Answer: nm(m-n)
Step-by-step explanation:
m^2n-mn^2=
n*m(m)-m*n(n)=
n*m(m-n)=nm(m-n)
A school has 360 students, 4/9 of whom are boys. How many of the students are boys? How many are girls?
Answer:
There are 160 boys and 200 girls
Step-by-step explanation:
its a proportion
Write an expression that represents the total owed for 4 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $35?
Answer:
4c + 35
Step-by-step explanation:
What every the monthly amount is (c) you would multiply that by 4 to find the cost for 4 months and then you have to add in the one time cost of 35
How much of a(n) 70% orange juice drink must be mixed with 18 gallons of a 30% orange juice drink to obtain a mixture
that is 50% orange juice?
Answer:
18 gallons
Step-by-step explanation:
Start with x gallons of 70% juice and 18 gallons of 30% juice.
Result: x + 18 gallons of 50% juice
0.7x + 0.3 × 18 = (x + 18)(0.5)
0.7x + 5.4 = 0.5x + 9
0.2x = 3.6
x = 18
Answer: 18 gallons
Rearrange the formula to make x the subject y=4(x-1)
By rearranging the formula using algebraic operations, the value of x is [tex]\frac{y}{4}[/tex] - 1.
What is an Algebraic Expression?When operations like addition, subtraction, multiplication, division, etc. are performed on variables and constants, the result is a mathematical statement known as an algebraic expression.
To find the value of x, use the same operations on both sides of the equation.
For making x the subject
Divide by 4 on both sides
[tex]\frac{y}{4}[/tex] = (x-1)
On both sides of the equation, add 1.
[tex]\frac{y}{4}[/tex] - 1 = x
As a result, by rearranging the equations, the value of x is [tex]\frac{y}{4}[/tex] - 1.
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A manufacturing company has decided to be carbon free by 2030. what can it do to achieve this goal?
The manufacturing company has decided to be carbon free by 2030. so, it can reduce its pollution rate by using environmentally friendly equipment to achieve this goal.
Pollution:
The term pollution refers any substance that negatively impacts the environment or organisms that live within the affected environment.
Given,
A manufacturing company has decided to be carbon free by 2030.
Here we need to find the solution to achieve this goal.
To achieve this goal the company can take many measures this includes,
To completely switching to alternative sources of energy. The company can reduce its pollution rate by using environmentally friendly equipment.
By making maximum use of renewable energy in the company, in which energy can be emitted using solar energy, windmill etc.
And by planting more and more trees, the amount of oxygen in our environment should be increased.
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Given last periods forecast of 65, and last periods demand of 62, what is the simple exponential smoothing forecast with an alpha of. 4 for the next period?.
The exponential smoothing forecast for next period is 63.2.
What is exponential smoothing?A time series forecasting technique called exponential smoothing can be expanded to support data with a systematic trend or seasonal component.
Now,
Given:
Last period forecast = 65Last period demand = 62α = 0.4To find: Simple exponential smoothing forecast with α = 0.4 for next period.
Finding:
Now, by the concept of exponential smoothing, forecast for next period will be given by:
Ft + 1 = α Dt + (1 - α)F,
where,
Ft+1 = the next forecast,
α = weighing factor,
Dt = actual value for this period,
F = forecast value for the current period,
Substituting the values in the above expression:
=> Ft + 1 = 0.4 (65) + (1 - 0.4) 62
=> Ft + 1 = 26 + 37.2
=> Ft + 1 = 63.2
Hence the exponential smoothing forecast for next period is 63.2.
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Please help thank youuu
Answer:
f(-7) = -15
g(-3) = 27
Step-by-step explanation:
We see that the functions defined are:
f(x) = 2x - 1
AND
g(x) = 2x^2 - 3x
This problem asks to find f(-7) and g(-3). To find this, we have to plug the respective numbers into the respective functions.
f(-7) = 2 (-7) - 1
f(-7) = - 14 - 1
f(-7) = -15
g(-3) = 2(-3^2) - 3(-3)
g(-3) = 2(9) + 9
g(-3) = 18+9
g(-3) = 27
FINAL ANSWER: f(-7) = -15, g(-3) = 27
use mathematical symbols to write 3 different expressions to represent three groups of five
The different expressions to represent three groups of five are 3 * 5, 5 + 5 + 5 and 3 + 3 + 3 + 3 + 3
How to write different expressions to represent three groups of five?The mathematical statement is given as:
three groups of five
The statement three groups of five means
Three multiplied by 5
i.e. 3 * 5
This can also be written as
5 + 5 + 5
Also, it can be expressed as
3 + 3 + 3 + 3 + 3
Hence, the different expressions to represent three groups of five are 3 * 5, 5 + 5 + 5 and 3 + 3 + 3 + 3 + 3
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Shifting data, by adding a constant to each data value, does not change the _________.
A. quartiles
B. mean
C. standard deviation
D. median
The standard deviation is a measure of a collection of values' variance or dispersion. The correct option is C, standard deviation.
What is a standard deviation?The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.
Shifting data, by adding a constant to each data value, do not change the standard deviation. This is because the standard deviation is a measurement of how much a group of values varies or is dispersed.
Hence, the correct option is C, standard deviation.
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A loaf of bread 9 in. long is cut into slices 3/8 in. thick.
Answer:
32
Step-by-step explanation:
There is nothing this but the answer is 32.
The finances of a group of pet owners were analyzed to determine how much they were spending on their pet(s) each year. A graph of that data is shown:
A graph with Number of Owners on the x axis and Yearly Cost of Pets, in hundreds, on the y axis. The x axis has a scale from 1 to 10 with an increment of 1. The y axis has a scale of 5 to 15 with increments of 1. A curved line connecting 1, 15, approx 3, 7, and 10, 0 is drawn.
Would (3, 7.2) be a realistic solution for the function? Explain.
Group of answer choices
Yes, it is realistic to have 7.2 owners who spend $300 dollars on their pet(s).
No, it is not realistic to have 3 owners.
Yes, it is realistic that 3 owners spend $720 a year on their pet(s).
No, it is not realistic that owners spend $720 a year on their pet(s).
It is realistic that 3 owners spend $720 a year on their graph
C) Yes, it is realistic that 3 owners spend $720 a year on their pet(s).Given that
In the displayed graph, the y-axis shows the annual cost of pets in hundreds of dollars, while the x-axis shows the number of pet owners.The graph's path through the points(1,15),(3,7), and (10,0).To find
Would (3, 7.2) be a realistic solution for the function?So, according to the question
We can say that,
3 owners are present and,
A pet's annual cost is $720.
So, the option C (Yes, it is realistic that 3 owners spend $720 a year on their pet(s) ) is correct explanation of it.
Because no fractional value can represent the number of owners. Therefore, having 7.2 owners is not feasible and other options showing only one value. So A, B, and D are wrong answer.
C) Yes, it is realistic that 3 owners spend $720 a year on their pet(s).
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Write and simplify an expression for the ratio of the volume of the cylindrical tank to its surface area (including the bases).
The ratio of the volume of the cylindrical tank to its surface area will be r / 2.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
Let r be the radius and h be the height of the cylinder.
Then the volume of the cylinder will be
V = π r²h cubic units
Then the surface area of the cylinder will be
SA = 2πrh square units
Then the ratio of the volume of the cylindrical tank to its surface area will be
V / SA = π r²h / 2πrh
V / SA = r / 2
The ratio of the volume of the cylindrical tank to its surface area will be r / 2.
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(PLEASE HELP!) A car travels 76 km due north and then 25 km due east.
(a) What is the cars current bearing from the starting point correct to the nearest degree?
(b) How far is the car from the starting point correct to the nearest km?
Answer:
Step-by-step explanation:
Look at the File I attached. The Question says that a car travels 76 km north then 25 km east. Now think of this as the Right angled triangle I attached in the file.
a) Bearing from the staring point to the means the degrees of the part i marked with a question mark.
Now SOH CAH TOA
76 km is the ADJACENT
25 km is the OPPOSITE
and x is the HYPOTENUSE
We have the values of the ADJACENT and the OPPOSITE.
Now see which rule has both, It is TOA(tan rule) which is:
tan(y) = OPPOSITE/ADJACENT (y is the degrees we will get)
tan(y) = 25/76 ( opposite of the degree we need is 25 and adjacent is 76)
tan inverse(25/76) = y (inverse will be given as to the power -1 on the calculator)
FINAL ANSWER OF (a) = 18.21°
b) This part is asking for the length of the hypotenuse, which i denoted as x in the attached file.
For this part, you will use the Pythagoras Theorem
Which is :
a² + b² = c²
Where c is the hypotenuse and a and b are the opposite and adjacent.
So
76² + 25² = x²
6401 = x²
√6401 = x
x = 80.01
Consuelo is buying flavored coffee and plain coffee. the total amount of money she spends on coffee is t = 5.50p + 7f, where p represents the cost of a package of flavored coffee.
Answer is
(a) She can buy 7 packages of plain coffee or 5 packages of coffee.
(b) f = [tex]\frac{T- 5.50 p}{7}[/tex]
(c) she can buy 3 packages of flavoured coffee
(a) she spent on coffee is $ 40
amount of money she spends on coffee is 5.50
then, packages of plain coffee = [tex]\frac{40}{5.50}[/tex] ≈ 7.2
so she buy 7 packages of plain coffee.
she spent on coffee is $ 40 and amount spends on flavoured coffee is 7
then , packages of flavoured coffee = [tex]\frac{40}{7}[/tex] ≈ 5.7
so she can buy 5 packages of flavoured coffee.
(b)According to question ,
T = 5.50 + 7f
so 7f = T - 5.50
then , f = [tex]\frac{T - 5.50}{7}[/tex]
(c) we get the value of f = [tex]\frac{T - 5.50}{7}[/tex]
given that , f is equal to 3
then, f = [tex]\frac{T - 5.50}{7}[/tex]
= [tex]\frac{T - 5.50}{7}[/tex]×3
we get = [tex]\frac{T - 16.5}{7}[/tex]
when T is equal to 40
then , f = [tex]\frac{40 - 16.5}{7}[/tex] ≈ 3.35
so she can buy 3 packages of flavoured coffee.
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The functions are defined:
f(x) = -2x
g(x) = 2x + 5
h(x) = x² + 3x-10
Calculate the indicated function values.
ƒ(6²)
The indicated function value is f(6²) = -72
How to calculate the indicated function values?The function definitions are given as
f(x) = -2x
g(x) = 2x+ 5
h(x) = x^2 + 3x - 10
The function f(6²) means that x = 6² in f(x)
So, we have
f(6²) = -2(6²)
Evaluate
f(6²) = -72
Hence, the indicated function value is f(6²) = -72
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Write an equation of the line satisfying the given conditions. the line passes through (25,24)(25,24) and is perpendicular to y=6y=6.
The equation of the line is x = 25, in accordance with the given conditions.
What is the equation of a line?It is a first-order equation with the variables x and y. The coordinates of the point on the line shown in the coordinate plane are represented by the values of x and y.Given:
Line passes through (25,24)Line is perpendicular to y =6.To find: Equation of the line.
Finding:
Let the equation of the line be: (y - y') = m (x - x'),
where, (x',y') = point through which the line passes and m = slope of the line.
Since the given line is perpendicular to y = 6; the slope of this line = 0.The slope of the first line = [tex]\frac{1}{0}[/tex] , i.e., the y-intercept of this line does not exist and it is a vertical line.
Hence, the equation of the line is 0 = 1 (x - x')
Since the line passes through (25,24), x' = 25Thus, the equation of the line => 0 = 1 (x - 25)
=> x = 25.
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The brady family received 31 31 pieces of mail on april 22. the mail consisted of bills, letters, magazines, and ads. how many bills did they receive if they received the same number of bills as magazines, five more ads than letters, and three more letters than magazines?
The number of bills received by brady family are 781.
What is Linear equation in one variable?A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable with the form an x + b = 0 are solved utilizing basic algebraic operations.
Let x equal the number of letters obtained,
(x - 3) equal the number of bills obtained,
(x + 5) equal the number of advertisements received, and also
the number of magazines did receive is also given (x - 3).
The following equation can be derived:
x + (x - 3) + (x + 5) + (x - 3) = 3131
4x - 1 = 3131
4x = 3132
x = 784
Thus, number of bills received are-
(x - 3) = 784 - 3
number of bills received = 781.
Therefore, the number of bills obtained by brady family are 781.
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Find the rate of change for each set of ordered pairs. What is
the average rate of change of all the sets?
(2,3.5), (6,5.5)
(-1,0), (0, 3)
(3,-3), (4,4)
Write your answer to the average rate of change as a fraction,
a/b.
Enter the answer
SCRATCHPAD
Check it
Improve this question
The rate of change for each set of ordered pairs is:
a. 1/2
b. 3
c. 7
How to Find the Average Rate of Change?The average rate of change = change in y / change in x.
