64x³+125y³
= (4x+5y)( 16x²-20xy+25y²)
a³ + b³ = ( a + b )( a² - ab + b² )
64x³ + 125y³
= ( 4x )³ + ( 5y )³
= ( 4x+5y )[ (4x)²- (4x)(5y)+(5y)²]
= (4x+5y)( 16x²-20xy+25y² )
Two times the sum of a number and 3 is 8.
Use the variable c for the unknown number.
My answer is : 2(c+3)=8
The " is" throwing my brain off, thanks so much
Two times or Twice the sum of a number and 3 is 8. The value of the number will be 1.
Let the value of the unknown number or variable be c.
Given,
"Two times the sum of a number and 3 is equal to 8", which means when you add the unknown number with 3 and then multiply it by 2, then the final answer will come as 8.
If we form the statement into an equation, then finding the value of the unknown variable will be a lot easier.
The equation will be:
2(c + 3) = 8
=> 2c + 6 = 8
=> 2c = 8- 6
=> 2c = 2
=> c = 2/2
=> c = 1.
Hence, the value of the unknown number c will be 1.
To learn more about questions including unknown variables and equations:
https://brainly.com/question/20712267
4. Solve the equation m² = 14.
Answer:
m=3.7
Step-by-step explanation:
m²=14
m=√14
m=3.7416573868
m=3.7(2 d.p)
Select all the terms which are equivalent to the slope in a proportional relationship.
The terms which are equivalent to the slope in a proportional relationship include:
Constant of proportionalityOriginRise over runWhat is a proportional relationship?Proportional relationships are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."
The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope formula is the rise over run formula, where the fraction consists of a rise, whether the line is going up or down, divided by the run.
Learn more about constant on
https://brainly.com/question/15618632
#SPJ1
Complete question
Select all the terms which are equivalent to the slope in a proportional relationship.
Constant of proportionality
Origin
Inverse
Rise over run
Unit rate
Write in vertex form and state the vertex of the graph:
f(x)=20x+9+5[tex]x^{2}[/tex]
The vertex is (-2, 11), then the vertex form of the quadratic is:
f(x) = 5*(x + 2)^2 - 11
How to write the quadratic equation in vertex form?A quadratic equation with a leading coefficient a and a vertex (h, k) can be written in vertex form as:
y = a*(x - h)^2 + k
And for a quadratic equation of the form:
y = a*x^2 + b*x + c
The vertex is at:
h = -b/2a
In this case, our equation is:
f(x) =5x^2 + 20x + 9
Then:
h = -20/2*5 = -2
Evaluating in x = -2 we get:
f(-2) = 5*(-2)^2 + 20*-2 + 9
f(-2) = 5*4 - 40 + 9
f(-2) = 20 - 40 + 9 = -20 + 9 = -11
The vertex is (-2, -11), and the leadin coefficient is a = 5, then the vertex form is:
f(x) = 5*(x + 2)^2 - 11
Learn more about quadratic equations:
https://brainly.com/question/1214333
#SPJ1
Encuentra el área de la región coloreada.
A human disease known as cystic fibrosis is inherited as a recessive trait. For example, the possible outcomes of a child inheriting cystic fibrosis genes are CC Cc cC cc if the child’s parents had one copy of each version of the gene so the probability of having a disease is ¼. Find the probability that 3 out of 6 children of these parents will have a cystic fibrosis.
The probability that 3 of the 6 children of this parents has the genes would be 0.1318
How to solve for the probabilityThe possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.
The total number of children from the family is n = 6
and the probability of those with the cystic fibrosis is x = 3,
Probability of the disease = 0.25
We have the formula as
[tex]^{6} C_{x} *P^{x} *(1-p)^{n-x}[/tex]
The probability is 1/4 = 0.25
This is then written as
6C3 x 0.25³ x (1 - 0.25)⁶⁻³
= 20 x 0.015625 0.421875
= 0.1318
The probability that 3 out of the 6 children would have this gene is 13.18%
Read more on probability here: https://brainly.com/question/24756209
#SPJ1
5. We have 3 coins: 1 normal coin, 1 trick coin with 2 heads and 1 trick coin with 2 tails. A coin is drawn at random and put on a table and you see that it is
heads. What is the probability you have the real coin? (4 points)
Answer:
1/3
Explanation:
Imagine you repeat the experiment 100 times.
It is expected that half of the times (50) you take the fair coin and half of the times (50) the trick coin.
When you take the fair coin, half of the times you get heads, that is 25 times from 100 you “get the fair coin AND you get heads with the fair coin”.
