$495 was shared amongst 3 friends in the ratio of 3:7:10, find the sum of money shared

Answer: x=12

Step-by-step explanation:

Answer:

  x=1

Step-by-step explanation:

The equation can be simplified and solved using the rules of exponents and the usual inverse operations.

__

Interpreted according to the Order of Operations, your equation is ...

  ((2^2)x)^3 = 64

  (4x)^3 = 64x^3 = 64 . . . . . . use (ab)^c = (a^c)(b^c)

  x^3 = 1 . . . . . . . . . . . . . . divide by 64

  x = ∛1 = 1

__

Perhaps you want x in the exponent:

  (2^(2x))^3 = 64

  2^(6x) = 2^6 . . . . . . . . . use (a^b)^c = a^(bc)

  6x = 6 . . . . . . . . match exponents

  x = 1 . . . . . . divide by 6

_____

Additional comment

Folks are often not careful about identifying exponents. It is helpful if you write the exponent in a way that leaves no ambiguity.

Answer:

Does the answer help you?

If the common difference is 2, then the sum of the first 8 terms is 88 and If the common difference is 3, then the sum of the first 8 terms is 116.

To find the sum of the first 8 terms of the sequence, we need to identify a pattern in the sequence so that we can find the 8th term and then use the formula for the sum of the first n terms of an arithmetic sequence.

Looking at the given sequence, we can see that each term is increasing by a certain amount. To find that amount, we can subtract consecutive terms:

6 - 4 = 2

9 - 6 = 3

So, the sequence has a common difference of 2 or 3. Since we have only three terms, it is not clear which of the two is the correct common difference. Therefore, we will assume both and calculate the sum for each.

If the common difference is 2, then the 8th term is:

\(a_{8}\) = \(a_{1}\) + 7d = 4 + 7(2) = 18

If the common difference is 3, then the 8th term is:

\(a_{8}\) = \(a_{1}\) + 7d = 4 + 7(3) = 25

Now, we can use the formula for the sum of the first n terms of an arithmetic sequence:

\(S_{n}\) = n/2(\(a_{1}\) + \(a_{n}\))

If the common difference is 2, then:

\(S_{8}\) = 8/2(4 + 18) = 88

If the common difference is 3, then:

\(S_{8}\) = 8/2(4 + 25) = 116

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The upper control limit for the 3 standard deviation chart is approximately 10.53%. Any sample percentage above this value should be investigated for potential problems with the drilled holes.

To calculate the upper control limit for a 3-standard deviation chart, we first need to find the overall average and standard deviation of the sample percentages. The overall average is simply the average of the sample percentages:

Overall average = (2.0 + 7.0 + 5.0 + 3.0 + 4.0) / 5 = 4.2%

To find the overall standard deviation, we first need to calculate the sample standard deviations:

sample 1: s1 = sqrt(2.0*(1-2.0/100))

sample 2: s2 = sqrt(7.0*(1-7.0/100))

sample 3: s3 = sqrt(5.0*(1-5.0/100))

sample 4: s4 = sqrt(3.0*(1-3.0/100))

sample 5: s5 = sqrt(4.0*(1-4.0/100))

Using a calculator or spreadsheet, we can calculate these to be:

s1 ≈ 1.398

s2 ≈ 2.449

s3 ≈ 2.108

s4 ≈ 1.673

s5 ≈ 1.936

Next, we need to calculate the average of the sample standard deviations, which is called the average range:

average range = (s1 + s2 + s3 + s4 + s5) / 5 ≈ 2.113

Finally, we can calculate the upper control limit using the formula:

upper control limit = overall average + 3 * average range

upper control limit = 4.2% + 3 * 2.113% ≈ 10.53%

Therefore, the upper control limit for the 3 standard deviation chart is approximately 10.53%. Any sample percentage above this value should be investigated for potential problems with the drilled holes.

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Answer: 41.5692

Hope I helped :)

At Maryland, the mean number of points per player per game is greater than the median number of points per player per game. The mean number of points per player per game is the same at all 3 schools.

Given that in Baylor's University that there are 6 players who each score 12 points per game, and 6 players who each score 0 points per game.

The scores are 0, 0, 0, 0, 0, 0, 12, 12, 12, 12, 12, 12.

Mean = Sum/Count = 72/12 = 6.

Median is the average between the nth  and (n+1)th  term.

(0+ 12)/2 = 6

In Maryland university 1 player scores 58 points per game, 1 player scores 14 points per game, and the rest of the 10 score 0 points per game,

58, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Mean = Sum/Count = 72/12 = 6.

Median is 0

In Dartmouth, university, 4 players score 5 points per game, 4 players score 6 points per game, 4 players score 7 points per game.

The scores are

5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7

Mean = Sum/Count = 72/12 = 6

Median =(6+6)/2= 6

​

At Maryland, the mean number of points per player per game is greater than the median number of points per player per game.

The mean number of points per player per game is the same at all 3 schools.

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Step-by-step explanation:

I hope this answer is helpful ):

To answer these questions, we need to use the formula for the uniform distribution, which is:
f(x) = 1/(b-a)
where a is the lower bound of the distribution and b is the upper bound.

a. To find the probability that a randomly selected videotape will be returned between 3 and 4 days late, we need to calculate the area under the curve between 3 and 4 on the x-axis. Since the uniform distribution is a rectangle, the area of the rectangle is equal to the height times the width. In this case, the height is f(x) = 1/(4-0) = 0.25 and the width is 4-3 = 1. Therefore, the probability is:
P(3 ≤ x ≤ 4) = height × width = 0.25 × 1 = 0.25
So the answer is 0.25.

b. To find the probability that a randomly selected videotape will be returned more than 1 day late, we need to calculate the area under the curve to the right of 1 on the x-axis. Since the distribution is uniform, the area to the right of 1 is equal to the width of the rectangle from 1 to 4, which is 4-1 = 3. Therefore, the probability is:
P(x > 1) = 3/(4-0) = 0.75

So the answer is 0.75.
In summary, the probability that a randomly selected videotape will be returned between 3 and 4 days late is 0.25, and the probability that a randomly selected videotape will be returned more than 1 day late is 0.75.

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Answer:

The answer is almost certainly 5 years. People might, however, pursue a Master of Architecture degree, which takes two to three years to accomplish.

Step-by-step explanation:

Architecture is a five-year degree that requires a keen interest in the topic.  A five-year undergraduate architecture degree, known as a B. Arch., or a two- or three-year post-college master's program, known as an M. Arch., are the two alternatives for those who wish to get an architectural degree that will help them get licensed as an architect. You'll have to labor every day and night. Of course, your performance in class will have an impact. Some instructors may offer homework that are beyond your grasp and abilities. Everything you do must be carefully thought out, imagined, and built.

1. AABBCCDD: The probability of this happening is \(1/16\), since each parent would need to contribute a dominant allele for each gene.

2. AABBCcDD:  This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is  = 1/128.

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

3. The probability of this happening is 1/32.

AaBbCcDd : The probability of this happening is  1/256.

4. aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is  1/128.

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is  1/32.

To solve this problem, we need to use the principles of probability and Punnett squares.

For a tetrahybrid cross, we need to consider the four genes independently and combine the probabilities of each gene's alleles.

Assuming that A, B, C, and D are dominant alleles, and a, b, c, and d are recessive alleles, we can create a Punnett square for each gene, which would look like this:

A  |  A  |  a  |  a  

---|-----|-----|----

B  |  B  |  b  |  b  

---|-----|-----|----

C  |  C  |  c  |  c  

---|-----|-----|----

D  |  D  |  d  |  d  

Each box in the Punnett square represents a possible combination of alleles from the two parents.

For example, the top-left box represents offspring that inherit an A allele from the mother and an A allele from the father.

We can use these Punnett squares to calculate the probabilities of each genotype in the F2 offspring.

AABBCCDD - This genotype can only be produced if both parents are homozygous dominant for all four genes.

The probability of this happening is \((1/2)^4 = 1/16\) , since each parent would need to contribute a dominant allele for each gene.

AABBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128\)

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is\(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32\)

AaBbCcDd - This genotype can be produced in 16 ways, since each gene can be inherited in two different ways (dominant or recessive).

The probability of this happening is \((1/2)^8 = 1/256.\)

aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128.\)

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is \(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32.\)

Note that we have assumed independent assortment of the four genes, which means that the inheritance of one gene does not affect the inheritance of another gene.

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Answer:

(9, 5)

Step-by-step explanation:

subtract R off of midpoint (M) = (3, 1)

this is how long each side is, so add that to the midpoint M to find Q

6+3 = 9

4+1 = 5

Answer: the number of terms of the series is 201 numbers

              the sum of the first 20 terms is 890    

the number of terms of the series is \(\frac{805-5}{4}+1=201\)

the series have:

u1 = 5

d = 4

=> u(n) = 5 + 4.(n - 1)

=> u(20) = 5 + 19.4 = 81

so the sum of the first 20 terms is (81 + 5).20/2 = 890

( u1 is the first number of the series, d is the  distance between front and rear numbers, u(n) is the overall term of the sequence, u(20) is the 20th of the series)

Step-by-step explanation:

Answer:

m<1=115°(Alternative interior Angles)

Answer:

a cycle is a sequence of non-repeated vertices and the degree of a graph is the number of neighbors the vertex has.

