Answer:
[tex]3n^3(2-n^2)[/tex]
Step-by-step explanation:
Given expression:
[tex]6n^3-3n^5[/tex]
To factor out the expression completely.
Solution:
In order to factor out the expression, we will find the greatest common factor of each term.
To find the G.C.F. of the two terms, we will list down their factors and then find the common ones.
The factors of the terms can be given as:
[tex]6n^3=2\times 3\times n\times n\times n[/tex]
[tex]3n^5=3\times n\times n\times n \times n\times n[/tex]
The G.C.F. = [tex]3\times n\times n\times n=3n^3[/tex]
So, we factor out the G.C.F. and write the remaining factors inside the parenthesis.
The expression will be given using distributive property as:
⇒ [tex]3n^3(2-n^2)[/tex] (Answer)
Final answer:
To factor out [tex]6n^3 - 3n^5,[/tex] find the greatest common factor and simplify the expression.
Explanation:
A factor, in mathematics, refers to a number or algebraic expression that divides another number or expression evenly, meaning without leaving a remainder. When we say that one number is a factor of another, it means that when you divide the larger number by the factor, the result is an integer. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because each of these numbers divides 12 without leaving a remainder.
Factoring out [tex]6n^3 - 3n^5[/tex] involves finding the greatest common factor of the terms.
Step 1: Factor out [tex]n^3[/tex] from both terms to get [tex]n^3(6 - 3n^2).[/tex]
Step 2: Further simplify to [tex]n^3(2)(3 - n^2[/tex]) for the final factored form.
the age of a mother is three times that of her son. after 5 years sum of their ages will be 50 years. Express it as a linear equation in two variables.
Step-by-step explanation:
[tex]s-\text{age of son}\\m-\text{mother's age}\\3s-\text{mother's age}\\\\\boxed{m=3s}\\\\(s+5)-\text{age of son after 5 years}\\(m+5)-\text{mother's age after 5 years}\\50-\text{sum of their ages}\\\\\boxed{(s+5)+(m+5)=50}[/tex]
A lender wil verity and carefully consider your income before approving you for a loan because
a they need to be sure you will be able to pay the loan back
b government restrictons reoeam u salary to be approved for a dan
C. loan applicants with higher salaries are generally more trustworthy than other applicants
d. they need to be sure you make at least the minimum payment for the loan you applied for
Please select the best answer from the choices provided
Answer:
A
Step-by-step explanation:
A local flower shop is selling $1 raffle tickets and is donating all proceeds to the children's hospital. They sold 5,500 tickets and plan to give away 20 flower arrangements valued at $70 and 20 gift certificates valued at $25. Find the expected value of purchasing a raffle ticket.
Round to the nearest cent. Do not round until the final calculation.
The expected value of purchasing a raffle ticket is -0.647.
What is the Expected Value of a Probability & Statistical Analysis?The expected value is derived in probability analysis by the multiplication of each of the potential possibilities by the likelihood that each result will occur and then adding all of those values together.
Using the formula below, we can calculate the expected value as follows:
[tex]\mathbf{ E(X)= \sum^{n}_{i=1}X_i P(X_i)}[/tex]
However, the probability (Pr) of each event can be categorized as follows:
Pr (to win a flower arrangement ) [tex]\mathbf{=\dfrac{20}{5500}}[/tex]Pr (to gift a certificate) [tex]\mathbf{=\dfrac{20}{5500}}[/tex]Pr (no win) ) [tex]\mathbf{=\dfrac{5500 - 20 - 20}{5500}=\dfrac{5460}{5500}}[/tex]Thus;
[tex]\mathbf{E(X) = 70(\dfrac{20}{5500} \times 25 ((\dfrac{20}{5500} )- 1(\dfrac{5460}{5500} )}[/tex]
[tex]\mathbf{E(X) =-0.647}[/tex]
Learn more about finding the expected value of a probability here:
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State weather the equation represents exponential growth, exponential decay or neither, 30 POINTS EASY
Answer:
Exponential Decay
Step-by-step explanation:
It's exponential growth when your base value is > 1. Example:
1.3ˣ, 2ˣ, 7ˣ, 999ˣ
It's exponential decay when the base value is < 1. Example:
0.9ˣ, 0.45ˣ, (1/2)ˣ, 0.79ˣ, .999ˣ
It's neither when the base value = 1. Example:
1ˣ
Roy has decided to visit the new ice cream shop around the corner. When he goes in, he sees 16 big buckets full of ice cream behind the counter, each containing a different flavor. There are 6 flavors that contain chocolate.
