Complete Question
Four spinners are spun. Spinner 1 has outcomes {1,2,3,4,5,6,7,8} Spinner 2 has outcomes {1,2,3,4,5,6} Spinner 3 has outcomes {1,2,3,4,5,6} Spinner 4 has outcomes {1,2,3,4,5} The outcomes for each spinner are equally likely. S is the sum of the numbers that come up on the spinners. What is the expected value of S?
Answer:
[tex]E(s)=14.5[/tex]
Step-by-step explanation:
From the question we are told that:
Spinner 1 ={1,2,3,4,5,6,7,8}
Spinner 2= {1,2,3,4,5,6}
Spinner 3 = {1,2,3,4,5,6}
Spinner 4 {1,2,3,4,5}
Generally the equation for expected outcome is mathematically given by
[tex]E(s)=\sum P(x).x[/tex]
Where
[tex]x=\frac{n(n+1)}{2}[/tex]
For Spinner 1
[tex]E(s_1)=\sum \frac{1}{8}*\frac{8(8+1)}{2}[/tex]
[tex]E(s_1)=4.5[/tex]
For Spinner 2
[tex]E(s_2)=\sum \frac{1}{6}*\frac{6(6+1)}{2}[/tex]
[tex]E(s_2)=3.5[/tex]
For Spinner 3
[tex]E(s_2)=E(s_3)[/tex]
For Spinner 3
[tex]E(s_4)=\sum \frac{1}{6}*\frac{6(6+1)}{2}[/tex]
[tex]E(s_4)=3[/tex]
Therefore The Expected Value
[tex]E(s)=\sum E(s 1..4)[/tex]
[tex]E(s)=4.5+2(3.5)+3[/tex]
[tex]E(s)=14.5[/tex]
A health club sold ten memberships in one week for total of $3000. If male memberships cost $300 and female memberships cost $300, then how many male memberships and how female memberships were sold?
Answer:
Step-by-step explanation:
The reason you haven't gotten an answer to this is because in its current formatting, there is no answer. Here's what I mean:
The first equation is going to be concerning the NUMBER of memberships sold, where m is male and f is female. The total number of memberships was 10:
m + f = 10
Now for the money equation. The total amount of money made from that number of memberships was 3000, where male memberships cost $300 and so do the female memberships, giving us an equation of
300m + 300f = 3000
Go back to the first equation and solve for either m or f. I solved for m in terms of f:
m = 10 - f and sub that into the second equation for m to get:
300(10 - f) + 300f = 3000 and
3000 - 300f + 300f = 3000. Here is where you find the problem. The -300f and the 300f cancel each other out, leaving you with the fact that
3000 = 3000 which it does, but it doesn't give us any viable answer.
I would have to say that since we can't do math on this, that the most credible answer you'll find is that the same number of male and female memberships were sold because 5 male memberships cost $1500 (5 memberships at $300 a piece is $1500) and 5 female memberships also cost $1500.
1500 + 1500 = 3000
Which of the following numbers has the greatest value?
89 3/4
66 1/2
55 2/3
74 1/4
106 5/6
Answer:
106 5/6
Step-by-step explanation:
55 < 66 < 74 < 89 < 106
the fractions are irrelevant because the whole numbers are all different
The greatest of the numbers will be 106 5/6 since 106 is greater than the rest of the integers present in the mixed fractions.
Finding greatest value in a sequenceThe greatest value is the highest value in a given set of number.
Given the following numbers
89 3/4
66 1/2
55 2/3
74 1/4
106 5/6
The greatest of the numbers will be 106 5/6 since 106 is greater than the rest of the integers present in the mixed fractions.
