Answer:
18 ft* (1 piece/ 1 1/3 ft)= 13.5 pieces.
Step-by-step explanation:
Determine whether the variation between the indicated quantities is direct or inverse. The number of calories in a cheese pizza and the size of the cheese pizza
Answer:
The variance is direct.
Step-by-step explanation:
Since size of the pizza determines the amount of calories.
Let us say that a 2" x4" strip of pizza has 250 calories.
Then a pizza of twice the size (or 4" x 4") will have twice as many calories (500 calories) .
p and q are two numbers.whrite down an expression of. a.) the sum of p and q. b) the product of p and q
(2/3)x-1=27/8,find x
Answer:
x = 105/16
Step-by-step explanation:
2/3x - 1 = 27/8
Add 1 to each side
2/3x - 1+1 = 27/8+1
2/3x = 27/8 + 8/8
2/3x = 35/8
Multiply each side by 3/2
3/2 * 2/3x = 35/8 *3/2
x = 105/16
Home sizes in Anytown, USA have a mean of 2400 square feet and a standard deviation of 450 square feet. What is the probability that a random sample of 50 homes in Anytown, USA has mean square footage less than 2200 square feet
Answer:
0.00084
Step-by-step explanation:
We are given that
Mean,[tex]\mu=2400[/tex] square feet
Standard deviation, [tex]\sigma=450[/tex]square feet
n=50
We have to find the probability that a random sample of 50 homes in Anytown, USA has mean square footage less than 2200 square feet.
[tex]P(x<2200)=P(\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}<P(\frac{2200-2400}{\frac{450}{\sqrt{50}}})[/tex]
[tex]P(x<2200)=P(Z<\frac{-200}{\frac{450}{\sqrt{50}}})[/tex]
Using the formula
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]P(x<2200)=P(Z<-3.14)[/tex]
[tex]P(X<2200)=0.00084[/tex]
Hence, the probability that a random sample of 50 homes in Anytown, USA has mean square footage less than 2200 square feet=0.00084
What is the derivative of x^2?
Answer:
[tex]\displaystyle \frac{d}{dx}[x^2] = 2x[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = x^2[/tex]
Step 2: Differentiate
Basic Power Rule: [tex]\displaystyle \frac{dy}{dx} = 2x^{2 - 1}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = 2x[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
*REVERSE PROPORTION*
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Answer:
33.3%
Step-by-step explanation:
The selling price of £42 is (1 +40%) times the total purchase price.
1.40 × purchase price = £42
purchase price = £42/1.40 = £30
The total profit is 40% of this, so is ...
£30 × 40% = £12
The purchase price of the skirt is ...
total cost - glove cost = skirt cost = £30 -3 = £27
The profit on the skirt is ...
total profit - glove profit = skirt profit = £12 -100% × £3 = £9
Then the percentage profit on the skirt is ...
skirt profit % = skirt profit / skirt cost × 100% = £9/£27 × 100% = 33.3%
The percentage profit on the cost of the skirt was 33.3%.
I have 1/3 of my garden is parsely, I want to take 4/5 for lettuce. How much of my garden will be lettuce
A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance σ2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of σ2 = 23 months (squared) is most desirable for these batteries. A random sample of 30 batteries gave a sample variance of 16.3 months (squared). Using a 0.05 level of significance, test the claim that σ2 = 23 against the claim that σ2 is different from 23.
Answer:
Hence, we reject H_0 as There is sufficient evidence to show that population variance is not 23
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=30[/tex]
Variance [tex]\sigma= 16.8[/tex]
Significance Level [tex]\alpha=0.05[/tex]
[tex]\sigma = 23[/tex]
Genet=rally the Hypothesis are as follows
Null [tex]H_0=\sigma^2=23[/tex]
Alternative [tex]H_a=\sigma^2 \neq 23[/tex]
Generally the equation for Chi distribution t is mathematically given by
t test statistics
[tex]X^2=\frac{(n-1)\sigma}{\sigma^2}[/tex]
[tex]X^2=\frac{(30-1)16.8^2}{23}[/tex]
[tex]X^2=355.86[/tex]
Therefore
Critical Value
[tex]P_{\alpha,df}[/tex]
Where
[tex]df=29[/tex]
[tex]P_{\alpha,df}=16.0471 and 45.7223[/tex]
[tex]X^2=45.7223[/tex]
Hence, we reject H_0 as There is sufficient evidence to show that population variance is not 23
Consider the lists of length six made with the symbols P, R, O, F, S, where repetition is allowed. (For example, the following is such a list: (P,R,O,O,F,S).) How many such lists can be made if the list must end in an S and the symbol O is used more than once?
Answer:
96
Step-by-step explanation:
COMBINATIONS & PERMUTATIONS can be confusing but they always have a solution.
Key 1: Understand and/or rewrite the question
Consider the lists of 6 items (out of the 5 letters P,R,O,F, and S; where O is used twice).
NOTE: When they say O is used more than once, don't forget that each list must not exceed 6 items in total. So, O is used twice. Simple!
How many such lists can be made if each list must end in an S?
NOTE: This instruction requires that S doesn't move. It won't change position, and it won't be involved in the rearrangement!
Key 2: Solve the mysteries
Now, S won't move and O is doubled. These rules put a form of restriction on the "n" which is the total number of items involved in the operation. We are supposed to create lists of 6 items but the reality is - only 5 are moving. Recall also that the original number of items involved in the operation is 5.
In this case, n = 5
Then we have 4 items rotating - P, R, O and F - with 1 repeated.
What this means is that for every list starting with the first O, the different arrangements apply to the second O as well.
There is no distinction such as O₁ and O₂. O is O!
Let k = the extra O
(n - k) = 5 - 1 = 4
So each of these 4 letters has 4! (4 factorial) arrangements, that is (4 x 3 x 2 x 1) = 24 arrangements
Multiply 24 by 4 to get 96
in a group of boys the number of arrangments of boys 4 boys is 12 times the number of arrangment of 2 boys the number of boys in the group is
Answer:
4*12*2
Step-by-step explanation:
it will be the right answer
Answer:
There are 6 boys in group.
Step-by-step explanation:
Since we have given that
Number of arrangement of 4 boys = 12 times the number of arrangement of 2 boys.
So, Let the number of boys in the group be 'x'.
So, Number of boys in the group will be
\begin{gathered}x=\frac{12\times 2}{4}\\\\x=\frac{24}{4}\\\\x=6\end{gathered}
x=
4
12×2
x=
4
24
x=6
Hence, there are 6 boys in the group.
hope it helps you a follow would be appreciated
Determine the time necessary for P dollars to double when it is invested at interest rate r compounded annually, monthly, daily, and continuously. (Round your answers to two decimal places) r=8%
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Answer:
annually: 9.01 yearsmonthly: 8.69 yearsdaily: 8.67 yearscontinuously: 8.66 yearsStep-by-step explanation:
For interest compounded in discrete intervals, the formula is ...
A = P(1 +r/n)^(nt)
We want to find t for P=1 and A=2, so we have ...
2 = (1 +r/n)^(nt)
ln(2) = nt·ln(1+r/n)
t = ln(2)/(n·ln(1+r/n))
A table of values for r=0.08 is attached.
__
For continuous compounding, the formula is ...
A = Pe^(rt)
t = ln(A/P)/r = ln(2)/0.08 ≈ 8.66434 . . . . years
__
annually: 9.01 yearsmonthly: 8.69 yearsdaily: 8.67 yearscontinuously: 8.66 yearsThe value of a car will “depreciate” over time. For example, a car that was worth $24 000 when it was new, is being sold for $13 500 three years later. Determine the annual depreciation rate on this car. Express your final answer as a percent, rounded to one decimal place.
Answer:
The car will depreciate at a rate of 21.14% per year.
Step-by-step explanation:
Given that the value of a car will “depreciate” over time, and, for example, a car that was worth $ 24,000 when it was new, is being sold for $ 13,500 three years later, to determine the annual depreciation rate on this car the following calculation must be performed:
13,500 x (1 + X) ^ 1x3 = 24,000
13,500 x (1 + 0.2114) ^ 3 = 24,000
X = 21.14%
Therefore, the car will depreciate at a rate of 21.14% per year.
A finance journal, which publishes research on current financial topics, states that the maturity term for a certificate of deposit is, on average, 10 years. A banker believes the average maturity term at their bank is different than the amount quoted in the finance journal. After completing a study, the banker found that the average maturity term for a certificate of deposit is 8 years, on average.
Required:
As the banker sets up a hypothesis test to determine if their belief is correct, what is the banker's claim?
Answer:
Following are the solution to the given question:
Step-by-step explanation:
In this the hypothesis is:
[tex]H_{0}:\mu=10\\\\H_{1}:\mu\neq10[/tex]
The bankers assert that their bank's average maturity was distinct from that of ten years, that's why the hypothesis of the alternative.
please show steps in solving: B/3 + B/4 + B/6 =
Answer:
= 3b/4
Step-by-step explanation:
= b . 4/12 + b . 3/12 + b . 2/12
Apply the fraction rule: a/c + b/c = a + b/c
= b . 4 + b . 3 + b . 2/12
= 4b + 3b + 2b/12
Add similar elements: 4b + 3b + 2b = 9b
= 9b/12
Cancel 9b/12: 3b/4
= 3b/4
Find "n" if the Standard Error of M is 4 and the population standard deviation is 16.
Answer:
n = 16
Step-by-step explanation:
Givem that :
Population Standard deviation , σ = 16
Sample size, n =
Standard Error, S. E = 4
To obtain the standard Error, S. E, we use the relation :
S.E = σ / √n
4 = 16 / √n
√n * 4 = 16
Divide both sides by 4
(√n * 4) / 4 = 16 / 4
√n = 4
Square both sides
n = 4²
n = 16
Hence, Sample size = 16
Complete this
sentence: The shortest side
of a triangle is always opposite the
A. longest side
B. angle with the smallest measure
• C. second-longest side
•
D. angle with the greatest measure
Answer:
B
Step-by-step explanation:
The shortest side of a triangle is opposite the smallest angle
The longest side of a triangle is opposite the largest angle
find the area of the figure sides meet at right angles 8 cm, 3cm, 4cm, 5cm, 9cm
Answer:
umm is it a quadrilateral
Step-by-step explanation:
Answer:
if it's 8cm, 3m, 4cm, 5cm, and 9cm it's probably a quadrilateral
Use the fact that 1 square mile=640 acres to find the area of a property that measures 7 hectares is for sale.
a. How large is the property in acres?
b. If the property is selling for $150,000, what is the price per acre?
Answer:
a) The property has 17.3 acres.
b) The price per acre is of $8,670.5.
Step-by-step explanation:
The questions are solved by proportions, using a rule of three.
a. How large is the property in acres?
Each hectare has 2.47105 acres.
So 7 hectares will have:
7*2.47105 = 17.3.
The property has 17.3 acres.
b. If the property is selling for $150,000, what is the price per acre?
17.3 acres for $150,000. So
150000/17.3 = $8,670.5.
The price per acre is of $8,670.5.
If land the domain of the following peicewise function f(x)={x^2 +2 if -6
Answer:
? what is this question asking
Step-by-step explanation:
x -3,4,11,18 y -3,1,5,9
Is the relationship linear, exponential, or neither?
Choose 1 answer:
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Answer:
linear
Step-by-step explanation:
The points all lie on a straight line. The relationship is linear.