If he closes his eyes and picks out a bucket at random, what is the probability that the flavor he picks will contain chocolate?
A.
B.
C.
D.
Answer:
6/17
Step-by-step explanation:
To find the probability that Roy picks a chocolate flavor at random, we need to use the basic probability formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]
In this scenario:
- The favorable outcomes are the number of chocolate flavors.
- The total number of possible outcomes is the total number of flavors.
According to the given situation, there are a total of 16 flavors of ice cream, and out of these, 6 flavors contain chocolate.
Using the probability formula:
\[ \text{Probability of picking a chocolate flavor} = \frac{6}{16} \]
To simplify the fraction, we can divide both the numerator and the denominator by the greatest common divisor, which in this case is 2:
\[ \frac{6 \div 2}{16 \div 2} = \frac{3}{8} \]
Now, to express this as a decimal, we divide 3 by 8:
\[ 3 \div 8 = 0.375 \]
Therefore, the probability that Roy picks a chocolate flavor at random is 0.375. If you're looking at multiple-choice answers, you would choose the option that best fits this answer.
Estimate a 10% tip on a bill of $143.17 by first rounding the bill amount to the nearest ten dollars.
Estimated tip: $il
x
6
?
Answer:
Step-by-step explanation:
143.17
round the bill to the nearest $ 10..
that would make it $ 140
a 10% tip......its the same thing as multiplying by 0.1
and when u multiply any number by 0.1 ur actually starting at the decimal ( or the end of the number) and move one space to the left.
examples :
10% of 245 = 24.5
10% of 5010 = 501
10% of 76 = 7.6
10% of 88.5 = 8.85 .....if there is a decimal, start at the decimal
so.....10% of 140
start at the end of the number and move 1 space to the left...
ur answer is 14 <==
If f(x) = 4x+5 what is f(-3)
In this question, you're solving the given function.
In this case, you would plug in "-3" to the x variable, then solve.
Solve:
f(x) =4(-3) + 5
f(x) = -12 + 5
f(x) = - 7
When you're done solving, your answer should be -7.
Answer:
f(x) = - 7
Answer:
-7
Step-by-step explanation:
f(x) = 4 x + 5
f(-3) = 4 (-3) + 5
f(-3) = -12 + 5
f(-3) = -7
If u (x) = negative 2 x squared and v (x) = StartFraction 1 Over x EndFraction, what is the range of (u circle v) (x)?
(one-third, 0)
(3, infinity)
(negative infinity, 3)
(negative infinity, positive infinity)
The range of (u circle v) (x) is (negative infinity, 0).
Explanation:To find the range of (u circle v) (x), we need to substitute v(x) into u(x), which means replacing x in u(x) with v(x).
u(x) = -2x²
So, (u circle v) (x) = -2(v(x))² = -2(1/x)² = -2/x²
The range of (u circle v) (x) is (negative infinity, 0) because as x approaches 0 from the right, (-2/x²) approaches negative infinity, and as x approaches 0 from the left, (-2/x²) approaches positive infinity.
1. Will is 30 years old and works for a company that matches his 401(k) contribution up to 3%. The interest rate for
his 401(k) is 7.13%. If he puts away 9% of his $41,000 salary every year, how much would he have saved in 10
years? Round your answer to the nearest cent.
Oooo
$52,835.72
$56,602.91
$68,395.76
$73, 272.37
Answer:
C. $68,395.76
Step-by-step explanation:
ED2020
Final answer:
Will would have saved approximately $9,420.12 in 10 years by contributing 9% of his $41,000 salary annually, with a 3% employer match and a 7.13% interest rate.
Explanation:
To calculate how much Will would have saved in 10 years, we need to consider both his salary contribution and the employer's matching contribution. Will saves 9% of his $41,000 salary every year, which comes out to $3,690. The employer matches his contribution up to 3%, so the employer would contribute an additional $1,230 (3% of $41,000) every year.
To calculate the total savings after 10 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt). In this case, the principal P is the total annual contributions, the interest rate r is 7.13%, and n is the number of times interest is compounded per year, which we will assume to be once per year.
