Bronx Community College 1 of 9 123.5-D05 Final Exam Spring 2022 Professor Wickliffe Richards Instructions: Answer the following test items. Show your calculations as to how you get your answers, to get full credit for a correct answer. (1) (14 pts) The costs (in dollars) of 10 college math textbooks are listed below. 70 72 71 70 69 73 69 68 70 71 a) (4 points) Calculate the mean b) (2 points) Find the median c) (8 points) Calculate the sample standard deviation.

Solution

- The formula for finding the integral of a function using the trapezoidal rule is:

- Applying the formula, we have:

- Thus, we can find the Integral as follows:

Final Answer

The integral is 5.9

Answer:

355.94 cm2

Step-by-step explanation:

if it is the area of the shaded part, you have to find the area of rectangle and the area of the circle, then subtract the rectangle's area from the circle's.

area of circle = 3.14( i used this π because the radius is not divisible by 7) × 11 × 11 = 379.94.

area of rectangle = 6 × 4 = 24cm

379.94 - 24.00 = 355.94cm2.

Answer:

$45.

Step-by-step explanation:

When the TV is bought on hire purchase, you deposit $35 and pay $30 monthly. There are 12 payments. 12 * 30 = $360. 360 + 35 = $395.

Since cash would've cost $350, the amount of money saved by paying cash is 395 - 350 = $45.

Hope this helps!

Answer:

row 4 answer 6 i just took the quiz

Answer:

The slope is 2

Step-by-step explanation:

Every time the x unit goes up one the y unit is going up 2

As per the calculated confidence interval, the false statement is "A 90% confidence interval for (p<40K − p≥40K) would be wider than the (−0.16, 0.02) interval." (option c).

In this case, we are interested in the difference in the proportion of people not affected by the shutdown between two income groups, those who make less than $40,000 and those who make $40,000 or more. We can calculate a confidence interval for this difference using the formula:

(p₁ - p₂) ± z*(SE)

Where:

   • p₁ is the proportion of people not affected by the shutdown in the first income group (less than $40,000)

   • p₂ is the proportion of people not affected by the shutdown in the second income group ($40,000 or more)

   • z* is the critical value from the standard normal distribution corresponding to the desired level of confidence (in this case, 95%, so z* = 1.96)

   • SE is the standard error of the difference in proportions, calculated as:

SE = √((p₁*(1-p₁))/n₁ + (p₂*(1-p₂))/n₂)

Where:

   • n₁ is the sample size of the first income group (less than $40,000)

   • n₂ is the sample size of the second income group ($40,000 or more)

Using the data from the Survey USA poll, we can calculate the values needed to construct the confidence interval:

   • p₁ = 0.48

   • p₂ = 0.55

   • n₁ = n₂ = 307

Substituting these values into the formula, we get:

(0.48 - 0.55) ± 1.96√((0.48(1-0.48))/307 + (0.55*(1-0.55))/307) = -0.07 ± 0.05 = (-0.12, -0.02)

The width of a confidence interval depends on the sample size and the level of confidence.

Statement (c) is false.

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Complete Question:

The United States Federal Government Shutdown Of 2018–2019 occurred from December 22, 2018 Until January 25, 2019, A Span Of 35 Days. A Survey USA Poll Of 614 Randomly sampled Americans During This Time Period Reported That 48% Of Those Who Make Less Than $40,000 Per year And 55% Of Those Who Make $40,000 Or More Per Year Said The Government Shutdown Has Not At The United States federal government shutdown of 2018–2019 occurred from December 22, 2018, until January 25, 2019, a span of 35 days. A Survey USA poll of 614 randomly sampled Americans during this time period reported that 48% of those who make less than $40,000 per year and 55% of those who make $40,000 or more per year said the government shutdown has not at all affected them personally. A 95% confidence interval for (p<40K − p≥40K), where p is the proportion of those who said the government shutdown has not at all affected them personally, is (-0.16, 0.02). Based on this

information, determine if the following statements are true or false, and explain your reasoning if you identify the statement as false

(a) At the 5% significance level, the data provide convincing evidence of a real difference in the proportion who are not affected personally between Americans who make less than $40,000 annually and Americans who make $40,000 annually.

(b) We are 95% confident that 16% more to 2% fewer Americans who make less than $40,000 per year are not at all personally affected by the government shutdown compared to those who make $40,000 or more per year.

(c) A 90% confidence interval for (p<40K − p≥40K) would be wider than the (−0.16, 0.02) interval.

(d) A 95% confidence interval for (p≥40K − p<40K) is (-0.02, 0.16).

Given the expression :

To solve the given expression:

First add the numbers 52 and 8 then divide by 30

so, the result will be as following :

So, the answer is : 2

=========================================================

Also, we need two different word phrases for the expression

The first :

52 increased by 8 then divided by 30

The second :

The Quotient of the sum numbers (52 , 8 ) and 30

A function assigns the values. The value of (gof)(3) is -576.

A function assigns the value of each element of one set to the other specific element of another set.

Given f(x)=x+21 and g(x)=-x², therefore, the value of (gof)(x) will be,

(gof)(x) = g(f(x))

           = -(x+21)²

The value of (gof)(3) will be,

(gof)(3) = -(3+21)²

            = -576

Hence, the value of (gof)(3) is -576.

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Therefore, based on the given information, the estimated age of the tomb is approximately 3,970 years.

To estimate the age of the tomb based on the radioactive carbon-14 (C-14) content in the cypress beam, we can use the decay equation:

A = A₀ * e*(kt)

Where:

A = Final amount of radioactive substance (55% of the original C-14 content)

A₀ = Initial amount of radioactive substance (100% of the original C-14 content)

k = Decay constant (ln(2) / half-life of C-14)

t = Time (age of the tomb)

Given that the half-life of C-14 is approximately 5600 years, we can calculate the decay constant:

k = ln(2) / 5600 years

Now we can plug in the values:

0.55A₀ = A₀ * e*((ln(2) / 5600 years) * t)

Dividing both sides by A₀:

0.55 = e*((ln(2) / 5600 years) * t)

Taking the natural logarithm of both sides:

ln(0.55) = (ln(2) / 5600 years) * t

Now we can solve for t, the age of the tomb:

t = (ln(0.55) * 5600 years) / ln(2)

Evaluating the expression:

t ≈ 3,970 years

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Answer:

Arithmetic: 5,8,11,14,17

Geometric: 3,6,12,24,48

Neither: 4,7,12,19,31

Step-by-step explanation:

The arithmetic sequence is one that is adding or subtracting a specific amount. In this case, the common difference or that number we are adding each time is 3.

The geometric sequence is one that is multiplying or dividing a specific amount. In this case, the common ratio or the number that we are multiplying each time is 2.

The last sequence is none of the above, so we put it into neither.

Hope this helped :D

If the equation is 19-5=3z-11 then the value of z is 15/3.

Given an equation in terms of z is 19-5=3z-11.

We are required to find the value of variable z which exist in equation.

Equation is like a  relationship between two or more variables expressed in equal to form. Equations of two or more variables look like ax+by=c. It may be linear equation, quadratic equation,cubic equation,or many more depending on power of the variable.

The value of z can be find as under:

19-5=3z-11

4=3z-11

3z=4+11

3z=15

z=15/3

Hence if the equation is 19-5=3z-11 then the value of variable z is 15/3.

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Answer:

3.4

Step-by-step explanation:

Equation:

12x = 40.8

Isolate the variable:

x = 40.8/12

x = 3.4

Answer:

x = 3.4

Step-by-step explanation:

12x = 40.8

40.8 / 12 = 3.4

x = 3.4

The probability that your mom will get a text on three consecutive days is (1/6)^3, or approximately 0.00463.

The problem can be modeled as a sequence of independent events, where each event is the probability of being able to send a text during the professor's setup time. This probability is (30-5)/30, or 5/6. Therefore, the probability of sending a text on any given day is 5/6. Since the events are independent, the probability of getting a text on three consecutive days is (5/6)^3, which is approximately 0.00463 or 0.463%.

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Answer:

7,13,6

Step-by-step explanation:

you must take the number minus 4 then add 6 minus 7 then add 9, minus 10 then add 12.

Answer:

Addition expression: 58+(-27)

Subtraction expression: 58-27

Answer:

1: below its initial height.

2: if Jimmy has 20 balls and Chris take 15,how many balls does Jimmy have?

3: I would want Mrbeast to be the President because he would help everyone.

For taxable income of $49,020 or less, the tax rate is 15%. Any taxable income exceeding $49,020 will be subject to a different tax rate, which is not specified in the given information.

The provided information outlines the tax rates based on different taxable income brackets. For taxable income equal to or less than $49,020, the tax rate is 15%.

This means that if an individual or entity has a taxable income within this range, they will be required to pay 15% of their income as taxes. However, the information does not provide the tax rate for taxable income exceeding $49,020. To accurately calculate the tax liability for income above this threshold, the specific tax rate for that income range is required. Without knowing the tax rate for taxable income above $49,020, it is not possible to determine the exact tax liability for income in that range. The given information only provides the tax rate for taxable income up to $49,020, which is 15%.

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Answer:

200 in²

Step-by-step explanation:

To find the area, you need to split it into two squares. The upper square would be 10 inches times 10 inches which would give you 100 inches squared. Since both are the same size, you can add both square areas together to give you 200 inches squared.

The cost of metal per square foot for the water tank in the shape of a cylinder, we need to determine the total surface area of the tank and divide the total cost of metal by that surface area. Therefore, the cost of the metal per square foot for the water tank is approximately $36.95.

The water tank in the shape of a cylinder has a height of 2 and a diameter of 16. Since the diameter is given, we can calculate the radius by dividing the diameter by 2. Therefore, the radius (r) is 8.

To find the total surface area of the cylinder, we need to consider the curved surface area of the cylinder and the areas of the top and bottom circles. The formula for the surface area of a cylinder is given by 2πrh + 2πr^2, where π is approximately 3.14, r is the radius, and h is the height.

Substituting the values into the formula, we get:

Surface Area = 2 * 3.14 * 8 * 2 + 2 * 3.14 * 8^2

Surface Area = 100.48 + 402.24

Surface Area = 502.72 square feet

The total cost of the metal for the tank is given as $18,588.80. To find the cost per square foot, we divide the total cost by the surface area:

Cost per Square Foot = $18,588.80 / 502.72 square feet

Cost per Square Foot ≈ $36.95

Therefore, the cost of the metal per square foot for the water tank is approximately $36.95.

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Answer:

Step-by-step explanation:

Number of weeks

The (x – 1) represents the number of the week in the expression.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The linear system of the equation is given as,

y = mx + c

Where, m is the slope of the line and c is the intersection point of line and y-axis.

The cost of a camp is $300 for the first week and $125 for each week beyond the first.

The total cost can be modeled by the expression 300 + 125(x – 1).

In the above linear expression, 125 represents the slope and 300 represents the y-intercept pf the linear expression.

Then the (x – 1) represents the number of the week in the expression.

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The nonzero vector orthogonal to the plane through the points P, Q, and R is [-8/13, -8/13, -12/13].

To find a nonzero vector orthogonal to the plane through the points P, Q, and R, we can use the cross product of two vectors that lie in the plane.

Let's find the vectors PQ and PR, which can be found by subtracting the coordinates of P from the coordinates of Q and R:

PQ = Q - P = (-2, 1, 3) - (1, 0, 1) = (-3, 1, 2)

PR = R - P = (4, 2, 5) - (1, 0, 1) = (3, 2, 4)

Next, we'll take the cross product of these two vectors to find a vector orthogonal to the plane:

n = PQ x PR =

[(1)(4) - (2)(2), (2)(-3) - (3)(1), (3)(3) - (2)(-2)]

= [-8, -8, -12]

This vector is orthogonal to the plane through the points P, Q, and R. To make it a nonzero vector, we can scale it to have magnitude 1:

n = [-8, -8, -12] / sqrt((-8)^2 + (-8)^2 + (-12)^2) = [-8/13, -8/13, -12/13]

So, the nonzero vector orthogonal to the plane through the points P, Q, and R is [-8/13, -8/13, -12/13].

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Answer:

\(\boxed {d = 4}\)

Step-by-step explanation:

Solve for the value of \(d\):

\(-24 + 12d = 2(d - 3) + 22\)

-Use Distributive Property:

\(-24 + 12d = 2(d - 3) + 22\)

\(-24 + 12d = 2d - 6 + 22\)

-Combine like terms:

\(-24 + 12d = 2d - 6 + 22\)

\(-24 + 12d = 2d +16\)

-Take \(2d\) and subtract it from \(12d\):

\(-24 + 12d - 2d = 2d - 2d +16\)

\(-24 + 10d = 16\)

-Add both sides by \(24\):

\(-24 + 24 + 10d = 16 + 24\)

\(10d = 40\)

-Divide both sides by \(10\):

\(\frac{10d}{10} = \frac{40}{10}\)

\(\boxed {d = 4}\)

Therefore, the value of \(d\) is \(4\).

Answer:

d = 4

Step-by-step explanation:

Given

- 24 + 12d = 2(d - 3) + 22 ← distribute and simplify right side

- 24 + 12d = 2d - 6 + 22

- 24 + 12d = 2d + 16 ( subtract 2d from both sides )

- 24 + 10d = 16 ( add 24 to both sides )

10d = 40 ( divide both sides by 10 )

d = 4

Answer:

Has one solution

Step-by-step explanation:

3 x+1-1=10-1

3x=9

9÷3

x=3

In this implementation, we used a total of 7 NAND gates (N1, N2, N3, N4, N5, N6, and N7).

To implement the Boolean function AB+C using up to 4 NAND gates, we can break it down into multiple steps. Each step involves using NAND gates to perform logical operations and combine the inputs in a specific way. Here's one possible implementation:

Step 1:
Create the NAND gates for the individual inputs and their negations:
- Create NAND gate N1 with inputs A and A (A NAND A).
- Create NAND gate N2 with inputs B and B (B NAND B).
- Create NAND gate N3 with inputs C and C (C NAND C).

Step 2:
Combine the inputs using NAND gates:
- Create NAND gate N4 with inputs A and B (A NAND B).
- Create NAND gate N5 with inputs N4 (output of N4) and N4 (output of N4 NAND N4). This is equivalent to inverting the output of N4.
- Create NAND gate N6 with inputs N5 (output of N5) and N5 (output of N5 NAND N5). This is equivalent to inverting the output of N5.

Step 3:
Combine the outputs of Step 2 with the C input:
- Create NAND gate N7 with inputs N6 (output of N6) and C.
- The output of N7 represents the desired function AB+C.

In this implementation, we used a total of 7 NAND gates (N1, N2, N3, N4, N5, N6, and N7).

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Answer:

Step-by-step explanation:

Table I

Given function is,

f(x) = \(b^x\)

From the table attached,

For x = 0.827, value of function f(0.827) = 5,

f(0.827) = \(b^{0.827}\)

Therefore, \(b^{0.827}=5\)

\(\text{log}(b^{0.827})=\text{log}(5)\)

0.827[log(b)] = log(5)

log(b) = 0.8452

b = \(10^{0.8452}\)

b = 7

Therefore, function 'f' will be,

f(x) = \(7^x\)

For f(x) = 9,

9 = \(7^x\)

log(9) = log(\(7^x\))

log(9) = x[log(7)]

x = 1.129

Table II

Given function is g(x) = \(\text{log}_b(x)\)

From the given table,

For x = 7, g(x) = 1

1 = \(\text{log}_b(7)\)

\(b^1=7\)

b = 7

Therefore, the function 'g' will be,

g(x) = \(\text{log}_7(x)\)

For g(x) = 1.318

1.318 = \(\text{log}_7(x)\)

\(x=7^{1.318}\)

\(x=12.9968\)

\(x=13.997\)

Answer:

am confused so this is the best i can do with what was given.

Step-by-step explanation:

\(5x=y\\\)

x = number of questions correct

y = total number of points

Answer:

1. 8/$12=21/$x then cross multiply.

2. 1/$1.5, we're looking for cost so $1 is more reasonable

3. $31.5

Step-by-step explanation:

12x 21/ 8 = 31.5

The mean, median, and mode are:

Mean = 10

Median = 8

Mode = 8

To find the mean, median, and mode of the given set of numbers: 5, 8, 18, 1, 14, 6, 8, 13, 8, 19, we can perform the following calculations:

Mean: The mean is calculated by summing up all the numbers and dividing by the total count of numbers.

Mean = (5 + 8 + 18 + 1 + 14 + 6 + 8 + 13 + 8 + 19) / 10

= 100 / 10

= 10

Therefore, the mean is 10.

Median: The median is the middle value when the numbers are arranged in ascending order. If there are an odd number of values, the median is the middle number. If there are an even number of values, the median is the average of the two middle numbers.

Arranging the numbers in ascending order: 1, 5, 6, 8, 8, 8, 13, 14, 18, 19

Since there are 10 numbers, the median is the average of the two middle numbers, which are the 5th and 6th numbers:

Median = (8 + 8) / 2

= 16 / 2

= 8

Therefore, the median is 8.

Mode: The mode is the number(s) that appear(s) most frequently in the set.

In this case, the number 8 appears three times, which is more than any other number.

Therefore, the mode is 8.

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Answer:

the answer is 1

Step-by-step explanation: