If Alex and Brandon work together, they will finish cleaning the school in 15 hours. Working alone, Brandon can finish the same job in 20 hours. How long will it take Alex to do the job by himself?

Answer:

The cost of 1 eraser is $0.07.

Step-by-step explanation:

Given:

The school store sells erasers. If Mrs. McBryde purchases 1000 erasers for $70.00,

Now, to find the cost of 1 eraser.

Let the cost of 1 eraser be [tex]x.[/tex]

The cost of 1000 erasers is $70.00.

So, 1000 is equivalent to $70.00.

Thus, 1 is equivalent to [tex]x.[/tex]

Now, to solve by using cross multiplication method:

[tex]\frac{1000}{70} =\frac{1}{x}[/tex]

By cross multiplying we get:

[tex]1000x=70[/tex]

Dividing both sides by 1000 we get:

[tex]x=\$0.07.[/tex]

Therefore, the cost of 1 eraser is $0.07.

Final answer:

The cost of one eraser is found by dividing the total cost of $70.00 by the number of erasers purchased, which is 1000, resulting in a cost of $0.07 per eraser.

Explanation:

To find the cost of one eraser, we divide the total cost by the number of erasers Mrs. McBryde purchased. She bought 1000 erasers for $70.00. So, we need to perform the division $70.00 ÷ 1000 erasers = $0.07 per eraser. This means each eraser costs 7 cents.

Answer:

500000 people

Step-by-step explanation:

The population grew by 600,000 which is 120% the earlier prediction by the town council.

Using direct proportion

600,000  -------- 120%

X              --------- 100%

X = (600000 × 100) ÷ 120 = 500000

Therefore the earlier prediction by the town council is 500000 people

The student's question is a mathematical problem calculating population growth predictions. The town council of Grand Island originally predicted a growth of 500,000 people, which is 20% less than the actual growth of 600,000 people.

To determine the prediction made by the town council, we can use the fact that the actual growth exceeded the prediction by one fifth (or 20%). If the actual growth was 600,000 people, the predicted growth can be calculated by dividing 600,000 by 1.2, as the actual growth represents 120% of the predicted value (100% original prediction + 20% excess).

Calculating the Predicted Population Growth

To find the town council's predicted growth, we can set up the equation:

Therefore, the town council had originally predicted that the population of Grand Island, Nebraska, would increase by 500,000 people between 1995 and 2005.

Answer: the explicit formula is

Tn = 3 + 5(n - 1)

Step-by-step explanation:

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + d(n - 1)

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 3

d = 8 - 3 = 13 - 8 = 18 - 13 = 5

The explicit formula for the arithmetic sequence is

Tn = 3 + 5(n - 1)

Answer:

The equation for this trend line is N = -2/1 + 110

Step-by-step explanation:

We are able to find this answer through the equation used to find m

[tex]\frac{y2-y1}{x2-x1}[/tex]

We plug in our selected points

[tex]\frac{70-50}{20-30}[/tex]

From this, we get -2/1

Our y intercept is equivalent to 110 due to the point in which it crosses the y-axis

Hope this helps

Answer:

The answer to your question is the third option

Step-by-step explanation:

To know if two lines are parallel we must get their slopes if the slopes are equal, the lines are parallel.

Data

A (2,2)

B (3,6)

C(0,5)

D(1,9)

Formula

slope = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

Process

1.- Calculate the slope of line 1

slope 1 = [tex]\frac{6 - 2}{3 - 2}[/tex]

slope 1 = [tex]\frac{4}{1}[/tex]

slope 1 = 4

2.- Calculate slope 2

slope 2 = [tex]\frac{9 - 5}{1 - 0}[/tex]

slope 2 = [tex]\frac{4}{1}[/tex]

slope 2 = 4

3.- Compare the slope

slope 1 = 4 and slope 2 = 4, both slope are equals, then the lines are parallel.

Step-by-step explanation:

Hi,

Since there are multiple scenarios, lets first discuss the rules of developing expressions.

Using these rules we can develop the following expressions:

Tip:

In addition, the order of number doesn't matter however this is not the case in subtraction.

Answer:

E) Choco Dream faces increasing marginal opportunity cost in the production of liquor chocolates.

Step-by-step explanation:

When Choco Dream increased their production of liquor chocolates by 500 units (to 4,500 bars per month), their opportunity was 800 units of dark chocolate. But when they needed to increase liquor chocolates by 500 more units (to 5,000 bars per month), then the opportunity cost increased to 1,000 units of dark chocolate.

That means that for the first 500 extra liquor bars, the opportunity cost = 800 dark chocolate bars / 500 liquor bars = 1.6 dark chocolate bars for every extra liquor bar.

The second increased required a higher opportunity cost = 1,000 dark chocolate bars / 500 liquor bars = 2 dark chocolate bars for every extra liquor bar.

The question is incomplete because you haven't attached the map with it. I am attaching the photo of the map here and answering according to it.

Answer:

Before stopping to eat, Leon and Marisol biked a total distance of 12 [tex]\frac{1}{3}[/tex]   miles.

Step-by-step explanation:

Leon and Marisol first biked the Brookside Trail to the end an back. According to the map, this trail is 3 [tex]\frac{2}{3}[/tex] miles long and the distance from the trail to the end and back can be calculating by adding this distance twice. The distance is a mixed fraction and we need to convert it into a simple fraction to add it.

To convert the mixed fraction, we will first multiply the denominator with the whole number, i.e. 3x3 = 9 and then add the numerator to it i.e. 9 + 2 = 11. The new denominator will be the same as the previous denominator.

The fraction can now be written as [tex]\frac{11}{3}[/tex]. The distance of Brookside trail to the end and back is

[tex]\frac{11}{3}[/tex] +

Then, they biked the Forest Glen Trail to the end and back. The distance of this trail is 2 [tex]\frac{1}{2}[/tex] miles. We will add this distance twice as well to obtain the total distance traveled for this trail.

To convert the mixed fraction into a simple fraction, multiply the denominator with the whole number i.e. 2 x 2 = 4. Then add the numerator to this answer i.e. 4 + 1 = 5. This is the new numerator and the denominator stays the same. The fraction is [tex]\frac{5}{2}[/tex].

The distance of Forest Glen Trail to the end and back is:

[tex]\frac{5}{2}[/tex] +

The total distance traveled can be calculated by adding both the distances traveled in the individual trails. i.e.

[tex]\frac{22}{3}[/tex] + 5

This can be written as:

[tex]\frac{22}{3}[/tex] + [tex]\frac{5}{1}[/tex]

The denominators are different so we will find out the L.C.M (Lowest Common Multiple) of 3 and 1 which is 3.

We will multiply the numerator and denominator of second fraction with 3 to make the denominator equal to 3.

[tex]\frac{22}{3} + \frac{5 X 3}{1 X 3}[/tex]

= [tex]\frac{22}{3} + \frac{15}{3}[/tex]

= [tex]\frac{22+15}{3}[/tex]

= [tex]\frac{37}{3}[/tex]

To convert [tex]\frac{37}{3}[/tex] miles into a mixed fraction, divide 37 by 3 and write down the answer as a whole number, the remainder as the numerator and the previous denominator i.e. 3 as the new denominator.

3 x 12 = 36. So dividing 37 by 3 will yield 12 as the whole number. The remainder is 37-36 = 1. So, the mixed fraction will be 12 [tex]\frac{1}{3}[/tex]

Before stopping to eat, Leon and Marisol biked a total distance of 12 [tex]\frac{1}{3}[/tex]   miles.

Answer:

Step-by-step explanation:

The question is incomplete because you haven't attached the map with it. I am attaching the photo of the map here and answering according to it.

Answer:

Before stopping to eat, Leon and Marisol biked a total distance of 12    miles.

Step-by-step explanation:

Leon and Marisol first biked the Brookside Trail to the end an back. According to the map, this trail is 3  miles long and the distance from the trail to the end and back can be calculating by adding this distance twice. The distance is a mixed fraction and we need to convert it into a simple fraction to add it.

To convert the mixed fraction, we will first multiply the denominator with the whole number, i.e. 3x3 = 9 and then add the numerator to it i.e. 9 + 2 = 11. The new denominator will be the same as the previous denominator.

The fraction can now be written as . The distance of Brookside trail to the end and back is

+

Then, they biked the Forest Glen Trail to the end and back. The distance of this trail is 2  miles. We will add this distance twice as well to obtain the total distance traveled for this trail.

To convert the mixed fraction into a simple fraction, multiply the denominator with the whole number i.e. 2 x 2 = 4. Then add the numerator to this answer i.e. 4 + 1 = 5. This is the new numerator and the denominator stays the same. The fraction is .

The distance of Forest Glen Trail to the end and back is:

+

The total distance traveled can be calculated by adding both the distances traveled in the individual trails. i.e.

+ 5

This can be written as:

+

The denominators are different so we will find out the L.C.M (Lowest Common Multiple) of 3 and 1 which is 3.

We will multiply the numerator and denominator of second fraction with 3 to make the denominator equal to 3.

=

=

=

To convert  miles into a mixed fraction, divide 37 by 3 and write down the answer as a whole number, the remainder as the numerator and the previous denominator i.e. 3 as the new denominator.

3 x 12 = 36. So dividing 37 by 3 will yield 12 as the whole number. The remainder is 37-36 = 1. So, the mixed fraction will be 12

Before stopping to eat, Leon and Marisol biked a total distance of 12    miles.

Answer:

d = $5.50 - p

Step-by-step explanation:

Answer: d = $5.50 - p

Step-by-step explanation:

Vote me Brainlets pls!

Answer:

STANDARD FORM PEOPLE Ax + By =C

so

find slope

m=-3

then plug that and one of the two points into the equation

y - y1 = m(x - x1)

y-1= -3(x-6)

y-1=-3x + 18

y + 3x = 19

so your answer is

3x + y = 19

Answer:

The average age was minimum at 1954 and the average age is 25.5.

Step-by-step explanation:

The given quadratic function is

[tex]f(x)=0.0039x^2-0.42x+36.79[/tex]

It models the​ median, or​ average, age,​ y, at which men were first married x years after 1900.

In the above equation leading coefficient is positive, so it is an upward parabola and vertex of an upward parabola, is point of minima.

We need to find the year in which the average age was at a minimum​.

If a quadratic polynomial is [tex]f(x)=ax^2+bx+c[/tex], then vertex is

[tex]Vertex=(-\dfrac{b}{2a},f(-\dfrac{b}{2a}))[/tex]

[tex]-\dfrac{b}{2a}=-\dfrac{(-0.42)}{2(0.0039)}=53.846153\approx 54[/tex]

54 years after 1900 is

[tex]1900+54=1954[/tex]

Substitute x=54 in the given function.

[tex]f(54)=0.0039(54)^2-0.42(54)+36.79=25.4824\approx 25.5[/tex]

Therefore, the average age was minimum at 1954 and the average age is 25.5.

The year when the average age at first marriage was at a minimum in a specific U.S. city was approximately 1954. The average age at first marriage for that year was approximately 28.4 years.

To find the year when the average age at first marriage was at a minimum, we need to determine the x-value at the vertex of the quadratic function. The x-value at the vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function. For the given function f(x) = 0.0039x2 - 0.42x + 36.79, the x-value at the vertex is x = -(-0.42)/(2*0.0039) = 53.85. Since the x-value represents years after 1900, we add 1900 to get the year: 1900 + 53.85 ≈ 1954.

To find the average age at first marriage for that year, we substitute x = 53.85 into the quadratic function. f(53.85) = 0.0039(53.85)2 - 0.42(53.85) + 36.79 ≈ 28.4. Therefore, the average age at first marriage for the year 1954 was approximately 28.4 years.

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Final answer:

Data can be categorized as discrete or continuous. Discrete data consist of countable values, while continuous data can take on any value within a range and are measurable. Examples include the number of passengers (discrete) and air pressure of a tire (continuous).

Explanation:

When categorizing data, it's important to determine whether the data are discrete or continuous. A discrete variable is one that can only take on certain, typically countable, values. Continuous variables, on the other hand, can take on any value within a range and are measurable.

Examples:

Further examples:

Answer:

a. 2.28%

b. 30.85%

c. 628.16

d. 474.67

Step-by-step explanation:

For a given value x, the related z-score is computed as z = (x-500)/100.

a. The z-score related to 700 is (700-500)/100 = 2, and P(Z > 2) = 0.0228 (2.28%)

b. The z-score related to 550 is (550-500)/100 = 0.5, and P(Z > 0.5) = 0.3085 (30.85%)

c. We are looking for a value b such that P(Z > b) = 0.1, i.e., b is the 90th quantile of the standard normal distribution, so, b = 1.281552. Therefore, P((X-500)/100 > 1.281552) = 0.1, equivalently  P(X > 500 + 100(1.281552)) = 0.1 and the minimun SAT score needed to be in the highest 10% of the population is 628.1552

d. We are looking for a value c such that P(Z > c) = 0.6, i.e., c is the 40th quantile of the standard normal distribution, so, c = -0.2533471. Therefore, P((X-500)/100 > -0.2533471) = 0.6, equivalently P(X > 500 + 100(-0.2533471)), and the minimun SAT score needed to be accepted is 474.6653

Using the normal distribution, it is found that:

a) 0.0228 = 2.28% of students have SAT scores greater than 700.

b) 0.3085 = 30.85% of students have SAT scores greater than 550.

c) The minimum SAT score needed to be in the highest 10% of the population is 628.

d) The minimum SAT score needed to be accepted is 475.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

Item a:

This proportion is 1 subtracted by the p-value of Z when X = 700, thus:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{700 - 500}{100}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772.

1 - 0.9772 = 0.0228.

0.0228 = 2.28% of students have SAT scores greater than 700.

Item b:

This proportion is 1 subtracted by the p-value of Z when X = 550, thus:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{550 - 500}{100}[/tex]

[tex]Z = 0.5[/tex]

[tex]Z = 0.5[/tex] has a p-value of 0.6915.

1 - 0.6915 = 0.3085.

0.3085 = 30.85% of students have SAT scores greater than 550.

Item c:

This is the 100 - 10 = 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.28 = \frac{X - 500}{100}[/tex]

[tex]X - 500 = 1.28(100)[/tex]

[tex]X = 628[/tex]

The minimum SAT score needed to be in the highest 10% of the population is 628.

Item d:

This is the 100 - 60 = 40th percentile, which is X when Z has a p-value of 0.4, so X when Z = -0.25.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.25 = \frac{X - 500}{100}[/tex]

[tex]X - 500 = -0.25(100)[/tex]

[tex]X = 475[/tex]

The minimum SAT score needed to be accepted is 475.

A similar problem is given at https://brainly.com/question/24663213

Answer: The maturity value is $43743

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount that was taken as loan.

R represents interest rate.

T represents the duration of the loan in years.

From the information given,

P = 42000

R = 8.3

T = 6 months = 6/12 = 0.5 years

I = (42000 × 8.3 × 0.5)/100 = $1743

The maturity value is the total amount paid after the duration of the loan. It becomes

42000 + 1743 = $43743

Answer:

  about 29.7 minutes

Step-by-step explanation:

If it take c minutes for Charles to mow the lawn by himself, it takes c+16 minutes for Peter. The two of them working together can mow in one minute this fraction of the entire lawn:

  1/c + 1/(c+16) = 1/18

Multiplying by 18c(c+16), we get ...

  18(c +16) + 18(c) = c(c+16)/18

  36c +288 = c^2 +16c

  c^2 -20c = 288 . . . . . subtract 36c

  c^2 -20c +100 = 388 . . . . . add (20/2)^2 = 100 to complete the square

  (c -10)^2 = 388

  c = 10 +√388 ≈ 29.6977 . . . . . take the positive square root

It takes Charles about 29.7 minutes to mow the lawn by himself.

Answer:

Step-by-step explanation:

I'm not quite sure what the question is.

64% + 28% = 92%

100% - 92% = 8%

If 8% = 50

100% = x

8x = 5000

x = 625 pairs of shoes at the beginning

Answer:

Correct statement: a. x₁ + x₂ + x₃ > 2

Step-by-step explanation:

The variables x₁, x₂ and x₃ takes value 0 if the projects are not done and 1 if the projects are done.

Consider that at least two projects are done, i.e. 2 or more projects are done.

This can happen in:

x₁ = 0, x₂ = 1 and x₃ = 1

x₁ = 1, x₂ = 0 and x₃ = 1

x₁ = 1, x₂ = 1 and x₃ = 0

x₁ = 1, x₂ = 1 and x₃ = 1

The statement (x₁ + x₂ + x₃ > 2) will be true only when all the variables takes the value 1.

This statement implies that 2 projects are definitely done.

Thus, the correct statement is (a).

Jeff made $210 by selling 30 pumpkins.

Step-by-step explanation:

Given,

Selling price of each Pumpkin = $7

Number of pumpkins sold by Jeff = 30

We will multiply number of pumpkins sold by selling price per pumpkin.

Amount made by Jeff = Price per pumpkin * Number of pumpkins

Amount made by Jeff = 7 * 30 = $210

Therefore;

Jeff made $210 by selling 30 pumpkins.

Keywords: multiplication

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Answer:

The bus left New York city at 5:10pm

Step-by-step explanation:

First, we need to calculate the total number of hours the bus used to travel from New York to Washington.

Total number of hours traveled

= 2 1/3hr + 1 3/4hr + 5/6hr

= 7/3+7/4+5/6

=28+21+10/12

=59/12

= 4 11/12hours

Converting 11/12hours to minutes we will have 11/12×60 = 55minutes

Therefore the bus traveled for 4hours 55minutes.

If the bus arrived in Washington at 10:05 pm and the bus left New York 4hours 55minutes ago, this means that the bus did left New York at (10.05-4.55)pm i.e 5:10pm

4hours past 10:05pm will be 6:05pm

55minutes past 6:05pm will be 5:10pm

This means that the bus left New York city at 5:10pm

Answer:

The z-score = -3.7 and p (-3.7) = 0.00011 or 0.011%

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Mean of time to finish a test = 60 minutes

Standard deviation of time to finish a test = 10 minutes

Time that a student finishes the test = 23 minutes

2. What is the z-score for the student?

z-score = (Time that a student finishes the test - Mean of time to finish a test)/Standard deviation of time to finish a test

Replacing with the real values:

z-score = (23 -60)/10 = -37/10 = -3.7

z-score = -3.7 and p (-3.7) = 0.00011 or 0.011%

Answer: standard deviation is 6.96

Step-by-step explanation:

Let m be mean

M=mean=sum/n

M=525/5

M=103

The standard deviation formula is :

S.D = sqrt( Summation of |x-m|^2 / n-1)

Let start finding:

|x-m|^2

For 1st: |119-103|^2=36

For 2nd: |104-103|^2=1

For 3rd: |92-103|^2=121

For 4th: |97-103|^2=36

For 5th: |103-103|^2=0

Summation of |x-m|^2 = 194

The standard deviation formula is :

S.D = sqrt( Summation of |x-m|^2 / n-1)

S.D= sqrt(194 / 4)

S.D=sqrt(48.5)

S.D= 6.96

The standard deviation is approximately 9.1 ounces.

Calculating the Population Standard Deviation

To find the standard deviation of the population of newborn babies' weights in a hospital, we need to follow several steps. The weights of the babies (in ounces) are 119, 104, 92, 97, and 103.

Calculate the mean (average) weight: (119 + 104 + 92 + 97 + 103) / 5 = 103

Determine the squared deviations from the mean for each weight: ((119 - 103)²), ((104 - 103)²), ((92 - 103)²), ((97 - 103)²), ((103 - 103)²).

Sum the squared deviations: 256 + 1 + 121 + 36 + 0 = 414.

Since we have the entire population, divide by the number of data points, which is 5: (414 / 5 = 82.8).

Take the square root of 82.8 to find the population standard deviation: √82.8} =approximately 9.1 ounces.

The population standard deviation of the babies' weights is approximately 9.1 ounces, rounded to two decimal places.

Answer:

The information given is not enough to determine their ages explicitly, so, here their ages are given in terms of Anna's age, which is the best that could be determined.

Anna's age = x years

Robert's age = (x - 11) years

Sara's age = (x - 9) years

David's age = (x - 1) years

Step-by-step explanation:

Let Anna be x years old.

Anna's age = x

Because Anna is 11 years older than Robert, we can say Robert's age is Anna's age minus 11.

Robert = x - 11

But Robert is 2 years younger than Sara, we can say Sara's age is Robert's age plus 2

Sara = (x - 11) + 2

= x - 9

David is 8 years older than Sara, we can say David's age is Sara's age plus 8.

David = (x - 9) + 8

= x - 1

Step-by-step explanation:

[tex]\lim_{n \to \infty} \sum\limits_{k=1}^{n}f(x_{k}) \Delta x = \int\limits^a_b {f(x)} \, dx \\where\ \Delta x = \frac{b-a}{n} \ and\ x_{k}=a+\Delta x \times k[/tex]

In this case we have:

Δx = 3/n

b − a = 3

a = 1

b = 4

So the integral is:

∫₁⁴ √x dx

To evaluate the integral, we write the radical as an exponent.

∫₁⁴ x^½ dx

= ⅔ x^³/₂ + C |₁⁴

= (⅔ 4^³/₂ + C) − (⅔ 1^³/₂ + C)

= ⅔ (8) + C − ⅔ − C

= 14/3

If ∫₁⁴ f(x) dx = e⁴ − e, then:

∫₁⁴ (2f(x) − 1) dx

= 2 ∫₁⁴ f(x) dx − ∫₁⁴ dx

= 2 (e⁴ − e) − (x + C) |₁⁴

= 2e⁴ − 2e − 3

∫ sec²(x/k) dx

k ∫ 1/k sec²(x/k) dx

k tan(x/k) + C

Evaluating between x=0 and x=π/2:

k tan(π/(2k)) + C − (k tan(0) + C)

k tan(π/(2k))

Setting this equal to k:

k tan(π/(2k)) = k

tan(π/(2k)) = 1

π/(2k) = π/4

1/(2k) = 1/4

2k = 4

k = 2

Answer:

A

Step-by-step explanation:

The triangles are the same size but in a different form. Y= 50 and a and b equal eachother.

The option (D) Can't be determined is correct because we cannot determine the value of b because there are two unknowns b and y.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

We have a triangle shown in the picture.

From the triangle first we can find the value of a:

a = 180 - (50 + 45)

a = 85 degree

We cannot determine the value of b because there are two unknowns b and y.

Thus, the option (D) Can't be determined is correct because we cannot determine the value of b because there are two unknowns b and y.

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Answer:

7

Step-by-step explanation:

Regular polygons have the same number of lines of symmetry as they do sides.

Polygons with an even number of sides have a line of symmetry for each pair of opposite vertices, as well as a line of symmetry through midpoints of opposite sides.

Polygons with an odd number of sides have a line of symmetry for each vertex, passing through the midpoint of the opposite side.

A heptagon has 7 vertices, and therefore has 7 lines of symmetry.

Answer: The answer in simplest form is [tex] -6(1/4) [/tex]

Step-by-step explanation:

In Wyatt's method I observed the mixed fraction was converted to simple fraction in the second step.

Therefore Wyatt's solution will be:

[tex] 2/5 * -15(5/8) = 2/5 * -125/8 = -25/4 [/tex]

Distributive property was used in Abigail's method.

The solution would be:

[tex] 2/5 * -15(5/8) = 2/5(-15 -5/8) = 2/5(-15) + 2/5(-5/8) = -6(-1/4) [/tex]

Note: Complete question is contained in the image

Answer:

2/5

Step-by-step explanation:

Final answer:

3-day Simple Moving Averages are computed by taking the average of three consecutive closing prices. The process is repeated for each set of three days within the ten-day period, resulting in a smoothed series of averages.

Explanation:

The 3-day simple moving average (SMA) of a series of stock prices is calculated by taking the sum of three consecutive closing prices and dividing by three. For the input series 7.78, 7.90, 8.00, 7.97, 7.86, 7.67, 7.60, 7.65, 7.65, 7.70, we perform the following steps:

For days 1, 2, and 3, the SMA would be (7.78 + 7.90 + 8.00) / 3.

For days 2, 3, and 4, the SMA would be (7.90 + 8.00 + 7.97) / 3.

Continue this process until you calculate the SMA for the last three days in the series.

Here is how they are actually calculated:

Day 1-3: (7.78 + 7.90 + 8.00) / 3 = 7.8933

Day 2-4: (7.90 + 8.00 + 7.97) / 3 = 7.9567

Day 3-5: (8.00 + 7.97 + 7.86) / 3 = 7.9433

Day 4-6: (7.97 + 7.86 + 7.67) / 3 = 7.8333

Day 5-7: (7.86 + 7.67 + 7.60) / 3 = 7.7100

Day 6-8: (7.67 + 7.60 + 7.65) / 3 = 7.6400

Day 7-9: (7.60 + 7.65 + 7.65) / 3 = 7.6333

Day 8-10: (7.65 + 7.65 + 7.70) / 3 = 7.6667

These averages help show the trend by smoothing out fluctuations in the data.

Answer:

2.78hrs

Step-by-step explanation:

Volume of water in the pool =πr2h

V = 3.142 * 2.5² *1.7

V = 33.38m³

Emptying the pool out at 12m³ per hour

= 33.38/12

= 2.78hrs

A - B = 4

A + B = 64

__________ +

A - B + A + B = 64 + 4

2A = 68

A = 34

B = 34 - 4

B = 30

Answer:

45%

Step-by-step explanation:

For simplicity, let use assume there are 100 students in the school.

No. of students to complete college = (30/100) x 100 = 30 Students

President wants to increase by 50% = (50/100) x 30 = 15 Students

New set goal = 30 + 15 = 45 students.

Total number of students = 100 students

Therefore;

Rate goal % = (45/100) x 100% = 45%