Answer:
a) 3 standard deviations above 16
b) More than 2 standard deviations of the mean, so yes, 22 inches is faw away from the mean of 16 inches.
c) Less than 2 standard deviations, so not far away.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
If Z < -2 or Z > 2, X is considered to be far away from the mean.
In this question, we have that:
[tex]\mu = 16[/tex]
(a) Suppose the data come from a sample whose standard deviation is 2 inches. How many standard deviations is 22 inches from 16 inches?
This is Z when [tex]X = 22, \sigma = 2[/tex].
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{22 - 16}{2}[/tex]
[tex]Z = 3[/tex]
So 22 inches is 3 standard deviations fro 16 inches.
(b) Is 22 inches far away from a mean of 16 inches?
3 standard deviations, more than two, so yes, 22 inches is far away from a mean of 16 inches.
(c) Suppose the standard deviation of the underlying data is 4 inches. Is 22 inches far away from a mean of 16 inches?
Now [tex]\sigma = 4[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{22 - 16}{4}[/tex]
[tex]Z = 1.5[/tex]
1.5 standard deviations from the mean, so 22 inches is not far away from the mean.
Find the area of a triangle bounded by the y-axis, the line f(x)=9−2/3x, and the line perpendicular to f(x) that passes through the origin. Area =
Answer:
The area of the triangle is 18.70 sq.units.
Step-by-step explanation:
It is provided that a triangle is bounded by the y-axis, the line [tex]f(x)=y=9-\frac{2}{3}x[/tex].
The slope of the line is: [tex]m_{1}=-\frac{2}{3}[/tex]
A perpendicular line passes through the origin to the line f (x).
The slope of this perpendicular line is:[tex]m_{2}=-\frac{1}{m_{1}}=\frac{3}{2}[/tex]
The equation of perpendicular line passing through origin is:
[tex]y=\frac{3}{2}x[/tex]
Compute the intersecting point between the lines as follows:
[tex]y=9-\frac{2}{3}x\\\\\frac{3}{2}x=9-\frac{2}{3}x\\\\\frac{3}{2}x+\frac{2}{3}x=9\\\\\frac{13}{6}x=9\\\\x=\frac{54}{13}[/tex]
The value of y is:
[tex]y=\frac{3}{2}x=\frac{3}{2}\times\frac{54}{13}=\frac{81}{13}[/tex]
The intersecting point is [tex](\frac{54}{13},\ \frac{81}{13})[/tex].
The y-intercept of the line f (x) is, 9, i.e. the point is (0, 9).
So, the triangle is bounded by the points:
(0, 0), (0, 9) and [tex](\frac{54}{13},\ \frac{81}{13})[/tex]
Consider the diagram attached.
Compute the area of the triangle as follows:
[tex]\text{Area}=\frac{1}{2}\times 9\times \frac{54}{13}=18.69231\approx 18.70[/tex]
Thus, the area of the triangle is 18.70 sq.units.
Which of the following is an arithmetic sequence?
2.4.8. 16.
2.4.-6.8.
-8, -6,-4,-2
Answer:
-8,-6,-4,-2 is an Arithmetic sequence, because there common difference is 2.
someone answer this
Answer:
16
Step-by-step explanation:
The right triangle shown is a 30:60:90 triangle.
30:60:90 right triangles have a 1:sqrt(3):2 ratio between their sides.
Since the side opposite from the 30 degree is 8, and x is opposite from the 90 degree angle, 8 and x have a 1:2 ratio, or 8:16.
Solve the equation. 3= x/3.3 what is x=
Answer:
9.9
Step-by-step explanation:
remember your distribution rules.
x/3.3=3 make sure x is by itself. so take 3*3.3
When you have x divided by a number equaling a number take the number it equals to and multiply by the number that x is being divided by.
3=x/3.3
move 3.3 by multiplying it by 3 which gives you 9.9.
The solution of x in equation 3 = x / 3.3 is,
⇒ x = 9.9
We have to given that;
Expression is,
⇒3 = x / 3.3
Now, We can simplify the equation for x as;
⇒ 3 = x / 3.3
Multiply by 3.3 both side,
⇒ 3 × 3.3 = x
⇒ 9.9 = x
⇒ x = 9.9
Thus, Solution is,
⇒ x = 9.9
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Seventy million pounds of trout are grown in the U.S. every year. Farm-raised trout contain an average of grams of fat per pound, with a standard deviation of grams of fat per pound. A random sample of farm-raised trout is selected. The mean fat content for the sample is grams per pound. Find the probability of observing a sample mean of grams of fat per pound or less in a random sample of farm-raised trout.
Complete question is:
Seventy million pounds of trout are grown in the U.S. every year. Farm-raised trout contain an average of 32 grams of fat per pound, with a standard deviation of 7 grams of fat per pound. A random sample of 34 farm-raised trout is selected. The mean fat content for the sample is 29.7 grams per pound. Find the probability of observing a sample mean of 29.7 grams of fat per pound or less in a random sample of 34 farm-raised trout. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
Answer:
Probability = 0.0277
Step-by-step explanation:
We are given;
Mean: μ = 32
Standard deviation;σ = 7
Random sample number; n = 34
To solve this question, we would use the equation z = (x - μ)/(σ/√n) to find the z value that corresponds to 29.7 grams of fat.
Thus;
z = (29.7 - 32)/(7/√34)
Thus, z = -2.3/1.200490096
z = -1.9159
From the standard z table and confirming with z-calculator, the probability is 0.0277
Thus, the probability to select 34 fish whose average grams of fat per pound is less than 29.7 = 0.0277
What’s the correct answer for this?
Answer:
D: 17 times
Step-by-step explanation:
Volume of tank = 36×13×24
= 11,232 cubic inches
Now
Bucket = 693 cubic inches
Number of time Valeria will use the bucket = 11232/693
= 16.2
≈ 17
an=(−3n+4)n(−4n−8)n In this problem you must attempt to use the Root Test to decide whether the series converges. Compute L=limn→[infinity]|an|−−−√n Enter the numerical value of the limit L if it converges, INF if it diverges to infinity, MINF if it diverges to negative infinity, or DIV if it diverges but not to infinity or negative infinity. L= Which of the following statements is true? A. The Root Test says that the series converges absolutely. B. The Root Test says that the series diverges. C. The Root Test says that the series converges conditionally. D. The Root Test is inconclusive, but the series converges absolutely by another test or tests. E. The Root Test is inconclusive, but the series diverges by another test or tests. F. The Root Test is inconclusive, but the series converges conditionally by another test or tests. Enter the letter for your choice here:
Answer:
L = 3/4
Option A. The Root Test says that the series converges absolutely.
Step-by-step explanation:
By using the root test equation given in the question. L = 3/4
Since L < 1, the series converges absolutely.
For clarity of expression, the detailed calculation is contained in the attached file. Check the file attached for the complete calculation to this question.
Please help. I’ll mark you as brainliest if correct!!!!
Answer:
a= 0
b= [tex]-\frac{\sqrt{42} }{12}[/tex]
Step-by-step explanation:
We can rewrite the expression to be:
[tex]\frac{i\sqrt{7} }{i^{2}\sqrt{24} }[/tex]
We then can cancel out the i and we get
[tex]\frac{\sqrt{7} }{\sqrt{24} i}[/tex]
Can be rewritten as
[tex]\frac{\sqrt{7} }{2\sqrt{6} i}[/tex]
We then rationalize and get
[tex]-\frac{\sqrt{42} }{12} i[/tex]
An individual who has automobile insurance from acertain company is randomly selected. Let Y be thenumber of moving violations for which the individualwas cited during the last 3 years. The pmf of Y is y p(y) 0 0.6 1 0.25 2 0.10 3 0.05 Suppose an individual with Y violations incurs a surcharge of $ 100 Y squared. Calculate the expected amount of the surcharge.
Answer:
[tex] E(100 Y^2) =100 E(Y^2)[/tex]
And we have that :
[tex] E(Y^2) =\sum_{i=1}^n X^2_i P(X_i)[/tex]
And replacing we got:
[tex] E(Y^2) =0^2 *0.6 + 1^2 *0.25 +2^2*0.10 +3^2 *0.05 = 1.1[/tex]
And finally we have:
[tex] E(100 Y^2) =100 *1.1 = 110[/tex]
Step-by-step explanation:
For this case we have the following probability masss function given:
Y 0 1 2 3
p(Y) 0.6 0.25 0.10 0.05
And we can define the surcharge with this expression [tex] 100Y^2[/tex]
We want to find the expected value for the last expression and we can do it on this way:
[tex] E(100 Y^2) =100 E(Y^2)[/tex]
And we have that :
[tex] E(Y^2) =\sum_{i=1}^n X^2_i P(X_i)[/tex]
And replacing we got:
[tex] E(Y^2) =0^2 *0.6 + 1^2 *0.25 +2^2*0.10 +3^2 *0.05 = 1.1[/tex]
And finally we have:
[tex] E(100 Y^2) =100 *1.1 = 110[/tex]
What is StartFraction 7 Over 9 EndFraction divided by one-third
Answer:
7/3
Step-by-step explanation:
Write this symbolically as:
7/9
-------
1/3
Invert the denominator fraction and then multiply:
(7/9)(3/1)
Reducing this, we get 7/3
Answer:
the answer as a mixed number is 2 and 1/3 (2 1/3)
and as a normal fraction its 7/3
Suppose that the operations manager of a nose mask packaging delivery service is
contemplating the purchase of a new fleet of trucks. When
packages are efficiently stored in the trucks in preparation for delivery, two major constraints
have to be considered. The weight in pounds and volume in cubic feet for each item. Now
suppose that in a sample of 200 packages the average weight is 26.0 pounds with a standard
deviation of 3.9 pounds. In addition suppose that the average volume for each of these
packages is 8.8 cubic feet with standard deviation of 2.2 cubic feet. How can we compare the
variation of the weight and volume?
Answer:
Coefficient of variation (weight) = 15%
Coefficient of variation (volume) = 25%
Step-by-step explanation:
Let's begin by listing out the given information:
Population = 200, Average weight = 26 lb,
standard deviation (weight) = 3.9 lb,
Average volume = 8.8 ft³,
standard deviation (volume) = 2.2 ft³
Based on the data given, the manager will have to make a deduction by comparing the relative scatter of both variables due to the different units of measuring weight (pounds) and volume (cubic feet).
To compare the variation of the weight and volume, we use the coefficient of variation given by the formula:
Coefficient of Variation = (Standard deviation ÷ Mean) * 100%
⇒ [tex]C_{v}[/tex] = (σ ÷ μ) * 100%
For weight
σ = 3.9 lb, μ = 26 lb
[tex]C_{v}[/tex] (weight) = (3.9 ÷ 26.0) * 100% = 15%
[tex]C_{v}[/tex] (weight) = 15%
For volume
σ = 2.2 ft³, μ = 8.8 ft³
[tex]C_{v}[/tex] (volume) = (2.2 ÷ 8.8) * 100% = 25%
[tex]C_{v}[/tex] (volume) = 25%
∴ the relative variation of the volume of the package is greater than that of the weight of the package
help ,, I need help with this one ,, i’m soo confused
As the x values go up, the y values go down which means the line is higher on the left side than it is on the right side.
The 4th graph would be the correct one
The model represents x? - 9x + 14
Which is a factor of x2 - 9x + 14?
OX-9
OX-2
O x + 5
+
+
+
+
+
+
O x +7
+
+
+
+
+
+
+
Answer:
work is shown and pictured
The factor of the equation x² - 9x + 14 is,
⇒ (x - 2)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ x² - 9x + 14
Now, We can find the factor of the expression as;
⇒ x² - 9x + 14
⇒ x² - 7x - 2x + 14
⇒ x (x - 7) - 2 (x - 7)
⇒ (x - 7) (x - 2)
Thus, The factor of the equation x² - 9x + 14 is,
⇒ (x - 2)
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A car dealership decreased the price of a certain car by 4% . The original price was $43,600 . write the new price in terms of the original price.
Answer: The new price of the car is $41856
Step-by-step explanation:
So we know the the original price as 43,600 which is 100% and is being dropped by 4% so you would have to subtract 4% from a 100% and multiply it by the original price.
100% - 4% = 96%
Now 96% of the original price is the new price.
96% * 43,600= ?
0.96 * 43,600 = 41856
Analyze the diagram below and answer the question that follows.
Answer:
B. Complements of congruent angles are congruent.
Step-by-step explanation:
Angles <DCF and <FEG have angles measures that are complementary to to angles E and C.
What postulate would justify the following statement?
If D is between A and B, than AD+DB=AB
Answer:
A, D and B must be in a straight line.
Step-by-step explanation:
If D is between A and B, than AD+DB=AB
This would mean A, D and B would be in a straight line.
What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
Diameter = 11 inches.
Radius = D/2 = 5.5 inches
Volume = 4/3πr³
= 4/3(3.14)(5.5)³
= 696.6 in.³
How do I solve part b and c
Answer:
part a: 52%
part b: 0.4
part c: 0.24
Step-by-step explanation:
For part one, you find the frequency of the number of people that are less that 20. You add the number of tics in each bar and you divide by the total.
so for part a it is (7+6+9+4)/ (7+6+9+4+4+12+8)
for part b you add up the values that are greater than 25(less than 35)
(12+8)/total
part c you find the number of people between 25 and 30
that's 12
over total
12/total
Please help. I’ll mark you as brainliest if correct!
Answer:
product = 40
Step-by-step explanation:
The conjugate of (-2 + 6i) is (-2 - 6i)
You just need to change the sign
(-2 + 6i) (-2 - 6i)
Expand:
4 + 12i + -12i - [tex]36i^{2}[/tex]
4 + 12i + -12i + 36
product = 40
What is the value of x?
Answer:
x = 22
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the interior angles
6x+1 = 79+ 2x+10
Combine like terms
6x+1 = 2x+89
Subtract 2x from each side
4x+1 = 89
Subtract 1 from each side
4x = 88
Divide by 4
4x/4 = 88/4
x = 22
Answer:
The answer is
Step-by-step explanation:
We can cross out A. So it has to be either B, C, or D.
Two surveys are conducted to measure the effect of an advertising campaign for a certain brand of detergent.27 In the first survey, interviewers ask house- wives whether they use that brand of detergent. In the second, the interviewers ask to see what detergent is being used. Would you expect the two surveys to reach similar conclusions? Give your reasons.
Answer:
NO
Step-by-step explanation:
The objective of this surveys is to determine if the two surveys will reach a similar conclusion.
From the data given, we have two test surveys here:
The survey is to measure the effect of an advertising campaign for a certain brand of detergent.
Now in the first survey; interviewers ask house- wives whether they use that brand of detergent and in the second survey the interviewers ask to see what detergent is being used.
Let assume that the brand name of the detergent is KLIN ;
From this disparities of statement ; we anticipate that they will reach different conclusion. This is because; from the first survey people will either respond to the fact that they use the brand detergent (KLIN) or do not used the brand detergent. But in the second survey; when being asked to see what detergent that is being used. There are greater chance that they will bring out the detergent that is commonly used which will eventually result to the same detergent .
A 15-inch candle is lit and steadily burns until it is burned out. Let b represent the burned length of the candle (in inches) and let r represent the remaining length of the candle (in inches).
a. Write a formula that expresses r in terms of b.When 3.1 inches have burned from the candle, the remaining length of the candle is inches.
b. Graph the relationship between a and b
Answer:
(a)r=15-b
11.9 Inches
(b)See attached
Step-by-step explanation:
Length of the candle =15 inch
Let b represent the burned length of the candle (in inches)
Let r represent the remaining length of the candle (in inches).
Therefore:
(a) r+b=15
r=15-b
When b=3,1 Inches
Remaining Length, r=15-3.1=11.9 Inches
(b)The graph showing te relationship between r and b is shown below.
r is plotted on the y-axis while b is plotted on the x-axis as labelled.
Formula that express r in terms of b is
[tex]r=15-b[/tex]
Remaining length of candle is 11.9 inches
Given :
A 15-inch candle is lit and steadily burns until it is burned out
Let b represent the burned length and let r represent the remaining length
We need to write the formula
remaining length = initial length - burned length
[tex]r=15-b[/tex]
When 3.1 inches have burned from the candle, the remaining length of the candle is inches.
b is 3.1
remaining length [tex]r=15-3.1=11.9[/tex] inches
now we graph the relationship
Graph is attached below.
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You are a medical assistant in a pediatrician’s office and one of your responsibilities is evaluating the growth of newborns and infants. Your first patient, a baby girl named Ivy Smith, was 21.5 inches long at 3 months old. At 8 months, you measure her at 24 inches long. For your medical records, all measurements must be given both in inches and in centimeters: 1 inch = 2.54 cm
I need to come up with an equation for this.
Which ordered pair is the solution of the system of equations? 3x+2y=4, -2+2y=24, I need help Im very confused on how to solve this...
Answer:
x = -7.33 OR x = [tex]\frac{-22}{3}[/tex]
y = 13
Step-by-step explanation:
→You can use the substitution method. First, make y by itself in (-2 + 2y = 24):
-2 + 2y = 24
2y = 26
y = 13
→Then, plug in 13 for y into the other equation:
3x + 2y = 4
3x + 2(13) = 4
3x + 26 = 4
3x = -22
x = -7.33 OR x = [tex]\frac{-22}{3}[/tex]
Which of the following points is in the solution set of y
What is 1.036 that add up to 4
Answer:
2.964
Step-by-step explanation:
URGENT!! EASY IM DUMB MY LAST QUESTION WILL FOREVER BE GRATEFUL PLS HELP WILL GIVE BRANLIEST!! AT LEAST TAKE A LOOK!!!! PLS I AM BEGGING!!!
YOU HAVE TO LOOK CLOSLY TO SEE THE NUMBERS ON THE TRIANGLE
IN CASE YOU CANNOT ON THE LEFT IT IS 15CM AND ON THE BOTTOM IT IS 14 CM
Find the unknown side of the triangle below (round to the nearest tenth).
A) 20.5 cm
B) 210.5 cm
C) 5.4 cm
D) 16 cm
Answer:
A. 20.5
Step-by-step explanation:
We can use the Pythagorean theorem to solve this equation for the missing side length, X.
a^2 + b^2 = c^2
We have a and b, we just need c, the hypotenuse.
14^2 + 15^2 = c^2
196 + 225 = c^2
421 = c^2
Now, we will square both sides:
The answer is about 20.5
Suppose a county’s population can be approximated with the function () = 34(1.00804) where is the number of years since 2000, and is measured in millions of citizens.
Answer:
Population = 34.27336
Step-by-step explanation:
Given:
Population function (t) = 34(1.00804)^t
Number of year = 2000
Find:
Number of citizen in year 2000
Computation:
We know that, base year is 2000
So, t = 1
Population function (t) = 34(1.00804)^t
Population function (1) = 34(1.00804)^1
Population = 34(1.00804)
Population = 34.27336
Therefore, Population is 34.273636 million
Lines DE and AB intersect at point C.
What is the value of x?
SER
12
A.
(2x + 2) E
25
0 0 0 0
38
C
(5x + 3)
52
D
31
Answer:
B=25
Step-by-step explanation:
A powerful computer is purchased for $2000, but loses 20% of its value each year. How much will it be worth 4 years from now?
a. Growth or Decay?
b. What is your multiplier?
c. Is $2000 your zero term or first term? term
d. Write the equation. (do not use spaces in your response; example: f(x)=10.2(1.22)^x )
e. Solve
Answer:
(A)Decay
(b)0.8
(c)First Term
(d)[tex]f(t)=2000(0.8)^t[/tex]
(e)$819.20
Step-by-step explanation:
The exponential function for modelling growth or decay is given as:
[tex]A(t)=A_o(1\pm r)^t[/tex],
Where:
Plus indicates growth and minus indicates decay.
[tex]A_o$ is the Initial Value\\r is the growth/decay rate\\t is the time period[/tex]
For a powerful computer that was purchased for $2000, but loses 20% of its value each year.
(a)Since it loses value, it is a decay.
(b)Multiplier
Its value decays by 20%.
Therefore, our multiplier(1-r) =(1-20&)=1-0.2
Multiplier =0.8
(c)$2000 is our First term (or Initial Value [tex]A_o[/tex])
(d)The function for this problem is therefore:
[tex]f(t)=f_o(1- r)^t\\f(t)=2000(1- 0.2)^t\\\\f(t)=2000(0.8)^t[/tex]
(e)Since we require the worth of the computer after 4 years,
t=4 years
[tex]f(4)=2000(0.8)^4\\f(4)=\$819.20[/tex]
