Given:
a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰.
To find:
The GCF of given terms.
Solution:
Greatest common factor (GCF): To find the GCF of two or more numbers, we need to find the product of their prime factor with their maximum powers.
The given terms are
[tex]a^{12}b^{4},a^{4}b^8, a^{24}b^{16}, a^{12}b^{20}[/tex]
Here, each term has two prime factors a and b. The highest power of a is 24 and the highest power of b is 20. So, the GCF of given terms is
[tex]GCF=a^{24}\times b^{20}[/tex]
[tex]GCF=a^{24}b^{20}[/tex]
Therefore, the GCF of a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰ is a²⁴b²⁰.
A recent drug survey showed an increase in use of drugs and alcohol among local high school students as compared to the national percent. Suppose that a survey of 100 local youths and 100 national youths is conducted to see if the percentage of drug and alcohol use is higher locally than nationally. Locally, 65 seniors reported using drugs or alcohol within the past month, while 61 national seniors reported using them. Conduct a hypothesis test at the 5% level.
Answer:
The answer is "0.586"
Step-by-step explanation:
Please find the solution to the given question:
[tex]z= \frac{0.65-0.61}{\sqrt{\frac{0.65 \times 0.35}{100}+\frac{0.61 \times 0.39}{100}}}[/tex]
[tex]= \frac{0.04}{\sqrt{\frac{0.2275}{100}+\frac{0.2379}{100}}}\\\\= \frac{0.04}{\sqrt{0.002275+0.002379}}\\\\= \frac{0.04}{\sqrt{0.004654}}\\\\= \frac{0.04}{0.0682202316}\\\\=0.586336327\\\\[/tex]
Convert 199º to radians. Round to 2 decimal places.
Answer:
3.47
Step-by-step explanation:
Answer: 199π/180
Step-by-step explanation:
The formula for converting degrees to radians is [tex]x[/tex]°·[tex]\frac{\pi }{180}[/tex]
In this case, that gives you [tex]\frac{199\pi }{180}[/tex]. 199 is a prime number, so this can't be simplified down any further.
Also, the formula for converting radians to degrees is just the opposite: you multiply your radian measure by [tex]\frac{180}{\pi }[/tex] to cancel out pi.
Hope this helps :)
The length of a rectangle is 2 times it’s width. The area of the rectangle is 72 square inches. Find the dimensions of the rectangle
Answer: 72 divided by 2 is 9. So the length is 9
Step-by-step explanation:
Would this be infinite solutions or no solution?
a square is cut from rectangle the side length of the square is half of the unknown with W the area of the Shaded region is 84 square inches write an equation you can use to find the width in inches
Answer:
Step-by-step explanation:
Just give me the answer
Mori just replaced the showerhead in her bathroom. the old one used 5.75 gallons per minute of water. Her new showerhead uses 2.5 gallons per minute. how many times has much water did Mori's old showerhead use?
Answer:
3.25
Step-by-step explanation:
Jamie has white, blue, and pink shirts. She has black, white, and beige pants. She has black and brown shoes. If she chooses one shirt,
one pair of pants, and one pair of shoes, how many unique outfits can she make?
Answer:
She can make [tex]18[/tex] unique outfits.
Step-by-step explanation:
Jamie has [tex]3[/tex] options to choose from for a shirt (white, blue, or pink), [tex]3[/tex] options to choose from for pants (black, white, or beige), and [tex]2[/tex] options to choose from for shoes (black or brown). Therefore, she can make [tex]3*3*2=18[/tex] unique outfits from these options. Hope this helps!
Write the number 16408 in words.
Answer:
Step-by-step explanation:
Sixteen thousand, four hundred and eight
Hope this helps!
Find the mean. Round to the nearest tenth if necessary.
37.4, 11.7, 35.4, 18.6, 5.7, 48.8, 18.9, 30, 15.1, 26.6, 35.7, 40.2
Answer:
27
Step-by-step explanation:
The actual mean is 27.008333333333, round that as you will.
Answer:
27 is the answer
Step-by-step explanation:
Took the test and got it right
Solve the following system of linear equations by graphing:
2x + 2y = 10
8x + 8y = 24
Answer:
Step-by-step explanation:
-8x - 8y = -20
8x + 8y = 24
0 ≠ 4
2y = -2x + 10
y = -x + 5
8y = -8x + 24
y = -x + 3
inconsistent
please solve and receive brain list
Answer:
-1 and -4
Step-by-step explanation:
Answer:
x = -1 y = -4
Step-by-step explanation:
6x + 2y = -14
-12x + 5y = -8
x= -1
y = -4
Solve the system of linear equations by substitution.Check your solution.
Step-by-step explanation:
x=-2
y=-1
........................
A bag contains 3 blue marbles, 7 red marbles, and 5
yellow marbles. If Joe picks 1 marble from the bag at
random, what is the probability that it will be blue?
Answer:
3 out of 15 I believe is the answer
Step-by-step explanation:
there are 3 blue marbles so he already has a chance out of 3, then I believe you add them all together which is 15 :) hope this helps
-1/2x-(1/2x+4)+12=17x-6(3x+5/6) What value of x makes the equation true? Show your work please.
Answer:
No Solution
Step-by-step explanation:
Keep in mind that if the grouping isn't right, then my result will be wrong:
-1/2x-(1/2x+4)+12=17x-6(3x+5/6)
Let me just change the formatting for convenience, and then begin the calculations:
[tex]-\frac{1}{2}x-\left(\frac{1}{2}x+4\right)+12=17x-6\left(3x+\frac{5}{6}\right)\:[/tex]
[tex]-\frac{1}{2}x-\frac{1}{2}x-4+12=17x-18x-5[/tex]
[tex]-2\cdot \frac{1}{2}x-4+12=17x-18x-5[/tex]
[tex]-x-4+12=17x-18x-5[/tex]
[tex]-x+8=17x-18x-5[/tex]
[tex]-x+8=-x-5[/tex]
[tex]-x=-x-13[/tex]
[tex]0=-13[/tex]
Result: No Solution
Expand the expression -3 (4s+-7). Then select the correct answer.
A. 12s - 21.
B 12s + 21.
C -12s + 21.
D -12s - 21
Answer:
I think A is the correct answer because -3+4 is 1 because 4 has greater sign + and +- gives result - thus,-3-7 gives - 21. I hope that it would be meaning ful for you ...
The area of a rectangular garden is 120 square meters. The width is 4 meters longer than one-half of the length. Find the
length and the width of the garden. Use the formula, area = length • width.
Answer:
Step-by-step explanation:
“The area of a rectangular garden is 120 square meters.”
LW = 120
“The width is 4 meters longer than one-half of the length.”
W = 0.5L + 4
L = 2W-8
Substitution
(2W-8)W = 120
2W^2-8W-120 = 0
W^2 -4W-60 = 0
W = 10, -6
-6 is an extraneous solution.
W = 10 meters
L = 2W-8 = 12 meters
tan a= 12/15, a lies in quadrant 3, and cos x= -20/29, x lies in quadrant 2. find sin (a+x).
a) 345/377 b) 135/377 c) -152/377 d) 352/377
Answer:
c) -152/377
Step-by-step explanation:
yan po ang tamang sagot ko..
purple paint is made from using red paint and blue paint in the ratio 1:2
write an equation for y in terms of x to show the relationship between the amount of red paint (y) and the amount of blue paint (x)
Answer:
[tex]y = \frac{x}{2}[/tex]
Step-by-step explanation:
Given
[tex]y : x = 1 : 2[/tex]
Required
Represent as an equation
[tex]y : x = 1 : 2[/tex]
Represent as a fraction
[tex]\frac{y }{ x} = \frac{1}{ 2}[/tex]
Cross multiply
[tex]y * 2 = x*1[/tex]
Divide both sides by 2
[tex]y = \frac{x*1}{2}[/tex]
[tex]y = \frac{x}{2}[/tex]
Write an expression that shows 10 *4.
HELP PLEASE IT IS EASY I SWEAR PLEASE HELP I SWEAR IT EASY PEASY
Answer:
the answer is 15
Step-by-step explanation:
Donna guessed there were 400 jellybeans in a jar. There were really 480 jellybeans. What is her prevent of error
Answer:
Step-by-step explanation:
Donna guessed 400 but there were 480 so she was off by 80
What is the multiplier for a 30% decrease. *
Answer:
0.7
Step-by-step explanation:
Let the number to be decreased be x. To decrease x by 30 %, the result will be
= x - 30% * x
= x - 0.3x
= 0.7x
From above, the result is 0.7 multiplied by the number to be reduced. Hence the multiplier is 0.7
A store manager combines trail mix that is 30% raisins with a trail mix that is 55% raisins. He makes 800 lbs of trail mix that is 40% raisins. How many pounds of each trail mix does the manager use?
Answer:
320 pounds of 55% raisins trail mix
480 pounds of 30% raisins trail mix
Step-by-step explanation:
i did it on RSM and got it right
Sally is teaching a nursery rhyme to her kindergarten students. She found that 4 out of every 10 students know the rhyme. If Sally has a total of 20 students, how many students in her class know the rhyme?
Step-by-step explanation:
the answer is
[tex]= \frac{4}{10} \times 20 = 8[/tex]
Find the slope of the line for the angle.
330 degrees
A triangle has sides with lengths of 3 feet, 6 feet, and 8 feet is it a right triangle?
Answer:
[tex]Solution,\\Longest~side(h) = 8ft.\\Perpendicular(p) = 3ft.\\Base(b) = 6ft.\\Now, \\h^2 = (8)^2 = 64sq.ft.\\p^2+b^2 = 3^2+6^2 = 9+36 = 45sq.ft.\\Since, h^2\neq p^2+b^2, ~the~triangle~is~not~a~right~triangle.[/tex]
Describe a congruence transformation that mapsABCD to APQR.
Alison rolls two number cubes 90 times. How many times is he going to get a sum of 3?
15
Step-by-step explanation:
Answer:
I think 30 im so sure
Step-by-step explanation:
uhm i think its 90 divided by 3 cuz i looked it up and got 30 so yea bye
Paul has $30,000 to invest. His intent is to earn 11% interest on his investment. He can invest part of his money at 7% interest and part at 13% interest. How much does Paul need to invest in each option to make a total 11% return on his $30,000?
7% interest =$?
13% interest =$?
Answer:
A
Algebra For what values of the variables must ABCD be a parallelogram?
B
23. A 2y + 2 B 24. B
(3x + 10)
(8x + 5)º
3x + 6
54°
D
С
D
A
Зу - 9 с
ly+4
Can someone please help me
Answer:
A) 23cm.
B) 32.0625 square cm.
Step-by-step explanation:
Perimeter: Just add all the sides together like so:
4.75x2 + 6.75x2 = 23cm.
Area: Multiply the base and height together:
4.75 x 6.75 = 32.0625 square cm.
23cm
4.75 + 4.75 = 9.50
6.75 + 6.75 = 13.50
13.50 + 9.50 = 23.00