Factoring is an important process that helps us understand more about our equations. Through factoring, we rewrite our polynomials in a simpler form, and when we apply the principles of factoring to equations, we yield a lot of useful information. There are a lot of different factoring techniques.
Professor Cramer determines a final grade based on attendance, two papers, three major tests, and a final exam. Each of these activities has a total of 100 possible points. However, the activities carry different weights. Attendance is worth 7%, each paper is worth 9%, each test is worth 14%, and the final is worth 33%, (a) What is the average for a student with 64 on attendance, 82 on the first paper, 61 on the second paper, 72 on test 1, 64 on test 2, 93 on test 3, and 82 on the final exam? (Round your answer to one decimal place.) (b) Compute the average for a student with the above scores on the papers, tests, and final exam, but with a score of only 29 on attendance. (Round your answer to one decimal place.)
The average for a student with 64 on attendance, 82 on the first paper, 61 on the second paper, 72 on test 1, 64 on test 2, 93 on test 3, and 82 on the final exam is 77.31% and the average for a student with the above scores on the papers, tests, and final exam, but with a score of only 29 on attendance is 73.23%.
Averagea. Average:
Average: 82(0.07)+ 61(0.09)+ 72(0.14) +64(0.14) + 93(0.14)+ 82(0.33)÷0.07+0.09+3(0.14)+0.33
Average=5.74+5.49+10.08+8.96+13.02+27.06÷0.91
Average=70.35÷0.91
Average=77.31%
b. Average
Average= 29(0.07)+ 61(0.09)+ 72(0.14) +64(0.14) + 93(0.14)+ 82(0.33)÷0.07+0.09+3(0.14)+0.33
Average=2.03+5.49+10.08+8.96+13.02+27.06÷0.91
Average=66.64÷0.91
Average=73.23%
Therefore the average for both a and b is 77.31% and 73.23%.
Learn more about average here:https://brainly.com/question/20118982
#SPJ1
Use the diagram to find the value of the following. what is the value of x.
Angle A-
Angle B -
Angle C-
Answer:
x=29 angle a=63 Ang b=46 and c=71
Step-by-step explanation:
2x+5+x+17+3x-16=180 (sum of angles in triangles)
value of x is 29 substitute it in angle a b c
a=2*29+5
=63
b=29+17 = 46
c=3*29-16 = 71
What are the slope and the y-intercept of the linear function that is represented by the graph?
Answer:
Step-by-step explanation:
it would be great if u had the image, but at least I can give some advice: use the method of rise over run to find the slope. use 2 points and count the number of squares "rising" and turn right and count the number of squares "running". left and down if it's going downward.
for the y intercept, find the x that equals 0. your coodinate should look like this: (0, *insert y*)
Determine whether or not the distribution is a probability distribution and select the reason(s) why or why not. X 0 1 2 P(X) 0 1/3 2/3 Select all that apply: The given distribution is a probability distribution, since the probabilities lie inclusively between 0 and 1. The given distribution is not a probability distribution, since at least one of the probabilities is greater than 1 or less than 0. The given distribution is a probability distribution, since the sum of probabilities is equal to 1. The given distribution is not a probability distribution, since the sum of probabilities is not equal to 1.
The distribution is a probability distribution, and the reasons are
The given distribution is a probability distribution, since the probabilities lie inclusively between 0 and 1. The given distribution is a probability distribution, since the sum of probabilities is equal to 1. How to determine whether the distribution is a probability distribution?The probability distribution is given as:
X 0 1 2
P(X) 0 1/3 2/3
From the above table of probability distribution, we can see that each probability value is between 0 and 1 (inclusive)
Also, the sum of probabilities is 1
i.e. 0 + 1/3 + 2/3 = 1
Hence, the distribution is a probability distribution, and the reasons are
The given distribution is a probability distribution, since the probabilities lie inclusively between 0 and 1. The given distribution is a probability distribution, since the sum of probabilities is equal to 1.Read more about probability distribution at
https://brainly.com/question/14525371
#SPJ1
television and DVD player cost a total of $1242. The cost of the television is two times the cost of the DVD player. Find the cost of each item.
Answer: TV costs $828 and DVD player costs $414.
Step-by-step explanation: let x represent the cost of tv while y represents the cost of the player. x+y = 1242. since the tv costs twice as much as the dvd player, we can say that 2y=x. now replace x with 2y in our equation and we get 2y+y= 1242, 3y = 1242. now divide both sides by 3 and y = 414. Now that we now the value of y, just sub it into our original equation, x+y = 1242. x + 414 = 1242. x = 828.
Find the unit tangent vector for the following parameterized curves.
r(t)=cos(t)i+sin(t)j+sin(t)k, 0≤t<2π.
The unit tangent vector for the parametrized curve is [tex]\vec T(t) = - \frac{\sin t}{\sqrt{1 + \cos ^{2} t}}\,\hat{i} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{j} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{k}[/tex].
How to determine the unit tangent vector of a parametrized curveIn this question we know a three-dimension parametrized curve, of which we must derive its unit tangent vector in accordance with the following formula:
[tex]\vec T(t) = \frac{\vec R'(t)}{\|\vec R'(t)\|}[/tex]
Where:
[tex]\vec T(t)[/tex] - Tangent vector.[tex]\|\vec R'(t)\|[/tex] - Magnitude of the first derivative of the parametrized curve.First, determine the first derivative of the parametrized curve:
[tex]\vec R'(t) = -\sin t \,\hat{i} + \cos t \,\hat{j} + \cos t \,\hat{k}[/tex]
Second, derive the magnitude of the parametrized curve:
[tex]\|\vec R'(t)\|[/tex] = √[(- sin t)² + (cos t)² + (cos t)²]
[tex]\|\vec R'(t)\|[/tex] = √(1 + cos² t)
Third, substitute every term in the unit tangent curve formula:
[tex]\vec T(t) = - \frac{\sin t}{\sqrt{1 + \cos ^{2} t}}\,\hat{i} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{j} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{k}[/tex]
To learn more on parametrized curves: https://brainly.com/question/15565506
#SPJ1
Will mark u brainliest Question
Question
What is the turning point of the graph of f(x)=|x−2|+3?
(2, 3)
(−3, 2)
(3, 2)
(2, −3)
The turning point of the function f(x) = |x-2| + 3 will be (3, 2).
Here,
We have to find the turning point of the graph of function,
f(x) = |x−2|+3
What is an absolute function?
The non-negative value of real number without regard to its sign is known as its absolute value.
Now,
The absolute function is;
f(x) = |x+3| -2.
Since, When we plot the graph of the absolute function f(x) = |x+3| -2,
it will give two straight lines which is shown in the graph.
Clearly, The graph of the function changes its position at the coordinate
(3, 2).
Therefore, The absolute function having its turning point at the coordinate ( 3, 2).
To know more about absolute functions visit:
https://brainly.com/question/25971887
#SPJ1
The blueprint specifications for a machined part calls for its thickness to be 3.145 in.
with a tolerance of +-0.010 in. Find the limit dimensions of the part?
The limit dimensions of the part are 3.135 inches and 3.155 inches
How to find the limit dimensions of the part?The given parameters are
Thickness = 3.145 inchesTolerance = 0.010 inchesThe limit dimensions of the part are calculated as
Limit = Thickness +/- Tolerance
So, we have
Limit = 3.145 inches +/- 0.010 inches
Expand the above expression
So, we have
Limit = (3.145 inches - 0.010 inches, 3.145 inches + 0.010 inches)
Evaluate the sum
Limit = (3.135 inches, 3.155 inches)
Hence, the limit dimensions of the part are 3.135 inches and 3.155 inches
Read more about dimensions at
brainly.com/question/19819849
#SPJ1
A support pole for an ancient structure is found to have one-sixth of the carbon-14 of a modern, living tree. How long ago did the tree used to make the support pole die? Give your answer to the nearest whole number. (Assume that half-life of carbon-14 is 5770 years.)
14912 years ago, the tree that was used to kill the support pole died which is one-sixth of the carbon-14 of a modern, living tree.
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
One-sixth of a modern, living tree's carbon-14 is present in an ancient structure.
Assume that the half-life of carbon-14 is 5770 years
As per the given condition, the expression would be
[tex]A(t) = A_o}\dfrac{1}{2} ^{(\frac{t}{5770} )}\\A(t) = (0.167)A_o}[/tex]
[tex](0.167)A_o} = A_o}\dfrac{1}{2} ^{(\frac{t}{5770} )}[/tex]
[tex](0.167) = \dfrac{1}{2} ^{(\frac{t}{5770} )}[/tex]
Take the logarithms of both sides to get:
[tex]log(0.167) =log \dfrac{1}{2} ^{(\frac{t}{5770} )}[/tex]
Using logₐ(xⁿ) = n logₐx.
⇒ log 0.167= (t/5770) log (0.5)
⇒ log 0.167/ log (0.5)= (t/5770)
⇒ 3 = (t/5770)
⇒ t = 3 × 5770
⇒ t = 14912
Hence, 14912 years ago, the tree that was used to kill the support pole died.
Learn more about the logarithmic properties here:
brainly.com/question/24211708
#SPJ1
Determine the point(s), if any, at which the graph of the function has a horizontal tangent line. Y= 1/2x^2 +7x (Give the answer as x,y coordinates)
Answer:
i don't know how to attach the file
One pizza will feed 5 people. How many pizzas are needed for 40 people?
Answer:
8 pizzas
Step-by-step explanation:
If you spend 3.5 hours a week studying for English and 7.5 hours studying for math what is the ratio of time
spent studying in math to studying for English?
Answer:
7.5 : 3.5
Step-by-step explanation:
ratio of time spent studying in math to studying for English is ;
time spent studying in math. / time spent in studying English
[tex] \frac{7.5}{3.5} [/tex]
= 7.5 : 3.5
Helpp??
A playground has 2 slides,
3 swings, and monkey bars.
What's the probability that a kid
will decide to use a slide if they
pick at random?
What are the solutions to –24x – 24 = x3 + 8x2?
Answer:
–24x – 24 = x3 + 8x2
Step-by-step explanation:
-24x-24=x^3+8x^2
x^3+8x^2+24=-24x-24+24
x^3+8x^2+24=-24x
x^3+8x^2+24+24x=-24x+24x
x^3+8x^2+24x+24=0
Answer: x=-2
Step-by-step explanation:
[tex]-24x-24=x^3+8x^2\\-24x-24+24=x^3+8x^2+24\\-24x=x^3+8x^2+24\\-24x+24x=x^3+8x^2+24+24x\\0=x^3+8x^2+24x+24\\x^3+8x^2+24x+24=0\\x^3+8x^2+12x+12x+24=0\\(x)(x^2+8x+12)+(12)(x+2)=0\\(x)(x^2+2x+6x+12)+(12)(x+2)=0\\(x)((x)(x+2)+6(x+2))+(12)(x+2)=0\\(x+2)((x)(x+6)+12)=0\\ (x+2)(x^2+6x+12)=0\\x+2=0\\x+2-2=0+(-2)\\x=-2\\x^2+6x+12=0\\D=(-6)^2-(4)(1)(12)\\D=36-48\\D=-12\\Hence,\\The\ equation\ has\ no\ valid \ roots\\Thus,\\x=-2[/tex]
The system of equations graphed below has how many solutions?
y = 2x + 2
y= 2x
The given system has zero solutions.
Lines that never cross one other are said to be parallel. Hence, a pair of parallel lines must have the same slope but distinct intercepts. (On the other hand, identical lines have same intercept).
In the general equation of a line, y = mx + b, m represents the slope of the line.
The general equations of parallel lines would be of the form:
(1) y = mx + b
(2) y = mx + c
where b and c are any constants.
Now, we observe that the given equations are of the above form with m=2, b=2 and c=0, therefore, they are parallel lines. Since, parallel lines never intersect each other, they have no solution.
To learn more about parallel lines, visit:
https://brainly.com/question/16701300
#SPJ10
Find the measure of the missing angles.
Answer:
x=26, y=90
Step-by-step explanation:
This is what I did,
I knew that y = 90 because it is a Right Angle. I subtracted 90 - 64 and that got me = y 26
Question 7 of 20:
Select the best answer for the question.
7. Percent means "per
O A. 100
OB. 1000
O C. 1
O D. 10
11
K
OMark for review (Will be highlighted on the review p
6. A household spend 120 on purchase of a commodity when it price is 6 per unit. When the rises to 10 per unit his total expenditure on this commodity becomes 180.calculate price elasticity of demand by percentage change method.
Therefore, the price elasticity of demand by percentage change method is -0.025.
Given the price of a first commodity (p₁) = 6 rs
the price of a second commodity (p₂) = 10 rs
Expenditure on first commodity (s₁) = 120
Expenditure on second commodity (s₂) = 180
We need to find the quantity as
120 = 6 * Q₁. 180 = 10 * Q₂
Q₁ = 120 / 6 Q₂ = 180 / 10
Q₁ = 20 Q₂ = 18
price elasticity of demand by percentage change method as
Eₐ = P / Q * ΔQ /ΔP
ΔQ = Q₂ - Q₁ = 18 -20 = -2
ΔP = p₂ - p₁ = 10 - 6 = 4
Eₐ = 6 / 120 * -2 / 4
Eₐ = - 0.025
Therefore, the price elasticity of demand by percentage change method is -0.025.
To learn more about the price elasticity of demand by percentage refer below
https://brainly.com/question/5425317
#SPJ9
On the weekdays a grocery store has 14301 customers and on the weekends the grocery store has 11856 customers . How many more customers does the grocery store have on weekdays than on weekends?
Answer:
2445
Step-by-step explanation:
it would have 2445 more costumers
Answer:
2445
Step-by-step explanation:
Subtract.
14301 - 11856 = 2445 more people on weekdays
Draw the image of
ΔDEF
∆DEF
under the dilation with scale factor
−1/2
and the origin as the center of dilation. Label the image
ΔD'E'F'
∆D′E′F′
. Make sure to include the coordinates of D’, E’, and F’.
The image of triangle DEF after the dilation with a scale factor of -1/2 is given at the end of the answer.
What are transformations on the graph of a function?Transformations in the graph of a function involve operations in the vertices of the image, such as addition, subtraction, division or multiplication.
The transformation used in this problem is a dilation, in which the coordinates of the vertices of the original figure are multiplied by the scale factor.
For this problem, the vertices of the triangle are given as follows:
D(3,6), E(3,2) and F(5,4).
The dilation has a scale factor of -0.5 = -1/2, hence the coordinates of the image are given as follows:
D': (3 x -0.5, 6 x -0.5) = (-1.5, -3).E': (-1.5, -1).F': (-2.5, -2).The dilated triangle is given by the graph at the end of this answer.
More can be learned about transformations such as dilation at https://brainly.com/question/28687396
#SPJ1
Which number below is NOT equal to the others?
1/8
18/10
1.8
1 4/5
Answer:
1/8
Step-by-step explanation:
When worked out, all numbers are equal to 1.8 except 1/8. (1/8 is equal to .125)
1/8) 1 divided by 8 is .125
18/10) 18 divided by 10 is 1.8
1.8) 1.8=1.8
1 4/5) 4 divided by 5 is .8, and when you add the 1 it ends up as 1.8
Need help with D pls will give brainly
The length of the pen is 2√3 feet
Area of a triangleThe formula for calculating the area of a rectangle is expressed according to the formula below:
Area of a right triangle = 1/2 * base * height
A = 1/2 bh
Given the following parameters
Area = 20 square feet
If the height is five times the length, then;
h = 5b
Substitute
A = 1/2 bh
A = 1/2(b)5b
30 = 1/2(5b²)
60 =5b²
b² = 12
b = 2√3
Hence the length of the pen is 2√3 feet
Learn more on area of triangle here: https://brainly.com/question/17335144
#SPJ1
Find the domain of f(x) and the interval.
f(x)=√x² - 2x +48
Answer:
Step-by-step explanation:
go pathways gives all the answers
PLS ANSWER THIS QUESTION FAST
WILL MARK BRAINLIEST
Answer: x=18 ==> C
Step-by-step explanation:
19+15+11=14+15+?
19+11=14+?
30=14+?
?=16
?+11+x=19+15+11
x+?=19+15
x+16=34
x=18 ==> C
a box of cereal has a volume of 1250 cubic cm with a length of 20cm and a width of 5cm. what is the height of the box?
Define in words variables for the unknown values
create an equation
solve using algebra
The height of the box that has a volume of 1250 cubic cm with a length of 20cm and a width of 5cm will be 12.5cm.
How to calculate the height?It should be noted that the formula for the volume will be:
= Length × Width × Height
Therefore the height will be:
Volume = LWH
where
L = length = 20cm
W = width = 5cm
H = height = unknown
1250 = (20 × 5 × H)
1250 = 100H
Height = 1250/100
Height = 12.5 cm
Therefore, the height is 12.5cm.
Learn more about volume on:
brainly.com/question/1972490
#SPJ1
Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks.
Learn with an example
Susan is going to ship some gifts to family members, and she is considering two shipping
companies. The first shipping company charges a fee of $20 to ship a medium box, plus an
additional $1 per pound. A second shipping company charges $5 for the same size of box,
plus an additional $4 per pound. At a certain weight, the two shipping methods will cost tre
same amount. How much will it cost? What is that weight?
The two shipping methods both cost $
Submit
at a weight of
pounds.
The first company shipping charge is 5 $
the second company shipping charge is 2 $
let the size of the box be 'x'
Given the first company charged as below
20$ for medium-sized and an extra 1$ for one pound
= 20x + 1
The second company charged as below
$5 for the same size of the box, plus an additional $4 per pound
= 5x + 4
The price of the two shipping options will be same.
20x + 1 = 5x + 4
20x - 5x = 4- 1
15x = 3
x= 3 / 15
x = 1/5
x = 0.2
∴ 20x+1 = 20 * 0.2 +1 = 5
5x + 4 = 5 * 0.2 + 1 = 2
Therefore, The first company's shipping fee is $5, whereas the second company's fee is $2.
Learn more about these problems refer below
https://brainly.com/question/22826860
#SPJ9
Kathi and Robert Hawn had a pottery stand at the annual Skippack Craft Fair. They sold some of their pottery at the original price of $10.50 each, but later decreased the price of each by $2.00. If they sold all 98 pieces and took in $893.00
find how many they sold at the original price and how many they sold at the reduced price.
Answer:
See work below.
30 sold for full price and 68 sold for a discount.
Step-by-step explanation:
Point A appears on the number line as shown below:
Answer:
C) x² + y²Step-by-step explanation:
According to the graph, point A has a negative value, between - 1 and zero.
All the expressions could result in negative value apart from the sum of the squares, which is never negative.
Correct choice is C.
XZ is the perpendicular bisector of segment WY. Solve for k. Enter a NUMBER only.
Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 6.
What is the numerical value of K?A bisector divides a segment or angle into two equal halves.
Given the data in the question;
XZ is the perpendicular bisector of segment WYSegment WX = 3k + 17Segment XY = 7k - 7Value of k = ?Since XZ is a perpendicular bisector of segment WY,
Segment WX is equal to Segment XY
Segment WX = Segment XY
Plug in the given values and solve for k.
3k + 17 = 7k - 7
Collect like terms
3k - 7k = -7 - 17
-4k = -24
Divide both sides by the coefficient of k
-4k/-4 = -24/-4
k = 6
Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 6.
Learn more about bisectors here: https://brainly.com/question/13880193
#SPJ1
13x + 5 + 17x -4.5 + x
Answer:
31x+0.5
Step-by-step explanation:
In this problem, we must combine like terms to simplify the expression. We can begin by writing out the expression:
13x + 5 + 17x - 4.5 + x
Now that we have rewritten the expression, we can combine like terms to simplify the expression. This would look like:
13x + 17x + x = 31x
5 - 4.5 = 0.5
The answer would be “31x + 0.5” when simplified.