Answers
Answer:
The dimensions of the rectangle are:
2a^2b^2 and 3ab^2 + 5a + 7b
Step-by-step explanation:
The question is asking for the length and width of the rectangle, and gives you an equation that shows the area of the rectangle. It says to factor out the GCF to find these dimensions. In simpler terms, the question wants you to divide the equation for the area, 6^3b^4 + 14a^2b^3 + 10a^3b^2, into two different equations for the length and width, which can't be divided more.
We have three terms to find the greatest common factor (GCF) of. 6^3b^4, 14a^2b^3, and 10a^3b^2. First, let's factor out the 2. This leaves us with
2(3^3b^4 + 7a^2b^3 + 5a^3b^2)
It seems like we're done with factoring out coefficients, for 3, 5, and 7 are all prime. Now, variables. Each term has a factor of a^2b^2. (not more, for this is the limit of 14a^2b^2.)
2a^2b^2(3ab^2 + 7b + 5a) . (this is the same as the answer above, but I changed the order of 7b and 5a there because some online things are specific and don't like it if you don't put the equations in order.)
And that's it!
Related Questions
Find the surface area of the square pyramid.
S=
Answers
what is the lenght of rectangle whose area is 240cm
Answers
Answer:
16
Step-by-step explanation:
I don't know how to explain but it is 16
Answer:
Since the Width (W) of the rectangle is not given, the answer would be Length (L) = 240/W
Step-by-step explanation:
A = L*W
240 = L*W
240/W = L
A ski resort claims that there is a 75% chance of snow on any given day in January and that snowfall happens independently from one day to the next. A family plans a four-day trip to this ski resort in January. Let X represent the number of days it snows while the family is there. What are the mean and standard deviation of X?
Option Choices:
Answers
Answer:
Its D
Step-by-step explanation:
Using the binomial distribution, it is found that the mean and the standard deviation of X are given as follows:
[tex]\mu_X = 3, \sigma_X = 0.87[/tex]
What is the binomial probability distribution?The expected value of the binomial distribution is:
[tex]\mu_X = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sigma_X = \sqrt{np(1-p)}[/tex]
In this problem, the proportion and the sample size are given as follows:
p = 0.75.n = 4.Hence, the mean and the standard deviation are given by:
[tex]\mu_X = np = 4(0.75) = 3[/tex]
[tex]\sigma_X = \sqrt{np(1-p)} = \sqrt{4(0.75)(0.25)} = 0.87[/tex]
More can be learned about the binomial distribution at https://brainly.com/question/24863377
#SPJ2
A pollster believes that 20% of the voters in a certain area favor a bond issue. If 49 voters are randomly sampled from the large number of voters in this area, approximate the probability that the sampled fraction of voters favoring the bond issue will not differ from the true fraction by more than 0.08. (Round your answer to four decimal places.)
Answers
Answer:
The probability that the sampled fraction of voters favoring the bond issue will not differ from the true fraction by more than 0.08 is 0.7698
Step-by-step explanation:
Given
n = 64
p = 0.20
X/n -p < 0.06
x-np <0.06n
x-np <0.06 * 64
x-np <3.84
Z score
= (x-np)/sqrt (np(1-p))
= -3.84/ sqrt (64*0.20*0.80)
= -1.20
P (x/n-p<0.06) = P(-1.2<z<1.20) = 1-2*0.1151 = 0.7698
One recipe makes 8 1/2 cups of potato salad. If one serving is 1/2 cup, how many servings does the recipe make?
Answers
Answer:
17
Step-by-step explanation:
8.5 / 0.5
A marketing research firm would like to survey undergraduate and graduate college students about whether or not they take out student loans for their education. There are different cost implications for the region of the country where the college is located and the type of degree. The survey cost table is provided below:
Student type
Region undergraduate graduate
East $10 $15
Central $12 $18
West $15 $21
The requirements for the survey are as follows:
The survey must have at least 1500 students.
At least 400 graduate students.
At least 100 graduate students should be from the West
No more than 500 undergraduate students should be from the East
At least 75 graduate students should be from the Central region
At least 300 students should be from the West
The marketing research firm would like to minimize the cost of the survey while meeting the requirements. Let X1 = # of undergraduate students from the East region, X2 = # of graduate students from the East region, X3 = # of undergraduate students from the Central region, X4 = # of graduate students from the Central region, X5 = # of undergraduate students from the West region, and X6 = # of graduate students from the West region.
Required:
Clearly state the problem (objective function, constraints)
Answers
Answer:
Objective Minimize 10x1 +15x2 + 12x3+18x4+15x5+ 21x6
The central total cost $ 17586 due to the number of central undergraduate students 1458 is very high.
The total minimum cost would $ 17586 +$260+ $300= $ 18146
Step-by-step explanation:
Let
X1 = # of undergraduate students from the East region,
X2 = # of graduate students from the East region,
X3 = # of undergraduate students from the Central region,
X4 = # of graduate students from the Central region,
X5 = # of undergraduate students from the West region, and
X6 = # of graduate students from the West region.
Then the cost functions are
y1= 10x1 +15x2
y2= 12x3+18x4
y3= 15x5+ 21x6
According to the given conditions
The constraints are
x1 +x2 + x3+x4+ x5+ x6 ≥ 1500------- A
15X2 +18X4+21X6 ≥ 400---------B
21X6 ≥ 100
X6 ≥ 100/21
X6 ≥ 4.76
Taking
X6= 5
10X1 ≤ 500
X1 ≤ 500/10
X1≤ 5
18X4 ≥ 75
X4 ≥ 75/18
X4 ≥ 4.167
Taking
X4= 5
Putting the values
15X5+ 21X6 ≥ 300
15X5+ 21(5) ≥ 300
15X5+ 105 ≥ 300
15X5 ≥ 300-105
15X5 ≥ 195
X5 ≥ 195/15
X5 ≥ 13
Putting value of X6 and X4 in B
15X2 +18X4+21X6 ≥ 400
15X2 +18(5)+21(5) ≥ 400
15X2 +195 ≥ 400
15X2 ≥ 400-195
15X2 ≥ 205
X2 ≥ 205/15
X2 ≥ 13.67
Taking X2= 14
Now putting the values in the cost equations to check whether the conditions are satisfied.
y1= 10x1 +15x2
y1= 10 (5) + 15(14)= 50 + 210= $ 260
y3= 15x5+ 21x6
y3= 15 (13) + 21(5)
y3= 195+105= $ 300
x1 +x2 + x3+x4+ x5+ x6 ≥ 1500
5+14+x3+5+13+5≥ 1500
x3≥ 1500-42
x3≥ 1458
y2= 12x3+18x4
y2= 12 (1458) + 18 (5)
y2= 17496 +90
y2= $ 17586
The cost can be minimized if the number of students from
Undergraduate Graduate
East Region X1≤ 5 X2 ≥ 13.67
Central X3≥ 1458 X4 ≥ 4.167
West X5 ≥ 13 X6 ≥ 4.76
This will result in the required number of students that is 1500
Constraints:
East Undergraduate must not be greater than 5
East Graduate must not be less than 13
Central Undergraduate must be greater than 1458
Central Graduate must be greater than 4
West Undergraduate must be greater than 13
West Graduate must be greater than 4
The central total cost $ 17586 due to the number of central undergraduate students 1458 is very high.
The east region has a least cost of $260 and west region has a cost of $300.
The total minimum cost would $ 17586 +$260+ $300= $ 18146
A 10 foot ladder is leaning against a building. It forms a 30 degree angle with the ground. How far away from the building is the foot of the ladder? Round your answer to the nearest hundredth. 5 feet, 5.77 feet, 8.66 feet, or 20 feet
Answers
x = 8.66 ft
Step-by-step explanation:
cos 30 = adj/hyp = x/10
---> x = (10 ft)cos30
= 8.66 ft
Find the perimeter of a
hexagon with each side
measuring 184 ft.?
Answers
Answer:
P = 1104
a - Side
Step-by-step explanation:
P = 1104
a - Side
Answer:
P=1140
Step-by-step explanation:
P=1140 BANANA SORRY THE ANSWER I DONT HAVE IT BUT HAVE A GOOD DAY
A researcher collected data on years spent in college and yearly income. He found that the longer someone is in college, the lower his/her income is. Which of the following is true based on this research? Select all that apply.
The line of best fit for this data would be increasing from left to right on the scatter plot.
The slope of the line of best fit for this data would be negative.
The -intercept for the line of best fit for this data would be zero.
The line of best fit for this data is horizontal because the variables are not related.
If you divided the data into two groups and found the average years of college and average yearly income from each of the two groups, you could find the estimated slope of the line of best fit by using the slope formula on those representative points.
Answers
Answer:
A
Cdfvvbghnjmk,l.;/‘Step-by-step explanation:
[tex]\tt\red{See \; attachment!}[/tex]
hi what is the answerr??
Answers
Given:
The rule of input and output function is:
[tex]25-g[/tex]
To find:
The answer if we put 19.
Solution:
Consider the input and output function is:
[tex]f(g)=25-g[/tex]
Substitute [tex]g=19[/tex], we get
[tex]f(19)=25-19[/tex]
[tex]f(19)=6[/tex]
Therefore, the required answer is 6.
0.5 mg/mL = ___________ mcg/mL
Answers
Answer: 500 mcg/mL
Step-by-step explanation: 0.5 mg/mL = ___________ mcg/mL
0.5 mg/mL(1000)
500 mcg/mL
Answer:
500 mcg / mL
Step-by-step explanation:
this is the ansa when u do 0.5 mg/mL = ___________ mcg/mL
simplify: The question in photo
Answers
Answer:
Step-by-step explanation:
If the graph of f(x) = |x| is shifted up 5 units, what would be the equation of the new graph?
A. g(x) = |x + 5|
B. g(x) = |x| + 5
C. g(x) = |x| - 5
D. g(x) = |x - 5|
Answers
Answer:
B. g(x)= |x| + 5
Step-by-step explanation:
-5 represents a vertical shift down, so that narrows it down to either A or B. A shows a shift across the horizontal (X) axis, so it must be B.
Eight members of a school marching band are auditioning for 3 drum major
positions. How many ways can students be chosen to be drum major?
*
Answers
Answer:
Step-by-step explanation:
WITHIN THE NEXT 5 MIN I WILL GIVE U BRAINIEST
50 POINTS
1. Harold is at the bottom of the
Grand Canyon but he forgot his
phone at the top of the trail. We
decide to help him and lower his
phone to him. After the first
second, it is 16 feet closer to him,
after three seconds, it is 80 feet
closer to him. If the Grand
Canyon is 6000 feet deep, how
long will it take for the phone to
reach Harold?
Answers
Opps, wrong answer
Deleted
PLEASE HELP ILL GIVE BRAINLIEST AND A THANKS
Answers
Answer:
[tex]forth \: line \: - 5x - 3x + 3 = 6 \\ - 8x + 3 = 6 \\ - 8x = 3 \\ x = \frac{3}{ - 8} [/tex]
Find dy/dx if f(x) = x²+9²
Answers
Answer:
let y=x²+9²
dy/dx=dx²/dx+d9²/dx
=[tex]2 x^{2-1}+0[/tex]
=2x is a required answer.
Find the volume of this solid figure. Use π = 3.14.
WITH SOLUTION PLEASE AND NO LINKS!
Answers
Step-by-step explanation:
you can get simply V= ABh πr^2 h π3.14^2 x 17.9 then you get the answer Ihope I can help you
Find the probability that a randomly selected dog owner
spent $100 or more on health care and the dog was a
mixed breed. (Type your answer in SIMPLIEST form)
Answers
If the standard deviation of the data values in a sample is 13, what is the
variance of the data values?
A. 169
B. 225
C. 289
D. 361
Answers
Answer:
A. 169 is the correct answer
the store is selling lemons at 0.53 each. each lemon yields about 2 tablespoons of juice. how much will it cost to buy enough lemons to make three 9inch lemon pies, each requiring half a cup of lemon juice?
Answers
Answer:
$6.36
Step-by-step explanation:
3 pies require 3/2 cups of lemon juice
16 tablespoons = 1 cup
need 24 tablespoons of lemon juice
need 12 lemons at $0.53 each
total cost = 12 x 0.53 = $6.36
write and solve proportion answer the question.
25%of what number w is 9
□= 25
100
w= □
Answers
Answer:
Answer is 36.
You can simply get this by writing and expression for it
25/100 x w=9
25w/100=9
w= 9x100/25
w=36.
Answer:
36
Step-by-step explanation:
9/w=25/100
cross multiplication:
9*100=25w
900=25w
900=25w / 25
36=w
What is the total volume of this composite shape? Round your answer to the nearest tenth.
Answers
log(x)²=(logx)², find the value of x
Answers
Answer:
x = 7.39
Step-by-step explanation:
log(x)²=(logx)², find the value of x
log x² = log x * log x
2log x = log x * log x
2 = log x
Take the exponent pf both sides
e² = e^logx
e² = x
x = e²
x = 7.39
Find the volume of the cylinder. Find the volume of a cylinder with the same radius and double
the height.
The volume of the cylinder is __ in.³.
The volume of a cylinder with the same radius and double the height is __ in.³.
Answers
about 78.54
V=π·5^2·1 = 78.54
Answer:
Find the volume of the cylinder.
[tex]\star \: \: \purple{Volume_{(cylinder)} = \pi {r}^{2} h}[/tex]
[tex]\star \: \: \purple{Volume_{(cylinder)} = 3.14 \times ( {5)}^{2} \times 1 }[/tex]
[tex]\star \: \: \purple{Volume_{(cylinder)} =3.14 \times 25 \times 1 }[/tex]
[tex]\star \: \: \purple{Volume_{(cylinder)} =78.50 \: in {}^{3} }[/tex]
Find the volume of a cylinder with the same radius and double the height.
[tex]\star \: \: \purple{Volume_{(cylinder)} = \pi {r}^{2} h}[/tex]
[tex]\star \: \: \purple{Volume_{(cylinder)} = 3.14 \times {(5)}^{2} \times 2}[/tex]
[tex]\star \: \: \purple{Volume_{(cylinder)} = 3.14 \times 25 \times 2}[/tex]
[tex]\star \: \: \purple{Volume_{(cylinder)} = 157 \: in {}^{3} }[/tex]
4x+(3x+2)=3x(4+2)................................
Answers
how to go in minutes from hours and hours to minutes answer in picture welcome in advance
Answers
Answer:
trick:
1 hour = 60 minutes
ex if said to convert 25 minutes to hour so
1 hour/60=1minutes
multiply both sides with 25
25 x 1hour/60=25minutes
5/12 hours=25 minutes
just like that for hour
A freshly isolatedsample of 90Y was found to have an activity of 8.9 x 105 disintegrations per minute at 1:00pm on December 3, 2003. At 2:15pm on Dec, 17, 2003, its activity was redetermined and found to be 2.6 x 104 disintegrations per minute. Calculate the half-life of 90Y.
Answers
Answer:
3960 minutes
Step-by-step explanation:
From;
0.693/t1/2 = 2.303/t log No/N
t1/2 = half life of 90Y
No = initial activity of 90Y = 8.9 x 10^5 disintegrations per minute
N= activity of 90Y after time t = 2.6 x 10^4 disintegrations per minute
t = time taken
Since the time elapsed is 20,235 minutes, we substitute into the formula above.
0.693/t1/2 = 2.303/20235 log 8.9 x 10^5/2.6 x 10^4
0.693/t1/2 = 1.75 * 10^-4
t1/2 = 0.693/ 1.75 * 10^-4
t1/2 = 3960 minutes
oduced the test statistic χ2=8.95 with a corresponding p-value of 0.03. Which of the following is correct? There is sufficient evidence to reject the null hypothesis at the 0.05 level since the test statistic is greater than the p-value. Answer A: There is sufficient evidence to reject the null hypothesis at the 0.05 level since the test statistic is greater than the p -value. A
Answers
Answer:
The null hypothesis must be rejected
Step-by-step explanation:
Here the P value is less than 0.05
which means that the test results are statistically significant and there are sufficient evidence to reject the null hypothesis and accept the alternative hypothesis.
Hence, the null hypothesis must be rejected.
Please help!! Urgent!
Answers
Answer:
[tex] log_{3}( {x}^{3} + {2x}^{2})[/tex]
Answer:
Answer:
log_{3}( {x}^{3} + {2x}^{2})log
3
(x
3
+2x
2