The prime factorization of 72 using exponential notation is [tex]2^{3} *3^{2}[/tex].
It is required to find the prime factorization of 72.
What is a prime factorization ?Prime factorization of a number is breaking a number down into the set of prime numbers which multiply together to result in the original number. The fundamental theorem of arithmetic says that every positive integer has a unique prime factorization.
Given that:
The prime factorization for 72 is
=2×2×2×3×3 .
=[tex]2^{3} *3^{2}[/tex]
Hence, the prime factorization of 72 using exponential notation is [tex]2^{3} *3^{2}[/tex].
Learn more about prime factorization here:
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2, 4, 3, 6, 5, 10, 9, 16, does anyone know the next 3 numbers and the pattern ??????????????
Answer:
No
Step-by-step explanation:
Latrell has 14¢ in nickels and pennies. He has 6 coins altogether. How many coins of each kind does he have?
There are 4 granola bars. Three friends want to share them evenly.
How much would each friend get? Show your answer in two different ways.
Answer:
4/3 or 1 and 1/3 or 1.33333 repeating
Step-by-step explanation:
you have 4 granola bars and 3 friends and you want to divide them among 3 friends
4/3
Answer:
1.3recuring or 3/4
Step-by-step explanation:
hope it helps
(x-5^2)-7=93
Solve using square roots
I’m just unsure whether the answer will be x=-5+- 10 or x=5+-10
Answer:
Step-by-step explanation:
steps are stated below
step 1
(x-5^2)-7=93 equation
step 2
x-5^2-7=93 remove brackets
step 3
x-5^2-7=93 simplify
x+(-25)+(-7)=93
step 4
(x)+(-25+-7)=93 combine the tems
x+(-32)=93
step 5
x+(-32)=93 change the symbols
x-32=93
step 6
x-32(+32)=93(+32) add +32 to both sides so we can get our answer
x=-0=93+32
x=125
Answer:
x=15, x=-5
Step-by-step explanation:
Solve:
[tex](x-5)^2-7=93[/tex]
Adding 7:
[tex](x-5)^2=93+7[/tex]
[tex](x-5)^2=100[/tex]
Taking square roots:
[tex]x-5=\sqrt{100}[/tex]
Recall a square root has two possible answers:
[tex]x-5=\pm 10[/tex]
Adding 5:
[tex]x=5\pm 10[/tex]
There are two answers:
[tex]x=5+ 10=15[/tex]
[tex]x=5- 10=-5[/tex]
Answers: x=15, x=-5
Point G and point H are the same distance form point F. Which coordinates could be the location of point H?
Note: It seems, you missed to add the correct option. But, I am solving the question to clear your concept anways.
Answer:
The coordinates of H are:
(x₂, y₂) = (2, 0)Step-by-step explanation:
Given the points
F(3, 2)G(4, 4)Since Point G and point H are the same distance from point F, therefore the point F is the mid-point of G and H
using the mid-point formula
[tex]m\:=\:\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]
Since the point F is the mid-point of G and H, so
m = (3, 2)
as
(x₁, y₁) = (4, 4) = G (x₂, y₂) = H = ?Thus, substituting m = (3, 2), (x₁, y₁) = (4, 4) to determine coordinates of the point H (x₂, y₂)
[tex]m\:=\:\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]
[tex]\left(3,\:2\right)\:=\:\left(\frac{x_2+4}{2},\:\:\frac{y_2+4}{2}\right)[/tex]
so
[tex]\:\:3\:=\:\frac{x_2+4}{2}[/tex]
[tex]x_2+4=6[/tex]
subtract 4 from both sides
[tex]x_2+4-4=6-4[/tex]
[tex]x_2=2[/tex]
and
[tex]2=\:\frac{y_2+4}{2}[/tex]
[tex]\:y_2+4\:=\:4[/tex]
subtract 4 from both sides
[tex]y_2=0[/tex]
Thus, the coordinates of H are:
(x₂, y₂) = (2, 0)Note: It seems, you missed to add the correct option.
What percent of 855 is 990
Answer:
86.36%
Step-by-step explanation:
Answer:
116%
Step-by-step explanation:
990% of 855 = 1.15789473684 or
= about 116%
Two vectors with magnitudes of 6 and 9 have a dot product equal to –27.
Find the angle between the vectors.
150°
120°
60°
30°
Answer: 120
B
Step-by-step explanation: got it right on edge
Answer:
B.) 120
Step-by-step explanation:
a recipe uses 1 1/4 cups of milk to make 10 servings. if the same amount of milk is used for each serving, how many servings can be made using 1 gallon of milk? take 1 gallon to be equal to 16 cups. please show the work!
Answer:
128 servings can be made using 1 gallon of milk.
Step-by-step explanation:
Given that:
[tex]1\frac{1}{4}[/tex] cups of milk make 10 servings
[tex]1\frac{1}{4}[/tex] can also be written as 1.25
Ratio of cups of milk to servings = 1.25 : 10
1 gallon = 16 cups
Let,
x be the number of servings made from 1 gallon
Ratio of cups of milk to servings = 16 : x
This is a direct proportion
1.25 : 10 :: 16 : x
Product of mean = Product of extreme
10*16 = 1.25x
160 = 1.25x
1.25x=160
Dividing both sides by 1.25
[tex]\frac{1.25x}{1.25}=\frac{160}{1.25}\\x=128[/tex]
Hence,
128 servings can be made using 1 gallon of milk.
A candy machine can make 25.15 pounds of candy in an hour. How much candy can it make in 6.5 hours?
Answer:
i believe its 163.475 pounds of candy
Step-by-step explanation:
i multiplied 25.15 by 6.5
Answer:
163.475 pounds of candy.
Step-by-step explanation:
If the machine can make 25.15 pounds of candy in 1 hour, then you just multiply 25.15 pounds by 6.5 hours to get the answer.
A store charges customers $85 for a video game. This is 170% of what the store paid for the game.
can anyone help a girl out?
Answer:
I think it is $59.5
Step-by-step explanation:
Hope this helped have an amazing day!
One angle of an isosceles triangle measures 56°. Which other angles could be in that isosceles triangle? .
Answer:
68 or 62 degrees
Step-by-step explanation:
If the 56 degree angle is one of the base angles of the triangle, you can multiply it by two (because base angles of an isosceles triangle
are congruent), and then subtract 180 (because you must subtract the sum of two angles from 180 to get the measure of the third angle).
If the 56 degree is not a base angle, then you can use this equation to get the measurement of each base angle:
(180-56)÷2=measure of each base angle
180=sum of angle measures in a triangle
56=measure of third angle
With 180-56, you get the sum of the base angles, so you must divide by two. (Base angles of an isosceles triangle are congruent)
The other angles that could be in that isosceles triangle should be considered as the 56°, 68°, or 62°.
Calculation of the measurement of the angles:Since One angle of an isosceles triangle measures 56°.
So in the case when 56° angle is one of the two congruent angles, so the remaining angles are 56° and 180-2(56) = 68°
Now
In the case when the is 56° Is not congruent to either of the other angles, so each of the remaining two angles should be [tex](180-56)/2[/tex]= 62°.
hence, The other angles can be 56°, 68°, or 62°.
learn more about an angle here: https://brainly.com/question/24283305
Factor expression completely x^2+6x+9
guys give me a grade 6 division word probelm answers have to be correct
Answer:
Six division word problems answer had to be correct!
Got You✌
Simplify ( 5^2x7^4 ) 10
Answer:
5^20 • 7^40
Step-by-step explanation:
each exponent needs to multiply each 10.
Answer:
D. [tex]5^{20}[/tex] x [tex]7^{40}[/tex]
Step-by-step explanation:
Original Equation= [tex](5^2 \cdot 7^4)^{10}[/tex]
Apply exponent rule: [tex](a\cdot b) ^n[/tex] = [tex]a^n[/tex] [tex]b^n[/tex]
= [tex](5^2)^{10}[/tex] x [tex](7^4)^{10}[/tex]
Distribute them
= [tex]5^{20}[/tex] x [tex](7^4)^{10}[/tex]
= [tex]5^{20}[/tex] x [tex]7^{40}[/tex]
Hope this helps!
What is the answer to this problem?
Answer:
You are told you have a cumulative count of $400 for interest You gave $5000 in principal Principal + gained interest = Total Hence total = $5,400what is the average marks of 215
Answer:
Average marks are 60.❤️❤️❤️❤️
.......find 6.5% of 5.00 by multiplying $5 by 0.065. Round to the nearest cent
Answer:
0.32
Step-by-step explanation:
Because I know
Answer:
33 cents.
Step-by-step explanation:
Solve by elimination. 4x+6y=-12 2x+3y=4
Answer:
0 = 20 is false, therefore the system of equations has no solution.
NO SOLUTION
Step-by-step explanation:
Given the system of equations
[tex]\begin{bmatrix}4x+6y=-12\\ 2x+3y=4\end{bmatrix}[/tex]
solving the system by the elimination method
[tex]\begin{bmatrix}4x+6y=-12\\ 2x+3y=4\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}2x+3y=4\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:4x+6y=8[/tex]
[tex]\begin{bmatrix}4x+6y=-12\\ 4x+6y=8\end{bmatrix}[/tex]
subtracting the equations
[tex]4x+6y=8[/tex]
[tex]-[/tex]
[tex]\underline{4x+6y=-12}[/tex]
[tex]0=20[/tex]
0 = 20 is false, therefore the system of equations has no solution.
NO SOLUTION
-1/2y = 1/2x + 5 and y = 2x + 2
Answer:
x = -4
y = -6
Step-by-step explanation:
I just use my calculator to do this
Can someone show me how to do this problem and I need help!!
Thank you!!
Answer:
[tex] \frac{6}{19 } [/tex]
Step-by-step explanation:
6 + 5 + 7 + 1 + 0 = 19
Please need it finshed i will give brainliest to whoever right.
Answer:
40 + -40 = 0
Step-by-step explanation:
hope this helps!
Answer:
40 + -40 =0 (your answer)
2538494 + -2538494 = 0 (example)
4 + -4 = 0 (example)
-18 + 18 = 0 (example)
-82 + 82= 0 (example)
just as long as the first number and the second number are the same, and one is negative and the other is positive, added together the two numbers will equal zero.
20 of the 80 coffee mugs at Carson's Pancake House are dirty. What percentage of the coffee mugs at the pancake house are dirty?
Answer:
25%
Step-by-step explanation:
20/80 in can be reduced to 1/4 and 1/4 equals 25%.
We have:
[tex]\dfrac{20}{80} = \dfrac{\%} {100}[/tex]
Solving for %:
[tex]\% = \dfrac{20\cdot 100}{80} = 25\%[/tex]
R/ 25% of coffee mugs are dirty.
A line passes through the point (-4, 7) and has a slope of -5/4
Write an equation in slope-intercept form for this line.
Answer:
We conclude that the equation in slope-intercept form for this line will be:
[tex]y\:=\:\frac{-5}{4}x+2[/tex]
Step-by-step explanation:
Given
The point = (-4, 7)slope = m = -5/4We know that the slope-intercept form of the line equation is
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept
Using the slope-intercept form to find the y-intercept 'b'
substituting m = -5/4 and the point (-4, 7)
[tex]y = mx+b[/tex]
[tex]7=\:\frac{-5}{4}\left(-4\right)+b[/tex]
[tex]-\left(-5\right)+b=7[/tex]
[tex]5+b=7[/tex]
subtract 5 from both sides
[tex]5+b-5=7-5[/tex]
[tex]b=2[/tex]
now substituting b = 2 and m = -5/4 in the slope-intercept form
[tex]y = mx+b[/tex]
[tex]y\:=\:\frac{-5}{4}x+2[/tex]
Therefore, we conclude that the equation in slope-intercept form for this line will be:
[tex]y\:=\:\frac{-5}{4}x+2[/tex]
Use the following situation to answer the next 2 questions: A manufacturer claims that a particular car will get at least 50 miles per gallon on the highway. The researchers of a consumer-oriented magazine believe this claim is too high and plan a test with a simple random sample of 30 cars. Assume the population standard deviation for individual cars is 2.3 miles per gallon. The researchers found the sample mean to be 49 miles per gallon, and they decided on using a = 0.05. (Hint: H n SD = H. Find the value of the test statistic. A.-2.38 B.-1.645 C.-0.43 D. 0.0087 E. 2.38 What is the conclusion of the hypothesis test? There evidence to reject the manufacturer's claim because sufficient:________A. Is not; 49 miles per gallon is too close to the claimed 50 miles per gallon B. Is not; the p-value of 0.0087 is less than the significance level C. Is; the sample mean is less than the claimed mean D. Is; the p-value of 0.0087 is less than the significance level E. Is; the p-value of 0.0174 is less than the significance level
Answer:
First question
The correct option is A
Second question
The correct option is E
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 50 \ mpg \ (miles \ per \ gallon )[/tex]
The sample size is n = 30
The population standard deviation is [tex]\sigma = 2.3 \ miles[/tex]
The sample mean is [tex]\= x = 49 \ mpg[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 50 \ mpg[/tex]
The alternative hypothesis is [tex]H_a : \mu < 50 \ mpg[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 49 - 50 }{ \frac{2.3}{ \sqrt{30 } } }[/tex]
=> [tex]t = -2.38[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n - 1[/tex]
[tex]df = 30 - 1[/tex]
[tex]df = 29[/tex]
Generally from the student t distribution table the probability corresponding to -2.38 to the left at a degree of freedom of [tex]df = 29[/tex] is
[tex]p -value = P( t < -2.38 ) = 0.0174[/tex]
From the value obtained we see that
[tex]p-value < \alpha[/tex] hence
The decision rule
Reject the null hypothesis
The conclusion is
There evidence to reject the manufacturer's claim because the p-value of 0.0174 is less than the significance level E
Identify the pattern for the following sequence. Find the next three terms in the sequence. . a. -15, -11, -7, -3, ____, _____, _____,...
A: Subtract 4; -7, -11, -15
B. Add 4; 2, 6, 10
C. Subtract 4; 1, 5, 9
D. Add 4; 1, 5, 9
Please select the best answer from the choices provided.
Answer: c
Step-by-step explanation:
Answer:
B you add 4. a negative plus a positive is a negative. -15 +4 is -11
There are 28 rows in a corner section of a professional football stadium. Each row
contains 4 more seats than the row in front of it. If there are 15 seats in the first row, 19
seats in the second row, 23 seats in the third row, and so on, which equation represents
the number of seats “s”in the “nth” row?
A. s(n)= 11 +4n
B. s(n) = 15+41
С. s(n) = 28 + 4n
D. s(n) = 11n + 4
Answer: A. S(n) =11+4n
Step-by-step explanation:first row is 15 so 11+(1×4) and 11+(4×2)=19 and so onn.
Amanda buys a book for 24.97, a backpack for 17.23. and a set of markers for 7.55. she gives the cashier 50.00 how much change does amanda get
Answer:
She would get 0.25 cents
Step-by-step explanation:
what you would do is add 24.97, 17.23 and 7.55 together and get a total of 49.75 and subtract that from 50 and get 0.25
please mark me brainliest
Answer:0.25
Step-by-step explanation:
What is the nature of roots of x- 9x = 20 ?
a. nonreal
b. real, rational, and equal
c. real, rational, and unequal
d. real, irrational, and unequal
Answer:
Option C
Step-by-step explanation:
To find the nature of the roots we use the Discriminant formula which is:
[tex]D=b^2-4ac[/tex]
and given the equation and compare with the standard quadratic equation
[tex]x^2-9x=20\\x^2-9x-20=0\\ax^2+bx+c=0[/tex]
Here our a is 1 , b is -9 and c is -20 so we plug a, b, c into the Discriminant formula
[tex]D=b^2-4ac\\D=(-9)^2-4(1)(-20)\\D=81+80\\D=161[/tex]
Since D > 0 (greater than zero) our roots are real and unequal for the rational and irrational part we got know the the Discriminant's square root value if it is in decimals the nature of the roots are irrational if the Discriminant's value is a whole number then it is rational and so 161 has a square roots in points which is
[tex]D=\sqrt{161} \\D=12.6885[/tex]
So our answer is real , irrational and unequal which is Option C
Daisy used a wooden board for a craft project. The board was 9 feet 4 inches tall. How tall is the board in inches?
Answer:
112
Step-by-step explanation:
A foot is 12 inches so you do 12 times 9 and then plus the four already listed inches
Answer:
112 inches
Step-by-step explanation:
PLease help me i don't get it
Answer:
150 and -150
Step-by-step explanation:
For question number 2...
You started off with an energy level of 250 and something was added to make it 400.
To figure out what this "something" was, you simply subtract the numbers.
400 - 250 = 150
For question number 3...
You start off with 325 and end with 175. Here, the outcome is smaller or less than what you started with. So, you know that you took away a certain amount of energy. To figure that out, you again subtract.
325 - 175 = 150
To make the equation make sense, you would subtract 150.
So the answer would -150.