=====================================================
Explanation:
5624 is close to 5600
72 is close to 70
Therefore, 5624 ÷ 72 is close to 5600 ÷ 70 = 80
Think of it like saying 56 ÷ 7 = 8 but then we add the zeros onto each to get what is shown above.
--------
Use your calculator to find that
5624 ÷ 72 = 78.111 approximately
which isn't too far from the estimate value of 80. Our estimate is an over-estimate.
Answer: 80
Step-by-step explanation:
First change the equation to the nearest tenth,
5620 divided by 70
Now, break up the 70 into ( 10 * 7 )
So first do 5620 divided by 10
5620 divided by 10 = 562
Now if we round to the nearest tenth again we get 560
Now we can divide 560 by 7
Which comes out to 80
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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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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single letter from the word ALFALFA is chosen. What is the probability of choosing an For an A? Express your answer as a fraction in owest terms or a decimal rounded to the nearest millionth
ANSWER
5/7
EXPLANATION
The word ALFALFA has 7 letters, of which there are:
• 3 A
,• 2 L
,• 2 F
If we choose a single letter, the probability of choosing an F is,
[tex]P(F)=\frac{2}{7}[/tex]And the probability of choosing an A is,
[tex]P(A)=\frac{3}{7}[/tex]Since we are choosing a single letter, there is no event where we can choose both an F and an A at the same time, so the probability of choosing an F or an A is,
[tex]P(F\text{ }or\text{ }A)=P(F)+P(A)=\frac{2}{7}+\frac{3}{7}=\frac{5}{7}[/tex]Hence, the probability of choosing an F or an A is 5/7.
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
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.
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]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
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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4. Sampling students A statistics class with 30 students has 10 varsity athletes and 20 who are not. Choose 2 of th students in the class at random. Find the probability that both are not varsity athletes. a. Draw a tree diagram to model this chance process.
A combination is an arrangement of a set of numbers from a total set where the order of the set is not relevant.
The probability that the 2 students chosen are not varsity athletes is 38/87
What is a combination?It is an arrangement of a set of numbers from a total set where the order of the set is not relevant.
We have,
Number of students = 30
Number of varsity athletes = 10
Number of non-varsity athletes = 20
Number of students chosen at random = 2
The probability that the 2 students chosen are not varsity athletes:
= [tex]\frac{^{20}C_2}{^{30}C_2}[/tex]
= 10 x 19 / 15 x 29
= 2 x 19 / 3 x 29
= 38 / 87
Thus,
The probability that the 2 students chosen are not varsity athletes is 38/87
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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!!!
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]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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help meeeeeeeeeeeeee
Answer:b
Step-by-step explanation:
On her first day in a hospital, Kiri receives u, milligrams (mg) of a therapeutic drug. The amountof the drug Kiri receives increases by the same amount, d, each day. On the seventh day,she receives 21 mg of the drug, and on the eleventh day she receives 29 mg.(a)Write down an equation, in terms of u, and d, for the amount of the drug that she receives(0)on the seventh day;
Answer
The equation for the amount of drug received on the 7th day in terms of u and d is
a₇ = u + 6d
Explanation
The description of the amount of drug administered on the first day and how the amount increases each day by d shows that this is an arithmetic progression question.
For an arithmetic progression with first term, u, and common difference, d, the nth term is given as
aₙ = u + (n - 1) d
a) So, for the 7th day
a₇ = u + (7 - 1) d
a₇ = u + 6d
Hope this Helps!!!
In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 56.8 inches, and standard deviation of 9.4 inches.
The probability that a randomly chosen child has a height of less than 33.3 inches when mean height is 56.8 inches and standard deviation is 9.4 inches will be 98%.
As per the question statement, in the country of United States, the height measurements of ten-year-old children are approximately normally distributed with a mean of 56.8 inches and standard deviation of 9.4 inches. We are supposed to find the probability that a randomly chosen child has a height of less than 33.3 inches.
z = (X - μ) / σ, where X is the data data, μ = mean, σ = standard deviation
z = (66.09 - 56.8) / 9.4
z = 0.988 or 98%
So, the probability that a randomly chosen child has a height of less than 33.3 inches when mean height is 56.8 inches and standard deviation is 9.4 inches will be 98%.
Probability: The chance of happening of any event is its probability.Mean: The average of any given set of data is called mean and is calculated by dividing the sum of all observations by the total number of observations.Standard deviation: A number calculated to depict the degree of variation across the board for a group.To learn more about probability, click on the link given below:
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Use the equation of the polynomial function f(x)=−2x3−x to complete the following.(a) State the degree and the leading coefficient.(b) Describe the end behavior of the graph of the function.(c) Support your answer by graphing the function.
The function given is,
[tex]f(x)=-2x^3-x[/tex](a)We need to find the degree and leading coefficient of the function.
The degree is the highest power of the polynomial.
We can see that it is a cubic polynomial, or, a third degree function.
The leading coefficient is the coefficient of the highest degree term.
In our case, -2 is the leading coefficient because it is the coefficient of x^3.
(b)The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
Let's graph the function:
From the graph, we can see,
• As x approaches infinity, the function approaches negative infinity
,• As x approaches negative infinity, the function approaches positive infinity
This describes the end behavior of the function.
(c)From our function graphed above, we see that "D", from the answer choices, represents the correct graph of this function.
Answer(s)(a)The degree of the polynomial is 3 and the leading coefficient is - 2.
(b)The curve opens down to the right because the leading coefficient is negative. Because the polynomial is cubic, the graph has end behaviors in the opposite direction, so the other end opens up to the left.
(c)D
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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Directions: Rewrite the following expressions in factored form by determining the GCF5.) 63x12 - 35x^6Factored Form:
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 hoursThe 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
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.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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75 1/3% as a fraction in the simplest form
226/3 %
hope this helped
Answer:
The answer for this is 226/3%
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
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
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]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.
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
Hey does anyone mind helping me and explaining? I would Appreciate it!
Photo is attached
Answer:
A
Step-by-step explanation:
Corresponding sides of similar figures are in proportion.
Nick had $100 in his savings account.over the next 6 months, he worked at a seasonal store, where each month he earned $400 and spent $250.He put the remaining amount in his savings account each month.Now that the job is over, he plans to spend $200 per month. For how many months can he
Make withdrawals from his savings account until his balance is $0
After the 6 months of work he has $1000 on the account, and with that, he can spend $200 each month for 5 months.
For how many months can he make withdrawls?
We know that Nick initially had $100 on his savings account.
Then each month (for 6 months) he earns $400 and spends $250 and puts the rest in the savings account, the rest will be:
$400 - $250 = $150
If he saves this for 6 months, then he adds:
6*$150 = $900
And he already had $100 on the account, so now he has a total of:
$900 + $100 = $1000
For how many months can he take $200 of the account?
To see that, we need to take the quotient between the total amount and what he takes each month:
$100/$200 = 5
5 months.
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