Use the sequence {−1,171,875;−234,375;−46,875;−9375,…} to answer the question.What is the explicit rule that describes the sequence?

Answer:

Kyle filled 10 10-oz cups, 6 14-oz cups, and 13 20-oz cups

Step-by-step explanation:

In order to solve this question we first have to create a system of equations. If we let "a" represent the number of 10-oz cups, let "b" represent the number of 14-oz cups, and let "c" represent the number of 20-oz cups, then we can make the following 3 equations...

1.   a + b + c = 29                                      (29 is the total number of cups)

2.  10a + 14b + 20c = 444                       (444 is the total volume of the coffee)

3.  0.95a + 1.15b + 1.50c = 35.90           (35.90 is the total price of the coffee)

Now we can solve this system of equation by first representing "a" in terms of "b" and "c". We use the first equation, to do that...

a + b + c = 29

a = 29 - b - c

Now we substitute "a" with an equal value in terms of "b" and "c" which we found above.

10a + 14b + 20c = 444

10 (29 - b - c) + 14b + 20c = 444

290 - 10b - 10c + 14b + 20c = 444

4b + 10c = 154

Now we use the fully simplified equation above to represent "c" in terms of "b", and we get that...

4b + 10c = 154

10c = 154 - 4b

c = 15.4 - 0.4b

Now we take the third equation and substitute "a" and "c" with equivalent values, and we get an equation from which we can find the value of "b"...

0.95a + 1.15b + 1.50c = 35.90

0.95 (29 - b - c) + 1.15b + 1.50(15.4 - 0.4b) = 35.90

27.55 - 0.95b - 0.95c + 1.15b + 23.1 - 0.6b = 35.90

50.65 - 0.4b - 0.95(15.4 - 0.4b) = 35.90

50.65 - 0.4b - 14.63 + 0.38b = 35.90

36.02 - 0.02b = 35.90

0.02b = 36.02 - 35.90

0.02b = 0.12

b = 6

Now that we know what "b" equals to, we can find the value of "c".

c = 15.4 - 0.4b

(we found this formula when we represented c in terms of "b" previously)

c = 15.4 - 0.4(6)

c = 15.4 - 2.4

c = 13

Now we can find the value of "a" buy using the first formula and substituting "b" and "c" with their values...

a + b + c = 29

a + 6 + 13 = 29

a = 29 - 6 - 13

a = 10

Therefore Kyle filled 10 10-oz cups, 6 14-oz cups, and 13 20-oz cups.

Solution:

Given the function:

At initial temperature, x=0. Then;

The initial temperature is 18 degrees Celsius.

Also; after 15minutes, x=15. Then;

ANSWER: After 15 minutes, the temperature is at 20 degrees Celsius.

Answer:

1. 3/4 = 0.75

2. 49/4 = 12.25

3. 4/3 = 1.3333

4. 27

5. 6

6. 28

7. 18

8. 7

9. 3

10. 21/4 = 5.25

Answer:

\(a_{n}\) = 10+12(n-1)

Step-by-step explanation:

This is an arithmetic sequence. An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant.

The formula for an arithmetic sequence is:

\(a_n = a_1 + (n-1)*d\) where \(a_1\) is the first value in the sequence, n is the nth term of the sequence, and d is the universal addition/subtraction value between each number.

\(a_1\\\) is 10, and d is 12.

Plug the values in and you get:

10+12(n-1).

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The impact on Carns Company's income from eliminating the Small Tools Division would be a decrease of $1,209,000.

To determine the impact on Carns Company's income from eliminating the Small Tools Division, we need to consider the avoidable costs associated with the division.

The avoidable costs include all of the variable costs of the division and a portion of the fixed costs that are specifically related to the Small Tools Division. In this case, the variable costs of the division are $1,295,000, and $119,000 of the fixed costs are avoidable.

To calculate the impact on income, we subtract the avoidable costs from the loss reported by the division:

Impact on income = Loss - Avoidable costs

Impact on income = $205,000 - ($1,295,000 + $119,000)

Impact on income = $205,000 - $1,414,000

Impact on income = -$1,209,000

The negative sign indicates a decrease in income.

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Answer: 24 problems done before dinner

Step-by-step explanation:

Take the 32 total math problems and divide it by 3/4 (the amount of problems done before dinner) getting you 24 problems done before dinner

The required expression is (x / 5) + 9

Given that we have to build an equation for the statement "9 more than the quotient of x and 5,

So,

This expression represents the quotient of x divided by 5, and then adding 9 to the result.

Therefore,

"9 more than the quotient of x and 5" can be written mathematically as:

(x / 5) + 9

Hence the required expression is (x / 5) + 9

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Answer:

the additional cost to produce each phone

Answer:

219

Step-by-step explanation:

Applying the system of equations given, we can conclude that: a. Nikhil has been with the company for 16 years, while Mae has been there for 4 years.

To solve the system of equations, let's substitute the value of x from the first equation into the second equation:

x = 4y

8 + 2y = 4y

Simplifying the equation, we get:

8 = 2y

Dividing both sides by 2:

4 = y

Now, substitute the value of y back into the first equation to find x:

x = 4y

x = 4(4)

x = 16

Therefore, Nikhil has been employed by the company for 16 years, and Mae has been employed for 4 years.

The correct answer is option a. Nikhil has been with the company for 16 years, while Mae has been there for 4 years.

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We have to calculate the 90% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value

(NOTE: although we have a relatively big sample, so it wouldn't be too wrong to approximate the standard deviation of the population with the sample one.. Even though, we will use the Student's t test as usual for unknown population standard deviations).

When σ is not known, s divided by the square root of N is used as an estimate of σM:

The degrees of freedom for this sample size are:

The t-value for a 90% confidence interval and 244 degrees of freedom is t = 1.651.

The margin of error (MOE) can be calculated as:

Then, the lower and upper bounds of the confidence interval are:

The confidence interval for the population mean is:

If we compare this interval with the one calcualted for a smaller sample, we can see that the limits are very similar and both CI contain both sample means.

Answer:

27.8 hg < μ < 29.4 hg.

A. No, because the confidence interval limits are similar.

Answer:

It is "for every 4 boys in the school, there are 7 girls.

Step-by-step explanation:

If the ratio of boys to girls is 4(boys):7(girls), then that would mean for every 4 boys in the school, there are 7 girls.

Answer:

For every 4 boys in the school, there are 7 girls.

Step-by-step explanation:

It's a ratio.

There are 4:7 boys for 4:7 every 4:7 girls.

(a). The graph of y = -f(x) is shown in the image below.

(b). The graph of y = g(-x) is shown in the image below.

By reflecting the parent absolute value function g(x) = |x + 2| - 4 over the x-axis, the transformed absolute value function can be written as follows;

y = -f(x)

y = -|x + 2| - 4

Part b.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = rise/run

Slope (m) = -2/4

Slope (m) = -1/2

At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -1/2(x - 0)

g(x) = -x/2 + 5, -4 ≤ x ≤ 4.

y = g(-x)

y = x/2 + 5, -4 ≤ x ≤ 4.

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The total number of students who graduated from the Cincinnati universities and colleges are 15382.

We are given that 6.76 % of Cincinnati college and university graduates majored in Registered Nursing.

The number of the Cincinnati college and university graduates who majored in Registered Nursing = 1026.

We need to find the total number of students that graduated from the Cincinnati universities and colleges altogether in 2016.

Let the total number of students be x.

ATQ:

6.67 % x = 1026

6.67 x = 102600

667 x = 10260000

x = 10260000 / 667

x = 15382.309

Rounding off to the nearest whole number is:

x = 15382.

Therefore, we get that the total number of students who graduated from the Cincinnati universities and colleges are 15382.

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Answer:

0.22

Explanation:

Following the hint, we will calculate the probability that all four do use computers. Since 94% of the people working use computers, the probability that all 4 four use computers is equal to:

P(4 use computer) = 0.94 x 0.94 x 0.94 x 0.94

P(4 use computer) = 0.78

Then, by the rule for complementary events, the probability that at least one doesn't use computers is:

P(at least 1) = 1 - P(4 use computers)

P(at least 1) = 1 - 0.78

P(at least 1) = 0.22

Therefore, the answer is 0.22

Answer:

6.33 years

Explanation:

The formula for investment at compound interest is given below::

From the statement of the problem:

• The initial investment, P = $2500

• Annual Interest Rate, r = 7.5% = 0.075

• Compounding Period (Quarterly), k = 4

• Amount after t years, A(t) = $4000

• Time, t = ?

Substitute these values into the compound interest formula above:

We then solve the equation for the value of t.

It will take approximately 6.33 years for a $2500 investment to grow to $4000.

Answer:

-4 , 0

Step-by-step explanation:

y = - 4 x + 0

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Step-by-step explanation:

x/2- 12 = -14

x/2 = -14 + 12

x/2 = -2

x = -4

Answer:

Radius: 2.1Inches

Step-by-step explanation:

Circumference

Circumference is the linear distance around the circle edge.

Radius

The radius of a circle is any of the line segments from its center to its perimeter. The radius is half the diameter or r = d

2

.

Diameter

The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. The diameter is twice the radius or d = 2·r.

