Answer:
16ft by 16ft by 8ft.
Step-by-step explanation:
Let the total surface area of the rectangular tank be S = 2LW+2LH+2WH where;
L is the length of the box
W is the width of the box
H is the height of the box.
Since the box is openend at the top, S = lw + 2lh+ 2wh
If the base is a square base then, l = w
S = l(l) + 2wh+2wh
S = l²+4wh ............... 1
If volume = lwh
lwh = 2028 ft³
wh = 2048/l ................ 2
Substitute equation 2 into 1;
S = l²+4(2048/l)
S = l²+8192/l
dS/dl = 2l - 8192/l²
If dS/dl = 0 (since we are looking for dimensions of the tank with minimum weight.)
2l - 8192/l² = 0
2l = 8192/l²
2l³ = 8192
l³ = 8192/2
l³ = 4096
l =∛4096
l = 16 ft
Since the length is equal to the width, hence the width = 16ft (square based tank)
Given the volume V = lwh = 2048
lwh = 2048
16*16*h = 2048
256h = 2048
divide both sides by 256
256h/256 = 2048/256
h = 8ft
Hence, the dimensions of the tank with minimum weight is 16ft by 16ft by 8ft.
A girl has 98 beads, and all but 14 were lost. how many beads did she loose?
Answer:
84 beads
Step-by-step explanation:
She had 98 beads and lost all but fourteen. So it would be 98 - 14 which would get you 84 beads that the girl has lost
Factor the expression.
p^2 - 10pq + 16q^2
[tex]p^2 - 10pq + 16q^2=\\p^2-2pq-8pq+16q^2=\\p(p-2q)-8q(p-2q)=\\(p-8q)(p-2q)[/tex]
simplify use the multiplication rule
Answer:
3
Step-by-step explanation:
[tex] \sqrt[4] {27} \cdot \sqrt[4] {3} = [/tex]
[tex] = \sqrt[4] {27 \cdot 3} [/tex]
[tex] = \sqrt[4] {3^3 \cdot 3^1} [/tex]
[tex] = \sqrt[4] {3^4} [/tex]
[tex] = 3 [/tex]
log 7 (x^2 + 11) = log 7 15
Answer:
x = ±2
Step-by-step explanation:
log 7 (x^2 + 11) = log 7 15
We know that log a ( b) = log a(c) means b =c
x^2 + 11 = 15
Subtract 11 from each side
x^2 = 15-11
x^2 =4
Take the square root of each side
sqrt(x^2) =±sqrt(4)
x = ±2
A recent survey asked 1200 randomly selected U.S. adults if they believe that the U.S. federal government is doing enough to keep U.S. elections safe from outside interference. After analyzing the results, the researchers were able to state that they are 95% confident that between 52.5% and 59.5% of all U.S. adults believe that the U.S. federal government is not doing enough to keep U.S. elections safe. Which statement BEST describes how to interpret these results
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is D
Step-by-step explanation:
From the question the question we are told that
The researchers were able to state that they are 95% confident that between 52.5% and 59.5% of all U.S. adults believe that the U.S. federal government is not doing enough to keep U.S. elections safe.
Generally a confidence interval states to what extent the chances of the true population is within the a given range
So the 95% confidence interval given in the question as 52.5% and 59.5% means that the chances of the true population mean being with this given range is 95%
So given that the the true population mean is within this range then it means that the population mean will be greater than 50%
So the statement that best describe and interprets this result is
The results show significant statistical support that most U.S. adults (over 50%) believe that the U. S. Federal government is not doing enough to keep U.S. election safe.
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = 4 cos(x), a = 7π
Answer:
The Taylor series of f(x) around the point a, can be written as:
[tex]f(x) = f(a) + \frac{df}{dx}(a)*(x -a) + (1/2!)\frac{d^2f}{dx^2}(a)*(x - a)^2 + .....[/tex]
Here we have:
f(x) = 4*cos(x)
a = 7*pi
then, let's calculate each part:
f(a) = 4*cos(7*pi) = -4
df/dx = -4*sin(x)
(df/dx)(a) = -4*sin(7*pi) = 0
(d^2f)/(dx^2) = -4*cos(x)
(d^2f)/(dx^2)(a) = -4*cos(7*pi) = 4
Here we already can see two things:
the odd derivatives will have a sin(x) function that is zero when evaluated in x = 7*pi, and we also can see that the sign will alternate between consecutive terms.
so we only will work with the even powers of the series:
f(x) = -4 + (1/2!)*4*(x - 7*pi)^2 - (1/4!)*4*(x - 7*pi)^4 + ....
So we can write it as:
f(x) = ∑fₙ
Such that the n-th term can written as:
[tex]fn = (-1)^{2n + 1}*4*(x - 7*pi)^{2n}[/tex]
In this exercise we must calculate the Taylor series for the given function in this way;
[tex]f_n= (-1)^{2n+1}(4)(x-7\pi)^{2n}[/tex]
The Taylor series of f(x) around the point a, can be written as:
[tex]f(x) = f(a) + f'(a)(x-a)+\frac{1}{2!} f''(a)(x-a)^2+....[/tex]
Here we have:
[tex]f(x) = 4cos(x)\\a = 7\pi[/tex]
Then, let's calculate each part:
[tex]f(a) = 4cos(7\pi) = -4\\df/dx = -4sin(x)\\(df/dx)(a) = -4sin(7\pi) = 0\\(d^2f)/(dx^2) = -4cos(x)\\(d^2f)/(dx^2)(a) = -4cos(7\pi) = 4[/tex]
Here we already can see two things:
1) The odd derivatives will have a sin(x) function that is zero when evaluated in [tex]x=7\pi[/tex].
2) We also can see that the sign will alternate between consecutive terms.
So we only will work with the even powers of the series:
[tex]f(x) = -4 + (1/2!)*4*(x - 7\pi)^2 - (1/4!)*4*(x - 7\pi)^4 + ....[/tex]
So we can write it as:
[tex]f(x)=\sum f_n[/tex]
Such that the n-th term can written as:
[tex]f_n= (-1)^{2n+1}(4)(x-7\pi)^{2n}[/tex]
See more abour Taylor series at: brainly.com/question/6953942
Verify the identity. cot x / 1 + csc x = csc x - 1 / cot x
Step-by-step explanation:
cot x / (1 + csc x)
Multiply by conjugate:
cot x / (1 + csc x) × (1 − csc x) / (1 − csc x)
Distribute the denominator:
cot x (1 − csc x) / (1 − csc²x)
Use Pythagorean identity:
cot x (1 − csc x) / (-cot²x)
Divide:
(csc x − 1) / cot x
Give examples of two variables that have a perfect positive linear correlation and two variables that have a perfect negative linear correlation.
Answer:
answer below
Step-by-step explanation:
1. price per gallon of gasoline and total cost of gasoline
2. distance from a door and height of a wheelchair ramp
perfect positive linear relationship:
this is a relation that exists between two variables. The pearson correlation is used to check this relationship and if the relationship is 1.0 then it is established that a positive linear relationship exists
negative linear relationship
this is a relationship between variables where the pearson correlation is less than 0. if the value is -1.0 then a negative linear relatioship exists.
price per gallon of gasoline and total cost of gasoline move in the same direction so it is positive.
distance from a door and height of a wheelchair ramp are negative because they do not move in the same direction.
Adam’s house is 2 centimeters from Juan’s house on a map. If each centimeter on the map represents 6 kilometers, how far apart are the two houses?
Answer:
Since 1 cm represents 6 km
2 cm will represent 12 km
Hence Adam's house is 12 km away
Answer:
The answer is C. 3
Step-by-step explanation:
If u divide 6 divided by 2 it will get you 3
i also got it right bc i took the quiz.
Suppose we want to choose 6 colors, without replacement, from 14 distinct colors. (a) How many ways can this be done, if the order of the choices matters? (b) How many ways can this be done, if the order of the choices does not matter?
Answer:
(a) 2,162,160
(b) 3,003
Step-by-step explanation:
(a) order matters
You can choose from 14 for the first pick. Then you have 13 left for the second pick. Then you have 12 left for the third pick. Keep going until you have 9 left for the 6th pick. The number when order matters is:
total = 14 * 13 * 12 * 11 * 10 * 9 = 2,162,160
(b) Order does not matter
Start with the same number as above for picking 6 out of 14. Since order does not matter, we divide by the number of ways you can arrange 6 items.
Since there are 6! ways of arranging 6 items,
total = 2,162,160/6! = 3,003
The number of ways when the order matters are 121080960.
The number of ways when order does not matters are 3003.
Given,
Choose 6 colors, without replacement, from 14 distinct colors.
We have to find:
- How many ways can this be done, if the order of the choices matters.
