Answer:
let length be x
b = x - 3
perimeter = 2( l + b)
54 = 2(x+x-3)
27 = 2x - 3
30 = 2x
x = 15
l = 15
b = 15 - 3
b = 12
The 8th term in the arithmetic sequence is 17, the 12th term is 25. Find the first term, and the sum of the first 20 terms.
Answer:
First term a = 3
Sum of first 20 term = 440
Step-by-step explanation:
Given:
8th term of AP = 17
12th term of AP = 25
Find:
First term a
Sum of first 20 term
Computation:
8th term of AP = 17
a + 7d = 17 ....... EQ1
12th term of AP = 25
a + 11d = 25 ...... EQ2
From EQ1 and EQ2
4d = 8
d = 2
a + 7d = 17
a + 7(2) = 17
First term a = 3
Sum of first 20 term
Sn = [n/2][2a + (n-1)d]
S20 = [20/2][(2)(3) + (20-1)2]
S20 = [10][(6) + 38]
S20 = [10][44]
S20 = 440
Sum of first 20 term = 440
6. Find average of the following
expressions (4-2x), (-7-3x), and
(11x+6)
Answer:
2x + 1.
Step-by-step explanation:
Average = sum of the expression / number of expressions
= [(4 - 2x) + (-7 - 3x) + (11x + 6)] / 3
= (-2x - 3x + 11x + 4 - 7 + 6) / 3
= 6x + 3 / 3
= 2x + 1
Answer:
2x+1
Step-by-step explanation:
(4-2x), (-7-3x),(11x+6)
Add the three expressions
(4-2x)+ (-7-3x)+(11x+6)
Combine like terms
-2x-3x+11x+4-7+6
6x+3
Divide by the number of expressions which was 3
(6x+3)/3
2x+1
The average is 2x+1
The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.14 gallons. A previous study found that for an average family the standard deviation is 2 gallons and the mean is 16 gallons per day. If they are using a 95% level of confidence, how large of a sample is required to estimate the mean usage of water
Answer:
A sample of 784 is required to estimate the mean usage of water.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The standard deviation is 2 gallons
This means that [tex]\sigma = 2[/tex]
They would like the estimate to have a maximum error of 0.14 gallons. How large of a sample is required to estimate the mean usage of water?
This is n for which M = 0.14. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.14 = 1.96\frac{2}{\sqrt{n}}[/tex]
[tex]0.14\sqrt{n} = 1.96*2[/tex]
[tex]\sqrt{n} = \frac{1.96*2}{0.14}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*2}{0.14})^2[/tex]
[tex]n = 784[/tex]
A sample of 784 is required to estimate the mean usage of water.
Kevin has 17 trading cards. Billy has t more trading cards than Kevin. Choose the expression that shows how many trading cards
Billy has
Answer:
Step-by-step explanation:
Suppose point (4, −9) is translated according to the rule (, ) → ( + 3, − 2). What are the coordinates of ′? Explain
An ANOVA procedure is applied to data obtained from four distinct populations. The samples, each comprised of 15 observations, were taken from the four populations. The degrees of freedom for the numerator and denominator for the critical value of F are:___________
a. 3 and 56, respectively.
b. 3 and 59, respectively.
c. 4 and 21, respectively.
d. 4 and 60, respectively
Answer:
a. 3 and 56, respectively.
Step-by-step explanation:
The computation of the degrees of freedom for the numerator and denominator for the critical value of F is given below:
k = 4
n = 15
Total degree of freedom is
= nk - 1
= 59
For numerator, it is
= k -1
= 4 - 1
= 3
and for denominator it is
= T - (k -1 )
= 59 - 3
= 56
A day trading firm closely monitors and evaluates the performance of its traders. For each $10,000 invested, the daily returns of traders at this company can be modeled by a Normal distribution with mean = $830 and standard deviation = $1,781.
(a) What is the probability of obtaining a negative daily return, on any given day? (Use 3 decimals.)
(b) Assuming the returns on successive days are independent of each other, what is the probability of having a negative daily return for two days in a row? (Use 3 decimals.)
(c) Give the boundaries of the interval containing the middle 80% of daily returns: (use 3 decimals) ( , )
(d) As part of its incentive program, any trader who obtains a daily return in the top 2% of historical returns receives a special bonus. What daily return is needed to get this bonus? (Use 3 decimals.)
Answer:
a) 0.321 = 32.1% probability of obtaining a negative daily return, on any given day.
b) 0.103 = 10.3% probability of having a negative daily return for two days in a row.
c) (-$1449.68, $3109.68)
d) A bonus of $4,488.174 is needed.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normal distribution with mean = $830 and standard deviation = $1,781.
This means that [tex]\mu = 830, \sigma = 1781[/tex]
(a) What is the probability of obtaining a negative daily return, on any given day?
This is the p-value of Z when X = 0, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0 - 830}{1781}[/tex]
[tex]Z = -0.466[/tex]
[tex]Z = -0.466[/tex] has a p-value 0.321.
0.321 = 32.1% probability of obtaining a negative daily return, on any given day.
(b) Assuming the returns on successive days are independent of each other, what is the probability of having a negative daily return for two days in a row?
Each day, 0.3206 probability, so:
[tex](0.321)^2 = 0.103[/tex]
0.103 = 10.3% probability of having a negative daily return for two days in a row.
(c) Give the boundaries of the interval containing the middle 80% of daily returns
Between the 50 - (80/2) = 10th percentile and the 50 + (80/2) = 90th percentile.
10th percentile:
X when Z has a p-value of 0.1, so X when Z = -1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 830}{1781}[/tex]
[tex]X - 830 = -1.28*1781[/tex]
[tex]X = -1449.68[/tex]
90th percentile:
X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 830}{1781}[/tex]
[tex]X - 830 = 1.28*1781[/tex]
[tex]X = 3109.68[/tex]
So
(-$1449.68, $3109.68)
d) As part of its incentive program, any trader who obtains a daily return in the top 2% of historical returns receives a special bonus. What daily return is needed to get this bonus?
The 100 - 2 = 98th percentile, which is X when Z has a p-value of 0.98, so X when Z = 2.054.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.054 = \frac{X - 830}{1781}[/tex]
[tex]X - 830 = 2.054*1781[/tex]
[tex]X = 4488.174 [/tex]
A bonus of $4,488.174 is needed.
Help me complete the proof!
Answer:
Distributive Property means you can multiply the outside and inside of parenthesis.
Addition Property... means you can add the same value to both sides of the equation without changing it. In this case you add 3x.
Subtraction Property... same as addition property, but with subtraction. In this case subtract 10 from both sides.
Division property... same as addition and subtraction properties but with division. In this case divide both sides by 8.
Technically the addition property can be used for the subtract 10 because you just add -10 and multiplication property could be used for the division, because you just multiply both sides by 1/8, but for the purpose of this equation, you would say subtraction and division.
A sprinter travels a distance of 200 m in a time of 20.03 seconds.
What is the sprinter's average speed rounded to 4 sf?
Given:
Distance traveled by sprinter = 200 m
Time taken by sprinter = 20.03 seconds
To find:
The sprinter's average speed rounded to 4 sf.
Solution:
We know that,
[tex]\text{Average speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]
It is given that, the sprinter travels a distance of 200 m in a time of 20.03 seconds.
[tex]\text{Average speed}=\dfrac{200}{20.03}[/tex]
[tex]\text{Average speed}=9.985022466[/tex]
[tex]\text{Average speed}\approx 9.985[/tex]
Therefore, the average speed of the sprinter is 9.985 m/sec.
Answer:
9.985
Step-by-step explanation:
On a shelf at a gaming store, there are three Sony PlayStations and seven Nintendo Wii coasters left. If one gaming system is selected at random, find the probability that the system is a Wii console.
Answer:
hello
as probability is equal to number of favourable outcomes/total number of out comes,
Step-by-step explanation:
=7/10
HOPES THAT IT HELPS YOU
PLEASE MARK ME AS BRAINLIEST
Suppose a sample of 1453 new car buyers is drawn. Of those sampled, 363 preferred foreign over domestic cars. Using the data, estimate the proportion of new car buyers who prefer foreign cars. Enter your answer as a fraction or a decimal number rounded to three decimal places
Answer:
"0.250" is the appropriate answer.
Step-by-step explanation:
Given:
New car sample,
= 1453
Preferred foreign,
= 363
Now,
The amount of new automobile purchasers preferring foreign cars will be approximated as:
= [tex]\frac{363}{1453}[/tex]
= [tex]0.250[/tex]
If $6^x = 5,$ find $6^{3x+2}$.
If 6ˣ = 5, then
(6ˣ)³ = 6³ˣ = 5³ = 125,
and
6³ˣ⁺² = 6³ˣ × 6² = 125 × 6² = 125 × 36 = 4500
A packing plant fills bags with cement. The weight X kg of a bag can be modeled by a normal distribution with mean 50kg and standard deviation 2kg. 4.
a. Find the probability that a randomly selected bag weighs more than 53kg.
b. Find the weight that is exceeded by 98% of the bags.
c. Three bags are selected at random. Find the probability that two weigh more than 53kg and one weighs less than 53kg.
Answer:
a) 0.0668 = 6.68% probability that a randomly selected bag weighs more than 53kg.
b) The weight that is exceeded by 98% of the bags is of 45.9 kg.
c) 0.0125 = 1.25% probability that two weigh more than 53kg and one weighs less than 53kg.
Step-by-step explanation:
The first two questions are solved using the normal distribution, while the third is solved using the binomial distribution.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The weight X kg of a bag can be modeled by a normal distribution with mean 50kg and standard deviation 2kg.
This means that [tex]\mu = 50, \sigma = 2[/tex]
a. Find the probability that a randomly selected bag weighs more than 53kg.
This is 1 subtracted by the p-value of Z when X = 53. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{53 - 50}{2}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a p-value of 0.9332.
1 - 0.9332 = 0.0668.
0.0668 = 6.68% probability that a randomly selected bag weighs more than 53kg.
b. Find the weight that is exceeded by 98% of the bags.
This is the 100 - 98 = 2nd percentile, which is X when Z has a p-value of 0.02, so X when Z = -2.054.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-2.054 = \frac{X - 50}{2}[/tex]
[tex]X - 50 = -2.054*2[/tex]
[tex]X = 45.9[/tex]
The weight that is exceeded by 98% of the bags is of 45.9 kg.
c. Three bags are selected at random. Find the probability that two weigh more than 53kg and one weighs less than 53kg.
0.0668 = 6.68% probability that a randomly selected bag weighs more than 53kg means that [tex]p = 0.0668[/tex]
3 bags means that [tex]n = 2[/tex]
Two above 53kg, which means that we want P(X = 2). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{3,2}.(0.0668)^{2}.(0.9332)^{1} = 0.0125[/tex]
0.0125 = 1.25% probability that two weigh more than 53kg and one weighs less than 53kg.
Which side of the polygon is exactly 6 units long?
Answer:
AB is correct as It is the shorter parallel line
as the line measures 6 units.
Step-by-step explanation:
The polygon is a trapezoid / (trapezium Eng/Europe)
We see the given coordinates (2, 6) - (-4, 6) = x-6 y 0 = x = 6units
as x always is shown as x - 6 as x= 6
We can also show workings as y2-y1/x2-x1 = 6-6/-4-2 0/-6
y = 0 x = 6 = 6 units as its horizontal line.
when y is 6-6 = 0 then we know the line is horizontal for y = 0.
The difference of the measures -4 to 2 is 6units so if no workings we just add on from -4 to 2 and find the answer is 6 units long.
When looking at diagonal lines we still group the x's and y's and make the fraction whole.
When looking for solid vertical lines that aren't shown here we use the y values if showing workings and show x =0 to cancel out.
a triangle has sides of 6 m 8 m and 11 m is it a right-angled triangle?
Answer:
No
Step-by-step explanation:
If we use the Pythagorean theorem, we can find if it is a right triangle. To do that, set up an equation.
[tex]6^{2}+8^{2}=c^2[/tex]
If the triangle is a right triangle, c would equal 11
Solve.
[tex]36+64=100[/tex]
Then find the square root of 100.
The square root of 100 is 10, not 11.
So this is not a right triangle.
I hope this helps!
What is the explicit formula for the sequence ? -1,0,1,2,3
Answer:
B
Step-by-step explanation:
substitute the values in the eq. Ot is also arithmetic progression.
A large water tank has two inlet pipes (a large and a small one) and one outlet pipe. It takes
2
hours to fill the tank with the large inlet pipe. On the other hand, it takes
5
hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in
7
hours. Assuming that the tank is initially empty, what fraction will be filled in
1
hour if all three pipes are in operation? Your answer should be a fraction in simplest form, without spaces, e.g. 1/2.
Answer:2x+2
Step-by-step explanation:
Assuming that the sample mean carapace length is greater than 3.39 inches, what is the probability that the sample mean carapace length is more than 4.03 inches
Answer:
The answer is "".
Step-by-step explanation:
Please find the complete question in the attached file.
We select a sample size n from the confidence interval with the mean [tex]\mu[/tex]and default [tex]\sigma[/tex], then the mean take seriously given as the straight line with a z score given by the confidence interval
[tex]\mu=3.87\\\\\sigma=2.01\\\\n=110\\\\[/tex]
Using formula:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The probability that perhaps the mean shells length of the sample is over 4.03 pounds is
[tex]P(X>4.03)=P(z>\frac{4.03-3.87}{\frac{2.01}{\sqrt{110}}})=P(z>0.8349)[/tex]
Now, we utilize z to get the likelihood, and we use the Excel function for a more exact distribution
[tex]=\textup{NORM.S.DIST(0.8349,TRUE)}\\\\P(z<0.8349)=0.7981[/tex]
the required probability: [tex]P(z>0.8349)=1-P(z<0.8349)=1-0.7981=\boldsymbol{0.2019}[/tex]
Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.
n an
1 −4
2 20
3 −100
an = −5(−4)n − 1 where n ≥ 1
an = −4(−5)n − 1 where n ≥ 1
an = −4(5)n − 1 where n ≥ −4
an = 5(−4)n − 1 where n ≥ −4
Given:
The geometric sequence is:
[tex]n[/tex] [tex]a_n[/tex]
1 -4
2 20
3 -100
To find:
The explicit formula and list any restrictions to the domain.
Solution:
The explicit formula of a geometric sequence is:
[tex]a_n=ar^{n-1}[/tex] ...(i)
Where, a is the first term, r is the common ratio and [tex]n\geq 1[/tex].
In the given sequence the first term is -4 and the second term is 20, so the common ratio is:
[tex]r=\dfrac{a_2}{a_1}[/tex]
[tex]r=\dfrac{20}{-4}[/tex]
[tex]r=-5[/tex]
Putting [tex]a=-4,r=-5[/tex] in (i), we get
[tex]a_n=-4(-5)^{n-1}[/tex] where [tex]n\geq 1[/tex]
Therefore, the correct option is B.
is x^2+y-15=10 a relation and a function?
Answer:
it is
Step-by-step explanation:
yes, it is. every function is a relation
x²+y-15=10
y=25-x²
As one once said Another one
Answer:
f
Step-by-step explanation:
Answer:
S = 62.9
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan S = opp side / adj side
tan S = sqrt(42)/ sqrt (11)
tan S = sqrt(42/11)
Taking the inverse tan of each side
tan ^ -1( tan S) = tan ^-1(sqrt(42/11))
S=62.89816
Rounding to the nearest tenth
S = 62.9
40% of what number is 16.6?
easy! plz help me tho
In a survey, the wording of the questions can introduce
Validity
Randomness
Bias
Uniformity
Answer:
bias
Step-by-step explanation:
the wording of the question may be misleading. the way the question is phrased influences the way the person who is being surveyed answers.
The wording of the questions can introduce (C) Bias.
What are bias questions?A question that is worded or expressed in a way that affects the respondent's opinion is considered biased. Such inquiries could offer details that influence a respondent's perspective on the topic.What are the types of bias?Bias in selection- When a sample is used in research that does not accurately reflect the larger population, selection bias arises. Aversion to Loss - People with loss aversion, which is a widespread human tendency, dislike losing more than they enjoy winning.Anchoring Bias. Framing Bias.Learn more about Bias brainly.com/question/3749477 here
#SPJ2
Write the standard form of the equation of the circle with center (−7,10) that passes through the point (−7,7)
Answer:
(x+7)^2+(y-10)^2=9
Step-by-step explanation:
The distance between the two points is sqrt((-7+7)^2+(10-7)^2)=3 which is in turn the radius of the circle
The administration conducted a survey to determine the proportion of students who ride a bike to campus. Of the 123 students surveyed 5 ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus? Check all that apply.
a. The sample needs to be random but we don’t know if it is.
b. The actual count of bike riders is too small.
c. The actual count of those who do not ride a bike to campus is too small.
d. n*^p is not greater than 10.
e. n*(1−^p)is not greater than 10.
Answer:
b. The actual count of bike riders is too small.
d. n*p is not greater than 10.
Step-by-step explanation:
Confidence interval for a proportion:
To be possible to build a confidence interval for a proportion, the sample needs to have at least 10 successes, that is, [tex]np \geq 10[/tex] and at least 10 failures, that is, [tex]n(1-p) \geq 10[/tex]
Of the 123 students surveyed 5 ride a bike to campus.
Less than 10 successes, that is:
The actual count of bike riders is too small, or [tex]np < 10[/tex], and thus, options b and d are correct.
2/3y = 1/4 what does y equal?
Answer:
Step-by-step explanation:
2/3y=1/4 this means 3y=8 then you divide both sides by 8 you will get the value of y =8/3
If two marbles are selected in succession with replacement, find the probability that both marble is blue.
Answer:
1 / 9
Step-by-step explanation:
Choosing with replacement means that the first draw from the lot is replaced before another is picked '.
Number of Blue marbles = 2
Number of red marbles = 4
Total number of marbles = (2 + 4) = 6
Probability = required outcome / Total possible outcomes
1st draw :
Probability of picking blue = 2 / 6 = 1 /3
2nd draw :
Probability of picking blue = 2 / 6 = 1/3
P(1st draw) * P(2nd draw)
1/3 * 1/3 = 1/9
Describe the transformation of f(x) to g(x). Pleaseee helllp thank youuuu!!!
The transformation set of [tex]y[/tex] values for function [tex]f[/tex] is [tex][-1,1][/tex] this is an interval to which sine function maps.
You can observe that the interval to which [tex]g[/tex] function maps equals to [tex][-2,0][/tex].
So let us take a look at the possible options.
Option A states that shifting [tex]f[/tex] up by [tex]\pi/2[/tex] would result in [tex]g[/tex] having an interval [tex][-1,1]+\frac{\pi}{2}\approx[0.57,2.57][/tex] which is clearly not true that means A is false.
Let's try option B. Shifting [tex]f[/tex] down by [tex]1[/tex] to get [tex]g[/tex] would mean that has a transformation interval of [tex][-1,1]-1=[-2,0][/tex]. This seems to fit our observation and it is correct.
So the answer would be B. If we shift [tex]f[/tex] down by one we get [tex]g[/tex], which means that [tex]f(x)=\sin(x)[/tex] and [tex]g(x)=f(x)-1=\sin(x)-1[/tex].
Hope this helps :)
Help please, I attached the question. Is it a!?

Answer:
A
Step-by-step explanation:
Recall that for a quadratic equation of the form:
[tex]0=ax^2+bx+c[/tex]
The number of solutions it has can be determined using its discriminant:
[tex]\Delta = b^2-4ac[/tex]
Where:
If the discriminant is positive, we have two real solutions. If the discriminant is negative, we have no real solutions. And if the discriminant is zero, we have exactly one solution.We have the equation:
[tex]2x^2+5x-k=0[/tex]
Thus, a = 2, b = 5, and c = -k.
In order for the equation to have exactly one distinct solution, the discriminant must equal zero. Hence:
[tex]b^2-4ac=0[/tex]
Substitute:
[tex](5)^2-4(2)(-k)=0[/tex]
Solve for k. Simplify:
[tex]25+8k=0[/tex]
Solve:
[tex]\displaystyle k = -\frac{25}{8}[/tex]
Thus, our answer is indeed A.
What is the value of x?
Enter your answer in the box.
units
Answer:
25
Step-by-step explanation:
40/24 = x/15
x = 15•40/24
x = 25
Answer:
25
Step-by-step explanation:
just use the facts that both triangles are similar