Average rate of change for (2,3.5), (6,5.5):
Average rate of change = (5.5 - 3.5)/(6 - 2) = 2/4 = 1/2
Average rate of change for (-1,0), (0, 3):
Average rate of change = (3 - 0)/(0 - (-1)) = 3/1 = 3
Average rate of change for (3,-3), (4,4):
Average rate of change = (4 -(-3))/(4 - 3) = 7/1 = 7
Therefore, the rate of change for each set of ordered pairs is:
a. 1/2
b. 3
c. 7
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You have one box that is 1 3 11 feet tall and a second box that is 1.27 feet tall. Write the decimal expansion for 1 3 11. If you stack the boxes, about how tall will the stack be?
Answer:
Step-by-step explanation:
On a coordinate plane, solid circles appear at the following points: (negative 4, 2), (negative 2, 2), (negative 1, 4), (1, 1), (1, 3), (2, negative 3).
Which ordered pair could be removed from the graph to create a set of ordered pairs that represents a function?
We need to remove either (1, 4) or (1, 1) to create a function.
How to alter a relation in order to obtain a function
Relations are formed by two sets, an input set known as domain and an output set known as range and relationships between these sets. A relation is a function if and only if each element from domain is related to only one element of the range. Mathematically speaking, we must satisfy the following proposition:
x → f(x), x → f'(x) ⇒ f(x) = f'(x)
Based on this definition, there are two possibilities to create a function:
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1,3 is the answer I believe. :)
What should be added to -7/12 to get 9/16
Answer:
1/48 should be added.
Step-by-step explanation:
If you add 9/16 to -7/12 you will get -1/48. Then do -7/12 + 1/48 and it will give you 9/16.
The formula for the area of a trapezoid is given. Solve this equation for h, height. a=H(B1+B2)/2
The solution of the equation for h is H = 2a/(B1 + B2)
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to solve the equation for h?The equation is given as
a=H(B1 + B2)/2
The above means that the variable h is represented by the variable H
Multiply both sides of the equation by 2
So, we have
2a = H(B1 + B2)
Divide both sides of the equation by (B1 + B2)
H = 2a/(B1 + B2)
Hence, the solution of the equation for h is H = 2a/(B1 + B2)
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Two customers spent the same total amount of money at a resturant.
* The first customer bought 8 hot wings and left a $4 tip.
* The second customer bought 10 hot wings and left a $2.80 tip.
* Both customers paid the same amount per hot wing.
How much does one hot wing cost at this resturant in dollars and cents?
Considering the definition of an equation and the way to solve it, the cost of one hot wing is $0.6.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The solution of a equation means determining the value that satisfies it and the equality must be true.
To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.This caseBeing "x" the cost of one hot wing, and knowing that:
The first customer bought 8 hot wings and left a $4 tip. → First customer payment= 8x +4The second customer bought 10 hot wings and left a $2.80 tip. → Second customer payment= 10x + 2.80Both customers paid the same amount per hot wing.the equation in this case is:
First customer payment= Second customer payment
8x +4= 10x +2.80
Solving:
4 - 2.80= 10x - 8x
1.2= 2x
x= 1.2 ÷ 2
x=0.6
Finally, the cost of one hot wing is $0.6.
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a) down payment, b) amount of the loan, c) monthly payment, and d) finance charge.
Shelly Lemony obtains a small business equipment loan for $120,000. Her down payment is 20% and the APR is 8% for 12 months.
a) Shelly Lemony's down payment is $24,000.
b) The loan amount is $96,000.
c) The monthly payment is $8,350.89.
d) The finance charge is $4,210.68.
What is the down payment?The down payment represents the initial up-front partial payment for the purchase of the equipment on loan.
The down payment reduces the cost of the equipment to the loan amount. Finance companies demand a down payment to ascertain the buyer's willingness and ability to proceed with the loan arrangement.
It is a sign of commitment to meet the loan contract obligations.
Data and Calculations:Monthly Pay: $8,350.89
Total Loan Amount = $96,000.00
Upfront Payment $24,000.00
Equipment loan = $120,000
Number of periods = 12 months
APR = 8%
Total of 12 Loan Payments = $100,210.68
Total Loan Interest = $4,210.68
Total Cost (price, interest, tax, fees) = $124,210.68
Thus, Shelly will make a down payment of $24,000 or 20% of the equipment loan.
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Multiplying and dividing Decimals
In qualifying for an auto race, one driver had lap speeds of 195.3 mph, 190.456 mph,193.557 mph, and 192.575 mph. What was the driver's average speed for the laps driven?
Answer:
193.0 mph
Step-by-step explanation:
The average is defined as the sum of the items divided by the number of items. In this case the sum is 771.888. If we divide that by the number of items (4) we get 192.972. However, our answer typically cannot have more significant digits than the element having the least number of significant digits. Since one of the numbers has only one digit to the right of the decimal point, we would usually want to round our answer to one place as well. So 192.972 will round to 193.0.
Wyatt made a scale drawing of a picnic area near the river. The picnic area, which is 84 yards
long in real life, is 231 inches long in the drawing. What scale did Wyatt use?
11 inches : ? yards
The scale used by Wyatt is; 11 inches : 4 yards.
What is defined by the term scale factor?The Scale Factor is utilised to scale forms in various dimensions. The scale factor is a measurement for figures with similar appearances but distinct scales or measures. Assume two circles appear similar but have different radii.The scale factor specifies how much larger or smaller a figure is than the earlier figure.Now, for the given values in question.
For the area of picnic is 84 yards.= long.
The length in the drawing is 31 inches.
Let the scale for yards is 'x'.
Then;
231 inches: 84 yards = 11 inches: x yards
Write in the fraction form,
231/84= 11/x
Cross multiplying;
x = (11×84)/231
x = 4
Thus, scale becomes; 11 inches : 4 yards.
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factor the expressions:
1234567890123456789012345678901234567890
The half-life of phosphorus-32 is about14 days. there are 6.6 grams present initially.a.express the amount of phosphorus-32 remaining as a functionof time t.b.when will there be 1 gram remaining?
a. The expression of the amount of phosphorus-32 remaining as a function of time t is A(t) = [tex]6.6\left(\frac{1}{2}\right)^{t / 14}[/tex].
b. The time when 1 gram remaining is 38.1145 days.
What is the half-life?The half-life is the amount of time it takes for half of a unstable nuclei to decay. Each substance has its own half-life.
Now, as per the question;
Exponential growth is given by the formula;
[tex]A(t)=A_0(1+r)^t[/tex]
Where,
A(t) = amount at time t.
A₀ = Initial amount of the nuclei (= 6.6)
r = rate of increasing( = -1/2; as decay is always negative)
t = time (= t/14)
Part a. Calculate the expression for the amount of phosphorus-32 remaining as a function of time t as-
Substituting all the values in the equation;
[tex]\begin{aligned}&A(t)=6.6\left(1+\left(-\frac{1}{2}\right)\right)^{t / 14} \\&A(t)=6.6\left(\frac{1}{2}\right)^{t / 14}\end{aligned}[/tex]
This is the requires expression.
Part b. Calculate the time there be 1 gram remaining as;
This time can be written as A(t) = 1.
Substitute the value in the equation.
[tex]\begin{aligned}&A(t)=6.6\left(\frac{1}{2}\right)^{t / 14} \\&1=6.6\left(\frac{1}{2}\right)^{t / 14}\end{aligned}[/tex]
[tex]\left(\frac{1}{2}\right)^{t / 14}=\frac{10}{66}[/tex]
Further solving;
t = 38.1145 days.
Thus, the time taken by phosphorus-32 to remain as 1 gram is 38.1145 days.
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Segment AC has a length of 60. Find the following values.
DG = 60
Therefore,[tex]4x - 3 + 2x + 21 = 60[/tex]
→[tex]6x+18 = 60 \\ 6x = 60 - 18[/tex]
→[tex]6x = 42[/tex]
Divide both sides by 6
→[tex]x = 7[/tex]
DO =[tex]4x - 3 [/tex]
→[tex]4(7) - 3 \\ 28 - 3[/tex]
DO [tex]= 25[/tex]
OG [tex]= 2x + 21[/tex]
→[tex]2(7) + 21 \\ 14 +21[/tex]
OG [tex]= 35[/tex]
Therefore:
[tex]x = 7[/tex]
[tex]DO = 25 ft[/tex]
[tex]OG = 35 ft[/tex]
I hope this helpsmina's explanation: i counted up from 15.75 to 176.3 to find the difference. i underlined each number i added on each line.
160.55 is the difference. i underlined each number i added on each line.
What is an linear equation in math?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
The two numbers are 15.75 and 176.3
First we will compare the numbers.
1. A=176.3
2. B=15.75
one's place of A is greater than once place of B.
tens place of A is greater than tens place of B.
Hundred place of A is greater than hundred place of B.
So, A>B
So we will subtract 15.75 from 176.3.
176.30 -15.75=
176.30 ----A
- 1 5.75 ----B
Hundreths place of A - Hundreths place of B = 0-5=10-5=5
Tenth place of A - Tenth place of B =12-7=5
ones place of A - ones place of B=5-5=0
Tens place of A - Tens place of B =7-1=6
So the solution is 160.55
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