Solution
- The question tells us to factor out the greatest negative common factor of the expression below:
[tex]-8m^3n^5-40m^3n^4[/tex]- The greatest negative common factor is the negative monomial with the largest magnitude, which divides evenly into each term of the given expression.
- Let us factorize the expression to derive this greatest negative common factor below:
[tex]\begin{gathered} -8m^3n^5-40m^3n^4 \\ -8,m^3,\text{ and }n^4\text{ are all co}mmon\text{ in the expression above.} \\ \text{Thus, we have:} \\ \\ -8m^3n^4(n-5) \end{gathered}[/tex]Final Answer
The answer is
[tex]-8m^3n^4(n-5)[/tex]her player O oo Find the amount of simple interest that $400 would earn at 8% per year by the end of 3 years. O A. $96 OB. $11,200 O c. $3200 OD. D. $112 O E. $32
To answer this question, we need to use the next formula for simple interest:
[tex]FV=PV\cdot(1+in)[/tex]Where:
FV is the future value we need to find (in this case).
PV is the present value, that is, $400 (in this case).
i is the interest rate. In this case, we have 8% (0.08).
n is the number of periods (n = 3, in this case).
Then, we have:
[tex]FV=400\cdot(1+(0.08)\cdot3)\Rightarrow FV=496[/tex]That is, the FV is $496. Therefore, the simple interest is $(496-400 = 96).
Thus, the amount of simple interest that $400 would earn at 8% per year by the end of 3 years is $96 (option A).
In other words, the result can be obtained also if we have is $400 * (0.08)*3 = $96.
A teacher determines the linear equation y=12x + 40 best models the number of points a student should earn on a test, y, if the student studies for x hours. Which statement is true
Given the equation:
y = 12x + 40
Where x represents the number of hours and y represents the number of points the student should earn.
To find the correct statement substitute the number of hours and points given for x and y respectively. If the left hand side of the equation equals the right hand side then the statement is the true.
We have:
1. A student who studies for 3 hours should earn about 76 points.
x = 3
y = 76
Substitute 3 for x and 76 for y.
y = 12x + 40
76 = 12(3) + 40
76 = 36 + 40
76 = 76
This statement is true.
2.
1. (10 pts) The formula for calculating the distance, d, in miles that one can see to the horizon on aclear day is approximated by d = 1.22√x, where x, is the elevation in feet of a person's eyes.a. Approximate how far in miles can a person whose eyes are 5' 6" from the ground see tothe horizon when they are at sea-level. (Hint: Height is often measured with two units,feet and inches, but this formula does not allow for two units.) Figure out if you need toconvert to feet or inches and then do the conversion out as a multiplication problembefore you answer the question Round to the nearest hundredth if necessary.b. How far does the same person see when they are standing on top of an 8,000 footmountain? (Hint: Consider where are their eyes if the mountain is the given height)Round to the nearest hundredth if necessary.
1) We need to use one single unit to express the elevation of a person's eyes.
a)
[tex]5^{\prime}6"=5\:feet+6\:inches=66"=5.5^{\prime}[/tex]Remember that 1 foot is equal to 12 inches. And dividing 66" by 12 yields 5.5'
Now, let's plug into the formula we've been given:
[tex]d=1.22\sqrt{5.5}\Rightarrow d=2.86\:miles[/tex]b) Now, let's bear in mind that this same person has reached the top of a mountain, and now he's at 8,000 feet high:
[tex]d=1.22\sqrt{8000}\Rightarrow d=109.12\:miles[/tex]Note that x, is always given in feet, as well as, d is in miles.
I need help with this practice problem solving It is trigonometry I will send another picture with the graph that is included in the problem, it asks to use the graph to solve
Given the function
[tex]f(x)=\sin (\pi x+\frac{\pi}{2})[/tex]The graph of the function is as shown below:
Fifteen strips, 11/4" wide, are to be ripped from a sheet of plywood. If 1/8" is lost with each cut, how much of the plywood sheet is used in making the 15 strips? (Assume 15 cuts are necessary.)
The size of the plywood sheet used is;
[tex]\frac{37}{8}^{\doubleprime}[/tex]Here, we want to get the size of the part of the plywood sheet lost
From the question, we are told that 1/8 inches is lost
The size lost would be;
[tex]\frac{1}{8}\times\text{ 15 = }\frac{15}{8}[/tex]This is the size that was lost
To get the total part of the plywood used, we simply add the width of all the strips to the amount of the plywood lost
We have this as;
[tex]\frac{11}{4}\text{ + }\frac{15}{8}\text{ = }\frac{22+15}{8}\text{ = }\frac{37}{8}[/tex]tell whether you can prove that each quadrilateral is a parallelogram. Explain.
WE know that in any quadrilateral the interior sum of its angles is 360. The missing angle in this case is:
[tex]360-121-59-59=121[/tex]Now, we also know that if the oposite angles in a quadrilateral are equal then the quadrilateral is a parallelogram.
Therefore the figure shown is a parallelogram.
The lengths of two sides of an isosceles triangle are 8 and 10. The length of the third side could beA. either 8 or 10B. 6, onlyC. 8, onlyD. 10, only
From Triangle Inequality Theorem
The sum of any 2 sides of a triangle must be greater than the measure of the third side.
The sum of 2 sides is less than (or equal to) the measure of a third side.
In an isosceles triangle, two sides are equal.
Then we have an option the third side= 8. Let's analyze!
c+a> b - for a and c =8
8+8 > 10
16> 10
The second option is the third side= 10. Let's analyze!
c+a> b - for a and c =10
10+10> 8
20> 8
Answer
A. either 8 or 10
Find the quotient.8 / (1 1/3) (Type a whole number or a fraction.)
In order to calculate the result of this division, let's first convert the mixed number 1 1/3 into a fraction:
[tex]1\frac{1}{3}=1+\frac{1}{3}=\frac{3}{3}+\frac{1}{3}=\frac{4}{3}[/tex]Now, calculating the division, we have:
[tex]\frac{8}{\frac{4}{3}}=8\cdot\frac{3}{4}=2\cdot3=6[/tex]So the result is 6.
A random variable X follows a normal distribution with a mean of 150 and a standard deviation of sigma. If we know that P(120 < X < 180) = 0.95, then, according to the 68-95-99.7 rule, the value of sigma is approximately:
a.
20
b.
15
c.
40
d.
30
e.
60
The value of sigma according to the 68-95-99.7 rule is 15.
What is the 68-95-99.7 rule?This is the informal term that is used in statistics to remember the percentage of values that are in the interval of a distribution in statistics.
We have the mean = 150
the interval is given as P(120 < X < 180)
based on this rule, 95 percent of the data lies in the u - 20 and u + 20 region
Such that we would have
u - 2α < x < u + 2α = 0.95
we have
u - 2α = 120
150 - 2α = 120
2α = 150 - 120
2α = 30
divide through by 2
α = 15
Sigma is given as 15
Read more on normal distribution here:
https://brainly.com/question/4079902
#SPJ1
Susan has a job selling cars, and earns 1.25% commission on the first $100,000 in sales,The commission increases to 4.95% on the next $200,000. Last month her total sales were$387,000. How much was her commission if she received 7.25% for any sales over $300,000
Solution:
Susan earns a commission based on car sales made.
Given:
Total sales made for the month = $387,000
Her commission is calculated based on levels and commision rate for each level.
On the first $100,000, she earns 1.25% commission.
Total sales at this level is $100,000
[tex]\begin{gathered} \text{Commision made on the first \$100,000 is;} \\ \frac{1.25}{100}\times100000=\text{ \$1,250} \\ =\text{ \$1,250} \end{gathered}[/tex]On the next $200,000, she earns 4.95% commission.
Total sales at this level is $300,000
[tex]\begin{gathered} \text{Commision made on the next \$200,000 is;} \\ \frac{4.95}{100}\times200000=\text{ \$9,900} \\ =\text{ \$9,900} \end{gathered}[/tex]On the next $87,000, total sales at this level is $387,000. She earns 7.25% commission for sales above $300,000.
