Answer:
(a) 2.3
(b) 0.5245
(c) 0.7242
(d) 0.5245
Step-by-step explanation:
The data provided is:
S = {180.5, 181.7, 180.9, 181.6, 182.6, 181.6, 181.3, 182.1, 182.1, 180.3, 181.7, 180.5}
(a)
The formula to compute the sample range is:
[tex]\text{Sample Range}=\text{max.}_{x}-\text{min.}_{x}[/tex]
The data set arranged in ascending order is:
S' = {180.3 , 180.5 , 180.5 , 180.9 , 181.3 , 181.6 , 181.6 , 181.7 , 181.7 ,, 182.1 , 182.1 , 182.6}
The minimum value is, 180.3 and the maximum value is, 182.6.
Compute the sample range as follows:
[tex]\text{Sample Range}=\text{max.}_{x}-\text{min.}_{x}[/tex]
[tex]=182.6-180.3\\=2.3[/tex]
Thus, the sample range is 2.3.
(b)
Compute the sample variance as follows:
[tex]S^{2}=\frac{1}{n-1}\sum(x_{i}-\bar x)^{2}[/tex]
[tex]=\frac{1}{12-1}\times [(180.5-181.41)^{2}+(181.7-181.41)^{2}+...+(180.5-181.41)^{2}]\\\\=\frac{1}{11}\times 5.7692\\\\=0.524473\\\\\approx 0.5245[/tex]
Thus, the sample variance is 0.5245.
(c)
Compute the sample standard deviation as follows:
[tex]s=\sqrt{S^{2}}[/tex]
[tex]=\sqrt{0.5245}\\\\=0.7242[/tex]
Thus, the sample standard deviation is 0.7242.
(d)
Compute the sample variance using the shortcut method as follows:
[tex]S^{2}=\frac{1}{n-1}\cdot [\sum x_{i}^{2}-n(\bar x)^{2}][/tex]
[tex]=\frac{1}{12-1}\cdot [394913.57-(12\times (181.41)^{2}]\\\\=\frac{1}{11}\times [394913.57-394907.80]\\\\=\frac{5.77}{11}\\\\=0.5245[/tex]
Thus, the sample variance is 0.5245.
We are standing on the top of a 320 foot tall building and launch a small object upward. The object's vertical altitude, measured in feet, after t seconds is h ( t ) = − 16 t 2 + 128 t + 320 . What is the highest altitude that the object reaches?
Answer:
The highest altitude that the object reaches is 576 feet.
Step-by-step explanation:
The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be [tex]h(t) = -16\cdot t^{2} + 128\cdot t + 320[/tex], the first and second derivatives are, respectively:
First Derivative
[tex]h'(t) = -32\cdot t +128[/tex]
Second Derivative
[tex]h''(t) = -32[/tex]
Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:
[tex]-32\cdot t +128 = 0[/tex]
[tex]t = \frac{128}{32}\,s[/tex]
[tex]t = 4\,s[/tex] (Critical value)
The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:
[tex]h(4\,s) = -16\cdot (4\,s)^{2}+128\cdot (4\,s) +320[/tex]
[tex]h(4\,s) = 576\,ft[/tex]
The highest altitude that the object reaches is 576 feet.
SNOG PLEASE HELP! (x-1)(y+8)
Answer:
xy + 8x - y - 8
Step-by-step explanation:
We can use the FOIL method to expand these two binomials. FOIL stands for First, Outer, Inner, Last.
F: The First means that we multiply the first terms of each binomial together. In this case, that would be x · y = xy.
O: The Outer means that we multiply the outer terms, or the first term of the first binomial and the second term of the last binomial, together. In this case, that would be x · 8 = 8x.
I: The Inner means that we multiply the inner terms, or the second term of the first binomial and the first term of the second binomial, together. In this case, that would be (-1) · y = -y.
L: The Last means that we multiply the last terms of each binomial together. In this case, that would be (-1) · 8 = -8.
Adding all of these together, we get xy + 8x - y - 8 as our final answer.
Hope this helps!
Answer:
[tex]xy+8x-y-8[/tex]
Step-by-step explanation:
=> (x-1)(y+8)
Using FOIL
=> [tex]xy+8x-y-8[/tex]
PLEASE ANSWER FAST, THANKS! :)
Answer:
Step-by-step explanation:
k = 3 ; 2k + 2 = 2*3 + 2 = 6 + 2 = 8
k = 4; 2k + 2 = 2*4 + 2 = 8 +2 = 10
k =5; 2k + 2 = 2*5 +2 = 10+2 = 12
k=6; 2k +2 = 2*6 + 2 = 12+2 = 14
k = 7 ; 2k + 2 = 2*7 +2 = 14 +2 = 16
k = 8 ; 2k + 2 = 2*8 + 2 = 16 +2 = 18
∑ (2k + 2) = 8 + 10 + 12 + 14 + 16 + 18 = 78
Which expression represents the phrase 4 times the sum of 9 and 6
A. 4x (9+6)
B.4x 9+6
C.9+ 6x4
D. 9+ (6x4)
Answer:
The answer is option A
4 x ( 9 + 6)
Hope this helps you
Basic factoring. Please help!
Answer:
-1(3 - y)
Step-by-step explanation:
If you factor out a negative 1, you will get the opposite signs you already have, so -1(3 - y). To check, we can simply distribute again:
-3 + y
So our answer is 2nd Choice.
What is the measure of
Answer:
C. 35
55 degrees + 35 degrees= 90 degrees
Translate the following statements into symbolic form using capital letters to representaffirmative English statement.
If Maria Cantwell promotes alternative energy,then if Patty Murray supports wilderness areas, then Dianne Feinstein's advocating gun control implies that Susan Collins does so,too.
Answer:
Step-by-step explanation:
There are two distinct statements but put together, it is:
- If Maria Cantwell (MC) promotes Alternative Energy (AE) and if Patty Murray (PM) supports Wilderness Areas (WA) then Dianne Feinstein (DF) advocating Gun Control (GC), implies that Susan Collins (SC) does so too.
For Susan Collins, she advocates gun control too.
So the symbolic or algebraic representation is:
(SC = DF): (MC ~ AE), (PM ~ WA)
OR
(GC = GC): (MC ~ AE), (PM ~ WA)
Where ":" represents "such that" or "given that"
" ~ " represents "support or promotion of"
It can now be read thus;
Susan Collins has same or equal interest as Dianne Feinstein, given that Maria Cantwell promotes alternative energy and Patty Murray supports Wilderness Areas.
NEED UGANT HELP pls help me
An event that is impossible has a probability of 0
An event that is certain to happen has a probability of 1
The probability scales from 0 to 1, referring from no chance to will happen.
If x is a binomial random variable with n trials and success probability p , then as n gets smaller, the distribution of x becomes
Answer:
If the value of n gests smaller then the distribution of X would be more skewed, that's a property of the binomial distribution
Step-by-step explanation:
For this problem we are assumeing that the random variable X is :
[tex] X \sim Bin(n,p)[/tex]
If the value of n gests smaller then the distribution of X would be more skewed, that's a property of the binomial distribution and if we don't satisfy this two conditions:
[tex] n p>10[/tex]
[tex]n(1-p) >10[/tex]
Then we can't use the normal approximation
The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation σ = .000586 mm. Assume a random sample of 59 sheets of metal resulted in an x¯ = .2905 mm. Calculate the 95 percent confidence interval for the true mean metal thickness.
Answer:
The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm
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 Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
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.
[tex]M = 1.96\frac{0.000586}{\sqrt{59}} = 0.0002[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.2905 - 0.0002 = 0.2903 mm
The upper end of the interval is the sample mean added to M. So it is 0.2905 + 0.0002 = 0.2907 mm
The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm
Consider the following sample information from Population A and Population B. Sample A Sample B n 24 16 s2 32 38 We want to test the hypothesis that the population variances are equal. The test statistic for this problem equals a. .84. b. .67. c. 1.50. d. 1.19.
Answer:
Always the numerator for the statistic needs to be higher than the denominator. And replacing we got:
[tex]F=\frac{s^2_2}{s^2_1}=\frac{38}{32}=1.19[/tex]
And the best option would be:
d. 1.19.
Step-by-step explanation:
Data given and notation
[tex]n_1 = 24 [/tex] represent the sampe size 1
[tex]n_2 =16[/tex] represent the sample size 2
[tex]s^2_1 = 32[/tex] represent the sample variance for 1
[tex]s^2_2 = 38[/tex] represent the sample variance for 2
The statistic for this case is given by:
[tex]F=\frac{s^2_1}{s^2_2}[/tex]
Hypothesis to verify
We want to test if the true deviations are equal, so the system of hypothesis are:
H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]
H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]
Always the numerator for the statistic needs to be higher than the denominator. And replacing we got:
[tex]F=\frac{s^2_2}{s^2_1}=\frac{38}{32}=1.19[/tex]
And the best option would be:
d. 1.19.
CAN SOMEONE HELP ME ASAP
A. 5
B. 53‾√53
C. 10
D. 103√3
Answer:
n = 5
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 30 = n/ 5 sqrt(3)
5 sqrt(3) tan 30 = n
5 sqrt(3) * 1/ sqrt(3) = n
5 = n
The diagram shows the first four patterns of a sequence. Find an expression for the numbers of squares in the nth pattern of the sequence.
Answer:
n^2+3
Step-by-step explanation:
As we can see in the diagram
1st pattern consists from 1 square 1x1 +3 squares 1x1 each
2nd pattern consists from 1 square 2x2 +3 squares 1x1 each
3-rd pattern consists from 1 square 3x3 +3 squares 1x1 each
4-th pattern consists from 1 square 4x4 + 3 squares 1x1 each
We can to continue :
5-th pattern consists from 1 square 5x5+3 squares 1x1 each
So the nth pattern consists from 1 square nxn+3 squares 1x1 each
Or total amount of 1x1 squares in nth pattern N= n^2+3
The expression for the numbers of squares in the nth pattern of the sequence is [tex]n^{2} +3[/tex].
What is nth term of a sequence?"The nth term of a sequence is a formula that enables us to find any term in the sequence. We can make a sequence using the nth term by substituting different values for the term number(n) into it."
From the given diagram
We can see that every term is made up with a square which side is n and three small square side is 1.
So,
1st term is 1 × 1 + 3 = 4
2nd term is 2 × 2 + 3 = 4
3rd term is 3 × 3 + 3 = 12
4th term is 4 × 4 + 3 = 19
So, nth term is [tex]n^{2} +3[/tex]
Hence, The expression for the numbers of squares in the nth pattern of the sequence is [tex]n^{2} +3[/tex].
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11. If 4 < x < 14, what is the range for -x - 4?
Answer:
-18 < -x-4 < -8
Step-by-step explanation:
We start with the initial range as:
4 < x < 14
we multiplicate the inequation by -1, as:
-4 > -x > -14
if we multiply by a negative number, we need to change the symbols < to >.
Then, we sum the number -4, as:
-4-4> -x-4 > -14-4
-8 > -x-4 > -18
Finally, the range for -x-4 is:
-18 < -x-4 < -8
i-Ready
Sofia
The area of a rectangle is 7/9 square feet. The width of the rectangle is 2 1/3 feet. What is the length of the rectangle?
Answer:
1/3 feet.
Step-by-step explanation:
The length = area / width
= 7/9 / 2 1/3
= 7/9 / 7/3
= 7/9 * 3/7
= 3/9
= 1/3 feet,
A normally distributed data set with a mean of 35 and a standard deviation of 5 is represented by the normal curve. What is the z–score corresponding to 45?
Answer:
The z–score corresponding to 45 is z=2.
Step-by-step explanation:
We have a random variable X represented by a normal distribution, with mean 35 and standard deviation 5.
The z-score represents the value X relative to the standard normal distribution. This allows us to calculate probabilities for any given normal distribution with the same table.
The z-score for X=45 can be calculated as:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{45-35}{5}=\dfrac{10}{5}=2[/tex]
The z–score corresponding to 45 is z=2.
If the statement shown is rewritten as a conditional statement in if-then form, which best describes the conclusion? When a number is divisible by 9, the number is divisible by 3.
Answer:
when a number is divisible by 9, then the number is divisible by 3.
Step-by-step explanation:
They tell us "When a number is divisible by 9, the number is divisible by 3" we could change it by:
when a number is divisible by 9, then the number is divisible by 3.
Which makes sense because the number 9 is a multiple of the number 3, which means that the 9 can be divided by 3, therefore, if the number can be divided by 9, in the same way it can be divided by 3 .
Answer:
a
Step-by-step explanation:
Perform the indicated operation.
Answer:
√75 = 5√3 and √12 = 2√3 so √75 + √12 = 5√3 + 2√3 = 7√3.
Answer:
[tex] 7\sqrt{3} [/tex]
Step-by-step explanation:
[tex] \sqrt{12} \: can \: be \: simplified \: as \: 2 \sqrt{3} \: and \: \sqrt{75} \: canbe \: simplified \: as \: 5 \sqrt{3} \\ after \: simplifying \: we \: can \: add \: them \: up \\ 2 \sqrt{3} + 5 \sqrt{3} = 7 \sqrt{3} [/tex]
If AB= X and x=4, then the transitive property states
Answer:
AB=4
Step-by-step explanation:
The transitive property states if A=B and B+C than A+C Next substitute
AB=x and x=4 so AB=4
Hope this helps, if it did, please give me brainliest, it helps me a lot. :)
Have a good day!
Laura tiene las tres séptimas partes de la edad de su mamá dentro de 5 años la edad de su mamá será el doble que la edad de ella ¿Cuántos años tiene cada una?
Answer:
Laura tiene 15 años mientras que su madre tiene 35 años.
Step-by-step explanation:
Deje que la edad de Laura sea L.
Deje que la edad de su madre sea m.
Tiene 3/7 de la edad de su madre:
L = 3 m / 7
En 5 años, la edad de su madre será el doble de su edad:
(m + 5) = 2 (L + 5)
m + 5 = 2L + 10
m - 2L = 5
Pon el valor de L:
m - 2 (3 m / 7) = 5
m - 6 m / 7 = 5
Multiplica por 7:
7m - 6m = 35
m = 35 años
=> L = 3 * 35/7 = 15 años
Laura tiene 15 años mientras que su madre tiene 35 años.
a.) The perimeter of a rectangular field is 354 m. If the length of the field is 95m, what is its width? b.) The area of a rectangular painting is 8439 cm^2. If the width of the painting is 87cm, what is its length?
Answer:
a) 82
b) 97
Step-by-step explanation:
a) 354 - (95+95)
354 - 190
164
164 ÷ 2 = 82
(82+82+95+95=254)
b) 8439 cm^2 = 87x
8439 cm^2 ÷ 87 = 87x ÷ 87
97 = x
11.Which word or words best complete the sentence? Two lines that lie in parallel planes _____ intersect. Sometimes Always Never
Answer:
never intersect
Step-by-step explanation
parallel lines do not intersect and neither do parallel planes
Answer in POINT-SLOPE FORM:
Complete the point-slope equation of the line through (1,3) and (5,1) Use exact numbers!
Answer:
y - 3 = (1/2)(x - 1)
Step-by-step explanation:
As we go from (1, 3) to (5, 1), we see that x (the run) increases by 4 and y (the rise) decreases by 2. Hence, the slope is m = rise / run = 2/4, or m = 1/2.
Then the desired point slope equation is y - 3 = (1/2)(x - 1).
what is the gfc of 16 and 8
Answer:
Greatest common factor of 16 and 8 is 8 .....The first card selected from a standard 52-card deck was a king. If it is returned to the deck, what is the probability that a king will be drawn on the second selection
Answer:
[tex]\frac{1}{13}[/tex]
Step-by-step explanation:
The probability P(A) that an event A will occur is given by;
P(A) = [tex]\frac{number-of-possible-outcomes-of-event-A}{total-number-of-sample-space}[/tex]
From the question,
=>The event A is selecting a king the second time from a 52-card deck.
=> In the card deck, there are 4 king cards. After the first selection which was a king, the king was returned. This makes the number of king cards return back to 4. Therefore,
number-of-possible-outcomes-of-event-A = 4
=> Since there are 52 cards in total,
total-number-of-sample-space = 52
Substitute these values into equation above;
P(Selecting a king the second time) = [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]
16. How much money will I need to have at retirement so I can withdraw $60,000 a year for 20 years from an account earning 8% compounded annually? a. How much do you need in your account at the beginning b. How much total money will you pull out of the account? c. How much of that money is interest?
Answer:
starting balance: $636,215.95total withdrawals: $1,200,000interest withdrawn: $563,784.05Step-by-step explanation:
a) If we assume the annual withdrawals are at the beginning of the year, we can use the formula for an annuity due to compute the necessary savings.
The principal P that must be invested at rate r for n annual withdrawals of amount A is ...
P = A(1+r)(1 -(1 +r)^-n)/r
P = $60,000(1.08)(1 -1.08^-20)/0.08 = $636,215.95
__
b) 20 withdrawals of $60,000 each total ...
20×$60,000 = $1,200,000
__
c) The excess over the amount deposited is interest:
$1,200,000 -636,215.95 = $563,784.05
which of the following statements is false?
Answer:
A.
Step-by-step explanation:
It's the first one. The angles are supplementary not complementary.
Answer:
I would have to say A
Step-by-step explanation:
of the following fractions which is 50% greater than 3/7
Answer:
9/14
Step-by-step explanation:
3/7 + 50%×3/7 =
= 3/7 + 1/2×3/7
= 3/7 + 3/14
= 6/14 + 3/14
= 9/14
The required fraction which 50% grater than 3/7 is 9/14.
Fraction to determine that 50% grater than 3/7.
Fraction of the values is number represent in form of Numerator and denominator.
Here, fraction = 50% grater than 3/7
= 1.5 x 3/7
= 4.5/7
= 45/70
= 9/14
Thus, The required fraction which 50% grater than 3/7 is 9/14.
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The point P(7, −2) lies on the curve y = 2/(6 − x). (a) If Q is the point (x, 2/(6 − x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x.
(i) 6.9
mPQ = 1
(ii) 6.99
mPQ = 2
(iii) 6.999
mPQ = 3
(iv) 6.9999
mPQ = 4
(v) 7.1
mPQ = 5
(vi) 7.01
mPQ = 6
(vii) 7.001
mPQ = 7
(viii) 7.000
mPQ = 8
(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at
P(7, −2).
m = 9
(c) Using the slope from part (b), find an equation of the tangent line to the curve at
P(7, −2).
The equation of the tangent line to the curve at P(7, -2) is y = 2x -16.
For each given value of x, we substitute the coordinates of P and Q into the slope formula to find the slope mPQ.
(i) For x = 6.9:
mPQ = (2/(6 - 6.9) - (-2)) / (6.9 - 7)
= 2.22
(ii) For x = 6.99:
mPQ = (2/(6 - 6.99) - (-2)) / (6.99 - 7)
= 2.020
(iii) For x = 6.999:
mPQ = (2/(6 - 6.999) - (-2)) / (6.999 - 7)
= 2.002002
(iv) For x = 6.9999:
mPQ = (2/(6 - 6.9999) - (-2)) / (6.9999 - 7)
= 2.000200
(v) For x = 7.1:
mPQ = (2/(6 - 7.1) - (-2)) / (7.1 - 7)
= 1.818182
(vi) For x = 7.01:
mPQ = (2/(6 - 7.01) - (-2)) / (7.01 - 7)
= 1.980198
(vii) For x = 7.001:
mPQ = (2/(6 - 7.001) - (-2)) / (7.001 - 7)
= 1.998002
(viii) For x = 7.0001:
mPQ = (2/(6 - 7.0001) - (-2)) / (7.0001 - 7)
= 1.999800
By observing the pattern in the calculated slopes, we can see that as x approaches 7, the slope of the secant line PQ approaches 2.
Using the point-slope form, we have:
y - y₁ = m(x - x₁)
Substituting the values of P(7, -2), we have:
y - (-2) = 2(x - 7)
y = 2x -16
Therefore, the equation of the tangent line to the curve at P(7, -2) is y = 2x -16.
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A 12 sided die is rolled the set of equally likely outcomes is 123 456-789-10 11 and 12 find the probability of rolling a number greater than three
Answer:
6
Step-by-step explanation:
nerd physics