When you take the trick coin, all the times you get heads, that is 50 times from the original 100 you “get the trick coin AND you get heads with the trick coin”.
In total, it is expected you get heads 75 times. And from those, 50 times will be with the trick coin and 25 times with the fair coin.
Now, if you get one of those at random, what’s the likelihood it was the fair coin?
Well, you have 25 cases it was the first coin and 50 cases it wasn’t, so it is 25 from a total of 75 and that is 25/75 = 1/3. That is, about 33.33%
Also, with probability theory:
Bayes’ Theorem:
P(B|A) = P(A ∩ B) / P(A)
P(A|B) = P(A ∩ B) / P(B)
So: with just the definitions I prove Bayes:
P(B|A) = P(A|B) * P(B) / P(A)
In our case:
P(Fair| Heads) = P(Heads|Fair) * P(Fair) / P(Heads)
p = P(Fair | Heads) = 0.5 * 0.5 / P(Heads)
What is P(Heads) ??
We can apply this:
Heads = (Heads ∩ Fair) U (Heads ∩ Trick)
And those in the union are disjoint (mutually exclusive), so:
P(Heads) = P(Heads ∩ Fair) + P(Heads ∩ Trick) =
= P(Heads|Fair) * P(Fair) + P(Heads|Trick) * P(Trick) =
= 0.5 * 0.5 + 1.0 * 0.5 = 1/4 + 1/2 = 3/4
Then:
p = P(Fair | Heads) = 0.5 * 0.5 / P(Heads) = 1/4 / (3/4) = 1/3
The volume of cube depends on the length of its sides. This can be written in function notation as v(s). What is the best interpretation of v(2)=8
The best interpretation of the function v(2) = 8 is that the volume of a cube with side length of 2 units is 8 cubic units
What are function notations?Function notations are the representation of a function using expressions such as g(x), f(x), etc
How to determine the best interpretation of the function notation?From the question, we have the following function notation that can be used in our computation:
v(2) = 8
From the question, we have the following representation
v(s)
This means that the volume of a cube of side length s is v(s)
When the above function is compared to v(2) = 8, we have the following comparison
s = 2 and v(s) = 8
This means that a cube of side length 2 has a volume of 8
The above represents the best interpretation of v(2) = 8
Read more about function notation at
https://brainly.com/question/27834526
#SPJ1
I need help with this Question.
The number of quarts in 12 L is 12.684 qt.
Given that, 12 L to qt.
What is metric conversion?Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
Here,
There are 1.057 quarts in a liter, and there are 0.946 liters in a quart.
Now, 12 L=12×1.057
= 12.684 qt
Therefore, the number of quarts in 12 L is 12.684 qt.
To learn more about the metric conversion visit:
brainly.com/question/21244256.
#SPJ1
what is:
s . s + 0.5s . s
if s=8.2
Answer:
100.86
Step-by-step explanation:
8.2*8.2+0.5(8.2)*8.2
6. Solve the following equation: 28 ÷ 7 + 2 × 3 = ?
O A. 12
OB. 10
OC. 24
O D. 18
Answer:
B. 10
Step-by-step explanation:
According to BODMAS rule, the brackets have to be solved first followed by powers or roots, then Division, Multiplication, Addition, and at the end Subtraction.[tex]\rm \implies 28 \div 7 + 2 \times 3 \\ \\ \rm \implies 4 + 2 \times 3 \\ \\ \rm \implies 4 + 6 \\ \\ \rm \implies 10[/tex]
What is the image of (12,-12) after a dilation by a scale factor of 1/4 centered at the origin?
The image of (12, -12) after a dilation by a scale factor of 1/4 centered at the origin would have these coordinates (3, -3).
What is dilation?In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object based on the scale factor applied, but not its shape.
Next, we would dilate the coordinates of the preimage (12, -12) by using a scale factor of 1/4 centered at the origin (0, 0) as follows:
Coordinate A (12, -12) → Coordinate A' (12 × 1/4, -12 × 1/4) = Coordinate A' (3, -3).
In conclusion, the coordinates of the image after a dilation by using a scale factor of 1/4 are (3, -3).
Read more on dilation here: brainly.com/question/20482938
#SPJ1
help please??? brainlest
5. At PrintAll copying, a new copying machine can produce five more than twice the number of copies per hour of the old copy machine. If the new machine produces 205 copies per hour, how many copies can the old machine produce? Show the equation you used to determine the answers.
6. A recipe calls for 2 cups of milk for every 6 1/4 cups of flour. If you increase the flour to 43 3/4 cups, how many cups of milk will you use?
