PLEASE HELP ASAP!!!!! DUE SOON!!! FULL ANSWER!!!!!
One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 15 hours. How long will it take the pipe to fill the pool if the drain is left open? Express your answer as a reduced fraction.
_____________ hours
Answer:
10 hours
Step-by-step explanation:
we need to know how fast it is filling up per hour:so we do 100=6xwe divide 6 by both sides[tex]\frac{100}{6} =\frac{6x}{6}[/tex]we get x=16.66666667now we need to know what %will drain per hrso the equation is 100=15ynow we need to divide by both sides[tex]\frac{100}{15} =\frac{15y}{15}[/tex]and we get y=6.666666667now that we have the input (x) and output (y) per hour we are going to find the difference 16.66666667-6.666666667=10 now we know that if we leave the drain open while we fill it, each hour it will fill %10now we have to figure out how many hours it will take1=0.1x (0.1 is %10 in decimal form)(1 is %100 in decimal form)we divide 0.1 into both sides[tex]\frac{1}{0.1}=\frac{0.1x}{0.1}[/tex]and we get 10 hoursHow many times more robberies were there actually in year 2 compare to year 4 round your answer to2 decimal places
If we want to know how many times more robberies were in year 2 copare to year 4 we must take the number of robberies during year 2 and divide it by the number of robberies during year 4. If you take a look at graph A you'll notice that the bar above year 2 has its top at 285 and the bar corresponding to year 4 at 220. Then there were 285 robberies in year 2 and 220 in year 4 so we get the following:
[tex]\frac{285}{220}=1.295[/tex]AnswerIf we round to two decimal places the answer is 1.30 times more robberies.
the scale model of a rectangular garden is 1.5 ft by 4 ft. the scale model is enlarged by a scale factor of seven to create the actual garden period what is the area of the actual garden?6 ft squared42 ft squared252 fr squared294 ft squared
Answer
Option D is correct.
294 ft squared
Explanation
The scale model of the rectangular garden is 1.5 ft. by 4 ft.
The model is then enlarged by a scale factor of 7 to create the actual garden.
So, we can now find the length of the actual garden
The Length of the actual garden = 4 × 7 = 28 ft.
The Width of the actual garden = 1.5 × 7 = 10.5 ft.
The area of a rectangle is given as
Area = Length × Width
= 28 × 10.5
= 294 ft squared
Hope this Helps!!!
KAn ad for a device used to discourage car thefts stated that "This device reduces your odds of car theft by 300 percent." What is wrong with this statement?Choose the correct answer belowOA. The statement does not mention the initial amount of car theftsB. If the device eliminated all car thefts, it would reduce the odds of car theft by 100%, so the 300% figure is misleadingOC. The actual amount of the decrease in car thefts is less than 100%OD. If car thefts fell by 100%, it would be cut in half. Thus, a decrease of 200% means that it would be totally eliminated, and a decrease of more than 200% is impossible
Explanation
we can analyze the statement An ad for a device used to discourage car thefts stated that "This device reduces your odds of car theft by 300 per cent"
If the goal was to discourage car thefts, the maximum that the percentage can be reduced by is 100%
Thus, it is misleading to say it will red
help meeeeeeeeeeeeee
Answer:b
Step-by-step explanation:
KX
KY
GIVEN PROBLEM
F
Problem 1: Solving Equations with Variables on Both Sides!
Given the equation 5x + 1 = 3x + 5, order the steps
below to correctly solve for x.
5x-3x=5-1
2x=2
x=1
Step-by-step explanation:
make the xes one side and the numb one side first and solve:
Answer: Step by Step Explanation Step 1: take 3x to the right side of equals to whereas 1 to the left side of it i.e. 5x-3x=5-1
Step2: Apply arithmetic operations now, it comes as 2x=4
Step3: Now x will stay at the left side, 1 goes to the divide 4 i.e. X=4/2 which equals to 2
Answer
An executive wishes to take out a $1.2 m mortgage. The yearly interest rate on the loan is 1.95% and the loan is for 20 years. What will the monthly repayments be? Give your answer in dollars and cents. Do not include commas or the dollar sign in your answer.
Mortgages are calculated using simple interest, so:
[tex]A=P(1+rt)[/tex]P= principal amount
r= interest rate
t= time
For P=1.2mill
r=1.95%
t=20years
The simple interest will be:
[tex]A=1200000(1+0.0195\cdot20)=1668000[/tex]Now divide the calculated amount by 20 to get the yearly fee:
[tex]\frac{1668000}{20}=83400[/tex]And finally divide it by 12 to get the monthly fee:
[tex]\frac{83400}{12}=6950[/tex]The exercutive will pay 6950 monthly
what number is represented by the expanded form shown? write the number in the place-value chart 70+8+6/100+3/1000
Answer:
Step-by-step explanation:
Hundreds: None
Tens: 70
Ones: 8
Tenths: None
Hundreths: 6/100
Thousandths: 3/1000
Total: 78 63/1000
Or in Numbers only:
78.063
When Trina arrived to take her driving test, there was a 193 minute wait. If she has waited 88 minutes so far, how much longer does she have to wait to take her test?
Tina has to wait 105 minutes more before she can take the test.
What is subtraction?
Subtraction is one of the basic arithmetic operation which means minus or difference between two or more values.
We are given that when Trina arrive for the test she has to wait 193 minutes before she could take the test
Now she has waited 88 minutes so far
We have to subtract this two values to find how long she has to wait before she could take the test.
Therefore we get,
[tex]193-88=105[/tex]
Hence She has to wait 105 minutes before she could take the test.
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The highest temperature recorded in the town of Westgate this summer was 95°F. Lastwinter, the lowest temperature recorded was -5°F. Find the difference between theseextremes.
Given:
The highest temperature is 95° F.
Lowest temperature is -5° F.
The difference between these temperature is,
[tex]95^{\circ}-(-5^{\circ})=95^{\circ}+5^{\circ}=100^{\circ}[/tex]Answer: The between the temperature is 100° F.
75 1/3% as a fraction in the simplest form
226/3 %
hope this helped
Answer:
The answer for this is 226/3%
Classify the pair of numbered angles A consecutive interior B corresponding C alternate exterior D alternate interior
When we have a pair of angles on the same side of the transversal but one interior to the parallels and one exterior, we can deduct that those are angles are classify as corresponding angles, which are always congruent.
Therefore, the answer is B. corresponding angles.your sister is looking for a way to increase the amount she is earning on her savings account. what should she do?
The thing that she can do to increase the savings is A. Deposit money into her savings account each month.
What should she do?Your information is incomplete and the complete question is written below. Savings accounts offer interest based on the balance. Therefore, you can boost the interest you receive on a savings account by making a deposit each month. By doing so, you will increase the account's total balance and, consequently, the interest rate.
The alternate selections are incorrect since doing so will result in a decrease in the amount of money in the savings account and a reduced rate of interest. Instead, use the money to open a checking account.
Note that the complete question is attached.
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Your sister is looking for a way to increase the amount of interest she is earning on her savings account. What should she do?
A. Deposit money into her savings account each month
B. Use the money from her savings account to open a checking account instead
C. Switch to a savings account with a lower interest rate
D. Make monthly withdrawals from her savings account
Classify the system and identify the number of solutions.
x - 2y +z = -7
x - 5y-z = -5
x 8y-3z = -3
The system of equations is consistent and dependent.
The system of equations has infinitely many solutions.
How are the equations solved and classified?
x - 2y +z = -7 ----(1)
x - 5y-z = -5 ----(2)
x -8y-3z = -3 -----(3)
Consider equations (1) and (3) ,
(1) - (3)
(x - 2y +z = -7 )-( x -8y-3z = -3)
(x - 2y + z +7 -(x - 8y - 3z +3)
x -2y + z +7 -x +8y +3z -3
6 y +4z +4 = 0
6y +4z = -4
Removing G.C.F from both sides of the equation,
3y +2z = -2 ----(4)
Consider equations (2) and (3),
(2) - (3)
(x - 5y-z = -5 )-( x -8y-3z = -3 )
(x - 5y - z + 5) - [ x -8y - 3z +3)
(x - 5y - z + 5 - x + 8y +3z - 3)
3y +2z +2 = 0
3y +2z = -2 ----(5)
Consider equations (4) and (5),
(4) - (5)
(3y +2z) - (3y +2z) = -2-( -2)
(3y +2z - 3y -2z ) = -2+ 2
0 = 0
Thus, the system of equations has infinitely many solutions.A system of equations is deemed consistent if it has at least one solution. A consistent system of equations is dependent if it has an infinite number of solutions.
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A rich relative dios and you inherit $120,000. How much will you have for your retirement of age 60) if you invest the inheritance in an account paying 2.0% annual interest compounded monthlyassuming that you are 18 years old now?O A. 569,287,040,00OB. 5481,030.54O C. $287.040,00OD $1,700,400.00previow answors
To answer this question we will use the following formula for compounded monthly interest:
[tex]A=A_0(1+\frac{r}{12})^{12t},[/tex]where A₀ is the initial amount, r is the annual interest as a decimal number and 12 is the number of years.
Notice that:
[tex]60-18=42.[/tex]Therefore, substituting t=42, r=0.02, and A₀=120000 we get:
[tex]A=120000(1+\frac{0.02}{12})^{12\cdot42}\text{.}[/tex]Simplifying the above result we get:
[tex]\begin{gathered} A=120000(1.001\bar{6})^{504} \\ \approx120000\cdot2.314747889 \\ \approx277769.75 \end{gathered}[/tex]Answer: $277,769.75.
In a study of pain relievers, 20 people were given Product A, and all but 4 experienced relief. In the same study, 50 people were given Product B, and all but 6
experienced relief.
Fill in the blanks below to make the statement the most reasonable possible.
Product (choose one) performed worse in the study because % failed to get relief with this product, whereas only % falled to get relief
with Product (choose one)
The correct answer is Product (B) performed worse in the study because 90% failed to get relief with this product, whereas only 20% failed to get relief with Product (A).
How to solve study based problems?
In mathematics, the study based problems are analyzed with the given percentage data. The calculation is based on statistical result and comparison results.
According to the question, the detailed study of pain relievers states that the 20 people were given Product A, and all but 4 experienced relief. And in the same study, 50 people were given Product B, and all but 6 experienced relief.
Let us assume total number of people be 100.
For the Product B, only 6 people got the relief that means out of 100 people only 12 got the relief which means Product B is performed worst.
Similarly, for the Product A, only 4 people got relief that means out of 100 people almost 20 people got the relief which means it is better than the product B.
Hence, the correct answer is Product (B) performed worse in the study because 90% failed to get relief with this product, whereas only 20% failed to get relief with Product (A).
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I need help solving some equations
SOLUTION
Write out the expression
[tex]12y-18y[/tex]The expression above are like terms, hence we can subtract them together
[tex]12y-18y=(12-18)y=-6y[/tex]Therefore,
Answer: - 6y
What is the value of x in the triangle?
3 square root 2
x
1) Note that this is a right triangle, and we can tell an isosceles one by the marks on the triangle.
2) So, we can use the Pythagorean Theorem, to find the side lengths since all we know for now is the hypotenuse:
[tex]\begin{gathered} a^2=b^2+c^2 \\ (3\sqrt[]{2})^2=x^2+x^2 \\ 2x^2=9\cdot2 \\ 2x^2=18 \\ \frac{2x^2}{2}=\frac{18}{2} \\ x^2=9 \\ x=\sqrt{9},\: -\sqrt{9} \\ x=-3,3 \end{gathered}[/tex]We can discard the negative value for there is no negative length. So, the answer is 3
Vladimir is looking to retire in 10 years. He has a plan to put $25,000 into an investment today that earns interest at a fixed amount per year. What would be a reasonable domain and range for a function modeling the total amount of the investment, including interest?explain your answer
If Vladimir is looking to retire in 10 years and he has planned to put $25,000 into an investment from today itself, that earns interest at a fixed amount per year, considering the rate of interest to be (R%) per annum, the domain and range for a function modeling the total amount of the investment, including interest are as follows:
Domain [X = {0 ≤ years ≤ 10}]
Range (total amount), [Y = {$25,000 ≤ Y ≤ 25,000( 1 + 10R)}]
As per the question statement, Vladimir is looking to retire in 10 years and he has planned to put $25,000 into an investment from today itself, that earns interest at a fixed amount per year, and since there is no information about the rate of interest of that investment, we are considering the rate of interest to be (R%) per annum.
We are required to determine the domain and range for a function modeling the total amount of the investment, including interest using the question statement mentioned data and our assumptions.
Since the starting principal amount, say P is $25,000, given,
Time of investment, say T is 10 years, also given,
And considering the interest rate per year to be R (%),
Then after 10 years, the total amount Vladimir has is [25000( 1 + xR)].
Where, the Domain (No. of years ) is [X = {0 ≤ years ≤ 10}]
And Range (total amount), [Y = {$25,000 ≤ Y ≤ 25,000( 1 + 10R)}]
Domain of a Function: In mathematics, the domain of a function is the set or group of inputs that is accepted by the function.Range of a Function: In mathematics, the range of a function is the set or group of outputs produced by the function using values from its domain.To learn more about Domain and Range of a Function, click on the link below.
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Directions: Rewrite the following expressions in factored form by determining the GCF5.) 63x12 - 35x^6Factored Form:
A store purchased a piece of artwork then marked up the price 350% before selling to customers. If the artwork was sold for $52.50, what was its original price?
Determine if the table shows a proportional relationship.
Time (hours) 0 8 16 24 32
Pay (dollars) 0 96 192 312 416
Yes, it is proportional because the ratios for dollars per hour are all equivalent to 12 dollars per hour.
Yes, it is proportional because the ratios for dollars per hour are all equivalent to 13 dollars per hour.
No, it is not proportional because 96 over 8 does not equal 312 over 24.
No, it is not proportional because 312 over 24 does not equal 416 over 32.
Given table does not show a proportional relationship.
It is not proportional because 96 over 8 does not equal 312 over 24.
In this question, we have been given a table that shows a relationship between time in hours and Pay in dollars.
Time (hours) 0 8 16 24 32
Pay (dollars) 0 96 192 312 416
We can observe that,
0 = 0 * 12
96 = 8 * 12
192 = 16 * 12
312 = 24 * 13
416 = 32 * 13
The ratio of pay to time is not constant.
This means, given time and pay relationship is not proportional.
Therefore, given table does not show a proportional relationship.
It is not proportional because 96 over 8 does not equal 312 over 24.
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9+9+9+9+9+99+9+9+9+9+9+9+9+9+9
Answer:
9 x 16 is 144
Step-by-step explanation:
If the 99 in the middle wasn't mistaken, the answer is 225.
Hope this helps!
Answer:225
Step-by-step explanation:
9x16=144 then 144+99=225
Which of the following is the average rate of change over the interval [-5, 10] for the function g(x) = log2 (x+6)-3
A.4/5
B.5/4
C.4/15
D.15/4
It's answer is option(C) i.e, 4/15
What is Average rate of change?
The average rate of function f over the interval a≤x≤b is given by ,
(f(b) - f(a)) / (b - a)
It is the average amount by which the function changed per unit throughout that time period.
In this question the equation is given,
g(x) = log2 (x+6)-3
Solve this eq. by putting the values [-5, 10],
let, interval [-5, 10] = [a, b]
Then solve for g(a) and g(b), we know g(a) = g(-5),
g(-5) = log₂(-5+6) - 3
= log₂1 - 3
= 0 - 3
g(-5) = -3
Now, for g(b) = g(10)
g(10) = log₂(10+ 6) - 3
= log₂16 - 3
= 4 - 3
g(10) = 1
Now put these values in average rate formula,
Average rate = (g(b) - g(a)) / (b - a)
= (1 - (-3)) / (10 - (-5))
= (1 + 3) / (10 + 5)
= 4 / 15
Therefore, the average rate is 4/15 i.e, option(C)
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Answer: C. 4/15. I took the test and got it right.
Step-by-step explanation:
Help pls consider this matrix transformation what is the image of
The image under the given transformation is [tex]\left[\begin{array}{ccc}-7\\10\end{array}\right][/tex] .
A matrix that transforms one vector to another vector by the process of matrix multiplication is transformation matrix.
A = [tex]\left[\begin{array}{ccc}-1&-2\\4&-1\\\end{array}\right][/tex] is to be solved with [tex]\left[\begin{array}{ccc}3\\-2\\\end{array}\right][/tex]
In linear transformation, T(x) = Ax
Lets say, Ax = B
Here, B = image of x under this transformation
B = Ax
= [tex]\left[\begin{array}{ccc}-1&-2\\4&-1\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}3\\-2\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}3*-1+-2*-2\\4*3+-1*-2\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}-3+-4\\12+-2\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}-7\\10\end{array}\right][/tex]
Therefore, we can conclude that the image under the given transformation is [tex]\left[\begin{array}{ccc}-7\\10\end{array}\right][/tex].
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I will show you the pic
to determine the product between the 2 numbers we must write both numbers in scientific notation
[tex]800.5=8.005\cdot10^2[/tex]now we multiply both number without the tenth potency.
[tex]8.005\cdot2=16.01[/tex]now we add the tenth potencies
[tex]\begin{gathered} 16.01\cdot10^{6+2} \\ 16.01\cdot10^8 \end{gathered}[/tex]now we move 1 decimal place more to the left to make the number between 0 and 9.9
[tex]16.01\cdot10^8=1.601\cdot10^9[/tex]Question 3 Find the Area 64 G H r = 9 in
Answer:
[tex]A_{\sec tor}=45.216in^2[/tex]
Explanation: We need to find the area of the shaded sector that has an angle of 64 degrees:
We can reason that it must be the portion of the total area of the circle, and we also know the radius of the circle:
The area of the circle is:
[tex]A_{circle}=\pi r^2=\pi(9in)^2=81\pi=254.31in^2[/tex]The area of the sector is:
We know that 64 degrees are part of the full circle which is 360 degrees, therefore:
[tex]\begin{gathered} \frac{64}{360}=\frac{A_{\sec tor}}{A_{circle}}\rightarrow\frac{64}{360}=\frac{A_{\sec tor}}{254.31} \\ \therefore\rightarrow \\ A_{\sec tor}=\frac{254.31\times64}{360}=\frac{16,277.76}{360}=45.216in^2 \\ A_{\sec tor}=45.216in^2 \end{gathered}[/tex]The monthly service charge $S of mobile phone is the sum of two parts. One part is a constant and the other varies directly as the connection time t minutes. When the monthly service charge is $230, the connection time is 100 minutes. When the monthly service charge is $290, the connection time is 130 minutes.a) Express S in terms of t.b) Find the value of the connection time t when the monthly service charge$S is $330.
Since the monthly charge S is made from 2 parts,
A constant part, let it b
A part depends on a direct relationship between it and the time t
Then the form of S should be
[tex]S=mt+b[/tex]Where:
m is the rate of change
b is the constant amount
Since S = 230 at t = 100
Since S = 290 at t = 130
Substitute them in the equation above to make 2 equations of m, b and solve them
[tex]\begin{gathered} 230=100m+b\rightarrow(1) \\ 290=130m+b\rightarrow(2) \end{gathered}[/tex]Subtract equation(1) from equation (2) to eliminate b
[tex]\begin{gathered} (290-230)=(130m-100m)+(b-b) \\ 60=30m \end{gathered}[/tex]Divide both sides by 30 to find m
[tex]\begin{gathered} \frac{60}{30}=\frac{30m}{30} \\ 2=m \\ m=2 \end{gathered}[/tex]Substitute m in equation (1) by 2 to find b
[tex]\begin{gathered} 230=100(2)+b \\ 230=200+b \end{gathered}[/tex]Subtract both sides by 200
[tex]\begin{gathered} 230-200=200-200+b \\ 30=b \\ b=3 \end{gathered}[/tex]a) The equation of S is (substitute m by 2 and b by 30)
[tex]S=2t+30[/tex]b) Since the monthly fee is $330, then
S = 330
Substitute it in the equation to find t
[tex]330=2t+30[/tex]Subtract 30 from both sides
[tex]\begin{gathered} 330-30=2t+30-30 \\ 300=2t \end{gathered}[/tex]Divide both sides by 2 to find t
[tex]\begin{gathered} \frac{300}{2}=\frac{2t}{2} \\ 150=t \\ t=150 \end{gathered}[/tex]The value of the time is 150 minutes
Which proportion would use to find the area of the sector given the below figure
Explanation
From the question, we are given that
[tex]\begin{gathered} \bar{AC}=radius(r)=7 \\ \angle C=\theta=80^0 \end{gathered}[/tex]If the area of a sector is denoted by x, recall that its formula can be expressed as;
[tex]\begin{gathered} x=\frac{\theta}{360}\times\pi r^2 \\ \therefore\frac{\theta}{360}=\frac{x}{\pi r^2} \end{gathered}[/tex]We can then substitute the parameters into the above formula.
[tex]\begin{gathered} \frac{80}{360}=\frac{x}{\pi7^2} \\ \Rightarrow\frac{80}{360}=\frac{x}{49\pi^{}} \end{gathered}[/tex]Answer:
[tex]\frac{80}{360}=\frac{x}{49\pi^{}}[/tex]A purple paint requires a proportional
relationship of number of quarts of red paint, r,
to blue paint, b. This is represented by the
equation.
3r = 24b
Enter the number of quarts of red paint used
for one quart of blue paint. (1 pt)
The number of quarts of red paint used for one quart of blue paint is 0.125 quarts.
Given that:
A purple paint requires a proportional relationship of number of quarts of red paint, r, to blue paint, b. This is represented by the equation 3r = 24b.
3r = 24b
b = 3r/24
b = r/8
b = 0.125r
So 0.125 quarts of red paint used for one quart of blue paint.
Hence the number of quarts of red paint used for one quart of blue paint is 0.125 quarts.
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