Answer:
m - n + 3
Step-by-step explanation:
6m - 5m = 1m
n - 2n = -1n
3
Answer:
See below:
Step-by-step explanation:
Hello! My name is Galaxy and I will be helping you today. I hope you are having a nice day.
We can solve this in a single step, simplification. We can do that with the help of algebra.
\(6m+3-5m-2n+n\\m+3-2n+n\\m+3-n\\m-n+3\)
After using algebra to simplify, we get our answer of \(m-n+3\).
Cheers!
A pool in the shape of a cylinder with a height of 6 m and a base radius of 7 m is drained for repair. If the rate at which the pool is being drained is 3 m3/min, find the rate at which the water level is falling when the water is 4 m deep to the nearest hundredth.
Answer:
The rate at which the water level is falling when the water is 4 meters deep to the nearest hundredth is 0.02 meters per minute.
Step-by-step explanation:
The volume of a cylinder (\(V\)), measured in cubic meters, is represented by the following formula:
\(V = \pi\cdot r^{2}\cdot h\) (1)
Where:
\(r\) - Radius, measured in meters.
\(h\) - Height, measured in meters.
Then, we differentiate (1) in time:
\(\dot V = 2\pi \cdot r\cdot h \cdot \dot r +\pi \cdot r^{2}\cdot \dot h\) (2)
Where:
\(\dot V\) - Rate of change of the volume, measured in cubic meters per minute.
\(\dot r\) - Rate of change of the radius, measured in meters per minute.
\(\dot h\) - Rate of change of the height, measured in meters per minute.
Then, we clear the rate of change of the height:
\(\pi \cdot r^{2}\cdot \dot h = \dot V-2\pi \cdot r\cdot h \cdot \dot r\)
\(\dot h = \frac{\dot V - 2\pi \cdot r\cdot h\cdot \dot r}{\pi \cdot r^{2}}\)
\(\dot h = \frac{\dot V}{\pi \cdot r^{2}}-\frac{2\cdot h\cdot \dot r}{r}\)
\(\dot h = \frac{1}{r}\cdot \left(\frac{\dot V}{\pi \cdot r}-2\cdot h\cdot \dot r \right)\) (3)
If we know that \(\dot V = -3\,\frac{m^{3}}{min}\), \(r = 7\,m\), \(h = 4\,m\) and \(\dot r = 0\,\frac{m}{min}\), then the rate of change of the height is:
\(\dot h = \left(\frac{1}{7\,m} \right)\cdot \left[\frac{-3\,\frac{m^{3}}{min} }{\pi\cdot (7\,m)-2\cdot (4\,m)\cdot \left(0\,\frac{m}{min} \right)} \right]\)
\(h = -0.019\,\frac{m}{min}\)
The rate at which the water level is falling when the water is 4 meters deep to the nearest hundredth is 0.02 meters per minute.
35. Which of the following is a good reason to contribute to a retirement savings plan offered by an employer?
OA. The federal government allows your contribution to be tax deferred.
OB. Your employer will take over contributions once you have continuously contributed for 5 years.
OC. An employer will usually allow you to pay reduced taxes and premium deductions each pay cycle.
OD. You will receive stimulus funds from the federal government.
(C) "Your employer will typically allow you to pay reduced taxes and premium deductions each pay cycle" is an excellent justification for enrolling in an employer-sponsored retirement savings plan.
What is a retirement savings plan?You are permitted to contribute as much of your salary as you choose to the Retirement Savings Plan on a tax-advantaged basis, up to the yearly limit established by the Federal Revenue Agency (IRS).
A retirement savings plan (RSP), also known as an RRSP, is a form of financial account used in Canada to hold savings and investment assets.
When opposed to investing outside of tax-preferred accounts, RRSPs offer a number of tax benefits.
They were launched in 1957 to encourage both workers and independent contractors to save for retirement.
They are subject to a number of limitations outlined in the Canadian Income Tax Act.
Savings accounts, guaranteed investment certificates (GICs), bonds, mortgage loans, income trusts, mutual funds, corporate shares, exchange-traded funds, foreign currency, and funds sponsored by labor are examples of approved assets.
Therefore, (C) "your employer will typically allow you to pay reduced taxes and premium deductions each pay cycle" is an excellent justification for enrolling in an employer-sponsored retirement savings plan.
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Identify the number of solutions of the system of linear equations.
x=y+3z=6
x-2y = 5
2x - 2y + 5z = 9
no solution
exactly one solution
infinitely many solutions
Solve the system. If there are infinitely many solutions, write the ordered triple in terms of z. If there is no solution, lea
The solution is (x, y, z)
-1.2
3
The solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11). The system has exactly one solution.
Let's solve the system of linear equations correctly.
The given system of linear equations is:
x = y + 3z = 6
x - 2y = 5
2x - 2y + 5z = 9
To determine the number of solutions, we can analyze the system using the method of elimination or substitution. Let's use the method of elimination:
From equation 1, we have:
x = y + 3z
Substituting this value of x in equation 2:
(y + 3z) - 2y = 5
y + 3z - 2y = 5
-z + 3z = 5 - y
2z = 5 - y
Now, let's substitute the value of x in equation 3:
2(y + 3z) - 2y + 5z = 9
2y + 6z - 2y + 5z = 9
11z = 9
Simplifying the equation, we find:
z = 9/11
Now, substituting this value of z back into the equation 2z = 5 - y, we get:
2(9/11) = 5 - y
18/11 = 5 - y
18/11 - 5 = -y
18/11 - 55/11 = -y
-37/11 = -y
y = 37/11
Finally, we can substitute the values of y and z into equation 1 to find the value of x:
x = y + 3z
x = 37/11 + 3(9/11)
x = 37/11 + 27/11
x = 64/11
Therefore, the solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11).
The system has exactly one solution.
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Mariam is going bowling. She will have to pay $4.00 to rent shoes, and $3.00 for every game that she bowls, b. Mariam has a coupon for a 20% discount: if Mariam bowls 7 games how much does she pay in total
Answer:
Step-by-step explanation:
answer is 49 good luck :)
Answer:
she will have to pay $20
Step-by-step explanation:
if she rents the shoes that $4 then the game was $3 each and she played 7 so 3x7=21 so thats $21+$4=$25 so her total before the coupon would have been $25. Then the 20% off would take $5 off so she would pay $20
Hope this helps.
A conical container can hold 120 pie cubic centimeters of water the diameter of the base of the container is 12 centimeters the height of the containers centimeters. If the diameter and height were both doubled the containers capacity would be times its original capacity
URGENT
The table shows the derivation of tan(2x). Select the
correct reason for each step.
Reason 1 is
Reason 2 is
Reason 3 is
Answer:
Reason 1 is: Addition
Reason 2 is: Tangent Sum Identity
Reason 3 is: Simplify
Step-by-step explanation: ED 2020
Answer:
Reason 1 is: Addition
Reason 2 is: Tangent Sum Identity
Reason 3 is: Simplify
Step-by-step explanation:
HELPPPP
Solve for x using the figure to the right.
Answer:
x = 20 units
Step-by-step explanation:
By geometric mean theorem:
\( {x} = \sqrt{40 \times 10} \\ \\ \implies{x} = \sqrt{400} \\ \\ \implies{x} = 20 \: units \\ \\ \)
Which graphs represent functions?
What is the answer plz
Answer:
A = 180m²
Step-by-step explanation:
To find the area of the bottom rectangle subtract the height of the top rectangle. Hope that makes sense if you want a another just ask.
Sarah is borrowing money from a friend. She is paying 5% interest. after 18 months, she paid her friend the principal plus $45. what was the original amount she borrowed?
What is the batting average of a man who goes to bat 54 times and hits the ball 40 times
Answer:
40/54 simplified is
20/27
Step-by-step explanation:
Is anyone good with Math or History
The probability of passing at least one will be 0.70.
We know that,
Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
here, we have,
Probability of passing history course = 0.59
Probability of passing math course = 0.60
Probability of passing both courses = 0.49
so, we get,
Probability of passing at least one will be
⇒ 0.59 + 0.60 – 0.49
⇒ 0.70
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complete question:
A student is taking two courses, history and math. the probability the student will pass the history course is 0.59, and the probability of passing the math course is 0.60. the probability of passing both is 0.49. what is the probability of passing at least one?
1. A random sample of 64 customers at a drive-through bank window is observed, and it is found that the teller spends an average of 2.8 minutes with each customer, with a standard deviation of 1.2 minutes. Is there sufficient evidence to conclude that the teller spends less than 3 minutes with each customer slader
Answer:
\(t=\frac{2.8-3}{\frac{1.2}{\sqrt{64}}}=-1.33\)
The degrees of freedom are given by:
\(df=n-1=64-1=63\)
The p value for this case would be given by:
\(p_v =P(t_{63}<-1.33)=0.0942\)
If we use a significance level lower than 9% we have enough evidence to FAIL to reject the null hypothesis that the true mean is greater or equal than 3 but if we use a significance level higher than 9% the conclusion is oppossite we reject the null hypothesis
Step-by-step explanation:
Information given
\(\bar X=2.8\) represent the sample mean
\(s=1.2\) represent the standard deviation
\(n=64\) sample size
\(\mu_o =3\) represent the value to verify
\(\alpha\) represent the significance level
t would represent the statistic (variable of interest)
\(p_v\) represent the p value
Hypothesis to verify
We want to check if the true mean for this case is less than 3 minutes, the system of hypothesis would be:
Null hypothesis:\(\mu \geq 3\)
Alternative hypothesis:\(\mu < 3\)
The statistic for this case is given by:
\(t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}\) (1)
Replacing we got:
\(t=\frac{2.8-3}{\frac{1.2}{\sqrt{64}}}=-1.33\)
The degrees of freedom are given by:
\(df=n-1=64-1=63\)
The p value for this case would be given by:
\(p_v =P(t_{63}<-1.33)=0.0942\)
If we use a significance level lower than 9% we have enough evidence to FAIL to reject the null hypothesis that the true mean is greater or equal than 3 but if we use a significance level higher than 9% the conclusion is oppossite we reject the null hypothesis
(6.2 x 10²) x (3.5 x 10³)
Answer:
\(21.7 x 10^5\)
Step-by-step explanation:
(6.2 x 10²) x (3.5 x 10³)
First, multiply the coefficients: 6.2 x 3.5 = 21.7.
Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.
Therefore, the result is 21.7 x 10^5.
Answer:
3286000
Step-by-step explanation:
Amanda is saving to but a new bike that costs $300. Each week she saves $12. Which of the following could be used to determine how many weeks (w) it will take for her to save enough money for the bike?Options 1) 12w=3002) w - 12= 3003) 12+ w = 3004) w/12= 300
Each week Amanda saves $12, so, if "w" is the numberof weeks, she saves 12w in "w" weeks
Answer:
Option 1: 12w = 300
3.Paul owes his father $56.78. He borrows $20 more from his father. Write an expression to represent his debt. Helpp plzzz asap
Given the point with Cartesian coordinates, (3√3,−3), find the polar coordinates of the point.
Answer: (6,11π/6).
Step-by-step explanation:We need to find the radius r and the angle θ. Remember that r2=x2+y2, so
because of the signs of x and y, our angle is in quadrant IV. Therefore, we find that θ=11π/6.
So the final answer is (6,11π6).
Exercise 1: Mathematics and economics
In 2019, the manager of a beachside brasserie offers a menu for € 23.90 for lunch. This menu
was so successful that the manager decided to increase her price for the summer.
The average weekly number of covers according to the price of the menu (in €) is given
by: N (x) = - 18 x + 605.
1. The manager sets the price of the menu at 25 €. Calculate the weekly turnover achieved by
Brewery.
x
To know: The turnover of a company corresponds to the sum of the amounts of sales
carried out by it.
х
2. We denote by C (x) the weekly turnover (in €) for a menu price of
euros. Show that C (x) = - 18x? +605 x
3. The manager believes that for her formula to remain profitable, her turnover must exceed
€ 1,400 the first week. Determine the highest menu price the manager can
to stare
for
be profitable.
Answer:
economics
In 2019, the manager of a beachside brasserie offers a menu for € 23.90 for lunch. This menu
was so successful that the manager decided to increase her price for the summer.
The average weekly number of covers according to the price of the menu (in €) is given
by: N (x) = - 18 x + 605.
1. The manager sets the price of the menu at 25 €. Calculate the weekly turnover achieved by
Brewery.
x
To know: The turnover of a company corresponds to the sum of the amounts of sales
carried out by it.
х
2. We denote by C (x) the weekly turnover (in €) for a menu price of
euros. Show that C (x) = - 18x? +605 x
3. The manager believes that for her formula to remain profitable, her turnover must exceed
€ 1,400 the first week. Determine the highest menu price the manager can
to stare
for
be profitable.
Step-by-step explanation:
what adding and subtracting with unlike denominator is
We can only add and subtract fractions that have the same bottom numbers. If fractions have the same bottom numbers, we can add them by just adding the top numbers and and keeping the original bottom number.
If they don't have the same bottom number, we have to find the least common denominator for those fractions which is simply the least common multiple of the two or how ever many fractions there are.
For example, to add 1/2 and 1/3, we find the least common
denominator, which is 6, and we want to get a 6 in the denominator.
When we have the same denominator, just add
the numerators and keep the original denominator.
4. Malaki has a 'no interest-free period' credit card that charges 16.5% p.a. interest. On 9 January he purchases a phone costing K395.00. His January statement is dated 28 January and the phone is the only item on it.
a. How much interest is charged on the January credit card statement?
b. Malaki pays K100.00 off the amount owed on 28 January and makes no more purchases or payments before the next credit card statement arrives on 28 February. How much will this statement show that Malaki owes?
Answer:
K5.60.
