The length of a rectangle is four times its width.
If the area of the rectangle is 144 cm^2 , find its perimeter.
Answer:
Let width of rectangle be x cm.
Width = x cm
Length = 4x cm
Area of rectangle = length x width
4x × x = 144
4x² = 144
x² = 144 ÷ 4 = 36
x = √36 = 6
Width = 6 cm
Length = 6 × 4 = 24cm
Perimeter = 6 + 24 + 6 + 24 = 60 cm
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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If you divided a positive number by a negative number and then divided the result by another negative number, what would the sign of the final result be? Explain your reasoning.
Answer: Positive
Step-by-step explanation:
If a positive number is divided ( or multiplied ) by a negative number it is always a negative number. If you divide ( or multiplied) two negative numbers its always a positive so,
+/- = -
- / - = +
In 2008, Chris bought a new boat for $35,000. The boat was worth $19,000 in the year 2011. If Chris knows that the value of the boat depreciated linearly, what was the annual rate of change of the boat's value? Round your answer to the nearest hundredth if necessary.
The annual rate of change of the boat's value is $5334.
Given,
Chris bought a new boat in 2008.
The value of boat in 2008 (Initial value) = $35000
The value of boat in 2011 = $19000
Chris knows that the value of the boat depreciated linearly.
We have to find the annual rate of change of the boat's value, x.
Number of years, n = 2008 to 2011 = 3 years
Here, x be a constant.
So,
Value in 2011 = Initial value - nx
19000 = 35000 - 3x
3x = 35000 - 19000
3x = 16000
x = 16000/3
x = 5333.33
x = 5334
That is,
The annual rate of change of the boat's value is $5334.
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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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Which of the following expression gives a fine in dollars for a book that is n days overdue
The rate is given by
[tex]\text{ \$0.10 per day}[/tex]and since the one-time charge is $0.25, the expression is
[tex]0.25+0.10n[/tex]where n denotes the number of days. Then, the answer is the second option
What is [tex]lim_{x-0} (f(f(x))[/tex] closest to?
a. DNE
b. 1
c. 3
d. 5
Answer:
c. 3
Step-by-step explanation:
You want to know the limit of the composite function f(f(x)) as x approaches zero.
LimitThe function f(x) can be evaluated at x=0. The graph shows the value to be ...
f(0) = 2
The function f(x) can also be evaluated at x=2. The graph shows the value to be ...
f(2) ≈ 3
The nearest value to f(f(0)) is 3.
__
Additional comment
For a continuous function, the limit at a point is simply the value at that point. F(x) is continuous in the neighborhoods of the points of interest, so we simply need to find the function value.
A number is divided by 3, and then 4 is added to the quotient. The result is 8. Find the number
Answer: 4/3 or 1.33
Step-by-step explanation:
Change 4x + 7y= 14 to slope intercept form
(y=mx+b)
A random sample of individuals at an airport were asked, "Is your flight on time or delayed?" Below are the results of the survey in a joint relative frequency table.
On Time Delayed Total
Domestic 94 418
International 73
Total 145
Part A: Draw and complete the frequency table. (3 points)
Part B: What is the smallest joint frequency, and what does it represent in the context? (3 points)
Part C: Does the data show an association between the flight being on time and flying domestic? If so, is it positive or negative? Justify your answer mathematically. (4 points)
For the frequency table for a random sample answer of the following are given below:
A. Complete frequency table:
On Time Delayed Total
Domestic 324 94 418
International 73 51 124
Total 397 145 542
B. Smallest joint frequency is 51. It represent international flight has lowest number of delays.
C. Domestic flight has highest number of on time flight. It is positive.
As given,
From the random sample of the survey of joint relative frequency table.
On Time Delayed Total
Domestic ? 94 418
International 73 ? ?
Total ? 145 ?
A. Domestic on time = 418 -94
=324
International delayed =145 -94
=51
On time total =324 + 73
=397
International total =73+ 51
=124
Total = 418 + 124
=542
=397 +145
B. Smallest joint frequency is 51. It represent international flight has lowest number of delays.
C. Domestic flight has highest number of on time flight. It is positive as on time flights are more than the delayed.
Therefore, For the frequency table for a random sample answer of the following are given below:
A. Complete frequency table:
On Time Delayed Total
Domestic 324 94 418
International 73 51 124
Total 397 145 542
B. Smallest joint frequency is 51. It represent international flight has lowest number of delays.
C. Domestic flight has highest number of on time flight. It is positive.
The complete question is:
A random sample of individuals at an airport were asked, "Is your flight on time or delayed?" Below are the results of the survey in a joint relative frequency table.