Using the formula, we can calculate:
A = ($3,690 + $1,230)(1 + 0.0713/1)^(1*10)
A = $5,920 * 1.0713^10
A = $9,420.123296
Rounding to the nearest cent, Will would have saved approximately $9,420.12 in 10 years.
a city’s population is increasing at a rate of 5% each year. Which type of model describes this situation?
A. none of these
B. quadratic
C. exponential
D. linear
Answer:
Exponential
Step-by-step explanation:
Ir's exponential because linear would mean it is increasing by a specific number every year, in which this case does not. Quadratic would mean a vertex form would need to be used, and with the information given , that could not happen.
A group of friends bought 7 tickets to a dog show for $30 each. How much did they spend on the tickets?
Answer:
$210
Step-by-step explanation:
1 ticket= 30
7 tickets = 7*30=$210
What exponential expression is equal to 2 to the negative 5th power • 2 to the 8th power ?
Answer:
2^3
Step-by-step explanation:
2^-5×2^8=2^(-5+8)
= 2^3
Answer:
2³
Step-by-step explanation:
Written in numerical form:
2⁻⁵ · 2⁸
Since both exponents have the same base, one of the exponent rules apply. When multiplying exponents with the same base, you add the exponents.
xᵃ · xᵇ = xᵃ⁺ᵇ
2⁻⁵ · 2⁸
= 2⁽⁻⁵⁾ ⁺ ⁸
= 2³ Simplified exponent form
= 8 Most simplified form
simplify the expression-
3+ -10g –7g +2g
Step-by-step explanation:
3-17g+2g
3-15g
3(1-5)g
How many integers have a square root that is greater than 10 and less than 11?
Answer:
20
Step-by-step explanation:
We know that 10² = 100, so all integers above 100 have a square root greater than 10. Similarly, 11² = 121, so all integers below 121 have a square root less than 11. So, we want the integers from 101 through 120, inclusive. There are integers from through (just as there are 20 integers from 1 through 20).
Which graph represents the solution to the given system ? Y=- 6X - 2Y +2=- 6X
Answer: The graph is attached.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Given the first equation:
[tex]y=- 6x - 2[/tex]
You can identify that:
[tex]m=-6\\b=-2[/tex]
By definition, the line intersects the x-axis when [tex]y=0[/tex]. Then, subsituting this value into the equation and solving for "x", you get that the x-intercept is:
[tex]0=- 6x - 2\\\\2=-6x\\\\x=-\frac{1}{3}\\\\x=-0.333[/tex]
Now you can graph it.
Solve for "y" from the second equation:
[tex]y +2=- 6x\\\\y=-6x-2[/tex]
You can identify that:
[tex]m=-6\\b=-2[/tex]
Notice that the slopes and the y-intercepts of the first line and the second line are equal; this means that they are exactly the same line and the System of equations has Infinitely many solutions.
See the graph attached.
If someone makes $200,000 per year, receives a paycheck monthly and pays 25.6% in income tax, how much is deducted from each paycheck for income tax?
$4266.67 is deducted every month for income tax.
Step-by-step explanation:
Given,
Amount earned per year = $200,000
Income tax = 25.6%
Amount of income tax = 25.6% of amount earned
Amount of income tax = [tex]\frac{25.6}{100}*200000 = \frac{5120000}{100}[/tex]
Amount of income tax = $51200
As this amount is yearly, therefore, we will divide it by 12 to find monthly amount.
Income tax deducted per month = [tex]\frac{51200}{12}=\$4266.67[/tex]
$4266.67 is deducted every month for income tax.
Keywords: income tax, percentage
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Joey wants to get a 90 test average in Science. He has already had two tests and he earned
a 91 and 85 on those tests. Write and solve an equation to find out what Joey needs to get on
the third test in order to have a 90 test average in Science.
I NEED A FREE BRAINLIEST ASAP
Answer:
Joey must get a score of 94 to have a average test score of 90.
Step-by-step explanation:
Joey wants a average score of 90.
He already scored 91 and 85 on the previous two tests, and wants to know the score to get a 90 as an average.
Set the equation:
Average = (score of known tests + x)/(amount of tests in all).
Note that: x = score of the next test.
First, Plug in the corresponding numbers to the corresponding terms/variables:
90 = (91 + 85 + x)/(3)
Simplify. Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, multiply 3 to both sides:
90(3) = (91 + 85 + x)/(3) * 3
270 = 91 + 85 + x
Isolate the variable x. Combine like terms:
270 = (91 + 85) + x
270 = 176 + x
Subtract 176 from both sides:
270 (-176) = 176 (-176) + x
x = 270 - 176
x = 94
Joey must get a score of 94 to have a average test score of 90.
~
Find the solution to the following system of equations:
y+2x=3
y-4x=10
Answer:
x=-7/6, y=16/3. (-7/6, 16/3).
Step-by-step explanation:
y+2x=3
y-4x=10
-----------
y=4x+10
4x+10+2x=3
6x+10=3
6x=3-10
6x=-7
x=-7/6
y+2(-7/6)=3
y-14/6=3
y=3+14/6
y=18/6+14/6
y=32/6=16/3
ILL GIVE BRAINLEST AND EXTRA POINTS
Answer:
C'(1, 2 )
Step-by-step explanation:
The translation rule
(x, y ) → (x + 3, y - 2 )
means add 3 to the original x- coordinate and subtract 2 from the original y- coordinate, thus
C(- 2, 4 ) → C'(- 2 + 3, 4 - 2 ) → C'(1, 2 )
Good evening ,
Answer:
C’(1 ,2)
Step-by-step explanation:
Since the original coordinates of C are (-2,4) then the coordinates of C’ will be
(-2+3 , 4-2) = (1,2).
:)
dori left her house at 12:00 pm and walked at 50 steps per minute and malory left her house at 12:20 and walked 90 steps per minute what time did malory catch up to dori?
Final answer:
Malory catches up to Dori 25 minutes after starting her walk. Since Malory started at 12:20 pm, she catches up to Dori at 12:45 pm by walking at a faster pace.
Explanation:
To determine what time Malory caught up to Dori, we can set up an equation based on the distance each has traveled. Since distance equals speed multiplied by time, and steps per minute can be considered as speed, we need to find a point at which they have both covered the same distance.
Dori started walking at 12:00 pm and Malory started at 12:20 pm, so Malory starts walking 20 minutes later. We'll use t to represent the time in minutes that Malory has been walking when she catches up to Dori.
Thus, Dori has been walking for t + 20 minutes by the time Malory catches up.
We set up the following equation to find t:
Dori's distance = Malory's distance
50 steps/minute × (t + 20) = 90 steps/minute × t
Solving for t gives us:
50t + 1000 = 90t
1000 = 40t
t = 25 minutes
Therefore, Malory catches up to Dori 25 minutes after Malory started walking. Since Malory started walking at 12:20 pm, we add 25 minutes to this time to find out the catch up time is 12:45 pm.
A company set up a food booth and a game booth at a county fair the fee for the food booth is $100 +5 dollars per day the fee for the game booth is $50 +7 dollars per day write an expression for how both booths will cost for the same number of days.
The expression for how both booths will cost for the same number of days (d) is 150 + 12d
Step-by-step explanation:
A company set up a food booth and a game booth at a county fair
The fee for the food booth is $100 + 5 dollars per dayThe game booth is $50 + 7 dollars per dayWe need to write an expression for how both booths will cost for the same number of days
Assume that the number of days is d for both booths
∵ The fee for the food booth is $100 + 5 dollars per day
∵ It used for d days
∴ The cost of the food booth = 100 + 5(d) ⇒ (1)
∵ The fee for the game booth is $50 + 7 dollars per day
∵ It used for d days
∴ The cost of the game booth = 50 + 7(d) ⇒ (2)
To find the cost for both booths in d days add (1) and (2)
∵ The cost for both booths = 100 + 5d + 50 + 7d
- Add the like terms
∴ The cost for both booths = (100 + 50) + (5d + 7d)
∴ The cost for both booths = 150 + 12d
The expression for how both booths will cost for the same number of days (d) is 150 + 12d
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Solve for x when m LKM=90
Answer:
x= -15
Step-by-step explanation:
3x+10=2x-5
3(-15)+10=2(-15)-5
-45+10=-30-5
-35=-35
Each side of the angle is equal, that's how i knew the two were supposed to be equal. <3 Hope this helps!
(I found the picture.)
Answer:
17
Step-by-step explanation:
L 3x + 10 5875 =90 2x - 5 x=_17 5 5 - x =17 Use the image to answer questions 6-7. 125 Given that Xll Y use the figure below to answer questions 8 - 11. -40-40 normal Unit 2: Equations & Exponents Directions: 1. Solve each problem.
I need this please 64 points!
Answer:
None. Wanda's work is correct.
Step-by-step explanation:
The first is correct.
Answer:
Wanda converted the percent to a decimal incorrectly. It should be 0.73
Step-by-step explanation:
It has to be move two decimal place.
anything’s appreciated :)
Answer:
See explanation
Step-by-step explanation:
An inscribed angle is the angle with vertex and two endpoints lying on the circle.
1) This option shows an inscribed angle, because vertex A and endpoints B ans C lie on the circle.
2) This option doesn't show an inscribed angle, because vertex K doesn't lie on the circle.
3) This option shows an inscribed angle, because vertex X and endpoints V ans W lie on the circle.
4) This option doesn't show an inscribed angle, because vertex M doesn't lie on the circle.
5) Angle CAB is inscribed angle subtended on the arc BC with measure of 80°, so its measure is 40° (half of the measure of arc BC)
6) Angle WXV is inscribed in the circle and subtended on the arc WV. Hence, the measure of the arc WV is twice the measure of angle VXW and is equal to 84°.
Options 7) and 8) are not visible.
2. What are the next two terms of the following sequence?-2,4,-8, 16, ...
A. -32, 64 D . 32, – 64
B. -32, 64
C. 32, 64
Answer:
(A.B.)-32, 64Step-by-step explanation:
[tex]-2\\(-2)(-2)=4\\(-2)(4)=-8\\(-2)(-8)=16\\-----------------\\(-2)(16)=-32\\(-2)(-32)=64\\\vdots[/tex]
Each next term is created by multiplying the previous term by (-2).
Answer:
It's the geometric sequence so the following numbers are:
-32,64
d= -2(multiplication number)
Answer: i did not fully understand,since there are two similar answer options(it's wether A or B)
Good luck!
Intelligent Muslim,
From Uzbekistan.
A dilation has been performed on DEF. The length of segment EF is 10 cm and the length of segment E'F' is 5 cm. If segment DE has a length of 12 cm, what is the length of segment D'E'?
Answer:
length of segment D'E= 6
Step-by-step explanation:
The dilation of DEF is 1/2
5 is 1/2 of 10
6 is 1/2 of 12
Answer:
6 cm
~~~~~~~~~~~~~~~~
Step-by-step explanation:
i took the unit test :) trust me
a city has 4 new houses for every 9 old houses . if there are 36 new houses in the city , how many old houses are there
Answer:
There are EIGHTYONE old homes
Im hoping that this helps you
if this helped you please give a brainliest!
- Gigiblue2663 :)
The average test score of RSM students in September increased by 10%. In October it increased by another 15%. By what percent did the average score on the test increase during the two months? PLEASE HELP I NEED THE ANSWER QUICK
Answer:
26.5%
Step-by-step explanation:
Increasing Percentages
When sequential percentages increasing are computed, each increase applies to the previous result, instead of the first quantity. That is why sometimes the final results may be confusing. For example, increasing 10% and then 15% will not be the same as increasing a total of 25%.
The average test scores of RSM students first increased by 10%. It means that some quantity C increased by
[tex]10C/100=0.1C[/tex]
Now the average test scores are
[tex]C+0.1C=1.1C[/tex]
A new increasing occurred by 15%, and the previous quantity must be multiplied by 1.15, so the final average test scores are
[tex]1.15(1.1C)=1.265C[/tex]
It means that the total increasing was [tex]100(1.265-1)=26.5\%[/tex]
Answer:
26.5%
Step-by-step explanation:
IM SMART! :D
(-3)/-6
what is the value?
-2
2
1/2
-1/2
｡☆✼★ ━━━━━━━━━━━━━━ ☾
The negatives cancel each other out
Thus, your answer is C. 1/2
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Answer: 1/2
Step-by-step explanation: When dividing integers, if the signs are the same, the quotient is positive. So a negative divided by a negative always equals a positive. In this problem -3 ÷ -6 is 0.5.
However, there is no 0.5 on the list so we need to write the decimal as a fraction.
To write the decimal 0.5 as a fraction, we use the place value chart. 0.5 means 0 units and 5 tenths which can be written as the fraction 5/10.
Notice however that 5/10 is not in lowest terms so we need to divide the numerator and denominator by the greatest common factor of 5 and 10 which is 5 to get the equivalent fraction 1/2.
29.5 divided by four