Step-by-step explanation:
5.
xnew = 205 = 2×xold + 5
200 = 2×xold
xold = 100
the old city machine can produce 100 copies per hour.
6.
2 cups of milk relate to 6 1/4 cups of flour.
such recipes represent a direct dependency of one variable on the other. one variable is always the other variable multiplied by a constant factor.
m = cups of milk
f = cups of flour
m = n×f
2 = n×(6 1/4) = n×(6×4 + 1)/4 = n×25/4
8 = 25n
n = 8/25
now, f = 43 3/4 = (43×4 + 3)/4 = 175/4
so,
m = 8/25 × 175/4 = (8×175)/(25×4) = 2×7 = 14
you will need 14 cups of milk.
Once the fence is installed, Jason uses 6 gallons 3 quarts of paint. How many quarts does he use?
Answer:
Jason used 27 quarts of paintStep-by-step explanation:
We know that:
1 gallon = 4 quartsThen 6 gallons is:
6 gallons = 6*4 quarts = 24 quartsAdd 3 quarts to get total:
24 + 3 = 27 quartsAnswer:
27 quarts
Step-by-step explanation:
Now we have to,
→ find how many quarts does 6 gallons 3 quarts of paint measure.
Formula we use,
→ 1 gallon = 4 quarts
Now the required solution will be,
→ (6 × 4) + 3
→ 24 + 3
→ 27 quarts
Hence, the answer is 27 quarts.
2007 Federal Income Tax Table Single: Over But not over The tax is $0 $7,825 10% of the amount over $0 $7,825 $31,850 $788 + 15% of the amount over $7,825 $31,850 $77,100 $4,386 + 25% of the amount over $31,850 $77,100 $160,850 $15,699 + 28% of the amount over $77,100 $160,850 $349,700 $39,149 + 33% of the amount over $160,850 $349,700 And Over $101,469 + 35% of the amount over $349,700 Tim Tradesman had a taxable income of $82,500. He figured his tax from the table above.
Earned income is said to be $35,000, Base tax amount at that level is $4386, The amount over $31850 is $3150, Line 3 is multiplied by 25% is $787.50, The sum of lines 2 and 4 is $5173.50 and This amount divided by 12 is $431.13.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
The given Federal Income Tax Table Single: Over But not over The tax is $0 $7,825 10% of the amount over $0 $7,825 $31,850 $788 + 15% of the amount over $7,825 $31,850 $77,100 $4,386 + 25% of the amount over $31,850 $77,100 $160,850 $15,699 + 28% of the amount over $77,100 $160,850 $349,700 $39,149 + 33% of the amount over $160,850 $349,700 And Over $101,469 + 35% of the amount over $349,700
Earned income is said to be $35,000.
Base tax amount at that level is $4386.
The amount over $31850 is $35000-31850 = $3150
Line 3 is multiplied by 25%: $3150×0.25 = $787.50
The sum of lines 2 and 4 is $4386 +787.50 = $5173.50
This amount divided by 12 is ... $5173.50/12 ≈ $431.13
Hence, Earned income is said to be $35,000, Base tax amount at that level is $4386, The amount over $31850 is $3150, Line 3 is multiplied by 25% is $787.50, The sum of lines 2 and 4 is $5173.50 and This amount divided by 12 is $431.13.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
A Norman window is a window with a semicircle on top of a regular rectangular window as shown in the diagram. What should the dimensions of the rectangular part of a Norman window be to allow in as much light as possible if there is only 12 ft of the framing material available?
The dimensions of the rectangular window that gives a maximum area are as follows;
Width = [tex]\dfrac{12}{2+\pi }[/tex] feet and length = 3 feet
What is the maximum value of a function?The maximum value of a function is given by the point at which the graph of the function has the highest value.
The parameters of the window are;
Length of the framing material available = 12 ft.
The shape of the window = A semicircle on top of a regular rectangular window
Required; The dimension of the rectangular part of the Norman window that allows the most light
Solution;
Diameter of the semicircular part of the window = The width of the rectangular part
Let x represent the width of the window, we have;
Perimeter of the semicircle = π·x/2
Side length of the rectangular window = (12 - π·x/2 - x)/2
Area of the rectangular part of the window, A = x × (12 - π·x/2 - x)/2
Area of the semicircle = π·x²÷4
Area of the window, is therefore;
[tex]A =\dfrac{ x \times (12 - \dfrac{\pi \cdot x}{2} - x)}{2} +\dfrac{ \pi \cdot x^2}{4}[/tex]
At the maximum area, of the rectangular part, we have;
[tex]A_r' =\dfrac{d}{dx}\left( A =\dfrac{ x \times (12 - \dfrac{\pi \cdot x}{2} - x)}{2} \right) = -\dfrac{x\cdot \pi +2\cdot x-12}{2} = 0[/tex]
x·π + 2·x - 12 = 0
The width, x = [tex]\dfrac{12}{2+\pi }[/tex] feet
The length of the rectangle is therefore;
[tex](12 - \pi \cdot \dfrac{6}{2+\pi } - \dfrac{12}{2+\pi })/2 = 6 - \pi \cdot \dfrac{3}{2+\pi } - \dfrac{6}{2+\pi } = 3[/tex]
The length of the rectangular window = 3 feet
Learn more about the maximum value of a function here:
https://brainly.com/question/15300035
#SPJ1
How many numbers are there from 10 to 99 in which the difference between the largest digit and the smallest digit equals 4?
