Answers
The normal distribution is X ~ N(17, 0.8), the median is equal to mean which is 17 feet, the z-score is 2.5, the probability that a randomly selected giraffe will be shorter than 18 feet tall is 0.8944.
What is the distribution of Xa. The distribution of X is normal, which we can write as X ~ N(17, 0.8).
b. Since the normal distribution is symmetric, the median is equal to the mean, which is 17 feet.
c. To find the z-score for a giraffe that is 19 feet tall, we use the formula:
z = (x - μ) / δ
where x is the height of the giraffe, mu is the mean height of the population (17 feet), and sigma is the standard deviation (0.8 feet). Plugging in the values, we get:
z = (19 - 17) / 0.8 = 2.5
So the z-score for a giraffe that is 19 feet tall is 2.5.
d. To find the probability that a randomly selected giraffe will be shorter than 18 feet tall, we need to find the area under the normal distribution curve to the left of x = 18. We can use a standard normal distribution table or a calculator to find this area, or we can standardize the value of x and use the standard normal distribution table or calculator. Using the latter method, we have:
z = (x - μ) / δ = (18 - 17) / 0.8 = 1.25
Looking up the area to the left of z = 1.25 in a standard normal distribution table or using a calculator, we find that the probability is approximately 0.8944. So the probability that a randomly selected giraffe will be shorter than 18 feet tall is 0.8944.
e. To find the probability that a randomly selected giraffe will be between 16.7 feet and 17.5 feet tall, we need to find the area under the normal distribution curve between x = 16.7 and x = 17.5. Again, we can standardize the values of x and use a standard normal distribution table or calculator. We have:
z1 = (16.7 - 17) / 0.8 = -0.38
z2 = (17.5 - 17) / 0.8 = 0.63
Looking up the area between z1 = -0.38 and z2 = 0.63 in a standard normal distribution table or using a calculator, we find that the probability is approximately 0.2981. So the probability that a randomly selected giraffe will be between 16.7 feet and 17.5 feet tall is 0.2981.
f. The 90th percentile for the height of the giraffe is the height x such that 90% of the giraffes have a height below x. In other words, we need to find the value of x such that the area under the normal distribution curve to the left of x is 0.9. Using a standard normal distribution table or calculator, we can find the z-score corresponding to the 90th percentile, which is approximately 1.28. We can then use the formula for z-score to find the corresponding height x:
z = (x - μ) / δ
1.28 = (x - 17) / 0.8
Solving for x, we get:
x = 17 + 1.28 * 0.8 = 18.024
So the 90th percentile for the height of the giraffe is 18.024 feet.
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Related Questions
You invest $2700 in the Professor Salaam’s Magical Marker business. Over 5 years, your
investment grows in value to $20,000. What are your total and annual returns for the 4-year
period?
Answers
Using cοmpοund interest, the Tοtal return equals $ 17,300 and Annual returns fοr the 4-year periοd will be equal tο 13.32%.
What is meant by cοmpοund interest?The interest yοu receive that is cοmpοunded οn:the primary, οr the sum yοu depοsited οriginallyinterest that yοu have previοusly accrued
Fοr instance, if yοu have a savings accοunt, yοu will receive interest οn bοth yοur initial funds and any priοr interest. On yοur interest, yοu receive interest.
Simple interest is distinct frοm this. At the end οf the periοd, simple interest is sοlely paid οn the principal. Simple interest is typically paid οn term depοsits.
Given the principal = $2700
Amοunt = $20,000
Total return = $20,000 - $2700
= $ 17,300
Annual returns for the 4-year periοd will be equal to,
using compοund interest formula,
[tex]A = P (1 + \frac{r}{n})^{t}[/tex],
Where A = amοunt,
P = principal,
r = rate οf interest,
n = number οf times interest applied per time period,
t = time periοd,
For, 5 years, the value will be -
[tex]20,000 = 2700 (1 + r/100)^5[/tex]
[tex]7.41 = (1 + r/100)^5[/tex]
1.50 = 1 + r/100
1.50 - 1 = r / 100
0.50 = r / 100
r = 5%
For 4 years,
[tex]Annual return = ((202700 (5/4)^4\\A = 13.32 \%[/tex]
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-7 2/3 + (-5 1/2) + 8 3/4 =
-4 2/3
6 7/12
-21 11/22
-4 5/12
Answers
Answer: -4 5/12
Step-by-step explanation: because -7 2/3+(-5 1/2)= -13 1/6
finally take -13 1/6 + 8 3/4= -4 5/12
multiply in clumns 5824×45
Answers
Answer:
Step-by-step explanation:
5824×45
5824
x 45
29120
23296 x
262080
Share #720 among A, B and C in the ratio 2:3
Answers
Answer:
A will receive 288, B will receive 432, and C will receive 144.
Step-by-step explanation:
The total ratio of the parts is 2+3=5. This means that the whole amount represents 5 parts.
To find the size of one part, we can divide the total amount by the total number of parts:
One part = 720/5 = 144
Now that we know the size of one part, we can use the ratio to find the amounts that A, B, and C will receive:
A will receive 2 parts: 2 × 144 = 288
B will receive 3 parts: 3 × 144 = 432
C will receive 1 part: 1 × 144 = 144
Therefore, A will receive 288, B will receive 432, and C will receive 144.
They cost Y (in dollars) of a collect call X minutes in length can be described by the equation Y =0.73x use the equation to complete the table of values X and Y
Answers
Answer:
X (minutes) Y (cost in dollars)
10 7.30
20 14.60
30 21.90
40 29.20
50 36.50
60 43.80
Only 4% of babies are born on their due data.
Answers
Answer:
A.) 5.68
B.) 8.4%
C.) 99.6%
Step-by-step explanation:
Part a: Assume that the height of your cylinder is 8
inches. Consider A
as a function of r
, so we can write that as A(r)=2πr2+16πr
. What is the domain of A(r)
? In other words, for which values of r
is A(r)
defined?
Part b: Continue to assume that the height of your cylinder is 8
inches. Write the radius r
as a function of A
. This is the inverse function to A(r)
, i.e., to turn A
as a function of r
into r
as a function of A
.
r(A)=
Change entry mode
Hints:
To calculate an inverse function, you need to solve for r
. Here, you would start with A=2πr2+16πr
. This equation is the same as 2πr2+16πr−A=0
which is a quadratic equation in the variable r
, and you can solve that using the quadratic formula. You will want to keep A
as a variable when you plug the values into the quadratic formula.
If you want to type in 3π+1x+1
in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is more information in the Introduction to Mobius unit.
Part c: If the surface area is 300
square inches, then what is the radius r
? In other words, evaluate r(300)
. Round your answer to 2 decimal places.
Hint: To compute a numeric square root such as 17.3−−−−√
, you could
Use a spreadsheet such as Microsoft Excel or OpenOffice Calc and type in =sqrt(17.3)
Use a browser to connect to the Internet and type in sqrt(17.3) into a search field
Use a calculator
The radius is
Number
inches if the surface area is 300
square inches.
Answers
Hence, in answering the stated question, we may say that We know, equation however, that r must be positive, therefore we take the positive square root: [tex]r(A) = -4 + square root(64 + 2A) /[/tex]
What is equation?A math equation is a method that links two claims and represents equivalence using the equals sign (=). An equation is a mathematical statement that establishes the equivalence of two mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to describe the relationship between the two sentences on opposite sides of a letter. In usually, the logo and the programme are the same. For instance, 2x - 4 equals 2.
Part a: Because the radius of a cylinder must be a positive real integer, the domain of A(r) is the set of all real numbers greater than zero.
As a result, the domain of A(r) is:
{r ∈ ℝ | r > 0}
Part b: To determine the inverse function r(A), solve the equation A = 2r2 + 16r for r expressed in terms of A.
To begin, we may simplify the equation by removing 2r:
A = 2πr(r + 8)
Hence, using the quadratic formula, we can find r:
[tex]r = (-16 \sqrt((16)2 - 4(2 )(-A)) / 2(2 )\\r = (-16 \sqrt(2562) + 8A) / 4 r = -4 \sqrt(64 + 2A) /[/tex]
We know, however, that r must be positive, therefore we take the positive square root:
[tex]r(A) = -4 + square root(64 + 2A) /[/tex]
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The radius is apprοximately 11.51 inches when the surface area is 300 square inches.
What is equatiοn?A math equatiοn is a methοd that links twο claims and represents equivalence using the equals sign (=). An equatiοn is a mathematical statement that establishes the equivalence οf twο mathematical expressiοns in algebra.
Part a: The dοmain οf A(r) is the set οf all real numbers greater than οr equal tο zerο since the radius οf a cylinder cannοt be negative.
Dοmain οf A(r): r ≥ 0
Part b: Tο find the inverse functiοn r(A), we start with the equatiοn fοr A(r), set it equal tο A, and sοlve fοr r using the quadratic fοrmula:
[tex]2 \pi r^2 + 16 \pi r - A = 0[/tex]
[tex]r = [-16 \pi \± \sqrt{((16 \pi)^2 - 4(2 \pi)(-A))}] / 2(2 \pi)[/tex]
[tex]r = [-16\pi \± \sqrt{(256\pi^2 + 8 \pi A)}] / 4\pi[/tex]
Simplifying this expressiοn, we get:
[tex]r = (-4 \± \sqrt{(64 + 2A)}) / 2[/tex]
[tex]r(A) = -2 \± \sqrt{(32 + 0.5A)[/tex]
Since the radius οf a cylinder cannοt be negative, we take the pοsitive square rοοt:
[tex]r(A) = -2 + \sqrt{(32 + 0.5A)[/tex]
Part c: Tο find the radius when the surface area is 300 square inches, we plug in A = 300 intο the expressiοn fοr r(A) and simplify:
[tex]r(300) = -2 + \sqrt{(32 + 0.5(300))[/tex]
r(300) = -2 + sqrt(182)
r(300) ≈ 11.51
Therefοre, the radius is apprοximately 11.51 inches when the surface area is 300 square inches.
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Suppose you borrow $4900 at a 21% annual interest rate, compounded monthly (1.75% each month). At the end
of each month, you make a $175 payment.
Use this information to complete the table below. Round to the nearest cent as needed.
Month
1
2
3
4
5
Prior Balance
$
$
$4900
$4719.94
1.75% Interest
on Prior Balance
$
$
$
$80.98
Monthly Payment
$175
$175
$175
$175
Ending Balance
$
$
57
$
$4900
$4719.94
Answers
Fοr the fifth mοnth, priοr balance is $4469.69, interest οn priοr balance is $77.78, mοnthly payment is $175, and ending balance is $4389.72.
What is annual interest rate?Annual interest rate is the amοunt οf interest that is charged οn a lοan οr investment per year, expressed as a percentage οf the amοunt bοrrοwed οr invested.
Tο cοmplete the table, we can use the fοllοwing steps:
Fοr the first mοnth:
Priοr balance: $4900
Interest οn priοr balance: 1.75% οf $4900 = $85.75 (rοunded tο the nearest cent)
Mοnthly payment: $175
Ending balance: $4900 + $85.75 - $175 = $4710.75 (rοunded tο the nearest cent)
Fοr the secοnd mοnth:
Priοr balance: $4710.75
Interest οn priοr balance: 1.75% οf $4710.75 = $82.46 (rοunded tο the nearest cent)
Mοnthly payment: $175
Ending balance: $4710.75 + $82.46 - $175 = $4628.21 (rοunded tο the nearest cent)
Repeat the same prοcess fοr the next three mοnths:
Fοr the third mοnth, priοr balance is $4628.21, interest οn priοr balance is $80.89, mοnthly payment is $175, and ending balance is $4549.10.
Fοr the fοurth mοnth, priοr balance is $4549.10, interest οn priοr balance is $79.34, mοnthly payment is $175, and ending balance is $4469.69.
Fοr the fifth mοnth, priοr balance is $4469.69, interest οn priοr balance is $77.78, mοnthly payment is $175, and ending balance is $4389.72.
Mοnth Priοr Balance Interest Mοnthly Ending
οn Payment Balance
Priοr Balance
1 $4900 $85.75 $175 $4710.75
2 $4710.75 $82.46 $175 $4628.21
3 $4628.21 $80.89 $175 $4549.10
4 $4549.10 $79.34 $175 $4469.69
5 $4469.69 $77.78 $175 $4389.72
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If A is True, and B is True, what is C
Answers
Answer: True
Step-by-step explanation: That was a complete guess. Did you forget to include an image? Am I missing something?
Determine the circumference of the base of the tin?
Answers
By answering the given question, we may state that We can apply the formula if we know the radius: C = 2πr where the radius r is.
what is diameter?In geometry, a circle's diameter is any straight line segment whose endpoint is on the circle and which passes through its centre. Another name for it is the circle's longest chord. The diameter of a sphere can be defined using either idea. The diameter is the length of the line perpendicular to the two points at either end of the circle. If you think of length as the distance between two points, then diameter is length. The diameter of a circle is the separation between its two farthest points.
We must know the base's diameter or radius in order to calculate the circumference of the tin.
If we know the diameter, we can apply the following formula to determine the circle's circumference:
C = πd
where d is the diameter and C is the circumference.
We can apply the formula if we know the radius:
C = 2πr
where the radius r is.
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please help me i really need this
Answers
Answer:
The area is given by the expreesion:
A = 5f + 10
Step-by-step explanation:
Notice the height of the shaded area is 5. But the base is the difference between f+9 and 7
So the length of the shaded area will be f+9-7=f+2
then the area of a rectangle is given by A=height*length
This is
A = 5 (f+2) = 5f+10
Question: Write an expression for the area shaded section of this rectangle. Expand your brackets
The area of shaded section is 5f+10
To calculate the area of the rectangle, it is known that just multiply the measurement of the height by the length.
So, to calculate the value of the area of this rectangle considering that the shaded area is part of it, we would do [tex]\sf f+9\times5[/tex].
The area of the shaded section will be given by the difference between the area of the shaded area and the unshaded area.
That is, [tex]\sf(f+9-7)\times5[/tex]
Let's calculate[tex]\begin{array}{l}\sf(f+9-7)\times5\\\sf(f+2)\times5\\\sf 5f+2\times5\\\therefore \bf 5f+10\end{array}[/tex]
5f+10 is the shaded section area expression
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solve for the value of a
( pls help i dont get this at all)
Answers
Answer:
Given that
(5a+6 )°+90°+(7a)°=180°
(angles on a straight line sum up to 180°)
5a°+6°+90°+7a°=180°
5a°+7a°=(180-96)°
12a°=84°
Deviding both sides by 12° gives
a=84/12
a=7°
therefore the value of
a=7°
Solve question
answer is csca+seca
Show the steps
Answers
The solution to the trigonometric expression is given as follows:
sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = csc(x) + sec(x).
How to solve the trigonometric expression?The trigonometric expression for this problem is defined as follows:
sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)).
The tangent and the cotangent are represented as follows:
tan(x) = sin(x)/cos(x).cot(x) = cos(x)/sin(x).Hence:
sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = sin(x)[1 + sin(x)/cos(x)] + cos(x)[1 + cos(x)cot(x)]
sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = sin(x)+sin²(x)/cos(x) + cos(x) + cos²(x)/sin(x)
sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = [sin²(x)cos(x) + sin³(x) + sin(x)cos²(x) + cos³(x)]/(sin(x)cos(x))
sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = csc(x) + sec(x).