On Time Delayed Total
Domestic ? 94 418
International 73 ? ?
Total ? 145 ?
Part A: Draw and complete the frequency table. (3 points)
Part B: What is the smallest joint frequency, and what does it represent in the context? (3 points)
Part C: Does the data show an association between the flight being on time and flying domestic? If so, is it positive or negative? Justify your answer mathematically. (4 points)
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Answer:
Step-by-step explanation:
Be sure to contact your instructor if you have questions. :)
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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simplify 5x -6y - x + 3y
Step-by-step explanation:
collect like terms
[tex]5x - x - 6y + 3y \\ 4x - 3y [/tex]
what is the percent chance from 450 To 1188
Answer:
738
Step-by-step explanation:
1188 - 450 = 738
(CO 5) A company claims that its heaters last more than 5 years. Write the null andalternative hypotheses and note which is the claim.O H: = 5, H: 4 < 5 (claim)wO Hou = 5 (claim), H: 25O Hou = 5, H.: > 5 (claim)O Hou > 5 (claim), H: 35
Given:
The company claims that its heaters last more than 5 years.
Find: null alternative hypotheses.
Sol:
[tex]H_0:\mu=5,H_a|:\mu>5\text{ \lparen claim\rparen}[/tex]Use the sinking fund formula shown to the right to determine the monthly payment needed to accumulate 270,000 with 5% interest or combine did monthly for 28 years The monthly invested payment is 
Using the sinking fund formula, the monthly payment needed to accumulate 270,000 with 5% interest or combine did monthly for 28 years, the monthly invested payment is 369.65.
What is sinking fund formula?A sinking fund, also referred to as a sinking fund, is defined by its name. Fundamentally speaking, it is built to sink. Although there are some similarities between a sinking fund and a reserve fund, their purposes differ significantly. Unlike reserve funds, which typically serve no particular purpose, sinking funds have a designated purpose.
Simply put, a reserve fund is a company's method of saving its surplus funds. There are numerous uses for reserve funds. They can be applied to a variety of costs, including those related to emergency situations, asset purchases, business expansions, and capital expenditures.
Sinking fund (A) = P × [tex]\frac{(1+r/n)^{tn}-1}{r/n}[/tex]
Where
A – Money accumulated
P – Periodic contribution,
r – Interest rate
t – Number of years
n – Number of payments per year
So, periodic contribution P = A / (((1 + r / n) ^ (t * n) – 1) / (r / n))
Here given that,
A – 270,000
r – 5%
t – 28 years
n – 12
P – To find
Substituting the values we get
P = [tex]270000/(((1+0.05/12)^{\left(28\times 12\right)}-1)/(0.05/12))[/tex]
P = 369.649667
P = 369.65
Therefore, the monthly payment needed to accumulate 270,000 with 5% interest or combine did monthly for 28 years, the monthly invested payment is 369.65.
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Marie is choosing a bag of apples to make into a pie. She thinks the pie will be tastier if it has more apples. The bag of green apples weighs 4.75, point, 75 pounds. The bag of red apples weighs 4.54, point, 5 pounds.
Which bag of apples should she buy?
red apples or green?
(from khan academy)
Marie should buy the bag with green apples as it has more weight hence it will have more apples eventually making her pie tastier
Comparison: When we compare, we look for similarities among the characteristics of other items or objects. Mathematicians use the concept of comparing and ranking numbers to identify the smaller and larger numbers and to determine whether they should be arranged in ascending or descending order.
Weight of bag with green apples = 4.75 pounds
Weight of bag with red apples = 4.54 pounds
Since the bag with green apples weighs heavier and contains more apples overall, Marie should purchase it because it will make her pie taste better.
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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.
What is an equation of a line that passes through the given point and is perpendicular to the given line. (-2, 5) and x = 3
The equation of the line passing from found as y = 5.
What is referred as the slope of line?The slope of the line is a measurement of its steepness and direction. A line's slope is classified as the change in y coordinate with regard to the shift in x coordinate. The net y coordinate change is Δy, whereas the net x coordinate change is Δx. So the transformation in y coordinate in relationship to the shift in x coordinate is written as m.The formula for finding the slope is;
m = Δy/Δx
Where, m is the slope
The given equation of line is;
x = 3 comparing it with standard form of equation;
y = mx + c
As, the equation is a straight line passing parallel to x axis, the slop of line x = 3 is ∞.
Thus, m₁ = ∞.
Now, let the slops of the line passing from (-2, 5) is m₂,
The, as both line are perpendicular.
Thus,
m₁ x m₂ = -1
m₂ = -1/∞
m₂ = 0
The equation of line is found by
y - y₁ = m₂(x - x₁)
Put the values;
y - 5 = 0(x + 2)
y = 5
Therefore,the equation of the line passing from found as y = 5.
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CONFUSED ON THIS PLEASE HELP!! QUESTION DOWN BELOW!
many thanks!!!
Answer:
(a) ∠e +∠d = 180° is false
Step-by-step explanation:
You want to know which angle expression is not true.
Angle SolutionWe can figure the measures of all of the unknown angles, then check the given expressions.
Angles 'a' and 130° are corresponding angles, so congruent:
a = 130°
Angles 'a' and 'e' are vertical angles, so congruent:
e = a = 130°
Angle 'd' and 62° are vertical angles, so congruent:
d = 62°
Angles 'b' and 'd' are corresponding angles, so congruent:
b = d = 62°
Angles 'f' and 62° are corresponding angles, so congruent:
f = 62°
Angles 'c' and 130° are a linear pair, so supplementary:
c + 130° = 180°
c = 50° . . . . . . subtract 130°
Statement check(a) ∠e +∠d = 180° ⇒ 130° +62° = 180° . . . . false
(b) ∠d +∠b = 124° ⇒ 62° +62° = 124° . . . . true
(c) ∠a +∠c = 180° ⇒ 130° +50° = 180° . . . . true
(d) ∠ 180° -∠f = 118° ⇒ 180° -62° = 118° . . . . true
What is 7 x 10 ^-4 in standard notation?
Answer: 0.007
Step-by-step explanation: 70 x 10^-4= 0.0001
70 x 0.0001
7 x 0.001
0.007
Hope this helps!
The standard notation of 7 x [tex]10^{-4}[/tex] is 0.0007.
The given expression is;
7 x [tex]10^{-4}[/tex]
To write 7 x [tex]10^{-4}[/tex] in standard notation,
When multiplying an integer by a power of ten, the decimal point is moved to the right or left by the number of zeroes in the exponent.
So, for7 x [tex]10^{-4}[/tex],
Move the decimal point 4 places to the left.
Starting with 7, Move the decimal point 1 place to the left to get 0.7.
Move it another 3 places to the left to get 0.0007.
Therefore,
7 x [tex]10^{-4}[/tex] in standard notation is 0.0007.
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pls help i dont get it
Create an In-Out table with your findings. Make a table with the number of bagels she has when she gets home as the In and the number she had to start with as the Out.
How does the solution to Marcella’s Bagels depend on the number of bagels she has when she gets home?Try several numbers for the number she has when she arrives home to explore this expansion, such as 3, 4, 5, or even 0. You should presume that, other from this number, everything in the problem is the same as it was in the original problem.
Create an In-Out table with your findings. Make a table with the number of bagels she has when she gets home as the In and the number she had to start with as the Out. Once you've added numerous entries to the table, search for a connection between the Out and the In before attempting to identify a rule that can explain this connection.
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Suppose the current cost of gasoline is $3.10 per gallon. Find the current price index number, using the 1975 price of 56.7 cents as the reference value.
The current price index is _____
(Round to one decimal place as needed.)
The current price index is mathematically given as,$538.194
What is the current price index?By increasing the ratio of the current value to the reference value by 100, one can determine the index value.
Given that the current cost of gasoline is $3.10 per gallon. we need to find the current price index number, using the 1975 price of 56.7 cents as the reference value.
In regard to this issue, we have that:
Current value = $3.10
Reference value: $0.576
Typically, the mathematical formula for the Index price is,
I = (3.10/0.576) x 100
I= $538.194
The current price index number is 538.194
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if explain this question to me give those crown thingy points
it two pages
please help 20points
Answer:
1.) 12 yards (the one you selected is correct)
2.) 1.1 with the bar over the decimal (the one you selected is correct)
Step-by-step explanation:
1.) It looks like Aaron dropped back 5 yards from the line of scrimmage and threw to the 7 yard line for a total of 12 yards.
2.) If you enter 10 divided by 9 into your calculator you will get back 1.11111111111111 that keeps repeating for how ever many digits your calculator can show. We write this as 1.1 with the bar over the decimal.
Russell works at a football concession stand selling drinks for $2 and bags of chips for $3. At one football game, Russell makes a total of $246 and sells a total of 100 drinks and bags of chips.
The number of chips and drinks are 46 chips and 56 drinks respectively.
How to calculate the values?Let the number of drinks be d.
Let the number of chips be c.
From the information, he works at a football concession stand selling drinks for $2 and bags of chips for $3 and he makes a total of $246 and sells a total of 100 drinks and bags of chips.
This will be:
c + d = 100 ........ i
2d + 3c = 246 ........ ii
From equation i, c = 100 - d
Substitute this into equation ii
2d + 3c = 246
2d + 3(100 - d) = 246
2d + 300 - 3d = 246
Collect like terms
2d - 3d = 246 - 300
-d = -54
d = 54
Number of drinks = 54
Since c + d = 100
c + 54 = 100
c = 100 - 54 = 46
Chips = 46
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Complete question
Russell works at a football concession stand selling drinks for $2 and bags of chips for $3. At one football game, Russell makes a total of $246 and sells a total of 100 drinks and bags of chips. Calculate the number of drinks and chips sold.
a number is 8 more than 32. find the number.let n = number.
do the sum
[tex]n=40[/tex]the number is 40 because 40 is 8 more than 32
cuanto es : Dos veces mas cuatro es igual a seis ?
We are asked to solve for a number such that:
Twice that number plus 4 equals 6
Which can be written in math terms as:
2 x + 4 = 6
Now we proceed to isolate the unknown in steps.
First we subtract 4 from both sides:
2 x + 4 - 4 = 6 + 4
we combine like terms:
2 x = 10
Now we divide both sides by 2 so as to cancel the factor 2 that accompanies "x":
2 x / 2 = 10/ 2
perform the indicated operations:
x = 5
A phone keeps track of the number of steps taken and the distance traveled. based on the information in the table, is there a proportional relationship between the two qualities?
there is no proportional relationship between the two qualities
Explanation:For two quantities to be proportional, it must follow the formula:
y = kx
where k = proiportionality constant
k = y/x
if y = 950, x = 1
inserting in the equation:
950= 1k
k = 950
The equation becomes: y = 950 × x
We check for other values. if k is the same, it is proportional
when y = 2852, x = 3
2852 = k × 3
k = 2852/3 = 950.67
when y = 5.1, x = 4845
4845 = k × 5.1
k = 4845/5.1 = 950
From the above, the value of k which is different is for the 2nd value.
Since they are not all the same, we say there is no proportional relationship between the two qualities
This is a file of basic probability, as I start to study this subject I realize that I have forgotten all the basic knowledge, can someone please show me how to do questions (b) and (c)
The probability that a ball is not red is 3/5 and the probability that the ball is red or white is 2/3 .
Mathematical descriptions of the likelihood that an event will happen or that a proposition is true are dealt with in the discipline of mathematics known as probability.
The probability of an event is a number between 0 and 1, where 1 denotes a certainty and 0 denotes an impossibility of the event.Simply put, probability is the likelihood that something will occur. We may discuss the chances of various outcomes when we are unsure of how an event will turn out.Statistics is the study of events subject to probability.In the given question there are 6 red balls, 4 white balls, and 5 blue
balls.
Total number of balls = 6+4+5 = 15 balls (sample space)
Red balls = 6
Not red balls = 15 - 6 = 9
Probability that the ball is red = 9/15 = 3 /5
Red and white balls = 6 + 4 =10
Probability that the ball is red or white = 10 / 15 = 2 / 3
Hence the probability that a ball is red or white is 2 / 3.
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Disclaimer : The complete question is :
A ball is drawn at random from a box containing 6 red balls, 4 white balls, and 5 blue balls. Determine the probability that it is
(a) not red
(b) red or white
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given vectors u=(70.707,84.265) and u=(-56.382,20.521) use the dot product to multiply the vectors
Step 1
Given;
[tex]\begin{gathered} u=(70.707,84.265) \\ v=(-56.382,20.521) \end{gathered}[/tex]Required; To find the dot product
Step 2
Find the dot product
[tex]\begin{gathered} \begin{pmatrix}70.707 & 84.265\end{pmatrix}\begin{pmatrix}-56.382 & 20.521\end{pmatrix}= \\ =70.707\left(-56.382\right)+84.265\cdot \:20.521 \\ =-2257.400009 \\ \end{gathered}[/tex]The answer thus is;
[tex]-2257.400009[/tex]pls help i dont get it this is due today
Answer:
Part a: x + 17 = 52 Part b: He should guess the number 35.
Step-by-step explanation:
In the equation, x stands for the number he has to guess. He is given the clue, "17 more than the number is 52." Therefore x + 17 = 52. Another equation you could use is 52 - 17 = x. This equation would be used to solve the problem. 52 - 17 = 35