For example 15 and 51, where 5 – 1 = 4.
There are 9 numbers from 10 to 99 in which the difference between the largest digit and the smallest digit equals 4
How to determine the count of the numbers?The difference can be represented as
Largest - Smallest = 4
Also, we have two instances to be
15 and 51
And the range is given as
Range = 10 to 99
In a range of 10, there is only one number whose difference between the digits is 4
There are 9 ranges of 10 from 10 to 99
So, the count of the range is
Count = 9 range * one number
Rewrite as
Count = 9 * 1
Evaluate
Count = 9
Hence, there are 9 of such numbers from 10 to 99
Read more about numbers at
https://brainly.com/question/27672495
#SPJ1
solve the equation 619m + 313m = 2813for m.
Answer:
2813
m = ----------
932
Step-by-step explanation:
619m + 313m = 2813
932m = 2813
÷932 ÷932
2813
m = ----------
932
I hope this helps!
Answer:
[tex]m=\frac{2813}{932}[/tex]
Step-by-step explanation:
Combine like terms:
[tex]{619m}+{313m}=2813{932m}=2813[/tex]
Divide both sides by the same factor:
932m=2813
[tex]\frac{932m}{932}}=\frac{2813}{932}}\\[/tex]
Simplify
Cancel terms that are in both the numerator and denominator
[tex]m=\frac{2813}{932}[/tex]
A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.05.
If 202 are sampled, what is the probability that the sample proportion will differ from the population proportion by greater than 0.03? Round your answer to four decimal places.
The probability that the sample proportion of the number of people using the courier will differ from the population proportion by greater than 0.03 is 0.0504
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
mean, μ = p = 0.05
sample size, n = 202
standard deviation, σ
= √{(p(1 - p)) / n}
= √{(0.05(1 - 0.05)) / 202}
= √{(0.05 * 0.95) / 202}
= 0.01533
The probability
differ from the population proportion by less than 3%
|X - 0.05| > 0.03
X < 0.02 OR X > 0.08
P(z < 0.02) + P(z > 0.08 )
z score for z < 0.02
z = (0.02 - 0.05) / 0.01533
= -1.9569
p value for z < -1.9569 = 0.02518
z score for z > 0.08
z = (0.08 - 0.05) / 0.02196
= 1.9569
p value for z > 1.9569 = 1 - 0.9748 = 0.02518
The probability required = 0.02518 + 0.02518 = 0.0504 = 5.04%
Learn more about p - values at:
https://brainly.com/question/28940355
#SPJ1
kieran tried to shade all the multiples of 3 on the hundred chart, but he made a mistake. what mistake did kieran make?
Answer:
Kieran shaded the multiples of 9 instead of the multiples of 3
Step-by-step explanation:
Which is the BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3?
A) 2
B) 3
C) 4
D) 6
The BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3 is 2 so option A is correct.
Given:
1 ≤ x ≤ 3
we know x is between 1 and 3 so the best estimate is 2 even though the answer could also be 3 but that will be skewed.
1 ≤ 2 ≤ 3 is the best estimate.
Therefore the BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3 is 2 so option A is correct.
Learn more about the average rate and function here:
https://brainly.com/question/28744270
#SPJ1
Determine which integer will make the inequality x − 4 < 16 true.
Answer:
Any Integer less than 20 ( ex. 19 , 18 , 17 , 16 , ........)
Step-by-step explanation:
Solve the Inequality to find the Integers that satisfy the Inequality
x - 4 < 16
add 4 for both terms
x - 4 + 4 < 16 + 4
x < 20
So any Integer less than 20 will make the Inequality True
You need 1.25 cups of sugar to make 1 dozen cookies. If you want to make 78 cookies, how much sugar is needed? Round your answer to 1 decimal places as needed To make 78 cookies, you will need cups of sugar.
