Answers
First, we find the prime factorization of each number.
72/2 = 36
36/2 = 18
18/2 = 9
9/3 = 3
3/3 = 1
72 = 2^3 * 3^2
90/2 = 45
45/3 = 15
15/3 = 5
5/5 = 1
90 = 2 * 3^2 * 5
To find the GCF, use only common factors with the lower exponent.
Both 72 and 90 have 2 as a factor. 72 has 2^3, and 90 has 2. 2 has a lower exponent than 2^3, so we use 2.
Both 72 and 90 have 3 as a factor. The both have 3^2, so we use 3^2.
90 has 5 as a factor, but 72 does not, so 5 is not a common factor, so we do not use 5.
The GCF is the product of the factor we use.
GCF = 2 * 3^2 = 2 * 9 = 18
Answer: The greatest number of students he can place in a row is 18.
Related Questions
Katie has 16 3/4 hours to finish 3 school projects. How much time may sge spend in each project if she plans to spend the same amount of time on each.
Answers
(16 3/4 ) / 3 = 5.58
lars has been approved for$420,000, 20-year mortgage with an APR of 5.125%.What is his monthly payment ? How much interest would he expect to pay on the loan in one month?How much of the monthly payment will go towards the principal?
Answers
Answer:
Monthly Payment = $2,286.85
Interest on first month payment = $1,793.75
Principal value on first month payment = $493.10
Step-by-step explanation:
lars has been approved for $420,000 for loan.
Time for loan = 20-years
APR (Annual Rate of interest ) = 5.125%
We need to find monthly payment. First month interest and First month principle.
Formula for loan:
[tex]p=\dfrac{PV\cdot \frac{r}{n}}{1-(1+\frac{r}{n})^{-nt}}[/tex]
Where,
p is monthly payment.
PV = Loan Amount (PV=$420,000)
R = Rate of interest (R=0.05125)
t = Loan period ( t=30)
n = Mode of payment (n=12)
Substitute the value into formula and solve for p
[tex]p=\dfrac{420000\cdot \frac{0.05125}{12}}{1-(1+\frac{0.05125}{12})^{-12\cdot 30}}[/tex]
p=$2,286.85
Thus, Monthly Payment =$2,286.85
Interest for first month [tex]=420000\times \dfrac{0.05125}{12}=1793.75[/tex]
Interest pay on the loan in on month = $1,793.75
Principle value on first month payment = 2286.85 - 1793.75 = $493.10
The monthly payment will go towards the principal is $493.10
A random sample of size n = 64 is taken from a population with mean μ = −12.2 and standard deviation σ = 5.
a. calculate the expected value and the standard error for the sampling distribution of the sample mean. (negative values should be indicated by a minus sign. round "expected value" to 1 decimal place and "standard error" to 4 decimal places.)
Answers
The expected value for the sampling distribution of the sample mean is -12.2. The standard error for the sampling distribution of the sample mean is 0.6250.
Explanation:The expected value for the sampling distribution of the sample mean can be calculated using the formula µx = μ = -12.2. So, the expected value is -12.2.
The standard error for the sampling distribution of the sample mean can be calculated using the formula σx = σ/√n, where σ is the population standard deviation and n is the sample size.
Substituting the given values, we get σx = 5/√64 = 0.6250 (rounded to four decimal places).
The expected value and the standard error for the sampling distribution of the sample mean is 0.6250.
Expected Value: -12.2
Standard Error: 0.6250
1. The expected value (mean) of the sampling distribution of the sample mean is equal to the population mean, which is given as -12.2. Therefore, the expected value of the sampling distribution is also -12.2.
2. The standard error (SE) of the sampling distribution of the sample mean is calculated using the formula:
[tex]\[ SE = \frac{\sigma}{\sqrt{n}} \][/tex]
where [tex]\sigma[/tex] is the population standard deviation and n is the sample size.
Given [tex]\sigma[/tex] = 5 and n = 64, we can calculate the standard error as follows:
[tex]\[ SE = \frac{5}{\sqrt{64}} = \frac{5}{8} = 0.625 \][/tex]
Rounded to four decimal places, the standard error is 0.6250.
What is the answer to my math problem from my school for homework today?
Answers
To get the total amount of food served to all small-sized dogs, multiply a single serving amount (12.5 ounces) by the total amount of small-sized dogs (12).
12.5 × 12 = 150
Collectively, the small-sized dogs are served 150 ounces of dog food a day.
To find the total amount of dog food served to the medium-sized dogs, multiply the amount of one serving (18 ounces) by the total amount of medium-sized dogs (5).
18 × 5 = 90
Altogether, the medium-sized dogs are served 90 ounces of dog food daily.
Add those values together to get the amount of dog food served to both small- and medium-sized dogs in a day.
150 + 90 = 240
The animal shelter serves 240 ounces of dog food to small- and medium-sized dogs every day. But recall we need the answer in pounds. Remember there are 16 ounces in one pound, so if we divide our answer in ounces by 16, we'll have the same answer in pounds.
240 ÷ 16 = 15
Answer:
The shelter serves 15 pounds of dry food in one day.
Point E is located at (2, −3) and point F is located at (−2, −1). Find the y value for the point that is 3 over 4 the distance from point E to point F.
A. -2.5
B. -4.5
C. -3.5
D. -1.5
Answers
Y = (3/4)F -(3/4)E +E
Y = (3F +E)/4
Y = (3(-1) +(-3))/4 = -6/4 = -3/2
the appropriate choice is D. -1.5
The sum of two numbers is 45. One number is 4 times as large as the other. What are the numbers?
Answers
x = large number
y = small number
Now, set up a system of equations:
[tex]x + y = 45[/tex]
[tex]4y = x[/tex]
Solve the system. I'm going to use the second equation to substitute 'x' into the first one (x = 4y):
[tex]4y + y = 45[/tex]
[tex]5y = 45[/tex]
[tex]y = 9[/tex]
Plug that back into 2nd equation to find both numbers:
[tex]4y = x[/tex]
[tex]4(9) = x = 36[/tex]
So, x = 36 and y = 9.
We can check. 36 + 9 actually does equal 45 and 4 times 9 is 36. We match our initial criteria, so our answer is right.
The value of the variable x and y whose sum is 45 will be 9 and 36, respectively.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
The sum of the two numbers is 45. One number is 4 times as large as the other.
Let the two numbers be x and y. Then the equation is given as,
x + y = 45 ...1
y = 4x ...2
From equations 1 and 2, then we have
x + 4x = 45
5x = 45
x = 9
Then the value of y will be
y = 4(9)
y = 36
The value of the variable x and y whose sum is 45 will be 9 and 36, respectively.
More about the solution of the equation link is given below.
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A student taking a math class needs 6 minutes to solve each algebra problem. How many problems can the student solve in 72 minutes?
Answers
Here is your answer:
The proper answer to this question is "12 questions".
Here is How:
Just use this equation:
72/6=12
Which means the student will be able to solve 12 questions!
If you need anymore help feel free to ask me!
Hope this helps!
Final answer:
By dividing the total minutes (72) by the minutes per problem (6), we find that the student can solve 12 algebra problems in 72 minutes.
Explanation:
The student asking how many algebra problems can be solved in 72 minutes if each problem takes 6 minutes can be answered with a simple division operation. You divide the total available time by the time taken for each problem to find the number of problems that can be solved. In this case, 72 minutes ÷ 6 minutes per problem equals 12 problems.
In the equation x=8y , what is the unit rate?
Answers
Write an equation or inequality that best represents each statement below
6 times a number, x, is at least 22
Answers
6 times the number = 6x
at least 22 (it be 22 or more}
6x ≥ 22
Which is the standard form of the equation of the parabola that has a vertex of (–4, –6) and a directrix of y = 3?
Answers
focus=(-4,-15)
If focus =(a,b) and directrix y=k
the parabola is:
y=1/(2(b-k)) * (x-a)²+(b+k)/2
So y=1/(2*(-15-3))*(x+4)²+(-15+3)/2
y=-(x+4)²/36 -6
Answer:
The required equation is [tex](x+4)^2=-36(y+6)[/tex].
Step-by-step explanation:
The standard form of the equation of the parabola is
[tex](x-h)^2=4p(y-k)[/tex] .... (1)
where, (h, k) is vertex and y = k - p is directrix.
It is given that vertex of parabola is (–4, –6) and the directrix is y = 3.
[tex](-4,-6)=(h,k)[/tex]
On comparing both the sides, we get
[tex]h=-4,k=-6[/tex]
Directrix of the parabola is
[tex]y=k-p[/tex]
Put y=3 and k=-6 in the above equation.
[tex]3=-6-p[/tex]
[tex]3+6=-p[/tex]
[tex]9=-p[/tex]
[tex]-9=p[/tex]
Substitute h=-4,p=-9 and k=-6 in equation (1).
[tex](x-(-4))^2=4(-9)(y-(-6))[/tex]
[tex](x+4)^2=-36(y+6)[/tex]
Therefore the required equation is [tex](x+4)^2=-36(y+6)[/tex].
Jake ate 1/6 of the cookies at the valentines party. If he ate 5 cookies, how many cookies were there in all?
Answers
What is the y-value when x equals -11?
y = -200 – 12(x).
Answers
Hope this helps, have a great day!
Real Question:
You Make A Table To Use AS A Quick Reference Guide. [tex]\left[\begin{array}{ccc}y = -200 -12 (x)\end{array}\right][/tex]
Use The Table Tool To Answer The Question:
[tex]\left[\begin{array}{ccc}-8&-104\\-9&-92\\-10&-80\\-11&-68\\-12&-56\end{array}\right][/tex]
What is the y-value when x equals -11?
[tex]\left[\begin{array}{ccc}y = -200 -12 (x)\end{array}\right][/tex]
Step-By-Step Explanation:
Plug In The X-Value [tex]\left[\begin{array}{ccc}y=-200-12(x)\\y=-200-12(-11)\end{array}\right][/tex]
Then You'll Multiply [tex]\left[\begin{array}{ccc}-12(x) Or -12(-11)\\132\end{array}\right][/tex]
To Find The Y-Value Simplify [tex]\left[\begin{array}{ccc}y=-200+132\\y=-68\end{array}\right][/tex]
Answer:
[tex]\left[\begin{array}{ccc}y=-200-12(x)\\y=-200-12(-11)\\y=-200+132\\ y=-68\end{array}\right][/tex]
Kylie writes an equation to solve for the diameter, d, of the circle shown. Solve Kylie’s equation to find the diameter of the circle. 4 (d + 4) = 72 What is the diameter? 7.5 in. 8.25 in. 11.25 in. 13.25 in.
Answers
Answer:
8.25 in.
Step-by-step explanation:
In order to solve this you just have to clear the equation that Kylie created to calcuate the diameter of the circle for diameter, in this case, you just need to do the next steps:
[tex]4(d+4)=7^{2} \\4(d+4)=49\\d+4=\frac{49}{4} \\d+4=12.25\\d=12.25-4\\d=8.25[/tex]
Now we know that the diameter of the circle is 8.25 inches.
plez help What is the value of y in the equation 4 + y = −3?
7
1
−1
−7
Answers
The third side of an isosceles triangle is 2 inches shorter than each of the other two sides. if the perimeter of this triangle is 67 inches find the length of each side.
Answers
reuben deposits $700 into an account that pays simple interest at a rate if 5% per year. How much interest will he be paid in the first 3 years.
Answers
Reuben deposits $700 at a 5% annual interest rate for 3 years, using the simple interest formula, he will earn $105 in interest over that period.
Explanation:The question deals with calculating the simple interest Reuben will receive by depositing $700 into an account at a 5% annual interest rate over 3 years. To calculate simple interest, the formula used is Interest = Principal × Rate × Time. In this scenario, the principal (P) is $700, the rate (R) of interest per year is 5% or 0.05 when expressed as a decimal, and the time (T) is 3 years.
Substituting these values into the formula provides us with: Interest = $700 × 0.05 × 3. Simplifying this gives us: Interest = $105.
Therefore, Reuben will be paid $105 in interest over the first 3 years.
The population of a particular town is given by the function P(t) = 920(1.06)2t, where t is the time in years and P(t) is the population after t years. What is the current population, the percentage growth rate, and the population size (rounded to the nearest whole person) in 4 years?
A: 920, 6% annually, and 1,161
B:920, 6% semiannually, and 1,466
C: 920, 0.6% per year, and 7,801
D:920, 60% semiannually, and 4,135
Answers
Selection B is appropriate.
_____
The 2 in the exponent means the growth factor 1.06 is applied twice for each increment of t, that is, twice in 1 year (semiannually).
What are the slope and the y intercept of the graph of the liner function shown on the grid
Answers
It rises 2 units and runs 1 unit, so your slope is
2 or 2/1
To find the y-intercept just find where the line crosses the y-axis
it crosses at the -4 mark
Your slope is 2 and y-intercept is -4
y2 = 4
y1 = 0
x2 = 4
x1 = 2
Now we will subtract. 4 - 0 is 4/ 4 - 2 is 0. 4/2 is 2. The slope is 2. Now, we find the y-intercept, where the line crosses when x = 0. Just by looking at the graph, we can see that -4 is the y-intercept. There. The slope is 2 and the y-intercept is -4. The answer is F.
About 12% of men and 10% of women are left-handed. if we select a person at random, are the event that the person is male and the event that the person is left-handed independt or associated?
Answers
The correct option is A. Gender and handedness are associated because men are more likely to be left-handed than women. This conclusion is drawn from the different probabilities of being left-handed based on gender, indicating an association rather than independence.
A. Gender and handedness are associated because men are more likely to be left-handed than women - - This statement is correct based on the given information. Men have a [tex]12\%[/tex] likelihood of being left-handed compared to women who have a [tex]10\%[/tex] likelihood. This difference shows an association between gender and handedness.
The other incorrect options are:
B. Gender and handedness are independent because all of the possible combinations of each exist - This option is incorrect because independence between two events means that the occurrence of one event does not affect the occurrence of the other. In this case, the probability of being left-handed depends on whether the person is male or female ([tex]12\%[/tex] for men and [tex]10\%[/tex] for women), indicating an association rather than independence.
C. Gender and handedness are associated because the percentage is an estimate - This option is incorrect because the percentages given ([tex]12\%[/tex]for men and [tex]10\%[/tex] for women) are specific probabilities based on data, not estimates. The difference in these probabilities reflects an association between gender and handedness.
D. Gender and handedness are independent because they are both comprised of mutually exclusive events - This option is incorrect because being male or female (gender) and being left-handed (handedness) are not mutually exclusive events. One can be male or female and still be left-handed or right-handed. Independence would require that the probability of being left-handed is the same regardless of gender, which is not the case here.
The complete Question is
About 12% of men and 10% of women are left-handed. If a person is selected at random, are the event that the person is male and the event that the person is handed independent or associated?
Choose the correct answer below.
A. Gender and handedness are associated because men are more likely to be left handed than women
B. Gender and handedness are independent because all of the possible combinations of each exist
C. Gender and handedness are associated because the percentage is an estimate
D. Gender and handedness are independent because they are both comprised of mutually exclusive events
Determine whether it is possible to circumscribe a circle about the quadrilateral.
80 POINTS
Answers
2. No. Opposite angles are not supplementary.
what statement about this figure is true-- i know its one of the last two but they both seem right to me
Answers
A group of 30 bikers went on a trip. some rode bicycles and the others rode tandems. if the total number of bicycles and tandems was 23, how many tandems were used?
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I need help ASAP Please and thank you
Answers
Again you hope this is true, but much depends on where you are. You can have a mansion in a ghetto area and it is worth next to nothing.
I should hope so.
The 4th one is a physical relationship. If the person is driving all the time it is true. There is a positive relationship.
The last one would have a random result.
All of these or none of them could have positive results. If you treat it as a pure math question, 1 should, 2 should, 3 should, 4 should and 5 should not. This question is far too subjective to get 100%. If you say anything at all, arguing it is very worthwhile. State your case and then shut up if your marker disagrees.
Find z such that 6.8% of the standard normal curve lies to the left of z. (round your answer to two decimal places.)
Answers
Answer with explanation:
it is given that ,6.8% of standard normal curve lies to left of z.
6.8% [tex]=\frac{6.8}{100}\\\\=0.068[/tex]
We will use z table to calculate the value of z.
First we will go on y axis in z table to see value of 0.06 and then on 0.08 on x axis.Their point of intersection will give value of z at 0.068, which is equal to 0.2483.
Value of Z ,at 6.8% ,when the curve is normal = 0.25
⇒0.25 represents area in the left of ,z=0.068.
The z-score corresponding to 6.8% in the standard normal distribution is approximately -1.48, rounding to two decimal places, ensuring 6.8% lies to the left.
To find the z-score such that 6.8% of the standard normal curve lies to the left of it,
use a standard normal distribution calculator.
For the z-score corresponding to the cumulative probability of 0.068 (6.8%).
Using a standard normal distribution calculator:
The cumulative probability of 0.068 (or 6.8%) in the standard normal distribution calculator.
find the z-score associated with this probability.
The z-score corresponding to a cumulative probability of 0.068 is approximately -1.48 (rounded to two decimal places).
Therefore, the z-score z such that 6.8% of the standard normal curve lies to the left of it is approximately -1.48.
Learn more about z-score here
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A math teacher assigns 3 projects. She gives the students 5 project options to choose from. How many different groups of projects can the students choose from?
Answers
just learned this in class the other day
There are different ways to think about the meaning of speed.
Which description correctly completes this sentence?
Speed is ________________________.
A.time traveled times distance traveled
B.time traveled divided by distance traveled
C.the number of hours it takes to travel a certain distance
D.the distance traveled divided by the time it takes to travel that distance
30 POINTS
Answers
The answer is D
Hope this helps!
Answer:
D
Step-by-step explanation:
Find the coordinates of the point (x,y,z)(x,y,z) on the plane z=2x+3y+3z=2x+3y+3 which is closest to the origin.
Answers
.. (x, y, z) = t(2, 3, -1)
so the point of interest will satisfy
.. 2(2t) +3(3t) -(-t) = -3
.. 14t = -3
.. t = -3/14
and its coordinates are (x, y, z) = (-3/7, -9/14, 3/14)
To find the point closest to the origin on the plane with equation z = 2x + 3y + 3, an offset vector from the origin to a point on the plane is used. This vector's dot product with the plane's normal vector should be zero, since the shortest path to the plane will be perpendicular to it. This creates a system of equations that can be solved for x, y, and z.
Explanation:To find the closest point (x, y, z) on the given plane to the origin in three-dimensional Cartesian axes, we can start by creating an offset vector from the origin to an arbitrary point on the plane. Let's use the equation of the plane, z = 2x + 3y + 3. Let's presume a point P(x, y, z) on this plane. The vector to this point from the origin is (x, y, z - 3).
Because we want the shortest distance to the origin, the dot product of this vector and the normal vector to the plane (2, 3, -1) should be zero, because the shortest path to the plane will be perpendicular to it. So, the formula for the dot product gives us:
2*x + 3*y - (z - 3) = 0
This simplifies to:
2x + 3y - z + 3 = 0
Which combined with the equation of the plane (z = 2x + 3y + 3), provides a system of equations that can be solved using methods like Gaussian elimination or substitution.
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Find the average rate of change of the function
Answers
x2 = 9 so sqrt(9) = 3
3-2 = 1
9-4 = 5
rate of change = 1/5
[tex]\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\ -------------------------------\\\\ f(x)= \sqrt{x} \qquad \begin{cases} x_1=4\\ x_2=9 \end{cases}\implies \cfrac{f(9)-f(4)}{9-4}\implies \cfrac{\sqrt{9}-\sqrt{4}}{5} \\\\\\ \cfrac{3-2}{5}\implies \cfrac{1}{5}[/tex]
common factor for 4x+8
Answers
Last week,you finished level 2 of a video gamr in 32 minutes. Today, you finish level 2 in 28 minutes. What is your percent change
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if we take 32 to be the 100%, what is 4 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 32&100\\ 4&p \end{array}\implies \cfrac{32}{4}=\cfrac{100}{p}\implies p=\cfrac{4\cdot 100}{32}[/tex]
* 100%
= 12.5%