After solving the given equations the answer is an Infinite solution. Hence, option A is correct

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

8 + 4x = 2x + 8 + 2x

Firstly, let's write the given equation in a simplified manner,

8 + 4x = 8 + 4x  

As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.

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Answer:

B. 3 by 12

Step-by-step explanation:

\(x(4x) = 36\)

\(4 {x}^{2} = 36\)

\( {x}^{2} = 9\)

\(x = 3\)

\(4x = 12\)

So the length is 12 inches, and the width is 3 inches.

(a) If f(x) is a convex function with x ∈ ℝⁿ, then all local minima of f(x) are also global minima. In other words, if there exists a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo, then f(x) ≥ f(xo) for all x ∈ ℝⁿ.

(b) A graph of a non-convex function can be visualized to understand why the statement in part (a) is not true. It will show a scenario where a local minimum is not a global minimum.

(a) To prove that all local minima of a convex function are also global minima, we can utilize the property of convexity. Suppose there is a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo. We assume that xo is a local minimum. Now, consider any arbitrary point x in ℝⁿ. We can express x as a convex combination of xo and another point y in the neighborhood, using the convexity property: x = λxo + (1 - λ)y, where λ is a scalar between 0 and 1. Using this expression, we can apply the convexity property of f(x) to get f(x) ≤ λf(xo) + (1 - λ)f(y). Since f(x) ≥ f(xo) for all x in the neighborhood, we have f(y) ≥ f(xo). Therefore, f(x) ≤ λf(xo) + (1 - λ)f(y) ≤ λf(xo) + (1 - λ)f(xo) = f(xo). This inequality holds for all λ between 0 and 1, implying that f(x) ≥ f(xo) for all x ∈ ℝⁿ, making xo a global minimum.

(b) A graph of a non-convex function can demonstrate a scenario where the statement in part (a) is not true. In such a graph, there may exist multiple local minima, but one or more of these local minima are not global minima. The non-convex nature of the function allows for the presence of multiple valleys and peaks, where one of the valleys may contain a local minimum that is not the overall lowest point on the graph. This occurs because the function may have other regions where the values are lower than the local minimum in consideration. By visually observing the graph, it becomes apparent that there are points outside the neighbourhood of the local minimum that have lower function values, violating the condition for a global minimum.

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Since y varies directly with x then

So,

Then, 1/4 is the constant of proportionality. So that,

If you measure 5 inches on the map, the actual distance would be 150 miles.

According to the legend on the map, 1 inch on the map represents 30 miles in actual distance.

If you measure 5 inches on the map, we can calculate the actual distance by multiplying it by the scale factor.

5 inches * 30 miles/inch = 150 miles.

Therefore, if you measure 5 inches on the map, the actual distance would be 150 miles.

The scale factor allows us to convert the measurements on the map to their corresponding real-world distances.

It is important to keep in mind the scale of the map when interpreting distances and sizes on it, as it provides a proportional representation of the real world at a reduced scale.

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Answer:

525

Step-by-step explanation:

Let the number be " x ".

1 / 5 of x is 105

x / 5 = 105

x = 105 x 5

x = 525

Therefore,

the number is 525.

Answer:

Step-by-step explanation:

1/5 of a number is 105, and the number is

105 * 5 = 525

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

check

525 * 1/5 = 105

the answer is good

You have the following operation:

6x9

To solve the previous operation you consider that the expression means 6 times 9, that is, that is the sum of six 9s:

6x9 = 9 + 9 + 9 + 9 + 9 + 9 = 54

Hence, the simplied operation is 6x9 = 54

Answer:

y = -3x - 4

Step-by-step explanation:

y = mx + b

-10 = -3 (2) + b

-10 = -6 + b

b = -4

Answer:

6 people

Step-by-step explanation:

take the 18 and divide it by three because this will help you solve for one car so 18 divided by three is six

Answer: x=4

Step-by-step explanation: 5x-2x-2=10

3x-2=10

Add 2 to both sides

3x=12

divide both sides by 3

x=4

Answer:

it has a slope of 1/3 and a point on the graph is (2,-3)

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:  d=\(\sqrt{x1-x2)2+(y1-y2)2}\)

Step-by-step explanation:

Answer:

t=d/v

Step-by-step explanation:

v=d/t

vt=d

t=d/v

Answer:

$19.50

Step-by-step explanation:

(26÷100)75=19.50

Answer:

549 ft

Step-by-step explanation:

take 670ft away from 1,220 ft ( not all the way sure of I'm right)

Answer:

550

Step-by-step explanation:

1,220+(-670)= 550

Thank you! :)