[tex]\begin{gathered} \text{Commision made on the next \$87,000 is;} \\ \frac{7.25}{100}\times87000=\text{ \$6,}307.50 \\ =\text{ \$6,}307.50 \end{gathered}[/tex]Therefore, Susan's total commission received for the month is;
[tex]\begin{gathered} \text{ \$1250 + \$9900 + \$6307.50} \\ =\text{ \$17,457.50} \end{gathered}[/tex]Hence, her commission received in total for the sales made is $17,457.50
it says i need to find the shortest distance between the point and the line for geometry honors, how would i figure it out
The given line equation is,
[tex]3x-y=-6[/tex]The given point is ,
[tex](5,1)[/tex]The graph will look like this,
let us rewrite the line equtaion as ,
[tex]3x-y+6=0[/tex]now, let us compare with the general equation of line,
[tex]Ax+By+C=0[/tex]then, A= 3,B=-1 and c= 6.
let us use the formula,
[tex]\begin{gathered} d=\frac{|Ax+By+c|}{\sqrt[]{A^2+B^2}} \\ d=\frac{|3\times5+(-1)\times1+6|}{\sqrt[\square]{3^2+(-1)^2}} \\ d=\frac{|15-1+6|}{\sqrt[\square]{9+1}} \\ d=\frac{20}{\sqrt[\square]{10}} \\ d=6.32 \end{gathered}[/tex]The shortest distance is 6.32 .
Sketch the graph of each line.
24)
y=3/5x-4
The graph of the given line is attached below.
We are given the line:-
y = (3/5)x - 4
We will find the x and y intercepts of the line to plot in the graph.
As the equation is already in the slope intercept form, we can write,
The y-intercept of the line is -4.
Hence, the coordinates of the point will be (0,-4).
To find the x - intercept of the line we will put y = 0 in the given line.
0 = (3/5)x - 4
4 = 3x/5
x = 20/3
The coordinates of the point will be (20/3,0).
We can plot these points to get the desired graph.
To learn more about slope intercept form, here:-
https://brainly.com/question/9682526
#SPJ1
Simplify the numerical expression (3^2 * 5^-1)^2
Simplify the numerical expression
[tex](3^2\cdot5^{-1})^{2}[/tex][tex]\begin{gathered} (9\cdot\frac{1}{5})^{2}= \\ (\frac{9}{5})^{2}= \\ \frac{81}{25} \end{gathered}[/tex]A construction crew is lengthening a road. Let y represent the total length of the road (in miles). Let x represent the number of days the crew has worked. Suppose that x and y are related by the equation y=53 + 2x. Answer the questions below. Note that a change can be increased or a decrease. For an increase, use a positive number. For a decrease, use a negative number. What was the road’s length when the crew started working?What is the change per day in the road’s length?
Given the equation:
[tex]y=53+2x[/tex]Where y represents the total length of the road (in miles), and x represents the number of days the crew has worked.
(a) What was the road’s length when the crew started working?
When the crew started working we have x = 0. Then:
[tex]\begin{gathered} y=53+2\cdot0 \\ \therefore y=53\text{ miles} \end{gathered}[/tex]The road's length is 53 miles.
(b) What is the change per day in the road’s length?
The change per day in the road's length is 2 miles/day.
you have a table that shows a linear relationship, when can you read the value for b,in y = mx + rectly from the table without drawing a graph or doing any calculations? Complete the explanati there is a point ( (select) vy) in the table, then y = b because at the y-Intercept the value of x select) (select) 0 y
y=mx+b
Where:
m= slope
b= y-intercept
b= has coordinate points (0,y) where the line crosses the y-axis.
So:
If there is a point (0,y) in the table y=b because at the y-intercept the value of x is 0.
which number is divisible by "644532"
Answer:
2
Step-by-step explanation: 2 can be divided by 644532
The odds in favor of a horse winning a race are 7:4. Find the probability that the horse will win the race.A. 7/12B. 4/7C. 7/11D. 4/11
We have a reason for 7:4,
i.e. the total probability of winning is 7+4=11
If the horse has a probability of winning of 7 between 11
We can say that the Pw of the horse is as follows
[tex]\frac{7}{11}[/tex]The answer is the option C
Exercise 2 Find a formula for Y in terms of X
Given:
y is inversely proportional to square of x.
The equation is written as,
[tex]\begin{gathered} y\propto\frac{1}{x^2} \\ y=\frac{c}{x^2}\ldots\ldots\ldots c\text{ is constant} \end{gathered}[/tex]Also y = 0.25 when x = 5.
[tex]\begin{gathered} y=\frac{c}{x^2} \\ 0.25=\frac{c}{5^2} \\ 25\times0.25=c \\ c=\frac{25}{4} \end{gathered}[/tex]So, the equation of y interms of x is,
[tex]y=\frac{25}{4x^2}[/tex]When x increases,
[tex]\begin{gathered} \lim _{x\to\infty}y=\lim _{x\to\infty}(\frac{25}{4x^2}) \\ =\frac{25}{4}\lim _{x\to\infty}(\frac{1}{x^2}) \\ =0 \end{gathered}[/tex]Hence, the value of x increases then y decreases.
Find the total amount in the compound interest account $2650 is compounded annually at a rate of 11% for 1 year
The compound interest formula is:
[tex]A\text{ = P}(1+i)^t[/tex]where:
A is the final amount including the principal
P is the principal amount
i is the interest rate (as a decimal)
t is time in years
Replacing with P = $2650, i = 0.11, and t = 1, we get:
A = 2650*(1 + 0.11)
A = 2650*1.11
A = $2941.5
Find the area of the triangle. 30 cm 15 cm cm2
Area of the triangle is 225 sq. cm.
Given:
The base of the triangle is, b = 30cm.
The height of the triangle is, h = 15cm.
The objective is to find the area of the triangle.
The formula to find the area of the triangle is,
[tex]A=\frac{1}{2}\times b\times h[/tex]Now, substitute the given values in the above formula.
[tex]\begin{gathered} A=\frac{1}{2}\times30\times15 \\ A=225cm^2 \end{gathered}[/tex]Hence, the area of the triangle is 225 sq. cm.
Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. sin 16° = ___
We have round of to 100th place means up to 3 places
[tex]\sin (16\text{ degre}e)=0.27563[/tex]Now we will reduce the digit from right side upto 3 places
As last digit is 3 which is less than 5 so it will remove directly
[tex]\sin (16\text{ degr}e)=0.2756[/tex]Now the last digit is 6 which is greater than 5. So and is even so change we will simply remove this
[tex]\sin (16\text{ degre}e)=0.275[/tex]Sales representatives of a new line of computers predict that sales can be approximated by the function (0= 1350 + 6101n(31+ e), where is measured in years.What are the predicted sales in 15 years? Round your answer to the nearest whole number
It is predicted that sales over time can be approximated by the function:
[tex]S(t)=1350+610\ln(3t+e)[/tex]It is required to find the predicted sales in 15 years to the nearest whole number.
To do this, substitute t=15 into the given function:
[tex]S(15)=1350+610\ln(3\cdot15+e)=1350+610\ln(45+e)[/tex]Evaluate and round to the nearest whole number as required:
[tex]S(15)=1350+610\ln(45+e)\approx3708[/tex]The sales in 15 years is about 3708.
12. A teacher weighed 148 lbs. in 1999 and weighs 190 lbs. In 2020. What was the rate ofchange in weight?
Given,
The weight of the teacher in 1999 is 148 lbs.
The weight of the teacher in 2020 is 190 lbs.
The rate of change in weight is,
[tex]\begin{gathered} \text{Rate of change=}\frac{190-148}{2020-1999} \\ =\frac{42}{21} \\ =2 \end{gathered}[/tex]The teacher gained 2 pounds per year.
Hence, option A is correct.
A survey stopped men and women at random to ask them where they purchased groceries, at a local grocery store or online.Grocery OptionsStoreOnlineTotalWomen231235Men221537Total452772What percent of the people surveyed shop at a local grocery store? Round your answer to the nearest whole number percent
Given:
A survey stopped men and women at random to ask them where they purchased groceries, at a local grocery store or online. Grocery Options
Store Online Total
Women 23 12 35
Men 22 15 37
Total 45 27 72
Required:
To find the percentage of the people surveyed shop at a local grocery store.
Explanation:
The total number of people is 75.
And the total number of people surveyed shop at a local grocery store is 45.
Now the percentage of the people surveyed shop at a local grocery store is,
[tex]=\frac{45}{72}\times100[/tex][tex]\begin{gathered} =62.5\% \\ \\ \approx63\% \end{gathered}[/tex]Final Answer:
63% of the people surveyed shop at a local grocery store.
Find the equation of the linear function x 1 2 3 4 y 1 6 11 16
We solve as follows:
*We determine first the slope (m), that is:
[tex]m=\frac{6-1}{2-1}\Rightarrow m=5[/tex]Now, using the slope and one point of the line, we replace in the following expression:
[tex]y-y_1=m(x-x_1)[/tex]We can use any point of the line, but I will be using the point (1, 1), that is:
[tex]y-1=5(x-1)[/tex]Now, we solve for y:
[tex]\Rightarrow y-1=5x-5\Rightarrow y=5x-4[/tex]Jenny wants to earn $1,300by the end of the summer. How much more will she need to earn to meet her goal?
The most appropriate choice for subtraction of natural numbers will be given by-
Jenny needs $1172.95 to earn her goal.
What is subtraction?
At first, it is important to know about natural numbers.
Natural numbers are integers which are greater than or equal to 1
One of the operations on natural number is subtraction
The process of reducing one number from another number is called subtraction. Subtraction is used to find the difference between two numbers. The larger number is called minuend and the smaller number is called subtrehend.
Amount of money Jennyy had before = $127.05
Amount of money Jenny wants to earn = $1300
Amount of money Jenny needs to earn her goal = $(1300 - 127.05)
= $1172.95
To learn more about subtraction of natural numbers, refer to the link-
https://brainly.com/question/13378503
#SPJ9
Complete Question
Jenny wants to earn $1,300 by the end of the summer. How much more will she need to meet her goal?
(Jenny had $127.05 before.)
18. Yvonne paid $18.72 for 8 gallons of gas. How much would she have spent on gas if she had only needed 5 gallons of gas?
As given by the question
There are given that $18.72 for 8 gallons of gas.
Now,
Since, $18.72 for 8 gallons of gas;
Then,
First calculate the price of one-gallon gas
So,
[tex]\frac{18.72}{8}=2.34[/tex]The price og one g
Rosa needs to build a wall. She has to start the wall with one postand then every 5.75 feet put another post. The wall will be166.75 feet long. How many posts will she need?
For every 5.75 feet, here is one post.
Determine the number of posts in a wall of 166.75 feet.
[tex]\begin{gathered} p=\frac{166.75}{5.75} \\ =29 \end{gathered}[/tex]So 29 posts needed for the wall.
A solid plastic cube has sides of length 0.5 cm. Its mass is m g. Write a formula for its density in grams per cubic centimetres
The density of the cube is equal to ρ = m / L³.
What is the density of a plastic cube?
The density of the plastic cube (ρ), in grams per cubic centimeter, is equal to the mass of the cube (m), in grams, divide to the volume of the cube. The volume is equal to the cube of the side length (L), in centimeters. Then, the density of the plastic cube is:
ρ = m / L³
By using the definition of density, the density of the element is equal to ρ = m / L³.
To learn more on densities: https://brainly.com/question/15164682
#SPJ1
42. If a pipe can drain a tank in t hours, what part of the tank does foes it drain in 3 hours? A. 3t B. t/3C. t + 3D. 3/t
Let us assume that the volume of a full tank is 1
If the tank can drain the full tank in t hours, it means that
1 = t
Let x represent the volume of the tank that would be drained in 3 hours. It means that
x = 3
We would solve both equations for x
1 = t
x = 3
By crossmultiplying,
xt = 3
x = 3/t
Thus, the correct option is D