The quantity of sugar required to make 78 cookies is 8.1 cups.
Given that, you need 1.25 cups of sugar to make 1 dozen cookies.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here,
The quantity of sugar to make 1 cookie
= 1.25/12
= 0.10417
The quantity of sugar to make 78 cookies
= 78×0.10417
= 8.1 cups
Therefore, the quantity of sugar required to make 78 cookies is 8.1 cups.
To learn more about the unitary method visit:
brainly.com/question/22056199.
#SPJ1
The probability that a 50-year-old male in the U.S. will die within one year is about 0.00142. An insurance company is preparing to sell a 50-year-old male a one-year, $60,000 life insurance policy. How much should it charge for its premium in order to have an expectation of $0 for the policy (i.e., make no profit and make no loss)? (Round your answer to the nearest dollar.)
They should charge for its premium in order to have an expectation of $0 for the policy is $85.
Given that, the probability that a 50-year-old male in the U.S. will die within one year is about 0.00142.
What is the probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, probability of alive 100-0.00142
= 0.99858
P(A)=0.99858A+0.00142(A+60000)
Put A=0, in the obtained function, we get
P(0)=0.99858(0)+0.00142(0+60000)
=0.00142×(60000)
=$85.2
= $85
Therefore, they should charge for its premium in order to have an expectation of $0 for the policy is $85.
To learn more about the probability visit:
https://brainly.com/question/11234923.
#SPJ1
y=1/x+2 slope and y intercept
Answer:
Step-by-step explanation:
I think the slope and the y is not 1/x because 2 is not part of the slope, im not sure
carolina and her friends are training for a kayaking competition. the average distance and time traveled by each is shown in the table below. if the distance kayaked in the competition is 3 miles, predict who will win based on the rates shown. predict how long it will take the winner to complete the race if their rate remains constant
Carolina, 7/8 mi in 1/2 hr
Leslie, 1 mi in 1/3 hr
Bryan 3/4 mi in 3/4 hr
Javier 1 mi in 2/3 hr
The winner of the race among the friends would be Leslie.
Who would win the race?The person who has the highest average speed will win the race. Average speed is the total distance travelled per time.
Average speed = total distance / total time
Carolina's average speed = 7/8 ÷ 1/2
7/8 x 2 = 7/4 = 1 3/4 miles per hour
Leslie's average speed = 1 ÷ 1/3
1 x 3 = 3 miles per hour
Bryan's average speed = 3/4 ÷ 3/4
3/4 x 4/3 = 1 mile per hour
Javier's average speed = 1 ÷ 2/3
1 x 3/2 = 1 1/2 miles per hour
To learn more about average speed, please check: https://brainly.com/question/21734785
#SPJ1
what fraction of the numbers from 1 to 20 contain the digit 7
Answer:
2/20
Step-by-step explanation:
Only 7 and 17 contain the number 7
You can afford a $1100 per month mortgage payment. You've found a 30 year loan at 8% interest.
a) How big of a loan can you afford?
b) How much total money will you pay the loan company?
c) How much of that money is interest?
a) $149911.84 can be afforded
b) $39600 is the total money you will pay the loan company
c) $246088.16 is the interested amount
What is interest ?The cost of borrowing money is called interest, and it is typically stated as a percentage, such as an annual percentage rate (APR).Lenders may charge interest to borrowers for using their funds, or borrowers may charge interest to lenders for using their funds.Interest is frequently regarded as simple interest (based on the principal amount) or compound interest (based on principal and previously-earned interest).Credit cards, mortgages, auto loans, personal loans, savings accounts, and penalty assessments are all frequently linked with interest.The macroeconomic policy set by the Federal Reserve's federal funds rate has a significant impact on interest rates.Calculation
Given,
d=$1100
N= 30 years
r = 8% or 0.08
a) Loan amount that can be afforded
[tex]=\frac{d[1- (1+\frac{r}{k})^{-Nk} }{\frac{0.08}{12} }[/tex]
[tex]=\frac{1100[1- (1+\frac{0.08}{12})^{-30*12} }{\frac{0.08}{12} }[/tex]
= $149911.84
b) Total money you pay = d×N×k
=1100×30×12
=$39600
c) Interest paid = Total money paid – loan amount
⇒39600–14911.84 = $246088.16
Hence,
a) $149911.84 can be afforded
b) $39600 is the total money you will pay the loan company
c) $246088.16 is the interested amount
To learn more about interest, refer to
https://brainly.com/question/25793394
#SPJ1
Select the correct rational numbers.
-4 2/3 ,-3 2/3, -1 2/3 2/3