A private shipping company will accept a box for domestic shipment only if the sum of its length and girth (distance around) does not exceed 108 inches. Suppose you want to mail a box with square sides so that its dimensions are h by h by w and its girth is 2 h plus 2 w. What dimensions will give the box its largest volume?
Answers
Answer:
18×18×36
Step-by-step explanation:
According to the Question
108≥ 4h + w
Volume V is given by
V = wh^2
⇒V= (108-4h)h^2
⇒V= 108h^2 - 4h^3
Now differentiating and keeping = 0 we get
V' = 216h - 12h^2 = 0
h = 216/12 = 18
w = 108 - 4×18 = 36
V = 36×18^2 = 11664 from a box of 18×18×36.
Related Questions
What preserves a shapes orientation?
a. Vertical translation
b. Reflection across the shapes base
c. Rotation about its center
Answers
Answer:
a.vertical translation
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are Normally distributed with a mean of 6.5 inches and a standard deviation of 1.2 inches. According to the 68-95-99.7 rule, we expect 95% of head breadths to be:___________.
Answers
Answer:
"According to the 68-95-99.7 rule, we expect 95% [95.45%] of head breadths to be" between 4.1 inches and 8.9 inches.
Step-by-step explanation:
According to the 68-95-99.7 rule, approximately:
68% (more precisely, 68.27%) of the data from the normal distribution lie one standard deviation, [tex] \\ \sigma[/tex], above and below the population mean, [tex] \\ \mu[/tex].95% (more precisely, 95.45%) of the data lie two standard deviations, [tex] \\ 2\sigma[/tex], above and below the population mean, [tex] \\ \mu[/tex], and finally,99.7 (or more precisely, 99.73%) of the data lie three standard deviations, [tex] \\ 3\sigma[/tex], above and below the population mean, [tex] \\ \mu[/tex].Then, if we have--from the question--that:
The random variable is head breadths.This variable follows a normal distribution.The population's mean for this distribution is [tex] \\ \mu = 6.5[/tex] inches.The population's standard deviation is [tex] \\ \sigma =1.2[/tex] inches.We have to remember that two parameters characterize a normal distribution: the population's mean and the population's standard deviation. So, mathematically, the distribution we have from question is [tex] \\ N(6.5, 1.2)[/tex].
For 95% (95.45%) of the head breadths, we expect that they are two standard deviations below and above the population's mean.
For solving this, we need to use the cumulative standard normal distribution (in case we need to find probabilities) and also use standardized values or z-scores:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
A z-score "tells us" the distance from the mean in standard deviations units. If the z-score is positive, it is above the mean. If it is negative, it is below the mean.
Since 95% (95.45%) of the head breadths are two standard deviations (above and below the mean), we have (using [1]):
[tex] \\ \pm2 = \frac{x - \mu}{\sigma}[/tex]
But we already know that [tex] \\ \mu=6.5[/tex] inches and [tex] \\ \sigma=1.2[/tex] inches.
Thus (without using units) for values above the population's mean:
[tex] \\ 2 = \frac{x - 6.5}{1.2}[/tex]
Solving the equation for x, we multiply by 1.2 at each side of [1] :
[tex] \\ 2 * 1.2 = \frac{x - 6.5}{1.2} * 1.2[/tex]
[tex] \\ 2 * 1.2 = (x - 6.5)\frac{1.2}{1.2}[/tex]
[tex] \\ 2 * 1.2 = (x - 6.5)\frac{1.2}{1.2}[/tex]
[tex] \\ 2 * 1.2 = (x - 6.5)*1[/tex]
[tex] \\ 2 * 1.2 = x - 6.5[/tex]
Adding 6.5 at each side of the previous equation:
[tex] \\ (2 * 1.2) + 6.5 = x - 6.5 + 6.5[/tex]
[tex] \\ (2 * 1.2) + 6.5 = x + 0[/tex]
[tex] \\ (2 * 1.2) + 6.5 = x[/tex]
Therefore, the raw value, x, in the distribution that is two standard deviations above the population's mean is:
[tex] \\ x = (2 * 1.2) + 6.5[/tex]
[tex] \\ x = 2.4 + 6.5[/tex]
[tex] \\ x = 8.9[/tex] inches.
For two standard deviations below the mean, we proceed in the same way:
[tex] \\ -2 = \frac{x - 6.5}{1.2}[/tex]
[tex] \\ -2*1.2 = x - 6.5[/tex]
[tex] \\ (-2*1.2) + 6.5 = x[/tex]
[tex] \\ x = (-2*1.2) + 6.5[/tex]
[tex] \\ x = -2.4 + 6.5[/tex]
[tex] \\ x = 4.1[/tex] inches
Therefore, "according to the 68-95-99.7 rule, we expect 95% [95.45%] of head breadths to be" between 4.1 inches and 8.9 inches.
The graph below shows these values, and the shaded area represents 95% of the data, or, to be more precise, 95.45% (0.954499).
Look at the work shown for the division problem shown on the right. The remainder is 8 . Now, evaluate f (x) = 2x4 – 4x3 – 11x2 + 3x – 6 for x = –2. f (–2) = 8 Compare the values you entered above. f (–2) is the remainder when dividing the polynomial by x + 2. Divide 2x4- 4x3 - 11x2 + 3x - 6 by x + 2.
Answers
Answer:
1st : 8
2nd: 8
3rd: equal to
Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
The remainder of the polynomial when divided by x + 2 is -60.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
2[tex]x^{4}[/tex] - 4x³ - 11x² + 3x - 6 divide by x + 2.
Now,
x + 3 ) 2[tex]x^{4}[/tex] - 4x³ - 11x² + 3x - 6 ( 2x³ - 2x² - 5x + 18
2[tex]x^{4}[/tex] + 6x³
(-) (-)
-2x³ - 11x² + 3x - 6
-2x³ - 6x²
(+) (+)
- 5x² + 3x - 6
-5x² - 15x
(+) (+)
18x - 6
18x + 54
(-) (-)
-60
We see that,
The remainder is -60.
f(-2) = 2[tex]x^{4}[/tex] - 4x³ - 11x² + 3x - 6
f(-2) = 2 x 16 + 32 - 44 - 6 - 6 = 32 + 32 - 44 - 12 = 64 - 56 = 8
Thus,
The remainder of the polynomial when divided by x + 2 is -60.
Learn more about polynomials here:
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Find the lengths of the 2 Missing sides of each triangle
Answers
Green
x=14.7
y=8.5
Red
x=3.5
y=6
Complete this expression using the distributive property
5(4 + 8) =
O (5 + 4)(5 + 8)
O 5(4) + 8
O 5(4) + 5(8)
O (5+4) + (5 + 8)
Answers
Answer:
5(4) + 5(8)
Step-by-step explanation:
Through destributive property, 5 is multiplied by both 4 and 8
Answer:
the person above is right thank and five star them
Step-by-step explanation:
What is the slope-intercept equation of the line below?
Answers
When x is 0 look at the y, the y is the blue dot which means it’s -2
For the slope you calculate rise over run basically count up then left and see how many would hit the line at an exact point
Your slope is y= 4/5x -2
Hope this helps!
Answer:D
Step-by-step explanation:
-2=4/5(0)-2
-2=0-2
-2=-2
-6/5=4/5(1)-2
-6/5=4/5-10/5
-6/5=4/5-10/5
-6/5=-6/5
A fair spinner has 11 equal sections: 3 red, 4 blue and 4 green. It is spun twice. What is the probability of getting the same colour twice?
Answers
Answer:
The probability of getting the same colour twice is approximately 34%.
Step-by-step explanation:
The probability of getting each color is:
P(x=red) = 3/11 P(x=blue) = 4/11P(x=green) = 4/11Then, we can calculate the probability of getting the color red twice as:
[tex]P(x_1=R;x_2=R)=P(x=R)^2=(3/11)^2=9/121[/tex]
We have to repeat this for the color blue and green:
[tex]P(x_1=B;x_2=B)=P(x=B)^2=(4/11)^2=16/121\\\\P(x_1=G;x_2=G)=P(x=G)^2=(4/11)^2=16/121[/tex]
Then, the probability of getting the same color twice in two spins can be calculated as:
[tex]P=P(x_1=R;x_2=R)+P(x_1=B;x_2=B)+P(x_1=G;x_2=G)=\\\\P=9/121+16/121+16/121\\\\P=41/121\approx0.34[/tex]
Can anybody help me with this one?
Answers
Answer:
12 cm
Step-by-step explanation:
The rule regarding secants and/or tangents is that the product of distances from their common point to the two intersection points with the circle is the same.
For the tangent the "two" intersection points with the circle are the same point, so ...
product of tangent lengths = product of secant lengths
(8 cm)(8 cm) = (4 cm)(4 cm +x)
Dividing by 4 cm gives ...
16 cm = 4 cm + x
12 cm = x
A rocket moves through outer space at 10,500 m/s. At this rate how much time would be required to travel the distance from Earth to the moon, which is 380,000 km?
Answers
Answer:
The answer is around 27.63 seconds.
Step-by-step explanation:
1 km equals 1000 meters so we have to multiply 10,500 and 1,000 which would equal 10,500,000 km. 10,500,000 divided by 380,000 which is around 27.63 seconds.
Section Exercise 11-8 Sales of People magazine are compared over a 5-week period at four Borders outlets in Chicago. Weekly Sales Store 1 Store 2 Store 3 Store 4 102 97 89 100 106 77 91 116 105 82 75 87 115 80 106 102 112 101 94 100 Click here for the Excel Data File Fill in the missing data. (Round your p-value to 4 decimal places, mean values to 1 decimal place, and other answers to 2 decimal places.) Treatment Mean n Std. Dev Store 1 Store 2 Store 3 Store 4 Total One-Factor ANOVA Source SS df MS F p-value Treatment Error Total (a) Based on the given hypotheses choose the correct option. H0: μ1 = μ2 = μ3 = μ4 H1: Not all the means are equal α = 0.05 Reject the null hypothesis if F > 3.24 Reject the null hypothesis if F < 3.24 (b) Determine the value of F. (Round your answer to 2 decimal places.) F-value (c) On the basis of the above-determined values, choose the correct decision from below. Fail to reject the null hypothesis. Reject the null hypothesis. (d) Determine the p-value. (Round your answer to 4 decimal places.) p-value Next Visit question mapQuestion 1 of 2 Total1 of 2 Prev
Answers
Answer:
Step-by-step explanation:
Hello!
An ANOVA was conducted to analyze the variable
Y: sales of "People" magazine over a 5-week period
This was studied in 4 Borders outlets in Chicago.
So this test has one factor: "Borders outlets" and four treatments: "Store 1, store 2, store 3 and store 4"
For each store you have the data for the weekly sales over a 5-week period so the sample sizes are:
n₁=n₂=n₃=n₄= 5 weeks
Store 1
∑X₁= 540; ∑X₁²= 58434
X[bar]₁= 108
S₁²= 28.50
S₁= 5.34
Store 2
∑X₂= 437; ∑X₂²= 38663
X[bar]₂= 87.40
S₂²= 117.30
S₂= 10.83
Store 3
∑X₃= 455; ∑X₃²= 41899
X[bar]₃= 91
S₃²= 123.50
S₃= 11.11
Store 4
∑X₄=505; ∑X₄²= 51429
X[bar]₄= 101
S₄²= 106
S₄= 10.30
Totals
N= n₁ + n₂ + n₃ + n₄= 4*5= 20
∑Mean= 108+87.40+91+101= 387.4
∑Variance= 28.50+117.30+123.50+106= 375.30
∑Standard deviation= 5.34+10.83+11.11+10.30= 37.58
Hypothesis test:
H₀: μ₁= μ₂= μ₃= μ₄
H₁: At least one population mean is different.
α: 0.05
The statistic for this test is
[tex]F= \frac{MS_{Treatments}}{MS_{Error}} ~~F_{k-1;N-k}[/tex]
k-1= 3 Df of the treatments, k=4 number of treatments
N-k= 16 Df of errors, N=20 total number of observations in all treatments
[tex]F_{H_0}= \frac{441.78}{93.83}= 4.71[/tex]
The critical region and p-value for this test are one-tailed to the right.
Using the critical value approach:
[tex]F_{k-1;N-k;1-\alpha }= F_{3;16;0.95}= 3.25[/tex]
The decision rule is:
If [tex]F_{H_0}[/tex] ≥ 3.25, reject the null hypothesis.
If [tex]F_{H_0}[/tex] < 3.25, do not reject the null hypothesis.
Using the p-value approach:
Little reminder: The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).
So under the distribution F₃,₁₆ you have to calculate the probability of the calculated [tex]F_{H_0}[/tex]:
P(F₃,₁₆≥4.71)= 1 - P(F₃,₁₆<4.71)= 1 - 0.9847 = 0.0153
p-value= 0.0153
The decision rule for this approach is
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
The p-value is less than the level of significance, so the decision is to reject the null hypothesis.
I hope this helps!
Felicia walks 3 blocks west, 4 blocks south, 3 more blocks west, then
2 blocks south again. How far is Felicia from her starting point?
blocks
Answer:
Answers
The results of a linear regression are shown below.
y= ax + b
a = -1.15785
b= 139.3171772
r= -0.896557832
r2 = 0.8038159461
Which phrase best describes the relationship between x and y?
1)Strong Postive Correlation
2)Strong Negative Correlation
3)Weak Positive Correlation
4)Weak Negative Correlation
Answers
Answer:
2) Strong Negative Correlation
Step-by-step explanation:
With the value of r we have both the information about the sign of the relationship and the strength of this relationship.
As the value of r is negative, we can conclude that the correlation between x and y is negative.
Also, as the absolute value of r is close to 1, we can conclude that this relationship is strong.
The strength can also be seen in the value of r2, which is also close to 1, but this value does not give information about the sign.
The value of the slope a, being negative, can also tell us that the relation between x and y is a negative correlation.
42,000 as a multipul of a power of 10
Answers
Answer:
[tex] 4.2 \times {10}^{4} [/tex]
Step-by-step explanation:
[tex]42000 = 4.2000 \times \times {10}^{4} \\ = 4.2 \times {10}^{4} [/tex]
For which x is f(x)?=-3
-7
-4
4
5
Answers
Answer:
B.
✔ -4
Step-by-step explanation:
E 2021
Can someone plz help me solved this problem I need help ASAP plz help me! Will mark you as brainiest!
Answers
Answer:
2 & 8
-4 & -4
Step-by-step explanation:
x and y are the numbers, as per question:
x= 4+2y and xy= 16
y(4+2y)= 162y²+4y=16y²+2y - 8= 0y²+2y+1 =9(y+1)²=9y+1=3 ⇒ y= 2 ⇒ x= 4+2*2= 8y+1= -3 ⇒ y= -4 ⇒ x= 4+2*(-4)= -4The following data summarizes results from 1000 pre-employment drug screening tests. If one of the test subjects is randomly selected, find the probability that the subject had a positive test result or a negative test result.
Positive Test Result Negative Test Result
Subject Uses Drugs 76 6
Subject Is Not a Drug User 95 823
P (subject had a positive test result or a negative test result)= simplify your answer.
Answers
Answer:
P (subject had a positive test result or a negative test result) = 1
Step-by-step explanation:
Given
The table above
Required
P (subject had a positive test result or a negative test result)
This is calculated as follows;
P (subject had a positive test result or a negative test result) =
P (subject had a positive test result) + P (subject had a negative test result)
Calculating P (subject had a positive test result)
This can be calculated by number of subjects with positive results divided by 1000
Only data from the column of subjects with positive results will be considered.
Number of Subjects = Subjects that uses drugs + Subjects that do not use drugs
Number of subjects = 76 + 95
Number of Subjects = 171
P (Subject had a positive test Result) = 171/1000
Calculating P (subject had a negative test result)
This can be calculated by number of subjects with negative results divided by 1000
Only data from the column of subjects with negative results will be considered.
Number of Subjects = Subjects that uses drugs + Subjects that do not use drugs
Number of subjects = 6 + 823
Number of Subjects = 829
P (Subject had a negative test Result) = 829/1000
Hence, P (subject had a positive test result or a negative test result) =
P (subject had a positive test result) + P (subject had a negative test result) = 171/1000 + 829/1000
P (subject had a positive test result or a negative test result) = (171 + 829)/1000
P (subject had a positive test result or a negative test result) = 1000/1000
P (subject had a positive test result or a negative test result) = 1
Given ∠E≅∠P, K is the midpoint of EP Prove EG≅MP
Answers
Answer:
∠E≅∠P || Given
∠EKG≅∠PKM || Vertical angles
EK≅KP || Midpoint Theorem
EKG≅PKM || AAS(Angle Angle Side)
EG≅MP || CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
Step-by-step explanation:
help solve the above equation
Answers
Answer:
[tex]\dfrac{1}{27}[/tex]
Step-by-step explanation:
[tex]n^{-\frac{2}{3}}=9[/tex]
Rewrite:
[tex]\dfrac{1}{\sqrt[3]{n^2}}=9\\\\9\sqrt[3]{n^2}=1[/tex]
Cube both sides:
[tex]729n^2=1[/tex]
Divide both sides by 729:
[tex]n^2=\dfrac{1}{729}[/tex]
Take the square root of both sides:
[tex]n=\sqrt{\dfrac{1}{729}}=\dfrac{1}{27}[/tex]
Hope this helps!
What’s the correct answer for this question?
Answers
Answer:
C:
Step-by-step explanation:
In a circle, the measure of an inscribed angle is half the measure of the central angle with the same intercepted arc
So
AQD = ARC AD/2
<AQD = 78/2
<AQD = 39°
Please answer this correctly
Answers
Answer: 3 people, 2 people, 4 people, 6 people, 2 people, 3 people, 3 people
Step-by-step explanation:
3 given numbers within 30-39
32, 35, 38
2 given numbers within 40-49
45, 48
4 given numbers within 50-59
51, 52, 54, 59
6 given numbers within 60-69
60, 61, 65, 65, 66, 69
2 given numbers within 70-79
77, 78
3 given numbers within 80-89
83, 83, 84
3 given numbers within 90-99
95, 96, 98
Answer: see Frequency below
Step-by-step explanation:
This is a frequency table. How many times does a number appear in the data set that falls within the given interval?
Interval Data Frequency
30-39: 35, 38, 32 3
40-49: 48, 45 2
50-59: 59, 51, 52, 54 4
60-69: 61, 60, 66, 65, 65, 69 6
70-79: 77, 78 2
80-89: 83, 84, 83 3
90-99: 98, 96, 95 3
Check the total to make sure you included each number from the data set.
Total numbers in the data set = 23, Total Frequency = 23 [tex]\checkmark[/tex]
Find the number of possible outcomes if the numbers 1 through 7 are written on different pieces of paper and placed in a hat. Two of these numbered pieces of paper are selected without replacement, and a 2-digit number is formed using the first number drawn in the tens place and the second number drawn used in the ones place.
Answers
Answer:
The number of the possible outcomes are:
12,13,14,15,16,17
21,23,24,25,26,27
31,32,34,35,36,37
41,42,43,45,46,47
51,52,53,54,56,57
61,62,63,64,65,67
71,72,73,74,75,76
The total number of possible outcomes = 42
Step-by-step explanation:
Given that :
the numbers 1 through 7 are written on different pieces of paper; &
Two of these numbered pieces of paper are selected without replacement;
Also,
a 2-digit number is formed using the first number drawn in the tens place and the second number drawn used in the ones place.
Then:
if the first number drawn is 1 , then the possible outcomes will be :
12,13,14,15,16,17
If the first number drawn is 2; then the possible outcomes will be:
21,23,24,25,26,27
If the first number drawn is 3; then the possible outcomes will be:
31,32,34,35,36,37
If the first number drawn is 4; then the possible outcomes will be:
41,42,43,45,46,47
If the first number drawn is 5; then the possible outcomes will be:
51,52,53,54,56,57
If the first number drawn is 6; then the possible outcomes will be:
61,62,63,64,65,67
If the first number drawn is 7; then the possible outcomes will be:
71,72,73,74,75,76
The number of the possible outcomes are:
12,13,14,15,16,17
21,23,24,25,26,27
31,32,34,35,36,37
41,42,43,45,46,47
51,52,53,54,56,57
61,62,63,64,65,67
71,72,73,74,75,76
The total number of possible outcomes = 7 × 6 = 42
How far from zero would you move on the x-axis to reach the point (10, 8)?
Answers
Answer:
You would move 10 units to the right from zero on the x-axis.
The given point is 10 units from zero, when you move on the x-axis to reach the point (10, 8).
What is coordinate plane?A coordinate plane is a two-dimensional surface formed by two number lines. It is formed when a horizontal line (the X-axis) and a vertical line (the Y-axis) intersect at a point called the origin. The numbers on a coordinate grid are used to locate points.
The given coordinate point (10, 8).
The distance of any point from the x-axis is called the x-coordinate.
In the point (10, 8), 10 units from the x-axis
Therefore, the given point is 10 units from zero, when you move on the x-axis to reach the point (10, 8).
Learn more about the coordinate plane here:
https://brainly.com/question/24134413.
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A fair 6-sided die is colored in the following way: The faces of 1 - 3 are colored red. The faces of 4 and 5 are colored blue. The face of 6 is colored green. What is the probability that the face comes up red OR a prime number
Answers
Answer:
There are 6 total possibilities, 3 red faces and 3 prime numbers however, 2 and 3 are prime numbers and they are red as well so total successful outcomes = 3 + 3 - 2 = 4. This means that the answer is 4 / 6 or 2 / 3.
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]1 \: 2\:3[/tex] are red
[tex]5[/tex] is prime.
Total of [tex]4[/tex] possibilities out of [tex]6[/tex]
[tex]\frac{4}{6}[/tex]
Hello! I'm stuck on this problem. Can someone help me? Thanks!
The model below represents an equation.
2 long x tiles and 3 square 1 tiles = 3 long x tiles
Which represent like terms in the model of the equation?
2 long x tiles and 3 square 1 tiles
2 long x tiles and 3 long x tiles
3 long x tiles and 3 square 1 tiles
1 long x tile and 1 square 1 tile
Answers
Answer:
Answer is B
Step-by-step explanation:
This is because you can combine both the green tiles. With the other options, you can't combine them.
(also I did the test )
Answer:
The answer is in ur head lololol
Step-by-step explanation:
Its b
Please answer this correctly
Answers
Answer:
10 people
Step-by-step explanation:
Count the x's for more than 1 scarf, which is 2 or 3 scarfs
2 = 9
3 =1
total = 10
Use the following information for questions 34-36: Deanna is the principal at a Midwestern middle school and wants to know the average IQ of all female, seventh grade students. She does not know anything about what the population distribution looks like. She took a simple random sample of 31 seventh-grade girls in her school and found the average IQ score in her sample was 105.8 and the standard deviation was 15. Based on the interval you calculated in question 34, does it seem plausible that the true average IQ score for all seventh-grade female students at this school is 113
Answers
Answer:
Since, 113 is on the confidence interval obtained (97.502, 114.098), so, we can suggest that is plausible that the true average IQ score for all seventh-grade female students at this school is 113.
Step-by-step explanation:
The question isn't complete, the missing part asked us to obtain a 99.5% confidence interval for the true average IQ score
Finding the confidence interval using the sample data provided, we can answer the question of plausibility.
Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Sample Mean = 105.8
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.
To find the critical value from the t-tables, we first find the degree of freedom and the significance level.
Degree of freedom = df = n - 1 = 31 - 1 = 30
Significance level for 99.5% confidence interval
(100% - 99.5%)/2 = 0.25% = 0.0025
t (0.0025, 30) = 3.03 (from the t-tables)
Standard error of the mean = σₓ = (σ/√n)
σ = standard deviation of the sample = 15
n = sample size = 30
σₓ = (15/√30) = 2.739
99.5% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 105.8 ± (3.03 × 2.739)
CI = 105.8 ± 8.298
99.5% CI = (97.502, 111.387)
99.5% Confidence interval = (97.502, 114.098)
Since, 113 is on the confidence interval obtained, so, we can suggest that is plausible that the true average IQ score for all seventh-grade female students at this school is 113.
Hope this Helps!!!
The following simple linear regression analyzes the relationship between the number of classes students are taking (the independent variable, labeled in the following output as X[,2]) and the number of books they have in their backpack (the response) at randomly chosen times. Assume all relevant assumptions are met. Which of the following are correct interpretations of the slope?
a. Each additional class a student takes is associated with about a 58.7% increase in the number of books in their backpack on average.
b. Each additional class a student takes is associated with about an additional 0.587 books in their backpack on average.
c. Taking an additional class causes students to carry 0.587 extra books with them on average.
d. The population average number of books in a studentâs backpack is 0.587.
Answers
Answer:
The answer is B.
Step-by-step explanation:
Why do we say that the answer is B?
For each additional class there is a significant increase that represents a minimum value over a total of books, that is, 100% that will always remain, therefore the increase will be an additional average over the other "books" that are already in backpack.
find the vector reciprocal to set. a= i+2j+2k, b= 2i+3j+k, c= i-j-2k
Answers
Answer:
I just do a' as a sample. You calculate b' and c'
Step-by-step explanation:
[tex]a'=\frac{b\times c}{a\bullet (b\times c)}, b' = \frac{c\times a}{a\bullet (b\times c)}, c' = \frac{a\times b}{a\bullet (b\times c)}[/tex]
Now, calculate b x c
[tex]\left[\begin{array}{ccc}i&j&k\\2&3&1\\1&-1&-2\end{array}\right] =<-5, 5,-5>[/tex]
[tex]a'=\frac{<-5,5,-5>}{<1, 2, 2>\bullet <-5, 5,-5>}=\frac{<-5, 5, -5>}{-5} =<1,-1,1>[/tex]
I run 200m in 32 seconds, how long will it take to run 5000m
Answers
Answer:
It will take 800seconds to you to run 5000m
Step-by-step explanation:
Let time taken to run 5000m is x
Using ratio and proportion
200:32=5000:x
200/32=5000/x
200*x=5000*32
200x=160000
x=800seconds
Mrs Van Roijen decides to abseil down the Shard in London. The journey down normally takes 33 minutes. However, on her way down, she stops for 18 minutes to take some photos. Eventually she arrives at the bottom of the Shard. Looking at her watch she sees that it is now 12:15. At what time did she set off? 11: 34
11: 24
11: 44
11: 54
Answers
Answer:
11.24
Step-by-step explanation:
If she arrived at 12.15, to find the time of departure we have to deduct 33 mins and the time she spent for photos,18 mins from this to get time of departure.
Total time spent for journey
33mins +18 mins = 51mins
time of departure = 12.15 - 51mins
so the time of departure is 11.24