Learn more on mixed fractions here: https://brainly.com/question/414559
#SPJ6
welp I am getting graded for this
Answer:
it is summer how do y'all still have school,like don't they give y'all a break
what is the value of sum of 18 and 3 time the difference of 9 and 5 divided by 2 is subtracted from 30 ?
if u give right answer i will mark u as a brainlist
Answer:
12
Step-by-step explanation:
(18+3)=21
(9-5)=4
4x21=84
84/2=42
42-30=12
Answer:
12
Step-by-step explanation:
((18+3)x(9-5))/2-30
=((21)x(4))/2-30
=(84)/2-30
=42-30
=12
A normal distribution has a mean of 15 and a standard deviation of 2. Find the value that corresponds to the 75th
percentile. Round your answer to two decimal places.
N
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.5
0.6915
0.6950
0.6985
0.7019
0.7054
0.7088
0.7123
0.7157
0.7190
0.7224
0.6 0.7257
0.7291
0.7324
0.7357
0.7389 0.7422
0.7454
0.7486
0.7517
0.7549
0.7 0.7580
0.7611
0.76420.7673
0.7704
0.7734
0.7764
0.7794
0.7823
0.7852
0.8
0.7881
0.7910
0.7939
0.7967
0.7995
0.8023
0.8051
0.8078
0.8106
0.8133
Please I need help :(
Answer:
A. x-2y-3z = 1/2
Step-by-step explanation:
yess.. if you take solve every equation then you will get same equation from all the equations
someone help me pls i need to pass summer school
Answer:
A
Step-by-step explanation:
The be the inverse function the domain {4,5,6,7} becomes the range and the range {14,12,10,8} becomes the domain
14 → 4
12 →5
10 →6
8 →7
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s = 17.6 milligrams.
Required:
Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.
Answer:
CI ≈ (173.8 < μ < 196.2)
Step-by-step explanation:
We are told that laboratory tested twelve chicken eggs. Thus;
n = 12
Mean; x¯ = 185 mg
S.D; s = 17.6 mg
DF = n - 1 = 12 - 1 = 11
We have a 95% confidence level. Thus; α = 0.05
Since n < 30, we will use t-sample test.
Thus, from t-table attached at 95% Confidence level and DF = 11, we have;
t = 2.201
Thus,formula for Confidence interval is;
CI = (x¯ - t(s/√n)) < μ < (x¯ + t(s/√n))
CI = (185 - 2.201(17.6/√12)) < μ < (185 + 2.201(17.6/√12))
CI = (185 - 11.1825) < μ < (185 + 11.1825)
CI = (173.8175 < μ < 196.1825)
CI ≈ (173.8 < μ < 196.2)
how to solve this trig
Hi there!
To find the Trigonometric Equation, we have to isolate sin, cos, tan, etc. We are also given the interval [0,2π).
First Question
What we have to do is to isolate cos first.
[tex] \displaystyle \large{ cos \theta = - \frac{1}{2} }[/tex]
Then find the reference angle. As we know cos(π/3) equals 1/2. Therefore π/3 is our reference angle.
Since we know that cos is negative in Q2 and Q3. We will be using π + (ref. angle) for Q3. and π - (ref. angle) for Q2.
Find Q2
[tex] \displaystyle \large{ \pi - \frac{ \pi}{3} = \frac{3 \pi}{3} - \frac{ \pi}{3} } \\ \displaystyle \large \boxed{ \frac{2 \pi}{3} }[/tex]
Find Q3
[tex] \displaystyle \large{ \pi + \frac{ \pi}{3} = \frac{3 \pi}{3} + \frac{ \pi}{3} } \\ \displaystyle \large \boxed{ \frac{4 \pi}{3} }[/tex]
Both values are apart of the interval. Hence,
[tex] \displaystyle \large \boxed{ \theta = \frac{2 \pi}{3} , \frac{4 \pi}{3} }[/tex]
Second Question
Isolate sin(4 theta).
[tex] \displaystyle \large{sin 4 \theta = - \frac{1}{ \sqrt{2} } }[/tex]
Rationalize the denominator.
[tex] \displaystyle \large{sin4 \theta = - \frac{ \sqrt{2} }{2} }[/tex]
The problem here is 4 beside theta. What we are going to do is to expand the interval.
[tex] \displaystyle \large{0 \leqslant \theta < 2 \pi}[/tex]
Multiply whole by 4.
[tex] \displaystyle \large{0 \times 4 \leqslant \theta \times 4 < 2 \pi \times 4} \\ \displaystyle \large \boxed{0 \leqslant 4 \theta < 8 \pi}[/tex]
Then find the reference angle.
We know that sin(π/4) = √2/2. Hence π/4 is our reference angle.
sin is negative in Q3 and Q4. We use π + (ref. angle) for Q3 and 2π - (ref. angle for Q4.)
Find Q3
[tex] \displaystyle \large{ \pi + \frac{ \pi}{4} = \frac{ 4 \pi}{4} + \frac{ \pi}{4} } \\ \displaystyle \large \boxed{ \frac{5 \pi}{4} }[/tex]
Find Q4
[tex] \displaystyle \large{2 \pi - \frac{ \pi}{4} = \frac{8 \pi}{4} - \frac{ \pi}{4} } \\ \displaystyle \large \boxed{ \frac{7 \pi}{4} }[/tex]
Both values are in [0,2π). However, we exceed our interval to < 8π.
We will be using these following:-
[tex] \displaystyle \large{ \theta + 2 \pi k = \theta \: \: \: \: \: \sf{(k \: \: is \: \: integer)}}[/tex]
Hence:-
For Q3
[tex] \displaystyle \large{ \frac{5 \pi}{4} + 2 \pi = \frac{13 \pi}{4} } \\ \displaystyle \large{ \frac{5 \pi}{4} + 4\pi = \frac{21 \pi}{4} } \\ \displaystyle \large{ \frac{5 \pi}{4} + 6\pi = \frac{29 \pi}{4} }[/tex]
We cannot use any further k-values (or k cannot be 4 or higher) because it'd be +8π and not in the interval.
For Q4
[tex] \displaystyle \large{ \frac{ 7 \pi}{4} + 2 \pi = \frac{15 \pi}{4} } \\ \displaystyle \large{ \frac{ 7 \pi}{4} + 4 \pi = \frac{23\pi}{4} } \\ \displaystyle \large{ \frac{ 7 \pi}{4} + 6 \pi = \frac{31 \pi}{4} }[/tex]
Therefore:-
[tex] \displaystyle \large{4 \theta = \frac{5 \pi}{4} , \frac{7 \pi}{4} , \frac{13\pi}{4} , \frac{21\pi}{4} , \frac{29\pi}{4}, \frac{15 \pi}{4} , \frac{23\pi}{4} , \frac{31\pi}{4} }[/tex]
Then we divide all these values by 4.
[tex] \displaystyle \large \boxed{\theta = \frac{5 \pi}{16} , \frac{7 \pi}{16} , \frac{13\pi}{16} , \frac{21\pi}{16} , \frac{29\pi}{16}, \frac{15 \pi}{16} , \frac{23\pi}{16} , \frac{31\pi}{16} }[/tex]
Let me know if you have any questions!
What is the length of de?
Answer: length of DE = 18
Step-by-step explanation:
Since the angles of these two triangles are the same, we can assume that they are similar triangles. To solve for a missing side of a triangle that is similar, you can set up a proportion:
[tex]\frac{27}{15}=\frac{x}{10}[/tex]
To solve for x (the missing length), you would do:
27 × 10 ÷ 15 = 18
You can set up the proportion in any way between the two triangles as long as the two sides correspond to each other. For example, you could have also used the following proportion to solve for x:
[tex]\frac{x}{27} =\frac{10}{15}[/tex]
When you solve for x using this proportion, you would get the same value for x:
10 × 27 ÷ 15 = 18
If you apply the changes below to the absolute value parent function F(x)= |x|, What is the new function? Shift 5 units to the left, shift 4 units down.
solve x^3-7x^2+7x+15
Step-by-step explanation:
\underline{\textsf{Given:}}
Given:
\mathsf{Polynomial\;is\;x^3+7x^2+7x-15}Polynomialisx
3
+7x
2
+7x−15
\underline{\textsf{To find:}}
To find:
\mathsf{Factors\;of\;x^3+7x^2+7x-15}Factorsofx
3
+7x
2
+7x−15
\underline{\textsf{Solution:}}
Solution:
\textsf{Factor theorem:}Factor theorem:
\boxed{\mathsf{(x-a)\;is\;a\;factor\;P(x)\;\iff\;P(a)=0}}
(x−a)isafactorP(x)⟺P(a)=0
\mathsf{Let\;P(x)=x^3+7x^2+7x-15}LetP(x)=x
3
+7x
2
+7x−15
\mathsf{Sum\;of\;the\;coefficients=1+7+7-15=0}Sumofthecoefficients=1+7+7−15=0
\therefore\mathsf{(x-1)\;is\;a\;factor\;of\;P(x)}∴(x−1)isafactorofP(x)
\mathsf{When\;x=-3}Whenx=−3
\mathsf{P(-3)=(-3)^3+7(-3)^2+7(-3)-15}P(−3)=(−3)
3
+7(−3)
2
+7(−3)−15
\mathsf{P(-3)=-27+63-21-15}P(−3)=−27+63−21−15
\mathsf{P(-3)=63-63}P(−3)=63−63
\mathsf{P(-3)=0}P(−3)=0
\therefore\mathsf{(x+3)\;is\;a\;factor}∴(x+3)isafactor
\mathsf{When\;x=-5}Whenx=−5
\mathsf{P(-5)=(-5)^3+7(-5)^2+7(-5)-15}P(−5)=(−5)
3
+7(−5)
2
+7(−5)−15
\mathsf{P(-5)=-125+175-35-15}P(−5)=−125+175−35−15
\mathsf{P(-5)=175-175}P(−5)=175−175
\mathsf{P(-5)=0}P(−5)=0
\therefore\mathsf{(x+5)\;is\;a\;factor}∴(x+5)isafactor
\underline{\textsf{Answer:}}
Answer:
\mathsf{x^3+7x^2+7x-15=(x-1)(x+3)(x+5)}x
3
+7x
2
+7x−15=(x−1)(x+3)(x+5)
\underline{\textsf{Find more:}}
Find more:
A stick 1 meter long casts a shadow 1.3 meters long. A building casts a shadow 25 meters long. How tall is the building (to 2 decimal places)
Answer: 19.23 meters
Step-by-step explanation:
1/1.3 = x/25
(1) (25) / 1.3
= 19.23 meters
ty
This graph shows a portion of an even function.
Use the graph to complete the table of values.
6
f(x)
-1
4
-3
-5
-6
2
DONE
2
4.
6
Answers:
first box = 1second box = 1third box = 3fourth box = 3Refer to the graph below.
==========================================================
Explanation:
If f(x) is an even function, then f(-x) = f(x) for all x in the domain.
What this means is that we have symmetry about the y axis. We can reflect that given curve over the y axis to generate the missing left side.
The graph shows that (1,1) is on the orange curve. It reflects over to (-1,1). This means 1 goes in the first box.
Use the rule [tex](x,y) \to (-x,y)[/tex] to apply a y axis reflection. We simply just change the sign of the x coordinate from positive to negative, while keeping the y coordinate the same.
---------------
We can also see that (3,1) is also on the orange curve. It reflects over to (-3, 1) using that rule mentioned earlier.
1 goes in the second box
---------------
The graph your teacher gave you shows that if we plugged in x = 5, then we get y = 3. In other words, the point (5,3) is on the orange graph.
It reflects over to (-5, 3) to show that x = -5 leads to the output y = 3
3 goes in the third box
----------------
Lastly, the point (6,3) reflects to (-6,3) when reflecting over the y axis.
3 goes in the fourth box.
See the graph below.
Average person who drives car in United States drives 15, 350 miles which is 50% more than an average driver in Europe. We assume that the number of yearly miles by U.S. drivers is approximately a normal random variable of standard deviation of 4200 miles. Calculate percent of drivers who traveled between 10,000 to 12,000 miles in a year.
Answer:
7,675
that is your answer
5 times a certain number plus 6 has the same value as two times the same number minus 3 what is the number
Let the number be x
ATQ
[tex]\\ \sf\longmapsto 5x+6=2x-3[/tex]
[tex]\\ \sf\longmapsto 5x-2x=-3-6[/tex]
[tex]\\ \sf\longmapsto 3x=-9[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-9}{3}[/tex]
[tex]\\ \sf\longmapsto x=-3[/tex]
i need help ON THIS PLS
Answer:
No, because the ratio of pay to hours is not the same for each pair of value.
A physical trainer decides to collect data to see if people are actually weight changing weight during the shelter in place. He believes there will not be a meaningful change in weight due to the shelter in place order. He randomly chooses a sample of 30 of his clients. From each client, he records their weight before the shelter in place order, and again 10 days after the order. A summary of the data is below.
The trainer claims, "on average, there is no difference in my clients' weights before and after the shelter in place order." Select the pair of hypotheses that are appropriate for testing this claim.
H0: µd = 0
H1: µd < 0 (claim)
H0: µd = 0 (claim)
H1: µd ≠ 0
H0: µd ≠ 0 (claim)
H1: µd = 0
H0: µd = 0 (claim)
H1: µd > 0
H0: µd = 0
H1: µd > 0 (claim)
H0: µd = 0
H1: µd ≠ 0 (claim)
H0: µd = 0 (claim)
H1: µd < 0
H0: µd ≠ 0
H1: µd = 0 (claim)
b) Select the choice that best describes the nature and direction of a hypothesis test for this claim.
This is a right-tail t-test for µd.
This is a right-tail z-test for µd.
This is a two-tail t-test for µd.
This is a two-tail z-test for µd.
This is a left-tail t-test for µd.
This is a left-tail z-test for µd.
c) Find the standardized test statistic for this hypothesis test. Round your answer to 2 decimal places.
d) Find the P-value for this hypothesis test. Round your answer to 4 decimal places.
e) Using your previous calculations, select the correct decision for this hypothesis test.
Fail to reject the alternative hypothesis.
Reject the alternative hypothesis.
Fail to reject the claim.
Reject the claim.
Fail to reject the null hypothesis.
Reject the null hypothesis.
f) Consider the following statements related to the trainer's claim. Interpret your decision in the context of the problem (ignoring the claim) and interpret them in the context of the claim.
Answer:
H0: µd = 0 (claim)
H1: µd ≠ 0
This is a two-tail t-test for µd
Step-by-step explanation:
This is a paired (dependent) sample test, with its hypothesis is written as :
H0: µd = 0
H1: µd ≠ 0
From the equality sign used in the hypothesis declaration, a not equal to ≠ sign in the alternative hypothesis is used for a two tailed t test
The data isn't attached, however bce the test statistic cannot be obtained. However, the test statistic formular for a paired sample is given as :
T = dbar / (Sd/√n)
dbar = mean of the difference ; Sd = standard deviation of the difference.
A note card company has found that the marginal cost per card of producing x note cards is given by the function below, where C'(x) is the
marginal cost, in cents, per card. Find the total cost of producing 900 cards, disregarding any fixed costs.
C'(x) = -0.05x + 77, for x S 1000
The total cost is
cents
Answer:
49,050cents
Step-by-step explanation:
Given the expression for calculating the marginal cost per card of producing x note cards expressed as
C'(x) = -0.05x + 77
On intergrating the marginal cost, we will get the total cost
C(x) = -0.05x²/2 + 77x
Substitute x = 900 into the resulting expression
C(900) = -0.05(900)²/2 + 77(900)
C(900) = -20,250+69,300
C(900) = 49,050
Hence the total costs in cents is 49,050cents
can somebody help with this please
Answer:
"D"
Step-by-step explanation:
just add the two functions
5x^2 - 8x^2 = -3x^2 etc
Tuition. The tuition at a community college increased from $2,500 to $2,650 per semester. What was the percent of increase in the tuition?
Answer:
6 percent increase
Step-by-step explanation:
2650 divided by 2500 gives you 1.06 which means if 2500 is 100 percent 2650 would be 106 percent so the answer is a 6 percent increase
Answer:
6%
Step-by-step explanation:
another way of doing this type of calculation is...
NEW-OLD = 2650-2500 = 150 = .06 = 6%
OLD 2500 2500
Categorize the trigonometric functions as positive or negative.
Answer:
So, remember that:
cos(x) > 0 for -pi/2 < x < pi/2
cos(x) < 0 for pi/2 < x < (3/2)*pi
and
sin(x) > 0 for 0 < x < pi
sin(x) < 0 for -pi < x <0 or pi < x < 2pi
Also, we have the periodicty of the sine and cocine equations, such that:
sin(x) = sin(x + 2pi)
cos(x) = cos(x + 2pi)
Now let's solve the problem:
[tex]sin(\frac{13*\pi}{36} )[/tex]
here we have:
x = (13/36)π
This is larger than zero and smaller than π:
0 < (13/36)π < π
then:
[tex]sin(\frac{13*\pi}{36} )[/tex]
Is positive.
The next one is:
[tex]cos(\frac{7*\pi}{12} )[/tex]
Here we have x = (7/12)*pi
notice that:
7/12 > 1/2
Then:
(7/12)*π > (1/2)*π
Then:
[tex]cos(\frac{7*\pi}{12} )[/tex]
is negative.
next one:
[tex]sin(\frac{47*\pi}{36} )[/tex]
here:
x = (47/36)*π
here we have (47/36) > 1
then:
(47/36)*π > π
then:
[tex]sin(\frac{47*\pi}{36} )[/tex]
is negative.
the next one is:
[tex]cos(\frac{17*\pi}{10} )[/tex]
Here we have x = (17/10)*π
if we subtract 2*π (because of the periodicity) we get:
(17/10)*π - 2*π
(17/10)*π - (20/10)*π
(-3/10)*π
this is in the range where the cosine function is positive, thus:
[tex]cos(\frac{17*\pi}{10} )[/tex]
is positive.
the next one is:
[tex]tan(\frac{41*\pi}{36} ) = \frac{sin(\frac{41*\pi}{36} )}{cos(\frac{41*\pi}{36} )}[/tex]
here we have:
x = (41/36)*π
Notice that both functions, sine and cosine are negatives for that value, then we have the quotient of two negative values, so:
[tex]tan(\frac{41*\pi}{36} ) = \frac{sin(\frac{41*\pi}{36} )}{cos(\frac{41*\pi}{36} )}[/tex]
is positive.
The final one is:
[tex]tan(\frac{5*\pi}{9} ) = \frac{sin(\frac{5*\pi}{9} )}{cos(\frac{5*\pi}{9} )}[/tex]
Here:
x = (5/9)*π
The sin function is positive with this x value, while the cosine function is negative, thus:
[tex]tan(\frac{5*\pi}{9} ) = \frac{sin(\frac{5*\pi}{9} )}{cos(\frac{5*\pi}{9} )}[/tex]
Is negative.
Which rules of exponents will be used to evaluate the expression. Check all that apply.
[
1791
quotient of powers
product of powers
power of a power
power of a product
negative exponent
zero exponent
Answer:
product of power
Step-by-step explanation:
I think this will help you
Why is the value of -9 is not-3
Answer:
Because it's a negative.
Step-by-step explanation:
The value of a positive number is still a positive number.
13. 30 of the 100 iPads in an inventory are known to be cracked. What
is the probability you randomly select one that is not cracked?
Answer:
7/10 or 0.7
Step-by-step explanation:
a probability is always the ratio of possible cases over all cases.
"all cases" here is 100.
possible cases are all iPads not cracked in the inventory = 70 (because 30 are cracked, that leaves 100-30=70 not cracked).
so, the probability to select a non-cracked unit is
70/100 or simplified 7/10 (or 0.7)
Find the length of the missing sides
Answer:
f = 10
g = 2 sqrt(3)
h = 20
Step-by-step explanation:
The short leg is opposite the smaller angle so it is f
The longer leg is opposite the larger angle so it is g
The hypotenuse is opposite the right angle so it is 20
We know f = x
g = x sqrt(3)
h = 2x = 20
2x = 20 so x = 10
f = 10
g = 2 sqrt(3)
h = 20
PLEASE I NEED A REAL ANWSER NO LIES
Part A: The area of a square is (9a2 − 24a + 16) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points)
Part B: The area of a rectangle is (25a2 − 36b2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)
Answer:
(3a - 4 )^2
Step-by-step explanation:
(9a^2-24a+16)=(3a - 4 )^2
Therefore the length of each side of the square is (3a - 4 )^2
Answer:
Part A: (3a - 4)^2
Part B: (5a + 6b)(5a - 6b)
Step-by-step explanation:
Part A:
It looks like this is the square of a binomial. Now we check it.
9a^2 is the square of 3a.
16 is the square of 4 and of -4.
Check the middle term:
2 * 3a * 4 = 24a
2 * 3a * (-4) = -24a
Since we get -24a when we use 4, the second term of the binomial is 4.
Answer:
9a^2 - 24a + 16 = (3a - 4)^2
Part B:
25a^2 − 36b^2
This is a two-term polynomial. The two terms are perfect squares and there is a subtraction sign between them, so this is the difference of two squares. The difference of two squares factors into the product of a sum and a difference.
25a^2 is the square of 5a.
36b^2 is the square of 6b.
25a^2 − 36b^2 = (5a + 6b)(5a - 6b)
An expression is shown below:
6x2y − 3xy − 24xy2 + 12y2
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
Given:
The given expression is:
[tex]6x^2y-3xy-24xy^2+12y^2[/tex]
To find:
Part A: The expression by factoring out the greatest common factor.
Part B: Factor the entire expression completely.
Solution:
Part A:
We have,
[tex]6x^2y-3xy-24xy^2+12y^2[/tex]
Taking out the highest common factor 3y, we get
[tex]=3y(2x^2-x-8xy+4y)[/tex]
Therefore, the required expression is [tex]3y(2x^2-x-8xy+4y)[/tex].
Part B:
From part A, we have,
[tex]3y(2x^2-x-8xy+4y)[/tex]
By grouping method, we get
[tex]=3y(x(2x-1)-4y(2x-1))[/tex]
[tex]=3y(x-4y)(2x-1)[/tex]
Therefore, the required factored form of the given expression is [tex]3y(x-4y)(2x-1)[/tex].
scientist has two solutions, which she has labeled solution a and solution b. solution a is 60% salt and solution b is 85% salt. she wants to obtain 140 ounces of mixture that is 80% salt. How many ounces of each solution should she use?
Answer:
We have 60% salt and 85% salt solutions and we need 140 ounces of a solution that is 80% salt.
We set up 2 equations:
A) x + y = 140
B) .60x + .85y = .80 * 140
Multiply equation A) by -.60
A) -.60x -.60y = -84 then we add this to B)
B) .60x + .85y = 112
.25y = 28
y = 112 ounces of 85% salt
x = 28 ounces of 60% salt.
Double Check
112 * .85 = 95.2 AND 28 * .60 = 16.80
95.2 + 16.80 = 112
and 112/140 = 80 per cent!!
Source: http://www.1728.org/mixture.htm
Step-by-step explanation:
The answer the the question pictured
Answer:
x-1/2x-3
Step-by-step explanation:
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