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not any where else...... solve the equation for x: (x-4)-(x+7)=8
Answers
Answer:
(x-4)-(x+7)=8 is x = -19
Step-by-step explanation:
To solve the equation for x, we need to simplify the left-hand side by combining the like terms:
(x-4)-(x+7)=8
x - 4 - x - 7 = 8 (distribute the negative sign)
-x - 11 = 8 (combine like terms)
To isolate x, we need to get rid of the constant term on the left-hand side. We can do this by adding 11 to both sides:
-x - 11 + 11 = 8 + 11
-x = 19
Finally, we can solve for x by multiplying both sides by -1:
x = -19
Therefore, the solution for the equation (x-4)-(x+7)=8 is x = -19.
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 0\le x \le 150≤x≤15.
x f(x)
0 9
3 39
6 69
9 99
12 129
15 159
Answers
So the average rate of change of the function over the interval 0 ≤ x ≤ 15 is 4.4.
What is function?In mathematics, a function is a relationship between two sets of numbers, where each input in the first set (called the domain) corresponds to exactly one output in the second set (called the range). In other words, a function takes an input, performs a specific operation on it, and produces an output. A function is usually denoted by a symbol (often a letter) and is defined by a rule that specifies how to calculate the output value for any given input value.
Here,
To find the average rate of change of the function over the interval 0 ≤ x ≤ 15, we need to calculate the change in the function value divided by the change in x over the interval.
The change in the function value over the interval is f(15) - f(0), which is 159 - 93 = 66.
The change in x over the interval is 15 - 0 = 15.
Therefore, the average rate of change of the function over the interval 0 ≤ x ≤ 15 is:
average rate of change = change in f / change in x
= 66 / 15
= 4.4
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Jayla is training for the Seaview sprint race she runs the same route in her neighborhood every day and she makes her go on 80% of the time she plans to run every day for the next 10 days how likely that will she make her goal every day
Answers
If Jayla makes her goal 80% of the time, we can say that she has a probability of 0.8 of achieving her goal on any given day.
The probability of Jayla making her goal every day for the next 10 days can be calculated by multiplying the probability of her achieving her goal on each day.
Assuming each day's result is independent of the previous day, the probability of Jayla making her goal every day for the next 10 days is:
0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 = 0.1073741824
So, there is approximately a 10.7% chance that Jayla will make her goal every day for the next 10 days.
Please help with this pls
Answers
Answer:
Step-by-step explanation:
its c
Justin flips a coin and rolls a number cube with sides labeled 1, 2, 3, 4, 5, and 6. He repeats this experiment 40 times. How many times would you expect him to flip tails and roll an even number?
Answers
You expect him to flip tails and roll an even number 10 times
How many times would you expect him to flip tails and roll an even number?From the question, we have the following parameters that can be used in our computation:
Sample space 1 = 1, 2, 3, 4, 5, 6
Sample space 2 = H, T
Using the above as a guide, we have the following:
P(Even) = 3/6
P(Tail) = 1/2
So, we have
P(Even and Tail) = 3/6 * 1/2
P(Even and Tail) = 1/4
In 40 times, we have
Expected = 1/4 * 40
Expected = 10
Hence, the number of times is 10
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What is the exact circumference of the circle?
Answers
Answer: The circumference would be 62.83
Step-by-step explanation:
C=2πr=2·π·10≈62.83185
Margo borrows $1500, agreeing to pay it back with 6% annual interest after 6 months. How much interest will she pay?
Answers
Answer:
Step-by-step explanation:
1,500 times 0.06 = 90
90 divided by 2 = 45
What are the coordinates of the point on the directed line segment from (-6,4) to
(9,-8) that partitions the segment into a ratio of 5 to 1?
Answers
The required point's coordinates are (0,3).
What is an equation?A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.
It demonstrates the equality of the relationship between the printed statements on the left and right.
Left side equals right side in all formulas.
To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.
A statement is not an equation if it lacks the equals sign. When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.
Hence, The required point's coordinates are (0,3).
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Find the radius r………………………..
Answers
Answer:
r = 3
Step-by-step explanation:
Pythagoras' theorem states that for all right-angled triangles, 'The square on the hypotenuse is equal to the sum of the squares on the other two sides.
AO^2 = AB^2 + BO^2
(2 + r)^2 = 4^2 + r^2
r^2 + 4r + 4 = 16 + r^2
4r = 12
r = 12/4
r = 3
Need help with math
Answers
C=2πr
2(3.14x7) = 43.96
C. 14 πcm = 14x3.14 = 43.96
Answer:
to find are u need to do it this way: pie r sqare
Step-by-step explanation:
22/7x7x7
22/7 x49
cut 7 and 49
1 and 7
22/1x7
=22x7
=154
Five lemonades and two cookles cost $1.50. Two lemonades and five cookles cost $2.70. How much does one cookle and one lemonade cost?
Answers
Answer:
50¢/cookie, $1.00/lemonade
Step-by-step explanation:
Let l = cost of one lemonade
c = cost of one cookie
We have:
5l + 2c = 1.50 -------> 10l + 4c = 3.00
2l + 5c = 2.70 -------> 10l + 25c = 13.50
-----------------------
21c = 10.50
c = .50
5l + 2(.50) = 1.50
5l + 1.00 = 1.50
5l = 5, so l = 1.00
Each cookie costs 50¢, and each lemonade costs $1.00.
(b) Find the costs of supplying bins to 10%, 50%, and 85% of the
cost to supply 10%
C = $
X
cost to supply 50%
C = $25,000
cost to supply 85%
C = $ 141,667
Answers
Answer:
To find the cost of supplying bins to 10%, 50%, and 85% of the cost to supply 10%, we can use proportional reasoning.
Let X be the cost to supply 10%. Then:
The cost to supply 50% is 5 times the cost to supply 10%, so it is 5X.
The cost to supply 85% is 8.5 times the cost to supply 10%, so it is 8.5X.
The cost to supply 10% is X.
To find the cost of supplying bins to 10%, 50%, and 85% of the cost to supply 10%, we can substitute X = $1 and multiply by the appropriate percentages:
The cost to supply bins to 10% of the cost to supply 10% is 0.1 * X = 0.1 * $1 = $0.10.
The cost to supply bins to 50% of the cost to supply 10% is 0.5 * X = 0.5 * $1 = $0.50.
The cost to supply bins to 85% of the cost to supply 10% is 0.85 * X = 0.85 * $1 = $0.85.
Therefore, the costs of supplying bins to 10%, 50%, and 85% of the cost to supply 10% are $0.10, $0.50, and $0.85, respectively.
Answer:
Let the cost to supply 10% of the bins be X dollars.
To find the cost of supplying bins to 50% of the cost to supply 10%, we can set up the following proportion:
10% of the cost = X dollars
50% of the cost = Y dollars
We know that the two costs are proportional, so we can set up the following equation:
10% / 50% = X / Y
Simplifying this equation, we get:
0.1 / 0.5 = X / Y
0.2 = X / Y
Multiplying both sides by Y, we get:
Y * 0.2 = X
Y = X / 0.2
Y = 5X
Therefore, the cost of supplying bins to 50% of the cost to supply 10% is 5 times the cost of supplying bins to 10%.
Substituting X = C/10 (where C is the cost to supply 10% of the bins), we get:
Y = 5X = 5(C/10) = C/2
So the cost of supplying bins to 50% of the cost to supply 10% is C/2 dollars.
To find the cost of supplying bins to 85% of the cost to supply 10%, we can set up a similar proportion:
10% of the cost = X dollars
85% of the cost = Z dollars
We know that the two costs are proportional, so we can set up the following equation:
10% / 85% = X / Z
Simplifying this equation, we get:
0.1 / 0.85 = X / Z
0.1176 = X / Z
Multiplying both sides by Z, we get:
Z * 0.1176 = X
Z = X / 0.1176
Z = 8.5X
Therefore, the cost of supplying bins to 85% of the cost to supply 10% is 8.5 times the cost of supplying bins to 10%.
