5a - {3b - 5[a - (b + -4a)]}

Answers

Answer 1

Interesting problem. When computers first came out (when dinosaurs ruled the planet), we had to deal with problems that were many brackets deep. So this has practical applications.

Start at the very right and keep on removing brackets and collecting like terms.

5a - {3b - 5[a - (b - 4a)]} I just changed the sign on the right bracket.
5a - {3b - 5[a - b + 4a]}
5a - {3b - 5[5a - b]} Now deal with []. You are still on the right.
5a - {3b - 25a + 5b}
5a - {8b - 25a} Finally remove {}
5a - 8b + 25a
30a - 8b
If you can solve another like this, you are well on your way to being good in computer science.

Related Questions

If the cubic function P(x) includes the points (−4, 0), (0, 0), and (2, 0), which of the following represents this function?

Answers

Final answer:

The function cannot be determined with the given information.

Explanation:

The given points (-4, 0), (0, 0), and (2, 0) indicate that the function is a cubic function with three real roots. A cubic function is of the form P(x) = ax^3 + bx^2 + cx + d. Since the function passes through the x-axis at (-4, 0), (0, 0), and (2, 0), the roots of the cubic function are -4, 0, and 2. Therefore, the function can be written as P(x) = a(x + 4)(x - 0)(x - 2). However, since a cubic function with three real roots has an odd degree, the coefficient 'a' must be negative or positive. This means that the function can also be written as P(x) = -a(x + 4)(x - 0)(x - 2) or P(x) = a(x + 4)(x - 0)(x - 2). So, the correct representation of the function cannot be determined with the given information.

Dominic picks oranges from 18 trees. He picks 11.4 pounds of oranges from each tree. How many total pounds does Dominic pick?

Answers

205.2 lbs. 11.4*18 = 205.2

11.4 pounds from each tree, there were 18 trees
11.4 * 18 is 205.2

He picked a total of 205.2 pounds of oranges from the 18 trees.

Hope this helps

The height of a rock thrown off a cliff can be modeled by h=-16t^2-8t+120, where h is the height in feet and t is time in seconds. How long does it take the rock to reach the ground?

Answers

The rock hits the ground after 4 seconds.

----------------------
Here is the work in how you can find this answer...:
----------------------

The height, h, of an object thrown upward from an initial height, H, with an initial velocity, Vo, is given by the function h as a function of time, t:

h(t) = -16t^2 + Vot + H

Since Vo = 48 ft/sec and H 64 ft, then:

h(t) = -16t^2 + 48t + 64

You want to know at what time, t, will the rock hit the ground (h = 0). Set the above function = 0.

-16t^2 + 48t + 64 = 0

Solve this quadratic equation for t. First, factor -16.

-16 ( t^2 - 3t -4 ) = 0

Apply the zero products principle.

t^2 - 3t - 4 = 0

Factor.

( t - 4 )( t + 1 )

Again, apply the zero products principle.

t - 4 = 0 and/or t + 1 = 0

If t - 4 = 0, then t = 4 seconds

If t + 1 = 0, then t = -1 second...Discard this solution as negative time is not meaningful in this problem.

---
OVERALL = THE ROCK HITS THE GROUND AFTER 4 SECONDS
---

Weight Gain after gaining 25 pounds, a person is 115 pounds lighter than double his previous weight. How much did the person weigh before gaining 25 pounds? How could I write this problem

Answers

Equation: x + 25 = 2x - 115
Cross 115 over the 'bridge' and add it with 25: x+140 = 2x
Cross x over the 'bridge' and subtract with 2x: 140 = x

ANSWER: x

suppose that a pair of 7 sided dice is tossed. What is the expected value of the sum?

Answers

Final answer:

The expected value of the sum when rolling a pair of 7-sided dice is 8.

Explanation:

When rolling a pair of 7-sided dice, each die has numbers 1 through 7 on its faces. To find the expected value of the sum, we need to calculate the average of all possible sums.

The first die can have 7 possible outcomes, and for each outcome, the second die can also have 7 possible outcomes. This gives us a total of 7*7=49 possible outcomes. The sums of these outcomes range from 2 (1+1) to 14 (7+7).

To find the expected value, we multiply each sum by its probability and sum them up. Since each sum has an equal probability of occurring (1/49), we can simplify the calculation:

Expected value = (2*1/49) + (3*1/49) + (4*1/49) + ... + (14*1/49) = 8

Therefore, the expected value of the sum when rolling a pair of 7-sided dice is 8.

You owe $976.34 on a credit card that has an interest rate of 10.75% APR. You pay $100.00 at the end of each month.

You place the $100.00 in a savings account that earns a 2.75% APR. What is the difference in interest between savings earned and credit card interest paid

answer: $8.52

Answers

You already wrote the answer. Do you want to check if this answer is correct?

1. $976.34*1075= 104.96
976.34*104=871.38
2. 100.00*0275=2.75

Myron bought a dozen eggs for $1.75 per dozen. If he bought 8 dozen eggs, how much did they cost?]

Answers

That would be 8×1.75, which is 14. He bought 8 dozen eggs for $14.

Hey there!

So, if 1 (dozen) of eggs equal ($1.75), we would want to multiply this by (8).

[tex] \left[\begin{array}{ccc}\boxed{\boxed{1.75*8}}\end{array}\right] \ =\left[\begin{array}{ccc}\boxed{14}\end{array}\right][/tex]

This would cost then ($14).

Hope this helps you!

A box has dimensions of 3 inches, 5 inches and 7 inches what is the surface area

Answers

Formula: 2(l*b+b*h+h*l)
2(3*5+5*7+7*3)
2(15+35+21)
2(71)
SA= 142

Final answer:

The surface area of a box with dimensions of 3 inches by 5 inches by 7 inches is calculated using the formula 2lw + 2lh + 2wh, resulting in a total surface area of 142 square inches.

Explanation:

To calculate the surface area of a box with dimensions of 3 inches, 5 inches, and 7 inches, you would use the surface area formula for a rectangular prism. The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the prism.

In this case:

Length (l) = 3 inches

Width (w) = 5 inches

Height (h) = 7 inches

Now, plug these dimensions into the formula:

Surface Area = 2(3 inches × 5 inches) + 2(3 inches × 7 inches) + 2(5 inches × 7 inches)

Surface Area = 2(15) + 2(21) + 2(35)

Surface Area = 30 + 42 + 70

Surface Area = 142 square inches

Therefore, the surface area of a box with dimensions of 3 inches by 5 inches by 7 inches is 142 square inches.

how many books can you get in a storage bin that is 4 feet high and 9 feet long and 11 feet wide

Answers

Well, this depends on the size of the books. We can find the volume of the bin by using...
V=bh or l x w x h
So, 9 times 11 is 99.
99 times 4 is 396, which is the volume.
You did not specify the size of the books, so all we can say is that the volume of the bin is 396 cubic feet.

One drawer in a dresser contains 7 blue socks and 7 white socks. a second drawer contains 5 blue socks and 1 white socks. one sock is chosen from each drawer. what is the probability that they match? express the answer in decimals.

Answers

It is 7/14 times 5/1 because blue is the only one that can match. You get 35/14 or 2 7/14 which is 2.5.

What is the simplified form of the expression? x8 2y10 5x5

Answers

we have
x8* 2y10 * 5x5
product of two powers that have the same base is equal to a power of said base that has as exponent the sum of the exponents

x8* 2y10 * 5x5----------> (1)*(2)*(5)*[x^(8+5)]*y^10=10*[x^13]*y^10

the answer is 10*[x^13]*y^10

Julia is an intern at an architecture firm. She is given an assignment to create a bell-shaped structure that is symmetrical. She writes the function f(x)=3 squareroot -|x-2|+6 to model the structure. Find the piecewise function that matches this absolute value function. Then, graph the function using a graphing calculator and describe what you see.

Answers

Answer:

The given function is

f(x)= 3 [tex]\sqrt\left- |x \right-2 |+6[/tex] ⇒[Absolute value function]

F(x)= 1. 3[tex]\sqrt {-(x-2)+6}[/tex] =[tex]3\sqrt {-x+2+6}=3\sqrt{-x+8}[/tex] when (x-2≥0→x≥2) ⇒[ Piecewise function]

2. [tex]3\sqrt{-[-(x-2)]+6}=3\sqrt{x-2+6}=3\sqrt{x+4}[/tex] when [ x-2<0→x<2]⇒[ Piecewise function]

We see there is a shape which is is in the form of dome,point of intersection of two curves being (2,7.348), symmetrical on both side of line x=2.

A quality control engineer tests the quality of produced computers. suppose that 5% of computers have defects, and defects occur independently of each other.
a. what is the expected number of defective computers in a shipment of twenty? 1
b. find the probability of exactly 3 defective computers in a shipment of twenty.

Answers

Binomial distribution can be used because the situation satisfies all the following conditions:1. Number of trials is known and remains constant (n=20)2. Each trial is Bernoulli (i.e. exactly two possible outcomes) (defective/normal)3. Probability is known and remains constant throughout the trials (0.05)4. All trials are random and independent of the othersThe number of successes(defects), x, is then given by[tex]P(x)=C(n,x)p^x(1-p)^{n-x}[/tex]where[tex]C(n,x)=\frac{n!}{x!(n-x)!}[/tex]
For n=20, p=0.05,
the mean number of defects is np=20*0.05=1

[tex]P(x)=C(n,x)p^x(1-p)^{n-x}[/tex]
[tex]P(X=3)=C(20,3)0.05^3(1-0.05)^{20-3}[/tex]
[tex]=1140(1.25*10^{-4}(0.41812)[/tex]
[tex]=0.05958[/tex]

Answer: probability of exactly 3 defects in a sample of 20 is 0.05958

3 sin2(θ) + 16 sin(θ) − 35 = 0

Answers

[tex]\bf 3sin^2(\theta )+16sin(\theta )-35=0\impliedby \begin{array}{llll} \textit{notice this is just a quadratic }\\\\ax^2+bx+c=0 \end{array} \\\\\\\ [3sin(\theta )-5][sin(\theta )+7]=0\\\\ -------------------------------\\\\ 3sin(\theta )-5=0\implies 3sin(\theta )=5\implies sin(\theta )=\cfrac{5}{3} \\\\\\ \measuredangle \theta =sin^{-1}\left( \frac{5}{3} \right)[/tex]

now, before continuing on the first root, recall that the sine has a range of -1 ⩽ sin(θ) ⩽1, however 5/3 is greater than 1, and therefore is out of range, meaning, there's no such angle, so we've got zilch there.

now, let's check the second root,

[tex]\bf sin(\theta )+7=0\implies sin(\theta )=-7\implies \measuredangle \theta =sin^{-1}(-7)[/tex]

well, hell -7 is smaller than -1, so is also outside the range for sine, and so, the second root gave also zilch, so, in short, there's no such angle.

Write the equation of the line passing through (−1, 0) and (0, −3).

Answers

The equation of the line passing through (-1, 0) and (0, -3) is y = -3x - 3, where -3 is the slope, and -3 is also the y-intercept.

The equation of a line can be written in slope-intercept form as y = mx + b, where m is the slope of the line, and b is the y-intercept. To find the slope m, we can use the two points given; the slope is the change in y over the change in x, which is (-3 - 0)/(0 - (-1)) = -3/1 = -3. With the slope found, and knowing that the line passes through the point (0, -3), we can say the y-intercept b is -3. The equation of the line through the points (-1, 0) and (0, -3) is y = -3x - 3.

what is r divided by 8

Answers

That quotient is indicated as
r/8

given the equation W=CE2/2, solve for C

Answers

W=CE^2/2
CE^2 = 2W
C = 2W/E^2 Answer

Answer:

[tex]C=\frac{2W}{E^2}[/tex]

Step-by-step explanation:

[tex]W=\frac{CE^2}{2}[/tex]

Solve for C

To solve for C, we need to get C alone

LEts start with eliminating 2 from the denominator

Multiply the equation by 2 on both sides

[tex]2W= CE^2[/tex]

To isolate C, divide both sides by E^2

[tex]\frac{2W}{E^2} =C[/tex]

[tex]C=\frac{2W}{E^2}[/tex]

“Find the equation of the line passing through (8,-2) & (7,-4). Write your equation in point-slope AND slope intercept forms.
Point slope form using (8,-2) _____
Point slope form using (7,-4) _____

Slope intercept form: y=2x-18

Answers

we know that
the equation of the line in point-slope------------> (y – y1) = m(x – x1)
the equation of the line in slope intercept forms. -----> y =mx+b

find the slope m
point (8,-2) & (7,-4).
m=(y2-y1)/(x2-x1)---------> (-4+2)/(7-8)=-2/-1----------> m=2

Part A)
find the equation of the line in point-slope using (8,-2)
(y – y1) = m(x – x1)---------> (y-(-2)) = 2*(x – 8)-------> y+2=2x-16
y=2x-16-2--------> y=2x-18

Part B)
find the equation of the line in point-slope using (7,-4)
(y – y1) = m(x – x1)---------> (y-(-4)) = 2*(x – 7)-------> y+4=2x-14
y=2x-14-4--------> y=2x-18

Part C)
find the equation of the line in slope intercept forms
using (7,-4)
y=mx+b--------> -4=2*7+b----------> -4=14+b-----------> b=-18
then
y=2x-18

Part D)
find the equation of the line in slope intercept forms
using (8,-2)
y=mx+b--------> -2=2*8+b----------> -2=16+b-----------> b=-18
then
y=2x-18

Find direction numbers for the line of intersection of the planes x + y + z = 1 and x + z = 0. (enter your answers as a comma-separated list.)

Answers

<1, 1, 1> × <1, 0, 1> = <1, 0, -1>

The cross product of the normals of the planes gives the direction vector of their line of intersection.

help!!!
All rectangles can also be classified as which of the following? Select all that apply. r

rhombus
square
parallelogram
trapezoid
quadrilateral

Answers

sqaure
rhombus
parallelogram
quadrilateral
hope it helps

Answer:

All rectangles can also be classified as which of the following? Select all that apply. r

rhombus

square

parallelogram

trapezoid

quadrilateral

Step-by-step explanation:

In plane geometry, a rectangle is a parallelogram.

Parallelogram: its opposite sides are parallel, it can also be a square, or a rhombus.

In Euclidean geometry, a quadrilateral is a polygon that has four sides and four vertices.

The answer is: Rhombus, square, parallelogram, and quadrilateral.

subtracting/adding mixed fractions

Answers

a)
= 3 2/4
= 3 1/2

b)
= 7 10/15 + 2 3/15
= 9 13/15

61/100in word form,decimal

Answers

Decimal form is 0.61 and word form is sixty- one one- hundredths

When 2/3 of a number is added to 10 the result is 5 more than the number find the number g?

Answers

[tex]g-the\ number\\\\\dfrac{2}{3}g+10=g+5\qquad\text{multiply both sides by 3}\\\\2g+30=3g+15\qquad\text{subtract 30 from both sides}\\\\2g=3g-15\qquad\text{subtract 3g from both sides}\\\\-g=-15\qquad\text{change the signs}\\\\\boxed{g=15}[/tex]

A trapezoid has an area of 15 square feet. If the bases are 4 feet and 6 feet , what is the height of the trapezoid? Hurry Big test tomorrow this the last one

Answers

the formula for a trapezoid is a=a+b/2 x h
so plug that back into the equation and you get
15=10/2 *h
15=5*h
from here, you know that 15/5 equals 3 and therefore the height of the trapezoid is 3.

Good Luck on ur Big Test!

Final answer:

The height of the trapezoid is 3 feet.

Explanation:

To find the height of a trapezoid with given bases and area, you can use the formula for the area of a trapezoid, which is the average of the two bases multiplied by the height. The formula is as follows:

Area = ½ × (base1 + base2) × height

Given that the area of the trapezoid is 15 square feet and the two bases are 4 feet and 6 feet, the formula becomes:

15 = ½ × (4 + 6) × height

This simplifies to:

15 = ½ × 10 × height

Therefore, we can calculate the height by dividing the area by 5 (which is half of 10):

height = 15 ÷ 5 = 3 feet

So, the height of the trapezoid is 3 feet.

20 POINTS!!

a triangle has side lengths 20cm, 27cm, 21cm. is the triangle a right angle? show your work

Answers

20^2 + 21^2 = 27^2
400 + 441 = 729
881 = 729 (does not equal)

Not a right traingle

use the Pythagoras Theorem

In the number 35.3816, the underlined three is __________ the other three.

Answers

Hey there! :D

The three in the tens place is 100 times bigger than the other three.

.3*100= 30

I hope this helps!
~kaikers

Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. a pollster contacts 92 people in the 18-21 age bracket and finds that 78 of them respond and 14 refuse to respond. when 284 people in the 22-29 age bracket are contacted, 265 respond and 19 refuse to respond. assume that 1 of the 376 people is randomly selected. find the probability of getting someone in the 22-29 age bracket or someone who refused to respond.

Answers

probability = (total 22-29 age bracket + number of not respond and aged 18- 21) / total people
= (284+14) / 376
= 0.792
= 0.79

Final answer:

The probability of selecting a person from the 22-29 age bracket or someone who refused to respond is approximately 79.3% out of the total number of people contacted.

Explanation:

The student is asking about finding the probability of selecting either a person from the 22-29 age bracket or someone who refused to respond from a combined group of people contacted in a survey. To solve this problem, we use the addition rule of probability. The total number of people is 376. The number of people who are in the 22-29 age bracket is 284, and the number of people who refused to respond is 14+19=33. However, this would include those who refused from the 22-29 bracket twice, so we subtract the 19 from the 22-29 age group who refused, leaving us with 33-19=14. Thus, the total number in either category is the sum of these, 284+14=298.

The probability (P) of picking someone from the 22-29 age bracket or someone who refused to respond is therefore calculated as:

P = Number in either category / Total number = 298 / 376 ≈ 0.793 or 79.3%

Jerome went on a hike. He climbed three-fourths of a mile in two-thirds of an hour. What was his hiking speed in miles per hour?

Answers

You could do this with fractions. I'll do decimals later.

d = 3/4 mile
t = 2/3 hour
r = ????

r = 3/4 // 2/3 Invert and multiply the denominator
r = 3/4 * 3/2 = 9/8 = 1 1/8

If your calculator handles fractions, you can use it to do this. If not you can change this to a decimal.
d = 3/4 = 0.75 miles
t = 2/3 hour = 0.666666666 hours.
r = ???

d = r*t
r = d/t
r = 0.75 / 0.66666667
r = 1.125 miles / hour
which gives you exactly the same answer 1.125 = 1 1/8

Final answer:

Jerome's hiking speed was calculated by dividing the distance he hiked, three-fourths of a mile, by the time it took him, two-thirds of an hour. This yielded a hiking speed of 1.125 miles per hour.

Explanation:

To calculate Jerome's hiking speed in miles per hour, we need to divide the distance he hiked by the time it took him. Jerome hiked three-fourths of a mile in two-thirds of an hour. To find the speed, we use the formula:

Speed = Distance ÷ Time

Speed = ¾ mile ÷ ⅓ hour

To divide fractions, we multiply by the reciprocal of the denominator:

Speed = ¾ × ⅔ = 3/4 × 3/2 = 9/8

This fraction simplifies to 1⅛ (1.125) miles per hour. So, Jerome's hiking speed was 1.125 miles per hour.

It is important to remember that when we talk about speed, we are referring to the distance traveled over a certain period of time regardless of the direction of travel.

What is the geometric mean of 6 and 13?

What is the Geometric mean a 5 and 45?

Answers

What is the geometric mean of 6 and 13?
√(6·13) = √78

What is the Geometric mean a 5 and 45?
√(5·45) = √225 = 15

Answer: [tex]\sqrt{78}[/tex] and [tex]15[/tex]

Step-by-step explanation:

Given: (1) two numbers [tex]6[/tex] and [tex]13[/tex].

(2) two numbers [tex]5[/tex] and [tex]45[/tex].

To Find: Geometric number of numbers in [tex](1)[/tex] and [tex](2)[/tex]

Solution:

Let first number be [tex]=\text{a}[/tex]

Let second number be [tex]=\text{b}[/tex]

Geometric mean of two numbers [tex]\text{a}[/tex] and [tex]\text{b}[/tex] is

[tex]\sqrt{\text{a}\text{b}}[/tex]

Now,

[tex](1)[/tex] First number is [tex]=6[/tex]

Second number is [tex]=13[/tex]

Geometric mean of both numbers is

[tex]\sqrt{6\times13}[/tex]

[tex]\sqrt{78}[/tex]

Geometric mean is [tex]\sqrt{78}[/tex]

[tex](2)[/tex] First number is [tex]=5[/tex]

Second number is [tex]=45[/tex]

Geometric mean of both numbers is

[tex]\sqrt{5\times45}[/tex]

[tex]\sqrt{225}[/tex]

[tex]15[/tex]

Geometric mean is [tex]15[/tex]

What is the approximate distance between the points (-5, 1) and (-2, 3) on a coordinate grid? A.7.81 units B.3.61 units C.2.23 units D.3.32 units

Answers

The formula for distance between point in a coordinate grid is the following:

[tex] \sqrt{(x2 - x1) {}^{2} + (y2 - y1) {}^{2} } [/tex]
Where 1 and 2 stands for the points, so in your case the formula is the following
[tex] \sqrt{( - 2 - - 5) {}^{2} + (3 - 1) } [/tex]
[tex] \sqrt{ {3}^{2} + 2 {}^{2} } [/tex]
[tex] \sqrt{9 + 4} [/tex]
[tex] \sqrt{13} =3.605...[/tex]
So your answer is about 3.61

Answer:

3.61

Step-by-step explanation:

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