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Answer:

Percent air is calculated as:

Solve for total amount of air:

Substitute the values in hand to get the answer

Answer: 4-4z

Step-by-step explanation: Coming the like terms in order to simplify the equation. There are four z's and they combine as they are like terms. Since we don't know the value of z, thats the most simplified form.

Answer:

Don't know if i did it right but i think it is:

a=14

b=6

c=5

The average cost function is C(x) = 5000x + 20,000/x, where x is the number of machines used in the production. The critical value is C(x) = 20,000 and it happens when x = 2.

If we have a function f(x), the critical point happens when its first derivative is equal to zero.

             f '(x) = 0

In the given problem, the function is:

C(x) = 5000x + 20,000/x

Take the derivative:

C '(x) = 5000 - 20,000/x² = 0

5000 x² = 20,000

x² = 4

x = ±2

Since x is within the interval: 0<x<∞, the solution is x = 2

Substitute x = 2 into the function:

C(2) = 5000 (2) + 20000/2

C(2) = 10000 + 10000 = 20,000

Hence, the critical value is C(x) = 20,000 and it happens when x = 2.

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Answer:

x = -8

Step-by-step explanation:

Add 12 on both sides

You get 3/4x = -6

Multiply 4/3 on both sides

You get x = -24/3

Simplify and you get -8.

Answer:

x=-8

Step-by-step explanation:

The reason why x is -8 is because

The first step is to isolate the x

To isolate the x you got to add 12 to both sides

\(\frac{3}{4}\)x-12+12=-18+12

the -12 gets canceled out by the positive twelve so all thats left now is

\(\frac{3}{4}\)x=-18+12,-18+12 is -6 so its  \(\frac{3}{4}\)x=-6

The second step is to divide

now you have to divide by \(\frac{3}{4}\) on both sides

\(\frac{\frac{3}{4} x}{\frac{3}4} } =\frac{-6}{\frac{3}{4} }\)

which \(\frac{3}{4}\) is taken out on the left side because its divided by itself so all thats left is a one,while on the right side -6 divided by three-fourths is -8

Answer:

18

Step-by-step explanation:

168 : 28 : : 108 : y

168 / 28 = 108 / y

6 = 108 / y

6 * y = 108

y = 108 / 6

y = 18

Answer:

y = 18

Step-by-step explanation:

Given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 28 when x = 168

28 = 168k ( divide both sides by 168 )

\(\frac{28}{168}\) = k , that is

k = \(\frac{1}{6}\)

y = \(\frac{1}{6}\) x ← equation of variation

When x = 108 , then

y = \(\frac{1}{6}\) × 108 = 18

Answer: 6*4 or 8*3

Step-by-step explanation:

12^2=24

Answer:

125.6 cubic inches

Step-by-step explanation:

The formula for volume of a cylinder is:

\(V = \pi r^2h\)

---------------------------------------------------------------------------------------------------------------

So:

\(\pi\) × 4 × 10 = 125.6

---------------------------------------------------------------------------------------------------------------

Have a good day :)

The simply supported reinforced concrete beam with the given specifications can safely carry the applied load. The beam section, size, and reinforcement details are sufficient to withstand the imposed loads without exceeding the allowable stress limits.

To determine the beam's safety, we need to calculate the maximum bending moment (M) and the required area of steel reinforcement (As). The maximum bending moment occurs at the center of the span and can be calculated using the formula M = (wL²)/8, where w is the total distributed load and L is the span length.

Substituting the given values, we find

M = (9.8kN/m + 3.2kN/m) × (4m)² / 8

M = 22.4kNm.

To calculate the required area of steel reinforcement, we use the formula As = (M × \(10^6\)) / (0.87 × fy × d), where fy is the yield strength of the steel, d is the effective depth of the beam, and 0.87 is a factor accounting for the partial safety of the material. The effective depth can be calculated as d = h - c - φ/2, where h is the total depth of the beam, c is the cover, and φ is the diameter of the reinforcing bars.

Substituting the given values, we have

d = 350mm - 60mm - 20mm/2

d = 320mm. Plugging these values into the reinforcement formula, we get As = (22.4kNm × \(10^6\)) / (0.87 × 375MPa × 320mm)

As ≈ 0.2357m².

Comparing the required area of steel reinforcement (0.2357m²) to the provided area of steel reinforcement (3 bars with a diameter of 20mm each, which corresponds to an area of 0.0942m²), we can see that the provided reinforcement is greater than the required reinforcement. Therefore, the beam is adequately reinforced and can safely carry the applied loads.

In summary, the given reinforced concrete beam with a span of 4m, subjected to a dead load of 9.8kN/m and a live load of 3.2kN/m, is safely able to carry the applied loads. The beam's section and reinforcement details meet the necessary requirements to withstand the imposed loads without exceeding the allowable stress limits. The calculations indicate that the provided steel reinforcement is greater than the required reinforcement, ensuring the beam's stability and strength.

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Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.

In the given question,

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base, h is the height, and π is approximately 3.14.

Substituting the given values, we get:

V = (1/3) × 3.14 × 3² × 3.8

V ≈ 35.63

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

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Answer:

The answer you're looking for is 1470.

Step-by-step explanation:

The method I used was PEMDAS

Since there was no parenthesis, I simplified the exponents.

2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?

After that, I multiplied all terms next to each other.

2.130 x 1000 - 6.6 x 100 = ?
2130 - 660 = ?

The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.

1470 = ?

I hope this was helpful!

The probability of having every bin filled with at least one ball if n balls are distributed randomly into m bins is given by the formula 1 - (m-1/m)^n.

Let's break it down step-by-step:

Step 1: Probability of a ball being put into a specific Bin Since there are m bins, the probability of a ball being put into a specific bin is 1/m. Therefore, the probability of a ball not being put into that bin is (m-1)/m.

Step 2: Probability of a ball not being put into a specific Bin Since there are m bins, the probability of a ball not being put into a specific bin is (m-1)/m. Therefore, the probability of a ball being put into that bin is 1/m.

Step 3: Probability of every bin being filled with at least one ball Using the above two probabilities, the probability of a specific bin not being filled with a ball is (m-1)/m. Therefore, the probability of all m bins not being filled with a ball is (m-1/m)^n. Finally, the probability of every bin being filled with at least one ball is 1 - (m-1/m)^n.

Therefore, the probability of having every bin filled with at least one ball if n balls are distributed randomly in to m bins is given by the formula 1 - (m-1/m)^n.

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By factoring out this common factor, we obtain the simplified expression 0.006(25c - 12).

We can start by determining the common factor between the two terms in order to factor the phrase 0.15c - 0.072. The common factor in this situation is 0.006, which we may factor out to obtain:

0.15c - 0.072 = 0.006(25c - 12) (25c - 12)

As a result, factoring the expression 0.15c - 0.072 gives 0.006 (25c - 12).

It is possible to utilise this factored form to further simplify calculations or to resolve equations that contain this statement. If we needed to find c in the equation 0.15c - 0.072 = 0, for instance, we could use the factored form to obtain:

0.006(25c - 12) = 0

25c - 12 = 0

c = 12/25

In conclusion, factoring the expression 0.15c - 0.072 involves finding the common factor between the two terms, which is 0.006. By factoring out this common factor, we obtain the simplified expression 0.006(25c - 12).

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Answer:

50.24

Step-by-step explanation:

a=(pi)r²

A =(pi)4²

A = 50.27

but I used the actual pi if you use 3.14 I think you'll get 50.24 but that's the closest answer.

Hope you get it right

Answer:

8.5

Step-by-step explanation:

this is a right triangle so we could use the formula, which is Pythagorean theorem

so it is \(13.5^{2} -10.5^{2} =72\\\sqrt{72} =8.5\)

Answer:

$305.9022863 or $305.90 (rounded to 2 decimal places)

Step-by-step explanation:

It is a compound interest, meaning an interest accumulates on an initial amount every period. The formula  

A= P(1+R)^n

A= the total amount P=Initial amount       R= rate  n=time period

P=$100 R=15% or 0.15(decimal)  n=8 (years)  

A= 100 (1.15)^8

A= 100(3.059022863)

A=305.9022863

The amount you will have after 8 years is $220

The formula for calculating simple interest is expressed as:

SI =PRT

P is the principal = $100

T is the time = 8 years

R is the rate. = 15%

SI = 100 * 8 * 0.15
SI = $120

Amount after 8years = $100 + $120
Amount after 8years = $220

Hence the amount you will have after 8 years is $220

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The estimate for the sum of the numbers is 230, and the actual sum of the numbers is 209.

To estimate the sum of the numbers, we can round each number to the nearest ten and then add them together. When rounding off to the nearest tens, we look at the number at the tenth position. If it is five and above, we round it off to the next nearest tens number and if it is below five, we round it off to the previous nearest tens number.

76 rounds to 80   since 6 is above 5
6 rounds to 10 since 6 is above 5
25 rounds to 30 since 5 is located at 5 and above interval
5 rounds to 10 since 5 is located at 5 and above interval
10 rounds to 10 since 0 is below 5
87 rounds to 90 since 7 is above 5

So, the estimate for the sum of the numbers is: 80 + 10 + 30 + 10 + 10 + 90 = 230

To find the actual sum of the numbers, we simply add them together without rounding:

76 + 6 + 25 + 5 + 10 + 87 = 209

The complete question is: 76. 6 25. 5 10. 87 =

What was Sela's estimate and what is the actual sum of the number?

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Step-by-step explanation: i dont have an explenation but i think its 2

Answer:

The correct answer is the "≥" sign.

Step-by-step explanation:

We know that the team must score at least 8 goals. This means, that they can earn 8 goals or more. The greater than or equal to sign means that the team can win either exactly 8 goals, or more than 8 goals.

Hope this helps! :D

Answer:

31/32 or 0.96875

Step-by-step explanation:

first you muliply 5/8 by 3/4 then the answer add it to 1/2

Answer:

Explanation:

The slope of the given line is 3/2

A line parallel to this has the same line but different y-intercept.

IIn point-slope form, it is:

Where

Using these, we have:

we are given a ring homomorphism f: R → R' between commutative rings R and R'. We need to show that if P is a prime ideal of R' and f^(-1)(P) ≠ R, then the ideal f^(-1)(P) is a prime ideal of R.

To prove this, we first note that f^(-1)(P) is an ideal of R since it is the preimage of an ideal under a ring homomorphism. We need to show two properties of this ideal: (1) it is non-empty, and (2) it is closed under multiplication.

Since f^(-1)(P) ≠ R, there exists an element a in R such that f(a) is not in P. This means that a is in f^(-1)(P), satisfying the non-empty property.

Now, let x and y be elements in R such that their product xy is in f^(-1)(P). We want to show that at least one of x or y is in f^(-1)(P). Since xy is in f^(-1)(P), we have f(xy) = f(x)f(y) in P. Since P is a prime ideal, this implies that either f(x) or f(y) is in P.

Without loss of generality, assume f(x) is in P. Then, x is in f^(-1)(P), satisfying the closure under multiplication property.

Hence, we have shown that f^(-1)(P) is a prime ideal of R, as desired.

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Answer:

y=-2x+5

Step-by-step explanation:

x-2y=2

2y=x-2

y=(x-2)/2

so the slope is 1/2

for lines to be perpendicular m1m2=-1 so the line must have a slope satisfying the condition

(1/2)m=-1

m=-2

the only line with a slope of -2

If is wrong i'm sorry

Answer:

Function 2, because Steve spends $5 each week and Ada spends $4 each week

Step-by-step explanation:

Function 1 shows a rate of change of using two points

(x1, y1) = (40,1)

(x2,y2) = (36,2)

m = (y2-y1)/(x2-x1) = (36-40)/(2-1) = -4

The rate of change is decreasing or spending at $4 per week

Function 2 shows an equation y=mx+b; where m is the slope or the rate of change

m=-5

The rate of change is decreasing or spending at $5 per week

Answer: its C

Function 2, because Steve spends $5 each week and Ada spends $4 each week

:

Answer:

\(x=-\frac{17}{28}\)

Step-by-step explanation:

\(\frac{1}{4}(4x-1)=-\frac{1}{7}-\frac{5}{7}\)

\(x-\frac{1}{4}=-\frac{6}{7}\)

\(x = -\frac{6}{7} + \frac{1}{4}\)

\(x = -\frac{17}{28}\)

plug \(x\) in the equation to make sure of your answer:

\(\frac{1}{4}(4x-1)=-\frac{1}{7}-\frac{5}{7}\\\frac{1}{4}(4(-\frac{17}{28}) -1)=-\frac{1}{7}-\frac{5}{7}\\-\frac{17}{28} -\frac{1}{4}=-\frac{6}{7}\\-\frac{6}{7}=-\frac{6}{7}\)

Answer:

-1/2

Step-by-step explanation:

lim x-> π/2 cos x /(2x-π) =

lim (x-π/2)->0 sin (π/2 - x) /2(x-π/2) =

lim (x-π/2)->0 - sin (x - π/2)/2(x-π/2) = -1/2

Answer:

3/10

To simplify a fraction, you need to find the  GCF (greatest common factor) between both numbers. The GCF between 9 and 30 is 3

9/10 divide by 3/3 is 3/10

Step-by-step explanation:

Hope this helps!! Mark me brainliest!!

Answer:

\(\frac{3}{10}\)

Hope this helps :)

Step-by-step explanation:

To simplify any fraction, you must first find the GCF of the numerator and denominator

9: 1, 3, 9

30: 1, 2, 3, 5, 6, 10, 15, 30

Both of them are divisible by three so we just have to divide the numerator by three and the denominator by three and we'll find our answer:

9/3 = 3

30/3 = 10

The new fraction is:

\(\frac{3}{10}\)

The distance between the two spheres is 6 - √5 units.

To find the distance between the spheres x² + y² + z² = 4 and x² + y² + z² = 8x + 8y + 8z - 47, first rewrite the second equation:

x² - 8x + y² - 8y + z² - 8z = -43

Now, complete the squares for x, y, and z terms:

(x - 4)² - 16 + (y - 4)² - 16 + (z - 4)² - 16 = -43

Combine the constants:

(x - 4)² + (y - 4)² + (z - 4)² = 5

Now, we have two spheres with centers (0, 0, 0) and (4, 4, 4) and radii 2 (from √4) and √5 (from √5), respectively. To find the distance between the spheres, subtract their radii from the distance between their centers:

Distance = √[(4 - 0)² + (4 - 0)² + (4 - 0)²] - 2 - √5
Distance = √(64) - 2 - √5
Distance = 8 - 2 - √5

So, the distance between the two spheres is 6 - √5 units.

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Answer:

11/12

Step-by-step explanation: