The number is 17.
Let's assume that the number is x.
So according to the question twice a number is 34 less than 4 times the number.
Then, the equation formed will be as follows
⇒ 2x = 4x - 34
Solving the equation we get the value of x which is the respective number.
Combine the like terms then proceed with calculations.
⇒ 4x - 2x = 34
⇒ 2x = 34
Divide both sides of the equation by 2.
⇒ x = 17
Hence the number whose twice is 34 less than 4 times the number is 17.
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Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 7 liters of natural oil for every 4 liters of synthetic oil. In order to make 671 liters of Petrolyn oil, how many liters of synthetic oil are needed?
For every 4 liters of synthetic oil, there are 7 liters of natural oil. 671 liters of Petrolyn oil. 244 liters of synthetic oil is needed and 427 liters of natural oil is needed.
Given that,
Petrolyn motor oil is a blend of synthetic and natural oil. For every 4 liters of synthetic oil, there are 7 liters of natural oil. 671 liters of Petrolyn oil are needed to produce it.
We have to find how much synthetic oil, in liters, is required.
According to the given values;
The ratio of natural to synthetic oil
= 7:4
If 671 liters have to be made then,
By adding 7+4=11
So, 7/11 of 671 liters will be = 427 liters of natural oil
and, 4/11 of 671 liters will be = 244 liters of synthetic oil
Therefore,244 liters of synthetic oil is needed and 427 liters of natural oil is needed.
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the length of a rectangle is four times it's width. if the perimeter is at most 106 centimeters, what is the greatest possible value for the width?
Lenght of a rectangle: L
Widht of the rectangle: W
Perimeter of the rectangle: P
length of a rectangle is four times it's width: L = 4W
Perimeter is at most 106: P <= 106
Perimeter is 2L + 2W: P = 2L + 2W
P <= 106
if we use the value of P = 2L + 2W, we can write:
2L + 2W <= 106
Since L = 4W, then we can write this equation:
2L + 2W <= 106
2(4W) + 2W <= 106
8W + 2W <= 106
10W <= 106
W <= 106/10 = 10.6
W <= 10.6
Therefore, the greatest possible value for the width is 10.6
Answer:
10.6
AB+C=85
A+BC=86
What’s the break down tonthis
Answer:
A = 28
B = 2
C = 29
Step-by-step explanation:
28×2+29 = 85
28+2×29 = 86
Use a law of exponents to write (-3mn^5)^4 as a product of powers
The exponent is 81[tex]m^{} 4[/tex] [tex]n^{20}[/tex]
An exponent is a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression.
Here we have to determine the sign for exponential or radical expression
(-3m[tex]n^{5}[/tex])^4
Simplify using the exponent rule with the same exponent [tex](ab)^{n}[/tex] = [tex]a^{n}[/tex] . [tex]b^{n}[/tex]
Similarly
(-3m[tex]n^{5}[/tex])^4
= [tex](-3)^{4}[/tex] . [tex]m^{4}[/tex]. [tex](n^{5} )^{4}[/tex]
Now using the exponent power rule [tex](a^{n} )^{m}[/tex] = [tex]a^{nm}[/tex]. We get
= 81 . [tex]m^{4}[/tex].[tex]n^{20}[/tex]
Therefore the exponent as a product of power is 81[tex]m^{4} n^{20}[/tex].
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Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
Several years ago Bill got a home mortgage of $116,000 with a term of 30 years at an APR of 9%. Use the Monthly Payments for Long-Term Loans Rule of Thumb to estimate his monthly payment.
$
Compare this estimate with what the monthly payment formula gives. (Round your answer to the nearest integer.)
The actual monthly payment is about $
greater than the estimated payment.
Bill's projected monthly payment under the Monthly Payments for Long-Term Loans using the Rule of Thumb is $870.00.
Bill's exact monthly payment using the Monthly Payments calculation is $933.36.
The real monthly payment is approximately $63.36 more than the predicted cost.
Simple procedures may be used to calculate the Monthly Payments for Long-Term Loans Rule of Thumb.
To begin, divide the annual percentage rate (APR) by 12 to obtain the monthly percentage rate (MPR).
Second, calculate the MPR on the principal amount. The product is the estimated monthly payment, which is similar to the real monthly payment and was computed using a financial calculator below.
Estimated Monthly Payment:
Home Mortgage = $116,000
Term of loan = 30 years
APR = 9%
Monthly interest rate = 0.0075 (0.09/12)
Estimated monthly payment based on the Monthly Payments for Long-Term Loans Rule of Thumb
($116,000 x 0.0075) = $870
Actual Monthly Payment Formula:
N (# of periods) = 360 months (30 x 12)
I/Y (Interest per year) = 9%
PV (Present Value) = $116,000
FV (Future Value) = $0
The outcome is given as:
PMT = $-933.36
Sum of all periodic payments = $-336,010.40
Total Interest = $220,010.40
Actual monthly payment = $933.36
Estimated monthly payment 870.00
Difference = $63.36
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Identify the property demonstrated by the equation.
4+5=5+4
A. Comm. Prop. of Add.
B. Assoc. Prop. of Add.
C. Comm. Prop. of Mult.
D. Assoc. Prop. of Mult.
The correct answer is commutative property of addition.
What is commutative property?
In mathematics, the commutative property states that the sum of the expression does not change by changing the order or position of the numbers. Basically, changing the order does not change the sum.
According to the question, the given equation for the property of identity is as follows: 4 + 5 = 5 + 4
For this equation, the commutative identity property of addition which states that: a + b = b + a
Therefore, using this property, the given equation can be written as:
4 + 5 = 5 + 4
Hence, the correct answer is commutative property of addition.
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Travis Gregg's co-payment for doctor visits
is $15. He also pays a $7.50 co-payment for
prescriptions. Last month he saw a doctor
4 times and had 5 prescriptions filled. How
much did Travis have to pay last month?
Answer: $97.5
Step-by-step explanation:
15(4) + 7.5(5) = $97.5
Answer:
97.5
Step-by-step explanation:
got it right
_ No_(Did_Not_Lie) Yes_(Lied)
Positive_test_results 10 45
Negative_test_results 34 12
The table below displays results from experiments with polygraph instruments. Find the positive predictive value for the test. That is, find the probability that the subject lied, given that the test yields a positive result.
The probability that the subject lied, given that the test yields a positive result is; 81.81%
How to interpret the probability from a table?
From the given table, we see that;
Number of people with a positive result who did not lie = 10
Number of people with a positive result who lied = 45
Total number of people with positive results = (10 + 45) = 55
Number of people with a negative result who did not lie = 34
Number of people with a negative result who lied = 12
Total number of people with negative results = (34 + 12) = 46
The probability that the subject lied, given that the test yields a positive result is;
Probability = 45/55 = 0.818 = 81.81%
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Please help I’ll mark you as brainliest if correct!!
The set of letters in the word 'woodpecker' using the listing (roster) method is {c, d, e, k, o, p, r, w}
Writing the elements of a SetFrom the question, we are to write the set of letters in the given word.
The given word is 'woodpecker'.
We are to write the set using either the listing (roster) method or the set builder notation.
The most concise way of writing the set is by using the listing (roster) method.
The roster method is a way to show the elements of a set by listing the elements inside of bracket.
The set of the letters in the given word is {c, d, e, k, o, p, r, w}
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When you first looked at the image, you saw that Dina has 24 tickets for carnival rides, and she wants to use all of them. Some rides have a height requirement, and some rides do not have a height requirement.
-Dina has 24 tickets and wants to use all of them. She plans to go on a ride most once.
-Rides with no height requirement cost 3 tickets.
-Rides with a height requirement cost 4 tickets.
Let's answer the question "How many rides can Dina go on using all of her tickets?"
To answer the question, think about the strategy you would use along with all the information you have. What answer do you get? Select all that apply.
Note that 3-ticket rides have no height requirement, and 4-ticket rides have a height requirement.
A. 3-ticket rides: 0; 4-ticket rides: 6
B. 3-ticket rides: 2; 4-ticket rides: 6
C. 3-ticket rides: 4; 4-ticket rides: 3
D. 3-ticket rides: 6; 4-ticket rides: 2
E. 3-ticket rides: 8; 4-ticket rides: 0
Find the volume of a cone with a height of 11 cm qnd a base radius of 3 cm.
Use the vale 3.14 for ~, and do not do any rounding. Be sure to include the correct unit in your answer.
Write the system of equations as a matrix equation AX=B, with A as the coefficient matrix of the system.x+2y=−112x+6y=−30
The matrix equation is given to be:
[tex]AX=B[/tex]where A is the coefficient matrix of the system.
To get the value of X, we need to multiply both sides of the equation by the inverse of A, since:
[tex]A\cdot A^{-1}=1[/tex]Therefore, we have:
[tex]X=A^{-1}\cdot B[/tex]he TLAST OPTION is correct.
Identify all extrema of this function: f(x) = 2/(3x-5).
Select one:
a. Max: 3; Min: -2
b. Max:2.52; Min: 1.23
c. Max:0.19; Min: -2.31;
d. No extrema
The correct option is d. No extrema, is obtained for the given function.
What is described as the extrema of a function?Extremum, plural Extrema, any point in calculus where the value of a function is greatest (a maximum) as well as smallest (a minimum) (a minimum). Absolute and relative (or local) maxima as well as minima exist. At a relative maximum, the function's value is greater than its value at directly adjacent points, whereas at an absolute maximum, the function's value is greater than its value any other point in the interval of interest.For the state question,
The function is defined as; f(x) = 2/(3x-5).
To estimated the extrema of the function, first find the critical points.
Differentiate the function with respect to x suing division rule.
f(x) = 2/(3x-5).
f'(x) = 3/(3x-5)²
Now, put the function equals to zero.
f'(x) = 3/(3x-5)² = 0.
3 = 0
But, 3 ≠ 0
Thus, there is no critical point found for the function.
The give function is independent of the value of the x, and thus called the constant function.
Therefore, there is no extrema obtained for the function.
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You are on an academic committee tasked to evaluate state employment math test questions. The following question has come to the attention of the committee:
"Each of the four digits 3, 4, 5, and 8 is placed in one of the boxes to form a fraction. The numerator and the denominator are two-digit whole numbers. What is the smallest value of all the common fractions that can be formed? Express your answer as a reduced fraction."
There are 4 boxes arranged in a square with 2 boxes side-by-side directly on top of the other 2 boxes. There is a horizontal line representing a fraction bar separating the top 2 boxes from the bottom 2 boxes.
Some committee members contend this is not a valid question.
Solve the problem. (If there is no solution, enter NO SOLUTION.)
Explain the solution to prove (or disprove) the question's validity.
The question is valid because to make the fraction as small as possible, you make the numerator as small as possible and make the denominator as large as possible.The question is valid because to make the fraction as small as possible, you make the numerator as large as possible and make the denominator as small as possible. The question is valid because to make the fraction as small as possible, you make both the numerator and the denominator as small as possible.The question is valid because to make the fraction as small as possible, you make both the numerator and the denominator as large as possible.The question is not valid because there is no solution.
Answer:
no solution that's my answer
The valid solution to the problem is: The smallest value of all the common fractions that can be formed using the digits 3, 4, 5, and 8 is 34/85.The smallest value of all the common fractions that can be formed using the digits 3, 4, 5, and 8 is 34/85.
Let's solve the problem step by step to determine the smallest value of all the common fractions that can be formed using the digits 3, 4, 5, and 8. We'll express the answer as a reduced fraction.
We have 4 boxes arranged in a square as described:
A B
C D
The fraction can be represented as AB/CD.
To make the fraction as small as possible, we need to arrange the digits in a specific way. We want to minimize the numerator (AB) and maximize the denominator (CD).
For the numerator (AB), we want the smallest two-digit number. The smallest two-digit number that can be formed using the digits 3, 4, 5, and 8 is 34.
For the denominator (CD), we want the largest two-digit number. The largest two-digit number that can be formed using the digits 3, 4, 5, and 8 is 85.
Therefore, the smallest fraction that can be formed is 34/85.
To ensure that this fraction cannot be further reduced, we need to check if 34 and 85 share any common factors greater than 1. If they do not share any common factors other than 1, then the fraction is in its reduced form.
Checking for common factors:
Factors of 34: 1, 2, 17, 34
Factors of 85: 1, 5, 17, 85
The only common factor is 1, which means the fraction 34/85 is already in its reduced form.
Thus, the valid solution to the problem is:
The smallest value of all the common fractions that can be formed using the digits 3, 4, 5, and 8 is 34/85.
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Evalúe the limit. Show steps
After evaluating the limit we have came to find that the limit of [tex]\lim_{x\rightarrow 1 }\frac{x-2}{x^2-10x + 25}[/tex] as x approaches 1 is −0.0625
What is limit?In mathematics, a limit is the value that a function, sequence, or index approaches as an input or as an index approaches a specific value. Limits are crucial to calculus and mathematical analysis and are necessary for the definitions of continuity, derivatives, and integrals.
The idea of a limit of a sequence is further generalized to include the idea of a limit of a topological network, in addition to sharing a connection with the category theory concepts of limit and direct limit.
A limit of a function is typically expressed in formulas as
[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]
To find the limit
⇒ [tex]\lim_{x\rightarrow 1 }\frac{x-2}{x^2-10x + 25}[/tex]
Evalúe 2 as x
⇒ [tex]\frac{1-2}{1^2-10(1) + 25}[/tex]
⇒ [tex]\frac{-1}{-9 + 25}[/tex]
⇒ [tex]\frac{-1}{16}[/tex]
⇒−0.0625
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A doctor wants to determine if a new medication for cholesterol is more effective than the previous medication. The doctor asks her patients if they would like to take part in a study for a new medication, and 30 patients currently taking medication for cholesterol volunteer to participate. Which of the following would be an appropriate procedure for this experiment?
(A)The doctor needs to randomly assign 15 patients to the new medication and 15 to the original medication to even out the variability between the patients.
(B)The doctor needs to assign the first 15 patients to the new medication and 15 to the original medication to even out the variability between patients.
(C)The doctor needs to let the 30 patients choose which medication they are going to take through use of a survey to determine whether they want to participate in the experiment.
(D)The doctor needs to randomly assign the 30 patients to the new medication to even out the variability between the patients and to determine if their cholesterol level is lowered.
The option that is an appropriate procedure for this experiment is D. The doctor needs to randomly assign the 30 patients to the new medication to even out the variability between the patients and to determine if their cholesterol level is lowered.
How to illustrate the information?From the information illustrated, the doctor wants to determine if a new medication for cholesterol is more effective than the previous medication.
In this case, it should be noted that it's important to prevent bias. Therefore, it's important that the doctor randomly assign the 30 patients to the new medication
In conclusion, the correct option is D.
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Answer:
answer is A got it right
Step-by-step explanation:
The average human heart beats 1.037 x 105 times per day. The approximate average mouse heart beats
1.008 × 10 times per day. On an average, how many beats more does the mouse heart beats in a day?
09.043 x 105
O 2.9 x 10¹
8.942 × 10¹
1.029 × 10²
On an average 9.043 [tex]\times10^{5}[/tex] beats more does the mouse heart beats in a day.
The average human heart beats = 1.037[tex]\times10^5[/tex] times per day.
The approximate average mouse heart beats = 1.008[tex]\times10^6[/tex] times per day.
We have to find the how many beats more does the mouse heart beats in a day.
Since we have to find the more heart beat of mouse comparing to the human heartbeats. So we subtract their heart beat.
The human heartbeats have [tex]10^5[/tex] while mouse heartbeats have [tex]10^6[/tex]. So we first equal the power of 10. After equal the power we can easily find the value of the more heart beat of mouse.
We can write,
The average human heart beats = 0.1037[tex]\times10^6[/tex]
Now,
The more heartbeats of mouse = average mouse heart beats − average human heart beats.
The more heartbeats of mouse [tex]= 1.008\times10^6-0.1037\times10^6[/tex]
The more heartbeats of mouse [tex]=(1.008-0.1037)\times10^{6}[/tex]
The more heartbeats of mouse = 0.9043[tex]\times10^{6}[/tex]
The more heartbeats of mouse = 9.043[tex]\times10^{5}[/tex]
Hence, on an average 9.043[tex]\times10^{5}[/tex] beats more does the mouse heart beats in a day.
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Please answer question fast (With steps preferred, not necessary)
Answer: your welcome
Step-by-step explanation:
Let x = the certain number
"A certain number was tripled 3x
"then decreased by 10": 3x - 10
"then doubled": 2*(3x-10)
"Then increased by 2": 2(3x-10)+2
"result was 5 times original number":
2(3x-10)+2 = 5x
6x - 20 + 2 = 5x
6x - 5x = 20 - 2
x = 18
Check (very important):
Is 2*(3*18 - 10) + 2:= 5*18 ?
2*(54-10) + 2 = 90 ?
2*(44) + 2 = 90 ?
90 = 90 ?yes
Given A and B are vertical angles with m /A = 20x + 10 and m/B = 30x - 10.
What is x?
Answer:
to solve for x, you gotta make the two equations equal to each other then you can move the numbers to get the value of x
20x+10=30x-10
20x-30x=-10-10
-10x=-20
x=2
Answer:
x=2
Step-by-step explanation:
if m/A and m/B are equal, to find x, your equation would be 20x+10=30x-10. doing two step equations, you would substract 20x from both sides, making your equation look like 10=10x-10. then you would add 10 from both sides making your equation 20=10x. then you would divide 10x from both sides making x=2.
Segment RS is rotated 90 counterclockwise about the origin and then reflected over the y-axis. The resulting segment R"S" has coordinates R" (3,2) and R" (6,-5) . What are the coordinates of the segment RS ?
The coordinates of RS are R(2, 3) and S(-5, 6)
What is rotation?A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point.
Given:
Segment RS is rotated 90 counterclockwise about the origin
So, When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x).
Also, the coordinates are reflected over y- axis.
So, The coordinates of RS before reflection over y- axis is
R(-3, 2) and S(-6, -5)
Now, the coordinates of RS before rotation is
R(2, 3) and S(-5, 6)
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answer yes or no and explain why or why not.if 4s - 2 = 12, does (4s - 2) + 2 = 12 ÷ 2
Here, we want to evaluate the given equation
Looking at what is given, the operations performed on both sides are different
The reason is because we have addition on one side and division on the other side
By the addition property of equality, we are supposed to have the same operation performed on both sides
Since it is different, then the two are not equal
9. FOOD Deandre has 7 apples and each apple
is divided evenly into eighths. How many
apple slices does Deandre have?
Four times the difference of some number and 3 amounts to the quotient of 144 and 12.
Written as an equation
The equation that can be derived is [tex]4(x-3)=12[/tex]
Given
Four times the difference of some number and 3 amounts to the quotient of 144 and 12.
Let us say some number is x
Quotient of 144 and 12,
Quotient = [tex]\frac{144}{12}[/tex]
Quotient = 12
Four times the difference of x and 3 is as follows
[tex]4(x-3)[/tex]
Writing this in the form of an equation we get
[tex]4(x-3)=12[/tex]
Hence the equation is obtained, also solving the equation for x
[tex]4x-12=12[/tex]
[tex]4x = 24[/tex]
[tex]x=\frac{24}{4}[/tex]
[tex]x=6[/tex]
Hence the equation for given conditions is obtained.
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Please help I’ll mark you as brainliest if correct!!
Answer:
9, 9, 9900
Step-by-step explanation:
In a certain lottery, you must correctly select 6 numbers (in any order) out of 35 to win. You purchase one lottery ticket. What is the
probability that you will win?
BOCCH
The probability of winning is
(Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to the nearest hundredth as needed.)
The probability of winning the lottery is 6.16*10^(-7).
There is a lottery. It is given that you must correctly select 6 numbers in any order out of 35 numbers to win.The total number of possible outcomes can be calculated by choosing 6 numbers from 35.The total number of possible outcomes is 35C6.The total number of possible outcomes is 35!/[6!(35-6)!].The total number of possible outcomes is 35!/[6!29!].The total number of possible outcomes is 1623130.There is only one ticket that will win the lottery.The number of favorable outcomes is 1.The probability of winning the lottery is the number of favorable outcomes divided by the total number of possible outcomes.The probability of winning the lottery is 1/1623130.The probability of winning the lottery is 6.16*10^(-7).To learn more about probability, visit :
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Which graph represents the solution set of the system of inequalities?
[_y< / {x
\y≥-x+2
Answer:
Step-by-step explanation:
Please help me factor.
49 - 9x²
Answer:
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
where
a
=
7
and
b
=
3
x
.
(
7
+
3
x
)
(
7
−
3
x
)
Step-by-step explanation:
What is the opposite of |-74|?
Answer:
|-74| = 74
yw:)
hope it helps
Tao buys almonds to prepare a sauce and serve it with noodles. Buy a 3/8 pound bag of almonds for $1.20.
What is the unit price per ounce that tao pays for almonds? (16 oz = 1 lb)
Or $0.15
Or $0.20
Or $2.40
Or $3.20
Answer:
Second option $0.2
Step-by-step explanation:
First we can convert 3/8 pounds to oz
since 16oz is in 1 pound
so 3/8 pound will be
3/8*16=6 oz
Then to find unit price per oz
we just take the total cost $1.20 divide by 6
$1.20/6=$0.2
Find the slope of the line passing through the points (3, 4) and (8,
3).
Answer:-7\5 IS THE ANSWER TO THAT
Step-by-step explanation: