Answer: The phrase "5 times a number, divided by 6" can be translated into the algebraic expression:
(5/6)x
This expression represents "5 times a number, divided by 6", where x is the unknown number.
Step-by-step explanation:
I run 3 miles in 20 minutes. What was my average speed in miles per hour?
Assume that the random variable X is normally distributed, with mean and standard deviation . Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.
Using the normal distribution, the probability that x is of at most 40, represented by option B, is given as follows:
[tex]P(X \leq 40) = 0.1587[/tex]
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation of the distribution are given, respectively, by:
[tex]\mu = 51, \sigma = 11[/tex]
The probability that x is of at most 40 is the p-value of Z when X = 40, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{40 - 51}{11}[/tex]
Z = -1
Z = -1 has a p-value of 0.1587.
Hence the probability is:
[tex]P(X \leq 40) = 0.1587[/tex]
Which is the part to the left of X = 40 of the distribution, hence option B is correct.
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Chris bought a new car for 12,500 he made 3,000 down payment and financed the rest for 14.5% for 36 months for 3 years how much less would his total be for same loan 24 months 2 years
The difference in total loan repayments between the two mortgage payment option is 771.12
The requirement here is to determine the difference between total loan repayments when the period of loan is 36 months and the total repayments when the period of loan is 24 months instead.
Note the loan amount is the excess of purchase price over the down payment required.
loan amount=12,500-3,000
loan amount=9,500
The monthly payment in each case can be determined using the present value formula of an ordinary annuity.
PV=monthly payment*(1-(1+r)^-N/r
36-month loan month payment
PV=loan amount=9,500
monthly payment=X
r=monthly interest rate=14.5%/12=0.0120833333333333
N=number of monthly payments=36
9,500=X*(1-(1+0.0120833333333333)^-36/0.0120833333333333
9,500=X*(1-(1.0120833333333333)^-36/0.0120833333333333
9,500=X*(1-0.6489543809903260)/0.0120833333333333
9,500=X*0.3510456190096740/0.0120833333333333
9,500=X*29.0520512283869000
X=9,500/29.0520512283869000
X=327.00
Total month repayments=327.00*36
Total month repayments=11,772.00
24-month loan month payment
PV=loan amount=9,500
monthly payment=X
r=monthly interest rate=14.5%/12=0.0120833333333333
N=number of monthly payments=24
9,500=X*(1-(1+0.0120833333333333)^-24/0.0120833333333333
9,500=X*(1-(1.0120833333333333)^-24/0.0120833333333333
9,500=X*(1-0.7495652524008220/0.0120833333333333
9,500=X*0.2504347475991780/0.0120833333333333
9,500=X*20.7256342840700000
X=9,500/20.7256342840700000
X=458.37
Total month repayments=458.37*24
Total month repayments=11,000.88
Difference in total payments=11,772.00-11,000.88
Difference in total payments=771.12
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Answer:
just 771.21
Step-by-step explanation:
to make it shorter credits to the og person who said the awnser 771.21
5/9+ (-4/5)
A. 1/4
B. 11/45
C. -9/14
D. -11/45
PLEASE HELP ILL GIVE BRAINLIST
Question 1 of 10
What is the slope of the line that contains the points (-2, 5) and (6,-3)?
OA. 8
OB. 1
O C. -1
OD. -8
Answer:
slope is -1
Step-by-step explanation:
Slope of the line is changes in y over changes in x. It can also be referred as rise over run.
We can express mathematically as:
[tex]\displaystyle{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
where m is slope.
Let (-2,5) be [tex]\displaystyle{(x_2,y_2)}[/tex] and (6,-3) be [tex]\displaystyle{(x_1,y_1)}[/tex]. Hence, apply the slope formula:
[tex]\displaystyle{m=\dfrac{5-(-3)}{-2-6}}\\\\\displaystyle{m=\dfrac{5+3}{-8}}\\\\\displaystyle{m=\dfrac{8}{-8}}\\\\\displaystyle{m=-1}[/tex]
Therefore, the slope is -1
tephen uses \dfrac{2}{25}
25
2
start fraction, 2, divided by, 25, end fraction kilograms of tofu in each serving of his famous tofu dish. He has 1\dfrac{1}{10}1
10
1
1, start fraction, 1, divided by, 10, end fraction kilograms of tofu.