- How many ways can this be done if the order of the choices does not matter.
What are permutation and combination?We use permutation when the order of the arrangements matters.
It is given by:
[tex]^ nP_r[/tex] = n! / r!
We use combination when order does not matter.
It is given by:
[tex]^nC_{r}[/tex] = n! / r! (n-r)!
Find the number of ways when order matters.
We have,
n = 14 and r = 6
[tex]^{14}P_{6}[/tex]
= 14! / 6!
= (14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6!) / 6!
= 4 x 13 x 12 x 11 x 10 x 9 x 8 x 7
= 121080960
Find the number of ways when order does not matter.
We have,
n = 14 and r = 6
[tex]^{14}C_{6}[/tex]
= 14! / 6! 8!
= 14 x 13 x 12 x 11 x 10 x 9 / 6 x 5 x 4 x 3 x 2
= 7 x 13 x 11 x 3
= 3003
Thus,
The number of ways when the order matters are 121080960.
The number of ways when order does not matters are 3003.
Learn more about combination here:
https://brainly.com/question/28134115
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nick cut a circular cookie into 5 equal slices. what is the angle measure of each slice?
Using concepts of circles, it is found that the angle measure of each slice is of 72º.
--------------------------------------------
The cookies have circular formats.A complete circle, which is the format of a cookie, has an angular measure of 360º.If it is divided into a number n of equal slices, the angles will be 360 divided by n.--------------------------------------------
5 equal slices, thus:
[tex]\frac{360}{5} = 72[/tex]
The angle measure of each slice is of 72º.
A similar problem is given at https://brainly.com/question/16746988
−(−49) = −49 true or false?
what is (2y + 5)(y - 3) in simplified form using the distributive property
Answer:
[tex]\boxed{2y^{2} - y - 15}[/tex]
Step-by-step explanation:
Use the FOIL technique in order to distribute the terms properly. FOIL stands for First Terms, Outside Terms, Inside Terms, and Last Terms. In order to properly distribute, multiply the common terms based on the steps in the FOIL technique. So, in this case:
The first terms are 2y and y. The outside terms are 2y and -3. The inside terms are 5 and y.The last terms are 5 and -3.Therefore, multiply the terms:
2y and y to get 2y²2y and -3 to get -6y5 and y to get 5y5 and -3 to get -15Then, add or subtract based on the signs:
2y² - 6y + 5y - 15
Then, add like terms to finish simplifying the expression. This leaves you with 2y² - y - 15.
Answer:
2y2 – y – 15
Step-by-step explanation:
(2y + 5)(y – 3)
= 2y(y – 3) + 5(y – 3)
= 2y2 – 6y + 5y – 15
= 2y2 – y –15
Hey guys! I have this problem and I dont really understand how to solve it, could you guys help me? :' )
Answer:
Step-by-step explanation:
Answer:
-7
Step-by-step explanation:
Finding Slope On a coordinate plane, a line goes through points (0, 1) and (4, 2). What is the slope of the line? m =
Answer:
slope = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (4, 2)
m = [tex]\frac{2-1}{4-0}[/tex] = [tex]\frac{1}{4}[/tex]
Answer:
the answer would be 1/4
Step-by-step explanation:
NEED ASAP I WILL GIVE BRAINLEYEST What is the value of the expression 22 + 82 ÷ 22? 8 10 17 20
Answer:
Exact Form:
283 /11
Decimal Form:
25. 72
Mixed Number Form:
25 8 /11
Step-by-step explanation:
Answer:
17
Step-by-step explanation:
A baking scale measures mass to the tenth of a gram, up to 650 grams. A cup of flour is placed on the scale and results in a measure of 121.8 grams. Which of the following statements is not true?
a.The exact mass of the cup of flour must be between 121.7 and 121.9 grams.
b.The cup of flour has a mass of exactly 121.8 grams.
c.Given the limitations of the scale, the measurement has an appropriate level of accuracy.
d.To the nearest gram, the cup of flour has a mass of 122 grams.
Answer
Is it C I may have done my math wrong lol
Step-by-step explanation:
two ratios equivalent to 27:9
Answer:
Those ratios could be 3:1
A sport jacket is on sale for 35% off, if the originsl price is $140, what is the sale price?
Answer:
$91
Step-by-step explanation:
If a jacket is on sale for 35% off, that means that the price of the jacket is [tex]100-35=65[/tex]% of its original price.
We can find 65% of 140 by making 65% into a decimal - 0.65, then multiply it by 140.
[tex]140\cdot0.65=91[/tex]
Hope this helped!
Answer:
$91.00
Step-by-step explanation:
The jacket is on sale for 35%. Usually, you pay for 100% of the jacket's price. Since it is on sale, we can subtract 35% from 100%.
100%-35%=65%
With the sale, you only pay for 65% of the price.
Now, we can multiply 65% and 140.
65% * 140
Convert 65% to a decimal. Divide 65 by 100 or move the decimal place 2 spots to the left.
65/100=0.65
65.0 --> 6.5 --> 0.65
0.65 * 140
Multiply
91
$91
The sale price for the sports jacket is $91.00
Find the equation with the given slope through the given point. Write the equation in the given form AX+BY=C m=1/9 (-6,2)
Answer:
x - 3y = 12
Step-by-step explanation:
Find the point-slope form of this equation and then convert the point-slope form into standard form (ax + by = c):
y - k = m(x - h) becomes y - 2 = (1/9)(x + 6).
Multiplying all three terms by 9 removes the fraction:
3y - 6 = x + 6, or x - 3y = 12
The paper usage at a small copy center is normally distributed with a mean of 5 boxes of paper per week, and a standard deviation of 0.5 boxes. It takes 2 weeks for an order of paper to be filled by its supplier. What is the safety stock to maintain a 99% service level?
Answer:
1.649 approximately 2
Step-by-step explanation:
S.d = standard deviation = 0.5
Time taken = lead time = 2 weeks
Mean = demand for week = 5 boxes
We are required to find the safety stock to maintain at 99% service level.
At 99% level, the Z value is equal to 2.326.
Therefore,
Safety stock = z × s.d × √Lt
= 2.326 × 0.5 x √2
= 1.649
Which is approximately 2.
Suppose 55 percent of the customers at Pizza Palooza order a square pizza, 72 percent order a soft drink, and 48 percent order both a square pizza and a soft drink. Is ordering a soft drink independent of ordering a square pizza?
Answer: No, the orders are not independent.
Step-by-step explanation:
If event 1 has some possible outcomes, suppose that we choose a given outcome 1 with a probability P1, and event 2, also with different possible outcomes, we can select an outcome 2, that has a probability P2, and the two events are independent (meaning that the outcome in event 1 does not affect the outcome in event 2, and vice versa)
Then the probability of outcome 1 and outcome 2 happening at the same time is equal to the product of their individual probabilities.
P = P1*P2.
In this case, event 1 is the selection of the pizza, and outcome 1 is the selection of the square pizza, with a probability of 55%.
Event 2 is the selection of the drink, outcome 2 is the order of a soft drink, with a probability of 72%.
If those two events were independent, then the probability that a customer orders a square pizza and a soft drink would be:
P = 0.55*0.72 = 0.396 (or 39.6%)
But we know that the actual probability is 48%.
So this is larger, which means that the outcomes are not independent.
True or false? induction is a kind of thinking you use to form general ideas and rules based on mathematical formuals
Answer:
Hey there!
True. You use individuals rules, pieces of evidence, and experimentally found ideas that can be combined to form a general mathematical statement.
Let me know if this helps :)
Which of the following is not a way of generating random numbers? A. random number tables B. using phone numbers selected at random in a local phone book C. using the internet D. books of random numbers
Answer:
well all of these look like a way so we have to use elimination method
A : random number tables : well it has random numbers so X out
B: PHONE NUMBERS: well phone numbers are random so X out
C: USing the internet : totally X out
D: books of random numbers: X out
so none of the above i guess
The only way that might not be used in generating random numbers is : (B). using phone numbers selected at random in a local phone book
Meaning of random numbersRandom numbers are numbers that occurs randomly without prediction. these numbers are impossible to predict using past values.
Random numbers are important for computer encryption and lotteries.
In conclusion, The only way that might not be used in generating random numbers is using phone numbers selected at random in a local phone book
Learn more about random numbers: https://brainly.com/question/10352102
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the square of a number is 3 less than four times the number. which values could be the number?
Answer:
x could be 3 or 1
Step-by-step explanation:
x²+3=4x
x²-4x+3=0
(x-3)(x-1)
x could be 3 or 1
The values could be 1 or 3.
Let the number be n.In this exercise, you're required to write a mathematical (algebraic) expression for the given word problem and determine which values could be the unknown number.
Translating the word problem into an algebraic expression, we have;
[tex]n^{2} = 4n - 3\\\\n^{2} - 4n + 3 = 0[/tex]
We would solve the quadratic equation by using the factorization method;
[tex]n^{2} - 3n -n + 3 = 0\\\\n(n - 3) - 1(n - 3) = 0\\\\(n - 1)(n - 3) = 0[/tex]
Therefore, the values could be 1 or 3.
Find more information: https://brainly.com/question/17215161
Which point slope form equations could be produced with the points (3,2) and (4,6)
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of a line given two points first find the slope of the line and use the formula
y - y1 = m( x - x1) to find the Equation of the line using any of the points given
Slope of the line using points
(3,2) and (4,6) is
[tex]m = \frac{6 - 2}{4 - 3} = \frac{4}{1} = 4[/tex]
So the equation of the line using point
( 3 , 2 ) and slope 4 is
y - 2 = 4( x - 3)Hope this helps you
evaluate -99 + 3^2•5
Answer:
= - 54
Step-by-step explanation:
- 99 + 3^2•5
- 99 + 9 × 5
- 99 + 45
= - 54
A study of the effect of television commercials on 12-year-old children measured their attention span, in seconds.
Clothes Food Toys
27 44 61
22 49 64
46 37 57
35 56 48
28 47 63
31 42 53
17 34 48
31 43 58
20 57 47
47 51
44 51
54
1. Find the values of mean and standard deviation.
2. Is there a difference in mean attention span of the children for various commercials?
3. Are there significance differences between pair of means?
Answer: Find answers in the attachment files
Step-by-step explanation:
Help and show work plz
Answer:
30
Step-by-step explanation:
If we have 4 integers that have an average of 9, then all the numbers will add up to [tex]9\cdot4=36[/tex].
If we want the greatest number possible, the other 3 need to be the lowest possible.
Since they are all different, the lowest possible values of the first 3 numbers are 1, 2, and 3.
[tex]1 + 2 + 3 = 6[/tex]
[tex]36 - 6 = 30[/tex]
So 30 is the greatest value of one of the integers.
Hope this helped!
A random sample of 12 second-year university students enrolled in a business statistics course was drawn. At the course's completion, each student was asked how many hours he or she spent doing homework in statistics. The data are listed below. 20, 29, 28, 22, 26, 22, 22, 18, 23, 21, 20, 27 It is known that the population standard deviation is 7. The instructor has recommended that students devote 2 hours per week for the duration of the 12-week semester, for a total of 24 hours. Test to determine whether there is evidence at the 0.07 significance level that the average student spent less than the recommended amount of time. Fill in the requested information below.A. The value of the standardized test statistic:Note: For the next part, your answer should use interval notation. An answer of the form (−[infinity],a) is expressed (-infty, a), an answer of the form (b,[infinity]) is expressed (b, infty), and an answer of the form (−[infinity],a)∪(b,[infinity]) is expressed (-infty, a)U(b, infty). B. The rejection region for the standardized test statistic:C. The p-value isD. Your decision for the hypothesis test: A. Reject H0. B. Do Not Reject H1. C. Do Not Reject H0. D. Reject H1.
Answer:
Reject H₀.
Step-by-step explanation:
In this case, we need to test whether the average student spent less than the recommended amount of time doing homework in statistics.
The provided data is:
S = {20, 29, 28, 22, 26, 22, 22, 18, 23, 21, 20, 27}
Compute the sample mean:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{12}\cdot [20+29+...+27]=23.167[/tex]
The population standard deviation is σ = 7.
The hypothesis for the test is:
H₀: The average student does not spent less than the recommended amount of time doing homework, i.e. μ ≥ 24.
Hₐ: The average student spent less than the recommended amount of time doing homework, i.e. μ < 24.
(A)
Compute the standardized test statistic value as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]=\frac{23.167-24}{7/\sqrt{12}}\\\\=-0.412[/tex]
Thus, the standardized test statistic value is -0.412.
(B)
The significance level of the test is:
α = 0.07
The critical value of z is:
z₀.₀₇ = -1.476
The rejection region is:
(-∞, -0.1476)
(C)
Compute the p-value as follows:
[tex]p-value=P(Z<-0.412)=0.34[/tex]
*Use a z-table.
Thus, the p-value is 0.34.
(D)
Since, p-value = 0.34 > α = 0.07, the null hypothesis was failed to be rejected at 7% level of significance.
Thus, the correct option is (A).
