Answer:
B
Step-by-step explanation
Find f(-11/5) if f(n) = 5n + 6
Answer:
f(-11/5) = -5
Step-by-step explanation:
f(n) = 5n + 6
Let x = -11/5
f(-11/5) = 5*-11/5 +6
= -11 +6
= -5
On a coordinate plane, Rectangles A B C D and E F G H are shown. The length of side A B is 6 units and the length of side B C is 3 units. The length of side E F is 8 units and the length of side F G is 4 units. Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin? Why or why not? Yes, because corresponding sides are parallel and have lengths in the ratio Four-thirds Yes, because both figures are rectangles and all rectangles are similar. No, because the center of dilation is not at (0, 0). No, because corresponding sides have different slopes
Answer:
Yes, because corresponding sides are parallel and have lengths in the ratio Four-thirds.
Step-by-step explanation:
Dilation is a transformation process in which the dimensions of a given figure are resized to produce an image with the same shape. This is done with respect to a scale factor and center of dilation.
In the given question, the center of dilation is at the middle of side DC of rectangle ABCD (i.e on side DC).
Given that the scale factor is [tex]\frac{4}{3}[/tex],
EF = HG = [tex]\frac{4}{3}[/tex] × AB = [tex]\frac{4}{3}[/tex] × 6 = 8 units
FG = EH = [tex]\frac{4}{3}[/tex] × BC = [tex]\frac{4}{3}[/tex] × 3 = 4 units
Therefore, rectangle EFGH is the result of dilation of ABCD.
Answer:
A. Yes, because corresponding sides are parallel and have lengths in the ratio Four-thirds
Step-by-step explanation:
According to Brad, consumers claim to prefer the brand-name products better than the generics, but they can't even tell which is which. To test his theory, Brad gives each of 199 consumers two potato chips - one generic, and one brand-name - then asks them which one is the brand-name chip. 92 of the subjects correctly identified the brand-name chip.
Required:
a. At the 0.01 level of significance, is this significantly greater than the 50% that could be expected simply by chance?
b. Find the test statistic value.
Answer:
a. There is not enough evidence to support the claim that the proportion that correctly identifies the chip is significantly smaller than 50%.
b. Test statistic z=-1.001
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the proportion that correctly identifies the chip is significantly smaller than 50%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi<0.5[/tex]
The significance level is 0.01.
The sample has a size n=199.
The sample proportion is p=0.462.
[tex]p=X/n=92/199=0.462[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{199}}\\\\\\ \sigma_p=\sqrt{0.001256}=0.035[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.462-0.5+0.5/199}{0.035}=\dfrac{-0.035}{0.035}=-1.001[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-1.001)=0.16[/tex]
As the P-value (0.16) is greater than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the proportion that correctly identifies the chip is significantly smaller than 50%.
Solve the system of equations below by graphing them with a pencil and
paper. Enter your answer as an ordered pair.
y= -x+5
y=x-3
Answer:
X+5= -x-3
2x = 2
X=1
then y1 is 4
y2 is -1
Answer:
Answer is 4, 1. If you graph the lines, they intersect at 4, 1.
Step-by-step explanation:
The amount of money that is left in a medical savings account is expressed by the equation y = negative 24 x + 379, where x represents the number of weeks and y represents the amount of money, in dollars, that is left in the account. After how many weeks will the account have $67 left in it? 10 weeks 13 weeks 15 weeks 21 weeks
Answer: 13 weeks
Step-by-step explanation:
y = -24x + 379
67 = -24x + 379
24x = 379 - 67
x = 312 / 24
x = 13
Answer:
the answer is 13 weeks
Step-by-step explanation:
y = amount left
y = 67
67 = -24x+379
-312 = -24x
x = -312 / -24
x = 13
A lake has a large population of fish. On average, there are 2,400 fish in the lake, but this number can vary by as much as 155. What is the maximum number of fish in the lake? What is the minimum number of fish in the lake?
Answer:
Minimum population of fish in lake = 2400 - 155 = 2245
Maximum population of fish in lake = 2400 + 155 = 2555
Step-by-step explanation:
population of fish in lake = 2400
Variation of fish = 155
it means that while current population of fish is 2400, the number can increase or decrease by maximum upto 155.
For example
for increase
population of fish can 2400 + 2, 2400 + 70, 2400 + 130 etc
but it cannot be beyond 2400 + 155.
It cannot be 2400 + 156
similarly for decrease
population of fish can 2400 - 3, 2400 - 95, 2400 - 144 etc
but it cannot be less that 2400 - 155.
It cannot be 2400 - 156
Hence population can fish in lake can be between 2400 - 155 and 2400 + 155
minimum population of fish in lake = 2400 - 155 = 2245
maximum population of fish in lake = 2400 + 155 = 2555
IF UR CLEVER PLEAZE HELP ME OUT I AM ON A LIVE LESSON . NEEDS TO BE ANSWERED STAT!!!!
Answer:
384cm2
Step-by-step explanation:
surface area
12×12=144
10×12/2=60
60×4=240
240+144=384cm2
In the diagram below, $RT:TS = 1:2$ and $SR = PQ = 20$. Find $UV$.
It's pretty easy not college levlel just some simple high school geomerty.
Answer: 12
Step-by-step explanation: Because $\overline{PQ}$, $\overline{UV}$, and $\overline{SR}$ are all perpendicular to $\overline{QR}$, we have $\overline{PQ} \parallel \overline{UV} \parallel \overline{SR}$. Therefore, we have $\angle UPQ = \angle UTS$ and $\angle UQP = \angle UST$, which means that $\triangle UPQ \sim \triangle UTS$. So, we have $UQ/US = PQ/ST$.
Because $ST/SR = 2/3$ and $PQ = SR$, we have
\[\frac{UQ}{US} = \frac{PQ}{ST} = \frac{SR}{ST} = \frac{3}{2}.\]Since $UQ/US = 3/2$, we have $UQ/QS = 3/5$.
We have $\triangle UQV \sim \triangle SQR$ by AA Similarity, so $UV/SR = UQ/QS = 3/5$. Therefore, we have $UV = (3/5)SR = \boxed{12}$.
An engineering study indicates that 8.5% of the bridges in a large state are structurally deficient. The state's department of transportation randomly samples 100 bridges. What is the probability that exactly 6 bridges in the sample are structurally deficient
Answer:
[tex]P(X=6)=(100C6)(0.085)^6 (1-0.085)^{100-6}=0.1063[/tex]
Then the probability that exactly 6 bridges in the sample are structurally deficient is 0.1063 or 10.63%
Step-by-step explanation:
Let X the random variable of interest "number of bridges in the sample are structurally deficient", on this case we now that:
[tex]X \sim Binom(n=100, p=0.085)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X=6)[/tex]
And if we use the probability mass function and we replace we got:
[tex]P(X=6)=(100C6)(0.085)^6 (1-0.085)^{100-6}=0.1063[/tex]
Then the probability that exactly 6 bridges in the sample are structurally deficient is 0.1063 or 10.63%
Consider the following sets of sample data: A: 431, 447, 306, 413, 315, 432, 312, 387, 295, 327, 323, 296, 441, 312 B: $1.35, $1.82, $1.82, $2.72, $1.07, $1.86, $2.71, $2.61, $1.13, $1.20, $1.41 Step 1 of 2 : For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.
Answer:
Dataset A
We have the following results:
[tex] \bar X_A = 359.786[/tex]
[tex]s_A= 60.904[/tex]
[tex] CV_A = \frac{60.904}{359.786}= 0.169 \approx 0.2[/tex]
Dataset B
We have the following results:
[tex] \bar X_B = 1.791[/tex]
[tex]s_B= 0.635[/tex]
[tex] CV_B = \frac{0.635}{1.791}= 0.355 \approx 0.4[/tex]
Step-by-step explanation:
For this case we have the following info given:
A: 431, 447, 306, 413, 315, 432, 312, 387, 295, 327, 323, 296, 441, 312
B: $1.35, $1.82, $1.82, $2.72, $1.07, $1.86, $2.71, $2.61, $1.13, $1.20, $1.41
We need to remember that the coeffcient of variation is given by this formula:
[tex] CV= \frac{s}{\bar X}[/tex]
Where the sample mean is given by:
[tex] \bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]
And the sample deviation given by:
[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
Dataset A
We have the following results:
[tex] \bar X_A = 359.786[/tex]
[tex]s_A= 60.904[/tex]
[tex] CV_A = \frac{60.904}{359.786}= 0.169 \approx 0.2[/tex]
Dataset B
We have the following results:
[tex] \bar X_B = 1.791[/tex]
[tex]s_B= 0.635[/tex]
[tex] CV_B = \frac{0.635}{1.791}= 0.355 \approx 0.4[/tex]
In a large sample of customer accounts, a utility company determined that the average number of days between when a bill was sent out and when the payment was made is 30 with a standard deviation of 7 days. Assume the data to be approximately bell-shaped.
Between what two values will approximately 68% of the numbers of days be?
Approximately 68% of the customer accounts have payment made between __________and________________ days
Answer:
Approximately 68% of the customer accounts have payment made between 23 and 37 days.
Step-by-step explanation:
We want to calculate what two values will approximately 68% of the numbers of days be.
For a bell shaped distribution, we can apply the 68-95-99.7 rule, which states that approximately 68% of the data will fall within 1 standard deviation from the mean.
Then, for a mean of 30 and standard deviation of 7, we can calculate the two values as:
[tex]X_1=\mu+z_1\cdot\sigma=30-1\cdot 7=30-7=23 \\\\X_2=\mu+z_2\cdot\sigma=30+1\cdot 7=30+7=37[/tex]
Answer:
The answer is 16 and 44 days.
Step-by-step explanation:
This is the correct answer for this question.
Jeff's net monthly income is $2550. His monthly expense for rent is $625. What percent of his net monthly income is his rent? (Round your answer to the nearest whole percent.)
Answer:
25%
I cannot really describe how I did it but I am pretty sure it is correct.
There is 0.3 probability that a group of insured motorists have an accident in a decade.
If there are 640 insured motorists, what is the mean number of accidents in a decade?
Answer:
192
Step-by-step explanation:
to find the mean you have to use this formula: mean= N(total number of trials) times P( probability of "success")
n=640
p=0.3
640x0.3= 192
in a church wing with 8 men and 10 women members find the probability that a 5 member committee chosen randomly will have.......
a).all men.
b).3men and 2 women
Answer:
a) Probability that a 5 member committee will have all men = 0.0065
b) probability that a 5 member committee chosen randomly will have 3 men and 2 women = 0.294
Step-by-step explanation:
Number of men = 8
Number of women = 10
Total number of members = 10 + 8 = 18
Probability = (Number of possible outcomes)/(Total number of outcomes)
Number of ways of selecting a 5 member committee from 18 people = [tex]^{18}C_5 = \frac{18!}{(18-5)!5!} = \frac{18!}{13!5!}[/tex] = 8568 ways
a) Probability that a 5 member committee will have all men
Number of ways of selecting 5 men from 8 men
= [tex]^8C_5 = \frac{8!}{(8-5)!5!} = \frac{8!}{3!5!}[/tex] = 56 ways
Probability that a 5 member committee will have all men = 56/8568
Probability that a 5 member committee will have all men = 0.0065
b)probability that a 5 member committee chosen randomly will have 3men and 2 women
Number of ways of selecting 3 men from 8 men
= [tex]^8C_3 = \frac{8!}{(8-3)!3!} = \frac{8!}{5!3!}[/tex] = 56 ways
Number of ways of selecting 2 women from 10 men
= [tex]^{10}C_2 = \frac{10!}{(10-2)!2!} = \frac{10!}{8!2!}[/tex] = 45 ways
Number of ways of selecting 3 men and 2 women = 56*45
Number of ways of selecting 3 men and 2 women = 2520
Probability of selecting 3 men and 2 women = 2520/8568 = 0.294
probability that a 5 member committee chosen randomly will have 3 men and 2 women = 0.294
Which of the following are point-slope equations of the line going through (3,
6) and (1,-2)? Check all that apply:
Answer:
y+2=4(x-1)
y-6=4(x-3)
Step-by-step explanation:
Slope between (3, 6) and (1, -2)
6-(-2)/3-1
8/2
4
y+2=4(x-1)
y-6=4(x-3)
PLEASE I NEED HELP ASAP sally drives for 2 hours at an average speed of 70 m/h. she then drives for half an hour at an average speed of 40 m/h work ot the total distance that sally has travelled
Answer:
Total Distance = 160 m
Average speed = 64 m/hr
Step-by-step explanation:
For first 2 hours:
Distance = Speed × Time
D = 70 × 2
D = 140 m
For the next half hour:
Distance = Speed × Time
Distance = 40 × 0.5
Distance = 20 m
Now total Distance:
Total Distance = 140+20
Total Distance = 160 m
After that,
Average Speed = Total Distance Covered/ Total Time taken
Average Speed = 160 m / 2.5 hours
Average speed = 64 m/hr
The diameter of a sphere is 4 centimeters, which represents the volume of the sphere?
Answer:
10 2/3π or 33.51
Step-by-step explanation:
the volume of a sphere is 4/3πr^3
if the sphere has a diameter of 4 the radius is half the diameter so it would be 2. 2^3 = 8 now multiply 8 by 4/3 to get 10 2/3. now multiply by pi to get 10 2/3 π or 33.5103 which rounds to 33.51
Answer:
32π/3 cubic cm
Step-by-step explanation:
help i give u brainliest
It is a 4 : 1 ratio of color to white
or a 1 : 4 white to colored
Explanation:
1cm = 10mm
1.2cm = 12mm
12 : 48 --> 1 : 4
Answer:
1:4
Step-by-step explanation:
1.2 cm of white fabric per 48 mm of colored fabric:
1.2 cm : 48 mm= 12 mm: 48 mm= 1:4
The ratio is: 1:4
add or subtract negative numbers
[tex]9+(-2)\\9-2\\=7[/tex]
[tex]-6+(-3)\\-6-3\\=-9[/tex]
[tex]4+(-9)\\4-9\\=-5[/tex]
Answer:
see below
Step-by-step explanation:
9 + -2 =
9 -2 = 7
-6 + -3
-6 - 3 =-9
4 + - 9
-9 +4 = -5
the mean of the prime factors of 24 is
Answer:
bad words
Step-by-step explanation:
it is your shet
Answer:
2.25
Step-by-step explanation:
Prime Factors of 24 is 2 x 2 x 2 x 3
2 + 2 + 2 + 3 = 9
9/4 = 2.25
A biologist conducting an experiment starts with a culture of 300 E. coli bacteria. 72 hours later the culture consists of 600,000 bacteria. What is the average increase in the number of E. coli bacteria per hour
Answer:
2,000
Step-by-step explanation:
if you divide 600,000 by 300 you get 2,000.
All applicants for admission to graduate study in business are given a standardized test. Scores are normally distributed with a mean of 460 and standard deviation of 80. What fraction of applicants would you expect to have scores of 600 or above
Answer:
The probability that applicants would you expect to have scores of 600 or above = 0.0401 or 4%
Step-by-step explanation:
Explanation:-
Let "x" Scores are normally distributed
Given mean of the Population = 460
standard deviation of the population = 80
Let X = 600
[tex]Z = \frac{x -mean}{S.D} = \frac{600-460}{80} =1.75[/tex]
The probability that applicants would you expect to have scores of 600 or above
P( X≥600) = P( Z≥ 1.75)
= 1- P( Z≤1.75)
= 1- ( 0.5 + A(1.75)
= 1- 0.5 - A(1.75)
= 0.5 - 0.4599 (from Normal table)
= 0.0401
The probability that applicants would you expect to have scores of 600 or above = 0.0401 or 4%
Which expanded expressions represent the exponential expression (–4)3 · p4? Select all that apply. (–4) · (–4) · (–4) · (–4) · p · p · p p · p · p · p · (–4) · (–4) · (–4) p · (–4) · (–4) · p · (–4) · p p · p · (–4) · (–4) · p · p · (–4) (–4) · p · p · p · (–4) · (–4) · (–4) (–4) · (–4) · p · (–4) · p · p · p
The expanded form of the given exponential expression is (-4)×(-4)×(-4)×p×p×p×p.
What is the exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
The given expression is (-4)³·p⁴.
Here, (-4)³= (-4)×(-4)×(-4)
p⁴=p×p×p×p
So, (-4)×(-4)×(-4)×p×p×p×p
= -64×p×p×p×p
Therefore, the expanded form is (-4)×(-4)×(-4)×p×p×p×p.
To learn more about an exponents visit:
https://brainly.com/question/15993626.
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Question from quadratic equation .
solve.
(x-3)(x+7)=0
Answer:
x = 3, -7
Step-by-step explanation:
Since you already have the factored form, all you need to do is set the equations equal to zero to find you roots:
x - 3 = 0
x + 7 = 0
x = 3, -7
Answer:
3 or -7
Step-by-step explanation:
For it to equal 0, x must be 3 or -7 because anything multiplied by 0 is 0. So you take each part, x-3 and see how you can make that a 0. x-3=0, therefore x must be 3. Other part x+7=0, x must be -7.
The shorter leg of a right triangle is 14 feet less than the other leg. Find the length of the two legs of the hypotenuse is 25 feet.
Answer:
9.233 ft, 23.233 ft
Step-by-step explanation:
If the shorter leg is x, then the longer leg is x+14 and the Pythagorean theorem tells you ...
x^2 + (x +14)^2 = 25^2
2x^2 +28x +196 = 625
x^2 +14x = 214.5
x^2 +14x +49 = 263.5
(x +7)^2 = 263.5
x = -7 +√263.5 ≈ 9.23268
The two leg lengths are √263.5 ± 7 feet, {9.23 ft, 23.23 ft}.
Answer: 9 ft, 23 ft
Step-by-step explanation:
We know the Pythagorean Theorem is a²+b²=c². Since one leg is 14 less than the other leg, we can use x-14 and the other leg would be x. We can plug these into the Pythagorean Theorem with the given hypotenuse.
(x-14)²+x²=25²
(x²-28x+196)+x²=625
2x²-28x+196=625
2x²-28x-429=0
When we solve for x, we get [tex]x=\frac{14+\sqrt{1054} }{2}[/tex] and [tex]x=\frac{14-\sqrt{1054} }{2}[/tex].
Note, since we rounded to 23, the hypotenuse isn't exactly 25, but it gets very close.
Preciso de ajudaa! Resolução também! - Considere as funções f e g tais que f(x)= x³+1 e g(x)= x-2 Determine: a)(fog)(0) b)(gof)(0) c)(fof)(1) d)(gog)(1)
Answer:
(fog)(x) means that we have the function f(x) evaluated in the function g(x), or f(g(x)).
So, if f(x) = x^3 + 1 and g(x) = x - 2.
we have:
a) (fog)(0) = f(g(0)) = (0 - 2)^3 + 1 = -8 + 1 = -7
b) (gof)(0) = g(f(0)) = (0^3 + 1) - 2 = -1
c) (fof)(1) = f(f(1)) = (1^3 + 1)^3 + 1 = 2^3 + 1 = 8 + 1 = 9
d) (gog)(1) = g(g(1)) = (1 - 2) - 2 = -1 -2 = -3
Which expression is equal to -3b(6b^-8)
Answer:a^2/b
Step-by-step explanation:
(a^6b^−3)1^/3
a^6 ^ 1/3 b ^ -3 ^ 1/3
using the power of power rule we can multiply the exponents
a ^ (6*1/3) b ^ (-3* 1/3)
a^ 2 b ^ -1
the negative exponent flips it from the numerator to the denominator
a^2* 1/ b^1
a^2/b
Answer:
A. -18b^-4
second answer is B. -18/b^-4
Step-by-step explanation:
2(3y+6)−3(−4−y) simplified
Answer:
9y+24
Step-by-step explanation:
2(3y+6)-3(-4-y)
Expand the brackets.
6y+12+12+3y
Rearrange.
6y+3y+12+12
Add like terms.
9y+24
Answer:
9y+24solution,
[tex]2(3y + 6) - 3( - 4 - y) \\ = 6y + 12 + 12 + 3y[/tex]
Collect like terms,
[tex]6y + 3y + 12 + 12[/tex]
Simplify
[tex]9y + 24[/tex]
hope this helps...
Good luck on your assignment..
HELP PLZ!! I NEED HELP!
Answer:
yes£18Step-by-step explanation:
The amount Lila and Wassim plan to save is ...
(£13 +13)(9) = £234
__
The charges they expect to incur are a per-person charge and a tent pitch charge. Since they expect to stay 10 nights, the special rate means they will only be charged for 8 nights.
per-person charge
per-person-per-night charge = (2 persons)(8 nights)(£6 per person-night)
= £96
tent pitch charge
To determine the tent pitch area required, we need to find the area of the tent:
A = LW = (4.2 m)(2.3 m) = 9.66 m²
This is less than 10 square meters, so we can expect the pitch charge to be £15 per night for 8 nights.
tent pitch charge = (£15/night)(8 nights) = £120
So, the total of camp site charges is expected to be ...
person charge + pitch charge = £96 +120 = £216
__
The expected savings exceeds the expected charges by ...
£234 -216 = £18
Lila and Wassim will have enough saved, with £18 extra.
A restaurant borrows from a local bank for months. The local bank charges simple interest at an annual rate of for this loan. Assume each month is of a year. Answer each part below.Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.
(a) Find the interest that will be owed after 4 months
(b) Assuming the restaurant doesn't make any payments, find the amount owed after 4 months
Complete Question:
A restaurant borrows $16,100 from a local bank for 4 months. The local bank charges simple interest at an annual rate of 2.45% for this loan. Assume each month is 1/12 of a year.
Answer each part below.Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.
(a) Find the interest that will be owed after 4 months
(b) Assuming the restaurant doesn't make any payments, find the amount owed after 4 months
Answer:
a) Interest that will be owed after 4 months , I = $131.48
b) Amount owed by the restaurant after 4 months = $16231.48
Step-by-step explanation:
Note that the question instructs not to round any intermediate computations except the final answer.
Annual rate = 2.45%
Monthly rate, [tex]R = \frac{2.45\%}{12}[/tex]
R = 0.20416666666%
Time, T = 4 months
Interest, [tex]I = \frac{PRT}{100}[/tex]
[tex]I = \frac{16100 * 0.20416666666 * 4}{100} \\I = 161 * 0.20416666666 * 4\\I = \$131.483333333\\I = \$131.48[/tex]
b) If the restaurant doesn't make any payments, that means after four months, they will be owing both the capital and the interest ( i.e the amount)
Amount owed by the restaurant after 4 months = (Amount borrowed + Interest)
Amount owed by the restaurant after 4 months = 16100 + 131.48
Amount owed by the restaurant after 4 months = $16231.48