The total number of servings Stephen can achieve with 1/10 kilograms of tofu at 2/25 kilograms per serving is 5/4 servings
Unit rateTofu per serving = 2/25 kilogramsTotal tofu Stephen has = 1/10 kilogramsNumber of servings = Total tofu Stephen has ÷ Tofu per serving
= 1/10 ÷ 2/25
= 1/10 × 25/2
= (1×25) / (10 × 2)
= 25/20
= 5/4 servings
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Which statement is true about the slope of the graphed line?
A graph is a line that extends from second quadrant to first quadrant with y-intercept at 4.
A.
The slope is negative.
B.
The slope is positive.
C.
The slope is zero.
D.
The slope is undefined.
Answer:
c
Step-by-step explanation:
because I had a test on these
There are 10 M&Ms of which 6 are green, in a bowl. You select 2 of them and eat each after it is selected. Is this a binomial experiment? Why or why not?
The experiment is not a binomial experiment.
What is a binomial experiment?
A binomial experiment is an experiment where there is a fixed number of trials, and the results are usually between two options- a yes or a no.
The conditions for a binomial experiment include:
1. Each trial should be classified either as a success or a failure.
2. There are a fixed number of observations
3. The trials are independent.
4. The number of trials are fixed.
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Suppose we want to choose 2 colors, without replacement from 3 colors red blue and green how many ways can this be done in the order of the choice is relevant and not relevant
The two colors can be chosen in 3 different ways.
In how many ways can we choose two colors?
If we have a set of N elements, the number of different sets of K elements (such that the order of the K elements does not matter) is:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
In this case, we have 3 colors, so N=3, and we want to choose 2, then K=2.
Replacing that we get:
[tex]C(3, 2) = \frac{3!}{(3- 2)!*2!} = \frac{3*2*1}{1*2*1} = 3[/tex]
The two colors can be chosen in 3 different ways.
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To find the quotient of two fractions, you first need to rewrite the division problem as an equivalent multiplication problem. Find this quotient using multiplication.
A tape manufacturer reduces the price of its Heavy Duty tape from $40 to $38 a reel and the price of Regular tape from $32 to $31 a reel. A computing center normally spends $1600 a month for tapes and 3/5 of this is for Heavy Duty tapes. How much will they save a month under the new prices?
Answer:
68
Step-by-step explanation:
Lets first find the quantity of tape the computing center is purchasing/month.
3/5 Of their 1600 dollar spending is on the heavy duty tapes, meaning they are spending 960 dollars/month on heavy duty tape, if we divide that by the original price, 40, it will give us the original quantity of heavy tape they are purchasing, 24/month.
The other 2/5 of their money, 640 dollars, are spent on regular tape, meaning they purchase 20 rolls of regular tape/month.
Given they are purchasing 24 rolls of heavy tape and 20 rolls of regular tape every month, we can simply multiple those by the new prices and sum the results.
24*38=912
20*31=620
912+620=1532
Then to find the money they are saving we subtract the new price from the original price.
1600-1532=68
How many words can be formed by using all the letters of the word AWILLO, if the two L's are to be separated?
483,800,000 place value of 4
Answer:
hundred million is the place value of 4 in 483800000
Suppose you are looking to purchase a new TV. You are placing it in an opening that is 136 cm wide but want to leave at least 2 cm of room on either side of the TV. If the TV screen measures 86 cm high, what is the largest size TVin inches, that you can purchase? TV's are measured based on the diagonal measure. (1inch = 2.54cm) Write your answer as an integer.
Answer:
62 inches
Step-by-step explanation:
Since we need to leave 2 cm of room on both sides, the maximum width of TV is 136 - 2 - 2 = 132 cm. Next, use the Pythagorean Theorem, a^2 + b^2 = c^2, to find the diagonal.
132^2 + 86^2 = c^2
c^2 = 17424 + 7396
c^2 = 24820
c = 157.543644746 cm
Finally, convert the value to inches using the given conversion factor.
157.543644746/2.54 = 62.0250569868 inches
if the area of the figure below is 400m. find x
Answer:
it's answer came 20000o
A class has $90 to spend on a field trip. The field trip costs $2.50 per person and there will be 5 chaperones on the trip. One student used the inequality 90 greater-than 2.50 (x + 5) to find x, the number of students that the field trip budget could accommodate. Which best describes the error in the student’s inequality?
Answer:
Step-by-step explanation:
x is the number of students
(x+5) is the number of students and chaperons
$2.50·(x+5) is the amount of money the number of students and chaperons will pay for the trip, and that number should be less or equal than $90 because those are all the money they have
2.50(x+5) ≤ 90 which is the same as 90 ≥ 2.50(x+5)
The inequality "90 greater-than 2.50 (x + 5) "
90 > 2.50(x+5) is an error becase it excludes the possibility that the trip can cost exact $90 so we need not just greater than > , yet greater and equal than ≥ sign
90 ≥ 2.50(x+5)
Solve for x: 4(x + 2) = 3(x - 2) (1 point)
0-2
O-4
O-10
O -14
Answer:
its -14
Step-by-step explanation:
Hooke's law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 11 lb stretches a certain spring 9 in., how much will a force of 22 lb stretch the spring?
Using proportions, it is found that a force of 22 lb stretches the spring 18 inches.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The measures are direct proportional, hence the rule of three is:
11 lb - 9 inches
22 lb - n inches
Applying cross multiplication:
11n = 9 x 22
n = 9 x 2
n = 18 inches.
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If 1st and 4th term of G.P is 500 and 32 respectively ,its 2nd term is
The second term of sequence is 200
Geometric equationGeometric sequence are sequence that differs in their term by a common ratio. The nth term of a geometric sequence is expressed as:
Tn = ar^n-1
where
a is the first term
n is the number of term
If 1st and 4th term of G.P is 500 and 32 respectively, hence;
T1 = ar^0 = 500
T3 = ar^3 = 32
From both expressions, the first term a = 500
Substitute into equation 2
ar^3 = 32
500r^3 = 32
r^3 = 32/500
r = ∛32/500
r = 0.4
Determine the second term
T2 = 500(0.4)
T2 = 200
Hence the second term of sequence is 200
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For what value of x is the rational expression below undefined x-4/3x2-75
The given expression is undefined when x = 5 OR x = -5
Undefined expressionFrom the question, we are to determine the value of x for which the given expression is undefined
The given expression is
x-4/3x²-75
An expression is undefined when the denominator equals zero
Thus, the expression is undefined when
3x² - 75 = 0
Now, we will determine the values of x in the equation above
3x² - 75 = 0
3x² = 75
x² = 75/3
x² = 25
x = ±√25
x = ±5
Hence, the given expression is undefined when x = 5 OR x = -5
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Make sure the answer is 100% correct. Then circle the answer in a circle.
Answer:
False
Any integers that the numbers 5, 10 , 15 but 20 can be used as a counter argument against the statement.
Step-by-step explanation:
The claim is that A⊆B which stands for that A is a SUBSET in B, or that B contains A.
The truth is that B⊆A since 5 has more possible outcomes than 20 in the number of integers.
So the list of all possible answers are r5, r10, and r15 where N⊆Z.
For example I choose r=3 and r15, 3(15)= 45. I can use the number 45 as a counter argument that the statement of A⊆B is false.
write the expression as the sine or cosine of an angle
pi/5 cos pi/2+sin pi/2\cos pi/5
The given expression as a sine function is [tex]sin(\frac{\pi}{5} +\frac{\pi}{2} )[/tex]
The addition formula for trigonometryThe given expression is:
[tex]sin(\frac{\pi}{5})cos(\frac{\pi}{2} ) + cos(\frac{\pi}{5})sin(\frac{\pi}{2} )[/tex]
Note that:
[tex]sin(A+B)=sinAcosB+cosAsinB[/tex]
Applying the addition principle to the given expression, we have:
[tex]sin(\frac{\pi}{5})cos(\frac{\pi}{2} ) + cos(\frac{\pi}{5})sin(\frac{\pi}{2} )=sin(\frac{\pi}{5} +\frac{\pi}{2} )[/tex]
Therefore, the given expression as a sine function is [tex]sin(\frac{\pi}{5} +\frac{\pi}{2} )[/tex]
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there were 936,795 bankruptcy filings in 2018. If there were 310,061 chapter 13 filings, what percent were not chapter 13
66.90% of the total bankruptcy fillings are not chapter 13 fillings.
What is bankruptcy?
This is a situation where the management of a company declares that it could no longer pay its debt obligations as it does have the cash resources to do so.
In this case, the total number of bankruptcy fillings is 936,795, out of which 310,061 are chapter 13 filings
fillings that were not chapter 13=936,795-310,061
fillings that were not chapter 13=626,734
fillings that were not chapter 13 as % of total fillings=626,734/936,795
fillings that were not chapter 13 as % of total fillings=66.90%
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9 and 1/9 subtracted by 1 and 4/5
Answer:
7 14/45
Step-by-step explanation:
9 1/9 - 1 4/5
82/9 - 9/5
410/45 - 81/45
329/45
7 14/45
Answer:
●7.31
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on a number line, suppose point E has a quotient of -1, and EG = 12. what are the possible coordinates of point G?
-13, or +11, because they are both 12 places away from -1.
For every 6,000 batches of 100 cards that are printed, she examines every 100th batch to make sure the logo is aligned and the magnetic strip works. Identify the population and the sample. a. population: 6,000 batches of 1000 cards sample: every 10,000 cards c. population: 6,000 batches of 1000 cards sample: every 100th batch b. population: 6,000 batches of 100 cards sample: every 10,000 cards. d. population: 6,000 batches of 100 cards sample: every 100th batch
Using sampling concepts, the population and the sample are given as follows:
d. population: 6,000 batches of 100 cards sample: every 100th batch.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
For example:
I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So I ask, lets say, 1000 randomly selected New York state residents whether they are Buffalo Bills fans, and then:
The population is: All New York State residents.The sample is the 1000 randomly selected New York state residents.Hence, in the situation described the population is the 6,000 batches of 100 cards, while the sample is every 100th batch, hence option d is correct.
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Melissa Costouras obtains a $3,000 loan for darkroom equipment. She makes six monthly payments of $511.18. Determine the APR.
Using simple interest, it is found that the APR is of 4.472%.
Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
[tex]A(t) = A(0)(1 + rt)[/tex]
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.The parameters are given as follows:
A(t) = 6 x 511.18 = 3067.08, A(0) = 3000, t = 0.5.
Hence the APR is found as follows:
[tex]A(t) = A(0)(1 + rt)[/tex]
[tex]3067.08 = 3000(1 + 0.5r)[/tex]
[tex]1 + 0.5r = \frac{3067.08}{3000}[/tex]
1 + 0.5r = 1.02236
r = (1.02236 - 1)/0.5
r = 0.04472.
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Sets A and I are defined as follows:
A = {-5, -2,0, 2, 5}
I = {−5, -1, 1, 5, 8}
Find the union of A and I.
Answer:
{-5,-2,0,2,5,-1,1,8}
Step-by-step explanation:
The union of two sets contains all elements that are in set A or in set B (possibly both).
{-5,-2,0,2,5} ∪ {-5,-1,1,5,8} = {-5,-2,0,2,5,-1,1,8}
Solutions greatest to smallest for function
=2+5−7
The greatest or maximum value for the given function = -8.25
The minimum or smallest value for the given function =-4
Calculation of greatest and smallest functionsThe maximum value of a function is the highest value of that function. To calculate the greatest function, the following equation is used,
Formula max = c - (b2 / 4a)
Where,
a = 2
b = 5
C = -7
Therefore maximum function
= -7 -(5*2/4*2)
= -7-(10/8)
= -7 - 1.25
= -8.25
The minimum value of a function is the least value of that function.
Formula for the minimum = c - b^2/4a.
= -7-5^2/4*2
= -32/8
= -4
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The sum of two numbers is 43 . The smaller number is 9 less than the larger number. What are the numbers?
Answer:
17 & 26
Step-by-step explanation:
The equation
[tex]x+(x+9)=43\\2x+9=43[/tex]
[tex]2x=43-9\\2x=34[/tex]
[tex]x=34/2=17[/tex]
One number is 17
The other number is:
[tex]x+9=17+9=26[/tex]
Hope this helps