Step-by-step explanation:
Suppose that there are 27 sophomores and 14 juniors in a Physiology class. Two students are chosen at random to participate in a class demonstration. What is the
probability of choosing two students at random and the first is a junior and the second one is a sophomore? Round your answer to four decimal places, if necessary.
Algebraic expression for 4less then 3x
When 'x' is 5, the Algebraic expression 3x - 4 evaluates to 11.
To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.
First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.
Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.
In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.
To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:
3(5) - 4
This simplifies to:
15 - 4 = 11
So, when 'x' is 5, the expression 3x - 4 evaluates to 11.
In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.
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Note the complete question:
Algebraic expression for 4 less than the product of 3 and some number
What is the algebraic expression for "4 less than the product of 3 and some number?
Please help me understand the meaning of how to calculate.
Brainliest! Jared uses the greatest common factor and the distributive property to rewrite this sum: 100 + 75 Drag one number into each box to show Jared's expression. Brainliest!
Answer:
25(4 + 3)
Step-by-step explanation:
100 = 2^2 + 5^2
75 = 3 * 5^2
GCF = 5^2 = 25
100 + 75 =
= 25 * 4 + 25 * 3
= 25(4 + 3)
c) The group is planning to build a fence around the garden. How many yards of
fencing materials do they need for the fence? Show your work. (3 points-2 points for
finding the value of side b and 1 point for finding the perimeter of the garden)
I
Based on the information, it should be noted that the perimeter that they need is 130 yds to build up the fence.
How to explain the valueAttached you can find a picture that will guide the explanation. We will assume that each line is supposed to be a fence. We will assume also that the diagonals that cross any subfield that has the same vegetable is unnecessary.
On the same fashion, the diagonal of the spinach-celery sector is 10. Recall that the field is a rectangle, so the perimeter of the outter fence is 2*(12+6)+2*(8+9) = 70 yds. Then, the total perimeter is given by
outter fence (70)+
fence spinach-watermelon (8) +
fence red peppers-watermelon(12)+
fence red peppers-carrots (15)+
fence carrots-tomatoes (9)+
fence celery-tomatoes(6) +
fence spinach-celery(10)
= 130 yds
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please help me answer this question thank you
Answer:
A
Step-by-step explanation:
Naji is trying to draw an isosceles triangle. He is
given point A at (-4,-2) and point B at (2,-2).
Plot these two points, then help Naji make the
isosceles triangle ABC by ploting point C. Give
your coordinates for point C. It must be on the
grid provided.
Answ
Step-by-step explanation:wirugf4
Please help me solve this I will give 100 points and give you Brainiest title ! It’s question 8 and please show your work!
Answer:
24
Step-by-step explanation:
0.25 * 16 = 4
40 - 4 = 36
36 divided by 1.5 = 24
\(\\ \rm\hookrightarrow c=\dfrac{40-1.5r}{0.25}\)
\(\\ \rm\hookrightarrow 16=\dfrac{40-1.5r}{0.25}\)
\(\\ \rm\hookrightarrow 40-1.5r=16(0.25)=4\)
\(\\ \rm\hookrightarrow 1.5r=36\)
\(\\ \rm\hookrightarrow r=36/1.5\)
\(\\ \rm\hookrightarrow r=24\)
What is the image of (-9,12)(−9,12) after a dilation by a scale factor of \frac{1}{3} 3 1 centered at the origin?
The image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).
In the given question,
We have to find the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin.
Since we have to find the image after a dilation.
So we learn about it now,
Any scale factor will dilate the image of any coordinate. A specific scale factor can be used to scale the coordinate up or down. To determine the answer, consider the scale factor in the equation and multiply or divide the coordinates of dilation by the appropriate scale factor.
So the given point is (-9,12).
Scale factor is 1/3.
So the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is define as
=(-9×1/3,12×1/3)
Simplifying
=(-3,4)
Hence, the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).
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in forming a 95% confidence interval for a population mean from a sample size of 20, we can proceed with large sample inference. True or False ?
As per the given confidence interval, the given statement "in forming a 95% confidence interval for a population mean from a sample size of 20, we can proceed with large sample inference" is false.
Confidence interval,
in probability , confidence interval refers the probability that a population parameter will fall between a set of values for a certain proportion of times.
Given,
in forming a 95% confidence interval for a population mean from a sample size of 20, we can proceed with large sample inference.
Here we need to find the given statement is true or false.
While we looking into the given question, we have identified that the value of
Confidence interval = 95%
Sample size = 20
Then the sample inference is calculated as, if we were to take 20 different samples and compute a 95% confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true mean value (μ).
Therefore, the statement is in correct.
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Kristen is creating a rectangular garden in her back yard. The length of the garden is 13 feet. The perimeter of the garden must be at least 54 feet and no more than 82 feet.