Does anyone know which is bigger for a poster Size: 22.375" x 34" or Size: 14.725" x 22.375"
Answer:
22.375" × 34" is the bigger size for a poster
Find f(5) for f(x) = 6 (3)
Answer:
5f=18
5f/5f=18/5f
f=3 2/5
The side lengths of a triangle are 5,10, and 13. Is this a right Triangle?
No because 5^2 +10^2 is not equavalent to 13^2
by using the pythagoras' theorem
When a < 0 in the quadratic function y = ax2 + bx + C, the graph of the quadratic function opens _____?
Answer:
downwards
Step-by-step explanation:
Given the quadratic function in standard form
y = ax² + bx + c ( a ≠ 0 )
• If a > 0 then the graph opens upwards
• If a < 0 then the graph opens downwards
find the result when six times the difference of 5 and 3 is added to the quotient of 12 by 3.with process
The cost function in a computer manufacturing plant is C(x) = 0.28x^2-0.7x+1, where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands. Determine the minimum production cost.
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Answer:
$562,500 per hour
Step-by-step explanation:
The cost will be a minimum where C'(x) = 0.
C'(x) = 0.56x -0.7 = 0
x = 0.7/0.56 = 1.25
The cost at that production point is ...
C(1.25) = (0.28×1.25 -0.7)1.25 +1 = -0.35×1.25 +1 = 0.5625
The minimum production cost is $562,500 per hour for production of 1250 items per hour.
_____
Additional comment
This is different than the minimum cost per item. This level of production gives a per-item cost of $450. The minimum cost per item is $358.30 at a production level of 1890 per hour.
6. A boy pushes his little brother in a box with a force of 500 N for 324 m How much work is this if the force of
friction acting on the sliding box is (a) 100 N (6) 250. N?
Answer:
(a) 129600 J
(b) 81000 J
Step-by-step explanation:
The work done is given by the product of force and the displacement in the direction of force.
Force, F = 500 N
distance, d = 324 m
(a) friction force, f = 100 N
The work done is
W = (F - f) x d
W = (500 - 100) x 324
W = 129600 J
(b) Friction, f = 250 N
The work done is
W = (F - f) d
W = (500 - 250) x 324
W = 81000 J
PLEASE HELP ME ASAP (72 POINTS)
Answer:
d=10.45t
Step-by-step explanation:
The last one is the answer.
Hope this helps!
--Applepi101
Answer:
D) d=10.45t
Step-by-step explanation:
His distance(d) was 100. And his time(t) was 9.58 seconds.
So 100=9.58x
x≈10.44
The answer is D, because 10.45 is greater than 10.44.
I hope this helps!
simplify. can someone help i am lost
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Answer:
[tex](S)\cdot(H)\cdot(E)\cdot(e)\cdot(\theta)\cdot(\epsilon+1+1)\cdot(\xi)\cdot(s)\cdot(h)[/tex]
Step-by-step explanation:
The inverse function of fun(x) is indicated using a -1 exponent. That is ...
[tex]\text{fun}(\text{fun}^{-1}(x)) = x\\\text{fun}^{-1}(\text{fun}(x)) = x[/tex]
The usual trig identities apply:
sin²(x) +cos²(x) = 1
sec²(x) -tan²(x) = 1
sin(x) = 1/csc(x)
__
So, the expression simplifies to ...
[tex](S)\cdot(H)\cdot(E)\cdot(e)\cdot(\theta)\cdot(\epsilon+1+1)\cdot(\xi)\cdot(s)\cdot(h)[/tex]
PLEASE CORRECT BEFORE ANSWERING I AM HAVING TROUBLE GETTING THINNGS RIGHT SO PLEASE HELP
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Answer:
3
Step-by-step explanation:
AB is 1 unit long.
A'B' is 3 units long.
The scale factor is the ratio of these lengths:
scale factor = A'B'/AB = 3/1 = 3
ABC is dilated by a factor of 3 to get A'B'C'.
