x² - 10x + 21 = 5 (x - 1)² + 16
which has a maximum value of 16 when x = 1 (and this happens to be the critical point (1, 0) we found earlier).
So, over the region R, f(x, y) has
• an absolute maximum of 61 at the point (-2, 0), and
• an absolute minimum of 16 at (1, 0)
What is (−47)−(−107)=?
please help
60
Step-by-step explanation:
(-47)-(-107)
(-47)-1(-107)
-47+107
=60
The vertex of a parabola is (-1, 4). What is the equation of the axis of symmetry of the parabola?
Answer:
x = - 1Step-by-step explanation:
The vertex is given (-1, 4).
The axis of symmetry is a vertical line and passes through vertex.
Since the x- coordinate of vertex is - 1, the line of symmetry is x = - 1.
Answer:
x=-1
Step-by-step explanation:
Parabola is symmetric on both sides of the vertex
The axis of symmetry is the x coordinate of vertex
Here the vertex is (-1,4)
So axis of symmetry is x=-1
i really need help with this quition
Answer:
I really need help with this question.*
Answer:
There is no question
Step-by-step explanation:
Hope you have a great day!!
on a photograph an ant is enlarged at scale 25:1 In the photo the ant leg is 15 cm what is the actual length of the ants leg
Answer:
0.6 cm
Step-by-step explanation:
15/25=0.6
Answer:
0.6 Is the answer
Step-by-step explanation:
Hope this helped ¬∪ω∪¬
a line that passes through the point (4, 2) and has the slope of -3/2
City planners are planning to build a new community pool. They agree that the pool will be rectangular in shape, but the proposed dimensions changed. At the most recent meeting, it was determined that the width would remain at 11.6 meters but that the length would increase by 3.7 meters. So, the pool would now cover an area of 205.85 square meters.
Which equation can be used to determine the original length of the pool, l?
205.85=2(l+15.3)
205.85=11.6(l+3.7)
205.85=3.7(l+11.6)
The equation that can be used to determine the original length of the pool is 205.85 = 11.6(l + 3.7)
Let l be the original length of the pool.
Since the length of the pool is increased by 3.7 m, the new length L = l + 3.7.
Also, the area of the pool A = 205.85 square meter and it is a rectangle with width, W = 11.6 meters,
So, A = LW
Substituting the values of the variables into the equation, we have
A = LW
205.85 = (l + 3.7)11.6
So, the equation that can be used to determine the original length of the pool is 205.85 = 11.6(l + 3.7)
Learn more:
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Answer:
Step-by-step explanation
205.85=11.6(l+3.7)
Determine the slope and y-intercept of a line that passes through the points (2, 4) and (–4, 1).
m = [ A. –2.5 , B. –1.5 , C. 0.5 ]
b = [ A. 3, B. 7, C. 9 ]
Answer:
m = [C. 0.5]b = [A. 3]Step-by-step explanation:
Slope- intercept form:
y = mx + b, where m is the slope, b is the y-interceptGiven points:
(2, 4) and (-4, 1)The slope is:
m = (1 - 4)/(- 4 - 2) = - 3/ - 6 = 1/2 = 0.5Use point (2, 4) to find the value of the y-intercept:
y = mx + b4 = 0.5*2 + bb = 4 - 1b = 3The points (-1, 4) and (2, 9) lie on a line.
What is the slope of the line?
Answer:
[tex]\displaystyle m = \frac{5}{3}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinate Planes
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]Step-by-step explanation:
Step 1: Define
Identify
Point (-1, 4)
Point (2, 9)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m.
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{9 - 4}{2 + 1}[/tex][Order of Operations] Simplify: [tex]\displaystyle m = \frac{5}{3}[/tex]What is the inequality shown?
-4<x>/=5
○ means either< or > but since the line is moving to the right it means that x is greater than -4 (<x)● means greater than or equal to since the line stoped at 5 it means x can be equal to 5 or less then 5
NEED HELP ASAP (WILL GIVD BRAINELST)
Answer:
5
Step-by-step explanation:
The answer is 60/12 becuase we can simfly both of theese mixed numbers into an improper fraction, wich will be 4/3*15/4. We do the multiplication, and we get 60/12. 60/12 can be simplifed to 5 becuase 60 divided by 12 is 5
Find the area of the square below when it is increased by a scale factor of 3
Answer:
To find the area of a square with the scale factor of 3, you multiply the side lengths by 3, so (3*L)*(3*W)= Area of your square.
Step-by-step explanation: I hope that this helps, ask questions in the comments below.(if you have any).
The area of the imagined square will be 90 units² by increased with a scale factor of 3.
What is the scale factor?You must specify the extent of the shape's enlargement when describing one.
The scale factor is the ratio of two dimensions such that one figure is large and another is small.
As per the imagined square with dimensions of 10 units.
Applied the scale factor 3 in the length of the square(since it has only one dimension).
10 x 3 = 30 units.
Thus, each side of the square will be 30 units in length.
Hence "By adding a scale factor of 3, the envisioned square's area will expand to 90 units²".
To learn more about scale factors,
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Glve the position of E on this number line. -- 1 Write a fraction for your answer. 昌 口号 Х ?
Answer:
3/8
Step-by-step explanation:
Please help pleasee right now
Ms. Mary spent $192 less than Ms.Mona on supplies for their class. Together they spent a total of $988. How much did each person spend?
Answer:
Mary:604
Mona:796
Step-by-step explanation:
Answer:
Ms. Mary spend $302
Ms. Mona spend $ 686
Step-by-step explanation: We know that Ms. Mary spend $192 less than Ms. Mona.
So we are to divide $988 by 2 which is 494
now both have $494 each but Ms. Mona spend 192 so we are to add 192 + 494 to get the right sum of how much money Ms. Mona have and take away 494-192 to get the right sum of how much money Ms. Mary spend.
192 + 494 = 686
494 - 192 = 302
Solve for the value of q.
Answer:
q=13
Step-by-step explanation:
(8q-5)°+81°=180° (angles on a str line)
8q-5+81=180
8q=180+5-81
=104
q=104÷8
=13
Using supplementary angle theorem
[tex]\\ \sf\longmapsto 8q-5+81=180[/tex]
[tex]\\ \sf\longmapsto 8q+76=180[/tex]
[tex]\\ \sf\longmapsto 8q=104[/tex]
[tex]\\ \sf\longmapsto q=13[/tex]
A business valued at $96 000 is purchased for a down payment of 25% and payments of $4000 at the end of every three months. If interest is 9% compounded monthly,
what is the size of the final payment?
Write your answer as 2,569.43.
Size of final payment is $6392.43
Given that formula for compound interest is P(1+r/n[tex])^{nt}[/tex]
where P is initial principal
r is interest rate
n is compound times per period
t is time in years
We find all the variables in the formula in order to get our answer.
Initial principal = 96000 less 25%= 72000
interest rate = 9%
number of compound times= 12
time in years =4.25 years (whole period is 4.5 years since number of payments to complete balance will take 54 months)
Hence principal and CI after 4 years and 3 months(the second to last payment)
72000(1+0.09/12)^12x4.25=$105,393.6
We use $105,393.6 as our principal to calculate the whole interest and principal for the period in order to find last payment
105393.6(1+0.09/12)^12x0.25=$107,786.03
interest for the final month = $107786.03-$105,393.6=$2392.43
To get our final payment, we add the principal payment of $4000 to final compounded interest =$6392.43
A patient has an illness that typically lasts about 24 hours. The temperature, T, in degrees Fahrenheit, of the patient t hours after the illness begins, is given by: T(t) = -0.013t^2 + 0.3172t +98.6. When does the patient reach its maximum value? what is the patient's maximum temp?
Answer:
no entiendo, perdóname, suerte
The sampling distribution of the ratio of two independent sample variances selected randomly from normal populations with equal variances is:
Answer: F distribution. chi-square distribution. t distribution. normal distribution.
Step-by-step explanation:
PLS HELP I NEED THIS DONE TODAY PLSSS WILL GIVE BRAINLY
Answer:
You need 6 lbs of red potatoes
32oz of cream cheese
43oz cream of potatoe soup
Step-by-step explanation:
Multiply all by 4
Due tomorrow answer using steps
[tex]\\ \sf\longmapsto (5x^3+5x^2+5)-(6x^3-6x^2+8x-5)[/tex]
[tex]\\ \sf\longmapsto 5x^3+5x^2+5-6x^3+6x^2-8x+5[/tex]
[tex]\\ \sf\longmapsto 5x^3-6x^3+5x^2+6x^2-8x+5+5[/tex]
[tex]\\ \sf\longmapsto -x^3+11x^2-8x+10[/tex]
[tex]\\ \sf\longmapsto x^3-11x^2+8x-10[/tex]
[tex]\large \boldsymbol{} \longmapsto (5x^3+5x^2+5) -(6x^3-6x^2+8x-5 ) \\\\\\ \longmapsto5x^3+5x^2+5-6x^3+6x^2-8x+5 \\\\\\ \longmapsto 5x^3-6x^3+5x^2+6x^2-8x+5+5 \\\\\\ \longmapsto \boxed{ - x^3+11x^2-8x+10}[/tex]
Quotient of 0 and 15
Answer:
15Step-by-step explanation:
cause the first number is zero so the answer is 15 #happy learningIsosceles triangle has , and a circle with radius is tangent to line at and to line at . What is the area of the circle that passes through vertices , , and
The circle that passes through the vertices of triangle ΔABC (A, B, C) is the
circumscribing circle of triangle ΔABC.
The area of the circle that passes through vertices A, B, and C, is (C) 26·π
Reasons:
The given parameters are;
Side length of isosceles triangle ΔABC; [tex]\overline{AB}[/tex] = [tex]\overline{AC}[/tex] = 3·√6
Radius of circle tangent to [tex]\overline{AB}[/tex] at B and [tex]\overline{AC}[/tex] at C = 5·√2
Required:
Area of the circle that passes through vertices A, B, and C
Solution:
Angle ∠BAO is given as follows;
[tex]\angle BAO = arctan\left(\dfrac{5 \cdot \sqrt{2} }{3 \cdot \sqrt{6}} \right) = \mathbf{arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)}[/tex]
Therefore;
[tex]\angle BOA = 90^{\circ} - arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)[/tex]
[tex]\overline{BC} = 2 \times 5 \cdot \sqrt{2} \times sin\left(90^{\circ} - arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right) = 15\cdot \sqrt{\dfrac{6}{13} }[/tex]
∠ABO' = ∠BAO' (Base angles of isosceles triangle ΔABO')
[tex]\angle BAO' = \angle BAO = \mathbf{arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)}[/tex]
Therefore;
[tex]\angle BO'A = 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)[/tex]
From sine rule, we have;
[tex]\dfrac{\overline{AB}}{sin \left(\angle BO'A \right)} = \mathbf{\dfrac{\overline{BO'}}{sin \left(\angle BAO' \right) \right)}}[/tex]
Which gives;
[tex]\mathbf{\dfrac{3 \cdot \sqrt{6} }{sin \left( 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right)}} = \dfrac{\overline{BO'}}{sin \left(arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right) \right)}[/tex]
Using a graphing calculator, we get;
[tex]\overline{BO'} = \dfrac{3 \cdot \sqrt{6} }{sin \left( 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right)} \times sin \left(arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right) \right) = \sqrt{26}[/tex]
The radius of the circumscribing circle [tex]\overline{BO'}[/tex] = √(26)
Therefore, area of the circumscribing circle, [tex]A_{O'}[/tex] = π·(√(26))² = 26·π
The area of the circle that passes through vertices A, B, and C, is (C) 26·π
Learn more here:
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The possible question options obtained from a similar question online are;
(A) 24·π (B) 25·π (C) 26·π (D) 27·π (E) 28·π
The rectangle shown has a perimeter of 64 cm and the given area. Its length is 8 more than five times its width. Write and solve a system of equations to find the dimensions of the rectangle.
Answer:
Length 28 cm, width 4 cmStep-by-step explanation:
Given:
P = 64 cmL = 5W + 8Simplify equation for perimeter and solve for W:
P = 2(L + W) = 2(5W + 8 + W) = 2(6W + 8) = 12W + 1612W + 16 = 6412W = 48W = 4 cmFind L:
L = 5*4 + 8 = 28 cm2/3 x 4/7 write the answer in the simplest form
Answer:
8/21
I don't think that it can be simplified further....
Answer:
⁸/₂₁
Step-by-step explanation:
²/₃ ·⁴/₇ = ⁸/₂₁
you just multiply the denominator with the denominator, and the numerator with the numerator.
This diagram models 3 friends who are sharing 2 turkey sandwiches equally.
How much does each friend get?
1/3 sandwich
2/3 sandwich
11/3 sandwiches
11/2 sandwiches
Answer:
2/3 sandwich.
Step-by-step explanation:
No Explanation
You and your best friend are both on the swim team. You want to beat your friend at the next swim meet so you decide to swim 151515 minutes longer than she does one day at practice.
Answer:
45
Step-by-step explanation:
15+15+15=45
that would increase her practice time by 45 minutes
¿De qué número es 60 el 80%?
Answer:
48
Step-by-step explanation:
The following data set has a mode of 2, a mean of 10, and a median of 7. Which of these three measures gives the best idea of the typical size of the numbers in the list?
2, 2, 2, 4, 6, 8, 10, 12, 14, 60
A. Median
B. Mode
C. Mean
Answer:
I should think the median
What is the perimeter of a rectangle with a length of 11.25 inches and a
width of 8 inches?
Answer:
38.5 in
Step-by-step explanation:
11.25 in + 11.25 in + 8 in + 8 in
= 38.5 in