The Greek letter π

π represents the number Pi which is defined as the ratio of the circumference of a circle to its diameter or π = C

d

. For simplicity, you can use Pi = 3.14 or Pi = 3.1415. Pi is an irrational number. The first 100 digits of Pi are: 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679

Answer:

The  chances of success for Archie is \(P(S|D) =  35\%\)

Step-by-step explanation:

From the question we are told that

 The distance of Sudland from Xhosas is   d =  100 miles

  The probability  of failure is  \(P(F) = 0.26\)

  The probability of choosing the desert route is   \(P(D) = \frac{1}{40} =  0.025\)

The probability of reaching Sudland through the mountain is  \(P(S|M) =0.75\)

Generally the probability of choosing the  mountains route is

         \(P(M) = 1 - P(D)\)

           \(P(M) = 1 - 0.025\)

             \(P(M) = 0.975\)

Generally the probability of success is mathematically represented as

       \(P(S) =  1- P(F)\)

         \(P(S) =  1- 0.26\)

          \(P(S) =  0.74\)

Generally the probability of success in reaching Sudland is also mathematically represented as

     \(P(S) =  P(S|M) * P(M) + P(S|D) * P(D)\)

=>   \(P(S|D) =  \frac{P(S) - P(S|M) * P(M)}{P(D)}\)

substituting values

=>  \(P(S|D) =  \frac{0.74 - 0.75 * 0.975}{0.025}\)  

=>  \(P(S|D) = 0.35 \)  

=>  \(P(S|D) =  35\%\)

Step-by-step explanation:

a= c-b pls let me know if it is correct or not

Answer:

He would have 48

Step-by-step explanation:

1 set: 8

2 sets: 16

3 sets: 24

4 sets: 32

5 sets: 40

5 sets: 48

OR

{4(8)} + 2(8)

32 + 2(8)

32 + 16

48

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Answers

48

Steps

4+2=6

8 times 6= 48

C=22cm

Step-by-step explanation:

circumference of circle=2πr or π×d

C=π×7=7π

C=7×22/7=22cm

There will be 12 slices of pizza left over, which can be expressed as 3/2 or 1 1/2 slices in fraction form.

To find out how much pizza will be left over, we need to calculate the total number of slices available and subtract the number of slices consumed by the players.

Given that there are six pizzas and each pizza has eight slices, the total number of slices available is 6 pizzas * 8 slices/pizza = 48 slices.

Since there are 36 players on the team, and each player has one slice, the total number of slices consumed is 36 slices.

To determine the remaining slices, we subtract the consumed slices from the total available slices: 48 slices - 36 slices = 12 slices.

Therefore, there will be 12 slices of pizza left over.

To express this as a fraction, we can write it as 12/1, which simplifies to 12. This means there will be 12 whole slices of pizza left over.

If you would like to express it as a fraction in its simplest form, you can write it as 12/8. By dividing both the numerator and denominator by their greatest common divisor, which is 4, we get 3/2. So, in fraction form, there will be 3/2 or 1 1/2 slices of pizza left over.

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Answer:

(x + i) (x - i)

Step-by-step explanation:

The expression x^2 + 1 is a sum of squares, which means that it cannot be factored using real numbers. However, it can be factored using complex numbers.

To factor x^2 + 1, we can use the fact that i^2 = -1, where i is the imaginary unit.

We can rewrite x^2 + 1 as:

x^2 + 1 = x^2 - (-1)

Now, we can use the difference of squares formula to factor x^2 - (-1):

x^2 - (-1) = (x + i)(x - i)

Therefore, the factored form of x^2 + 1 is:

(x + i)(x - i)

In multiple regression problem with two independent variables, value of one varible , b₁ is 2 then it means that the estimated mean of Y increases by 2 units for each increase of 1 unit of X₁, holding X₂ constant. So, second option is correct option.

Multiple Regression: Multiple regression is a statistical technique that can be used to analyze the relationship between a single dependent variable and multiple independent variables. The goal of multiple regression analysis is to use independent variables with known values to predict the value of each dependent value.

Y = b₁x₁+ b₂x₂ + … bₙxₙ + a

Here Y is the dependent variable, and X₁,…,Xₙ are the n independent variables. In calculating the weights, a, b₁,…,bₙ,

In the multiple regression b1 shows the coeffcient of independent variable X₁ in fitted model.

Here b₁ =+2.0 shows that for each unit increase in X₁, dependent variable Y is increased by 2 keeping other things constant.

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The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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Maureen's pension would be $50,035.20.

What is Percentage?

To compute a percentage, divide the value by the entire amount and multiply the result by 100. A percentage is a quantity or ratio that is stated as a fraction of one hundred. The percent sign, "%," is frequently used to represent it.

First, we need to calculate the average of Maureen's three highest salaries:

Average = (107,000 + 107,800 + 108,198) / 3

Average = 322,998 / 3

Average = 107,666

Next, we need to calculate 1.56% of this average:

Percentage = 1.56% * 107,666

Percentage = 1,667.84

Finally, we multiply this percentage by the number of years worked to find the pension:

Pension = 30 * 1,667.84

Pension = 50,035.20

So, Maureen's pension would be $50,035.20.

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