An expression is defined as a set of numbers, variables, and mathematical operations. The simplification of expression [(x+4)/(x²+3x-10)] - [(x-1)/(x²+2x-8)] is (4x+21)/(x³+7x²+1x-40).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The simplification of expression [(x+4)/(x²+3x-10)] - [(x-1)/(x²+2x-8)] can be done in the following manner,
[tex]\dfrac{x+4}{x^2+3x-10} - \dfrac{x-1}{x^2+2x-8}\\\\\\= \dfrac{x+4}{(x-2)(x+5)} - \dfrac{x-1}{(x+4)(x-2)}\\\\\\= \dfrac{(x+4)(x+4)- (x-1)(x+5)}{(x+4)(x-2)(x+5)} \\\\\\= \dfrac{x^2+16+8x-x^2-5x+x+5}{x^3+7x^2+2x-40}\\\\\\=\dfrac{4x+21}{x^3+7x^2+2x-40}[/tex]
Hence, the simplification of expression [(x+4)/(x²+3x-10)] - [(x-1)/(x²+2x-8)] is (4x+21)/(x³+7x²+1x-40).
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If a fair die is rolled 7 times, what is the probability, rounded to the nearest thousandth, of getting at least 4 threes?
Answer:
0.904
EX ; Each time the die is rolled, there are only two possible outcomes, either the result is a 2, or it is not. The result on a roll is independent of any other roll, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
- The parameters are:
x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.
In this problem:
- The die is rolled 7 times, hence .
One out of the 6 sides is a 2, hence
- Then:
0.905 = 90.5% probability of getting at most 2 twos.
Use polar coordinates to find the volume of the given solid. Inside both the cylinder x2 y2 = 1 and the ellipsoid 4x2 4y2 z2 = 64
The Volume of the given solid using polar coordinate is:[tex]\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta[/tex]
V= [tex]\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta[/tex]
What is Volume of Solid in polar coordinates?
To find the volume in polar coordinates bounded above by a surface z=f(r,θ) over a region on the xy-plane, use a double integral in polar coordinates.
Consider the cylinder,[tex]x^{2}+y^{2} =1[/tex] and the ellipsoid, [tex]4x^{2}+ 4y^{2} + z^{2} =64[/tex]
In polar coordinates, we know that
[tex]x^{2}+y^{2} =r^{2}[/tex]
So, the ellipsoid gives
[tex]4{(x^{2}+ y^{2)} + z^{2} =64[/tex]
4([tex]r^{2}[/tex]) + [tex]z^{2}[/tex] = 64
[tex]z^{2}[/tex] = 64- 4([tex]r^{2}[/tex])
z=± [tex]\sqrt{64-4r^{2} }[/tex]
So, the volume of the solid is given by:
V= [tex]\int\limits^{2\pi}_ 0 \int\limits^1_0{} \, [\sqrt{64-4r^{2} }- (-\sqrt{64-4r^{2} })] r dr d\theta[/tex]
= [tex]2\int\limits^{2\pi}_ 0 \int\limits^1_0 \, r\sqrt{64-4r^{2} } r dr d\theta[/tex]
To solve the integral take, [tex]64-4r^{2}[/tex] = t
dt= -8rdr
rdr = [tex]\frac{-1}{8} dt[/tex]
So, the integral [tex]\int\ r\sqrt{64-4r^{2} } rdr[/tex] become
=[tex]\int\ \sqrt{t } \frac{-1}{8} dt[/tex]
= [tex]\frac{-1}{12} t^{3/2}[/tex]
=[tex]\frac{-1}{12} (64-4r^{2}) ^{3/2}[/tex]
so on applying the limit, the volume becomes
V= [tex]2\int\limits^{2\pi}_ {0} \int\limits^1_0{} \, \frac{-1}{12} (64-4r^{2}) ^{3/2} d\theta[/tex]
=[tex]\frac{-1}{6} \int\limits^{2\pi}_ {0} [(64-4(1)^{2}) ^{3/2} \; -(64-4(2)^{0}) ^{3/2} ] d\theta[/tex]
V = [tex]\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta[/tex]
Since, further the integral isn't having any term of [tex]\theta[/tex].
we will end here.
The Volume of the given solid using polar coordinate is:[tex]\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta[/tex]
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Madison invests money in an account paying a simple interest of 3.2% per year.If she invests $160 and no money will be added or removed from the investment, how much will she have in one year, in dollars and cents?
The amount of interest she will earn in one year will be 5 dollars and 12 cents.
What is Simple interest?The normal interest levied on the amount borrowed from any bank on a yearly basis is called the simple interest.
Given that:-
The interest of 3.2% per yearInvests $160 and no money will be added or removed from the investment.The simple interest amount will be:-
SI = ( P x R x T ) / 100
SI = ( 160 x x 3.2 x 1 ) / 100
SI = $5.12
Therefore the amount of interest she will earn in one year will be 5 dollars and 12 cents.
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what is x+x+x+x+x+x+x+x+x+x+b+b+b+b+3=
Answer:
10x+4b+3
Step-by-step explanation:
x+x+x+x+x+x+x+x+x+x+b+b+b+b+3
There are 10 x
4 b
and one number
10x+4b+3
Answer:
10x+4b+3
Step-by-step explanation:
x+x+x+x+x+x+x+x+x+x+b+b+b+b+3
So when we add them we get 10x and 4b, which makes the equation
=> 10x+4b+3
Suppose that scores on a knowledge test are normally distributed with a mean of 60 anda standard deviation of 4.3. Scores on an aptitude test are normally distributed with a mean of 110 and a standard deviation of 7.1 Boris scored a 67 on the knowledge test and Callie scored 119 on the aptitude test. (a) Calculate the z-score for Boris. Round to the nearest hundredth. Show your work (b) Calculate the z-score for Callie. Round to the nearest hundredth. Show your work. (c) Who did relatively better on their test, Boris or Callie? Use the meaning of z-scores to explain
The Z-score for Boris is 1.627, and the Z-score value for the Callie is 1.267, Boris scored higher relatively.
What is Z-test?The Z test is a parametric procedure that is used on data that is dispersed in a normal fashion. For testing hypotheses, the z test can be used on one sample, two samples, or proportions. When the population variance is known, it analyzes if the means of two big groups are dissimilar.
We know the formula for the Z-test:
[tex]\rm Z = \dfrac{X-\mu}{\sigma}[/tex]
(a) For Boris:
[tex]\rm Z = \dfrac{67-60}{4.3}[/tex]
Z = 1.627
(b) For Callie:
[tex]\rm Z = \dfrac{119-110}{7.1}[/tex]
Z = 1.267
(c) Since the measures of two different data have been set to one measure and the value of the Z-score for Boris is higher relative to the Z-score value of Callie so Boris scored higher relatively.
Thus, the Z-score for Boris is 1.627, and the Z-score value for the Callie is 1.267, Boris scored higher relatively.
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please help! im a bit confused on this
There are 36 pieces of building blocks in a bag: 9 each of blue, green, red, and yellow. Four pieces are chosen at random. Identify the probability that all four of the pieces are red.
Answer:
2/935
Step-by-step explanation:
I have attached an image of the equation to use. Assuming that this is without replacement, we'll be taking out one piece out of the bag every time that one is chosen.
Therefore, for probability, the fraction is part/whole. We first have 9 red to 36 pieces in total, but if we take one out, we'll get 8 red left in the bag, and 35 pieces in total. This continues until we fulfill the prophecy (I don't know. qualifications?) that 4 of the pieces are red.
You can try this for yourself, but once simplified, it should be 3024/1413720, which simplifies to 2/935.
Please let me know if you need more clarification or have issues! probability can be confusing :)
Answer:
2/935
Step-by-step explanation:
dito^
What is the distance from the origin to point P graphed on the complex plane below?
Taylor has a punch bowl shaped like a cylinder, with a diameter of 22 inches and a height of 20 inches, she pours 8.25 gallons of punch into the bowl.
(note 1 gallon = 231 cubic inches)
How far from the top of the punch bowl is the top of the punch?
Answer:
1 gal =231 cu/in
r^2pi*ht=area
36pi*7= 791.68cu/in
231*3.25=750cu/in
41.68/(r^2pi)
=41.65/113.1=.368"
Step-by-step explanation:
Note that 1 gallon = 231 cubic inches.
Volume of liquid = 231 cubic inches = PI*R^2*H (equation for volume of a cylinder)
We have a radius (half diameter), so we can figure out the height of the liquid.
To figure how far below the top the liquid is, we subtract the height of the liquid from the height of the punch bowl (7 inches).
Is the following linear or nonlinear?
m = n 2 - 7n - 54
a) linear
b) nonlinear
I NEED HELP ASAP
====================================
[tex]\large \sf \underline{Problem:}[/tex]
Is the following linear or nonlinear?
m = n 2 - 7n - 54
a) linear
b) nonlinear
====================================
[tex]
\large \sf \underline{Answer:}[/tex]
A. Linear
====================================
[tex]\large \sf \underline{Explanation:}[/tex]
The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y).
====================================
Nine seconds elapsed from the time Mark saw the lightning until he heard the thunder. The lightning was about how many kilometers from Mark? (Sound travels about 331 meters per second in air.)
help statistics
no spam
Answer:
P = 20
Step-by-step explanation:
Mean
18.75 = 10(5) + 15(10) + P(7) + 25(8) + 30(2) / 3218.75 × 32 = 50 + 150 + 7P + 200 + 60600 = 460 + 7P7P = 140P = 20
A bus travels 9 miles north
and 4 miles west from its
original location.
How far is the bus from its
original location?
Answer:
3 miles?
Step-by-step explanation:
Here’s question two pls help
Answer:
Lake A
Step-by-step explanation:
FIrst off I am not sure how this connects with the lake but based on what I have seen and learned so far I would say that the Answer to #3 on the last question is Lake A and for the second part based on the data set I am unsure of how to do that but at least u got the answer to #3? sorry if this is no help.
Answer:
Total is 24
HALF THE TOTAL- 12
Impossible event- Picking a black marble
Certainty- Picking either one of a green, red, or blue marble
As likely as not event would be picking a blue marble(probability of that is 12/24= 1/2)
More likely than not event would be picking either a red or blue marble whose probability in total is 18/24= 3/4.
Unlikely event- You not picking anything at all
Step-by-step explanation:
Hi. Took me some time to attempt all problems, but the key to solving these problems is to ahve a firm foundation of basic probability. Things like likeliness and unlikelieness are all outskirts of probability, so I would reccomend getting yourself familiar with those basics. You GOT THIS!
i don’t understand how to find x
Find the output for the graph
y = -6x + 25
when the input value is 3.
=
y = [?]
Answer
[tex]x=\frac{11}{3}[/tex]
Explanation
Based on the given conditions, formulate:: [tex]y=3[/tex]
Substitute [tex]y=3[/tex] into [tex]y=-6x+25[/tex] :: [tex]3=-6x+25[/tex]
Rearrange variables to the left side of the equation: [tex]6x=25-3[/tex]
Calculate the sum or difference: [tex]6x=22[/tex]
Divide both sides of the equation by the coefficient of variable: [tex]x=\frac{22}{6}[/tex]
Cross out the common factor: [tex]x=\frac{11}{3}[/tex]
Can someone please help with my
Answer:
40%
Step-by-step explanation:
see photo for explanation of answer
A Crime scene investigator arrived at an auto accident to collect information. A car had hit a pedestrian sending a box he was carrying into the air. Luckily, the pedestrian was unharmed. In order to determine the speed the car was travelling at impact, the investigator needs to find out how high the box went into the air. Here aare the notes that he took from the scene. A 5 foot tall witness said that he saw the box fly up just above a tree next to where the accident happened. He was standing 25 feet from a tree. The angle of elevation as the witness looked up at the tree was 45. Determine the height of the tree, which will tell you the height the box flew into the air.
Answer:
no the height of the tree doesnt determine the heiht of the box, thatd be a pretty large box if so
If Alfonso increased his 401(k) plan contribution to 7%, how
much would be deducted each month for retirement?
Helpp
Answer:
20%
Step-by-step explanation:
sry if wrong byeeeeee
(Essay Worth 10 points) Below are the data collected from two random samples of 500 American students on the number of hours they spend in school per day (rounded to the nearest hour):
Meg concludes that students spend a mean of 7 hours in school each day. Tara thinks the mean is 6 hours. Who is correct—Meg or Tara? Explain your answer in two or three sentences. Make sure to use facts to support your answer.
The claim of Tara is correct about who thinks the mean of the students is 6 hours in school each day.
What is mean of the data set?The mean of the data is the average value of the given data. The mean of the data is the ratio of the sum of all the values of data to the total number of values of data.
The data which is collected from two random samples of a total 500 American students on the number of hours spend in school per day.
The mean of the data from sample A and B is,
[tex]\text{Mean}=\dfrac{4(70+80)+5(100+90)+6(125+120)+7(135+125)+8(70+85)}{70+80+100+90+125+120+135+125+70+85}\\\text{Mean}=\dfrac{6080}{1000}\\\text{Mean}=6.08[/tex]
The mean is approx 6 hours in school each day.
Now, Meg concludes that mean of students is 7 hours in school each day while Tara thinks the mean is 6 hours.
Thus, the claim of Tara is correct about who thinks the mean of the students is 6 hours in school each day.
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Plot the zeros of this function:
f(x)=(x-1)(x-7)
Answer:
The zeros of this function are x=(1,7)
Step-by-step explanation:
Mrs. Lee just bought a new rug. The rug is 7 feet long and 8 feet wide. What is the area of her rug?
What is the perimeter of the rhombus?
Answer:
20
Step-by-step explanation:
pythagorean theorum
a^2+b^2=c^2
4^2+3^2=c^2
16+9=25
[tex]\sqrt{25}[/tex]=5
5*4=20
help math grade 8 find the derivatives
Answer:
1. 7x^6
2. 25x^4
3. -3x^-4
4. -4x^-3
5. 20x
Step-by-step explanation:
Multiply the power by the coefficient, answer is your new coefficient. then reduce the power by 1.
Which equation represents a circle that contains the point (–2, 8) and has a center at (4, 0)? distance formula: startroot (x 2 minus x 1) squared (y 2 minus y 1) squared endroot (x – 4)2 y2 = 100 (x – 4)2 y2 = 10 x2 (y – 4)² = 10 x2 (y – 4)² = 100
The equation of a circle that contains the point (–2, 8) and has a center at (4, 0) is (x - 4)² + y² = 10²
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The circle contains the point (–2, 8) and has a center at (4, 0), hence:
[tex]radius=\sqrt{(0-8)^2+(4-(-2))^2}=10\ units[/tex]
The equation is:
(x - 4)² + (y - 0)² = 10²
(x - 4)² + y² = 10²
The equation of a circle that contains the point (–2, 8) and has a center at (4, 0) is (x - 4)² + y² = 10²
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Answer:
A
Step-by-step explanation:
the first one is the answer
A study you are reading gives the results of a 2 X 2 MANOVA with 6 dependent variables. Authors found significant omnibus main effects, but no significant interactions. What would be an appropriate next step according to materials covered in this course
The appropriate next step according to materials covered in this course is to examine post hoc pairwise comparisons.
What is a post hoc pairwise comparison?Pairwise Comparisons is known to be a kind or type of post-hoc analysis, where a person can compare the mean differences to that of a critical value.
Note that a post hoc tests tell a person, the key differences that exist between three or more set of means when an analysis of variance (ANOVA) F test is said to be significant just as in the case above.
See options below
Examine post hoc pairwise comparisons
Examine Levene’s test of equality of variance
Examine the results for each DV with 6 ANCOVAs
Examine the results for each DV with 6 ANOVAs
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How many different possible outcomes are there when five separate coins are tossed?
A. 16
B. 32
C. 8
D.4
Translate triangle ABC by the directed line segment from D to E. You may use digital tools or draw your answer and embed a screenshot of your work.
If you can observe
AB=BC=ACABC is an equilateral triangle
so
∆DEB is also equilateral triangle
DE=BD=BE=3.5There are 6 athletes at a track meet. How many different ways can they finish first or second?
A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 8
Blue 4
Green 17
Yellow 15
Purple 3
Based on these results, express the probability that the next spin will land on red or blue or green as a decimal to the nearest hundredth.