Substituting X = C/10 (where C is the cost to supply 10% of the bins), we get:
Z = 8.5X = 8.5(C/10) = 0.85C
So the cost of supplying bins to 85% of the cost to supply 10% is 85% of the cost to supply 10%, or 0.85C dollars.
Therefore, the costs of supplying bins to 10%, 50%, and 85% of the cost to supply 10% are:
- 10% of the cost: X dollars = C/10 dollars
- 50% of the cost: Y dollars = C/2 dollars
- 85% of the cost: Z dollars = 0.85C dollars
Please help me
Simplify this expression:
(In picture)
Answers
The simplified expression for given expression is x⁷/y¹⁰.
What is simplication of a expression?Simplification means reducing the expression in a simpler form using various operations while Approximation is simplifying the mathematical expression to its nearest value but not exactly correct.
Equation:To simplify the expression:
x³y⁻²x/x⁻³y⁸
Applying the properties, we get:
x³y⁻²x/x⁻³y⁸ = x⁽³⁻⁽⁻¹⁾⁾y⁽⁻²⁻⁸⁾/x⁻³x¹y⁰
Simplifying the exponents and the term with y, we get:
x⁴/y¹⁰ * x³ = x⁽⁴⁺³⁾/y¹⁰ = x⁷/y¹⁰
Therefore, the simplified expression is x⁷/y¹⁰.
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What describes this polygon?
A) Quadrilateral
B) Pentagon
C) Parallelogram
D) Hexagon
Answers
Factor the expression
ax+ay+az +3x+3y+3z
Answers
We can factor it by grouping.
=> ax+ay+az+3x+3y+3z
=> (ax+ay+az)+(3x+3y+3z)
=> a(x+y+z)+3(x+y+z)
=> (a+3)(x+y+z)
Thus, the given expression factored is (a+3)(x+y+z).
An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times the commercial is run on TV in each city and the number of car sales (in hundreds). Find the linear regression line for the data given in the table. Round any intermediate calculations to no less than six decimal places, and round the coefficients to two decimal places.
Number of TV commercials, x 3
5
11
16
19
Car sales, y (in hundreds) 2
3
8
9
6
Answers
According to the given problem, the linear regression line for the given data is y = -0.65 + 0.26x
What is linear regression?
Linear regression is a statistical method used to find the relationship between a dependent variable (y) and one or more independent variables (x). It assumes that there is a linear relationship between the variables, meaning that changes in the independent variable(s) are associated with proportional changes in the dependent variable.
The linear regression model can be represented as a straight-line equation:
y = b0 + b1*x + e
The equation of a linear regression line can be written as:
y = b0 + b1*x
where y is the dependent variable (car sales in this case), x is the independent variable (number of TV commercials), b0 is the intercept, and b1 is the slope of the line.
To find the values of b0 and b1, we need to calculate the following:
n = number of data points = 4
Σx = sum of x values = 54
Σy = sum of y values = 28
Σxy = sum of (x*y) values = 164
Σx^2 = sum of (x^2) values = 689
Using these values, we can calculate b1:
b1 = (nΣxy - ΣxΣy) / (n*Σx^2 - Σx^2)
b1 = (4164 - 5428) / (4*689 - 54^2)
b1 = 0.26 (rounded to two decimal places)
Next, we can use b1 to calculate b0:
b0 = (Σy - b1*Σx) / n
b0 = (28 - 0.26*54) / 4
b0 = -0.65 (rounded to two decimal places)
Therefore, the linear regression line for the given data is:
y = -0.65 + 0.26x
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write a mathematical sentence which relates to a real life scenario in business
Answers
Answer:
The profit (P) of a company is equal to the revenue (R) minus the cost (C): P = R - C.
Step-by-step explanation: