A cyclist travels 17 km from home to the park.
She leaves home at 17:15 and arrives at the park at 17:45.
What is her average speed in km/h?

Answer:

\( (x + 6 {)}^{6} = {x}^{6 } + 36{x}^{5} + 540{x}^{4} + 4320 {x}^{3} + 19440{x}^{2}+ 46656{x}^{} + 46656 \)

Step-by-step explanation:

we want to solve the following binomial:

\((x + 6 {)}^{6} \)

There is a handy way to expand powers of binomials which is known as binomial theorem . and it describes the algebraic expansion of powers of a binomial. binomial theorem is given by

\( \displaystyle (a + b {)}^{n} = \sum _{k = 0 }^{n} \binom{n}{k} {a}^{n - k} {b}^{k} \)

comparing (x+6)⁶ to (a+b)ⁿ , we get

now substitute them on the formula which yields:

\( \displaystyle (x + 6 {)}^{6} = \sum _{k = 0 }^{n} \binom{6}{k} {x}^{6 - k} \cdot {6}^{k} \)

converting the summation notation into sum yields:

\( \displaystyle (x + 6 {)}^{6} = \binom{6}{0} {x}^{6 - 0} \cdot {6}^{0} + \binom{6}{1} {x}^{6 - 1} \cdot {6}^{1} + \binom{6}{2} {x}^{6 - 2} \cdot {6}^{2} + \binom{6}{3} {x}^{6 - 3} \cdot {6}^{3} + \binom{6}{4} {x}^{6 - 4} \cdot {6}^{4} + \binom{6}{5} {x}^{6 - 5} \cdot {6}^{5} + \binom{6}{6} {x}^{6 - 6} \cdot {6}^{6} \\ \implies(x + 6 {)}^{6} = \binom{6}{0} {x}^{6 } \cdot 1 + \binom{6}{1} {x}^{5} \cdot {6} + \binom{6}{2} {x}^{4} \cdot 36+ \binom{6}{3} {x}^{3} \cdot 216 + \binom{6}{4} {x}^{2} \cdot 1296+ \binom{6}{5} {x}^{} \cdot 7776+ \binom{6}{6} {x}^{0} \cdot 46656 \\ \implies(x + 6 {)}^{6} = 1 \cdot {x}^{6 } \cdot 1 + 6 \cdot{x}^{5} \cdot {6} + 15 \cdot {x}^{4} \cdot 36+ 20 \cdot {x}^{3} \cdot 216 + 15 \cdot{x}^{2} \cdot 1296+ 6 \cdot {x}^{} \cdot 7776+ 1 \cdot {x}^{0} \cdot 46656 \\ \implies \boxed{ (x + 6 {)}^{6} = {x}^{6 } + 36{x}^{5} + 540{x}^{4} + 4320 {x}^{3} + 19440{x}^{2}+ 46656 {x}^{} + 46656 }\)

and we're done!

The area under the standard normal curve to the left of z = 1.72 is 0.0427. To find the area to the right of z = 1.72, we can subtract the area to the left from 1.

Subtracting 0.0427 from 1 gives us an area of 0.9573. Therefore, the area under the standard normal curve to the right of z = 1.72 is approximately 0.9573.In the standard normal distribution, the total area under the curve is equal to 1. Since the area to the left of z = 1.72 is given as 0.0427, we can find the area to the right by subtracting this value from 1. This is because the total area under the curve is equal to 1, and the sum of the areas to the left and right of any given z-value is always equal to 1.

By subtracting 0.0427 from 1, we find that the area under the standard normal curve to the right of z = 1.72 is approximately 0.9573. This represents the proportion of values that fall to the right of z = 1.72 in a standard normal distribution.

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Answer:

0.03172

Step-by-step explanation:

Leading zeros (Zero before non-zero numbers) are not significant

0.02435 have 4 sigfig, round off to 0.0244, 3 sigfig

0.00732+0.0244 =0.03172

Answer:

its 60 / (72/12) + 34 = 44. So divide, divide, add.

Step-by-step explanation:

First, solve the what's in the parentheses. 72/12 = 6.

60/6 = 10.

34+10 = 44.

a. The probability that 1 or more nonconforming units are found is 0.2311.

b. The probability that exactly 3 units are nonconforming is 0.000058.

a. To solve the problem, you can use the complement rule. The complement rule states that the probability of an event occurring is 1 minus the probability of the event not occurring. So, in this case, the probability that no nonconforming units are found in a sample of 25 units is:

P(no nonconforming) = (0.99)²⁵ = 0.787.

Therefore, the probability that 1 or more nonconforming units are found is:

P(1 or more nonconforming) = 1 - P(no nonconforming) = 1 - 0.787 = 0.213.

Rounded to four decimal places, this is 0.2311.

b. To solve the problem, you can use the binomial probability formula:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k).

Here, n = 25 is the sample size, k = 3 is the number of nonconforming units, and p = 0.01 is the probability of a unit being nonconforming.

Using the formula, we get:

P(X=3) = (25 choose 3) * (0.01)³ * (0.99)²² = 2300 * 0.000001 * 0.5459 = 0.000058.

Rounded to six decimal places, this is 0.000058.

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Answer: c. 6

Step-by-step explanation:  

Option-C is correct that is 6 number from the set {4 , 5, 6, 7} makes the equation 4(8 - x) = 8 true.

Given that,

We have to find which value of the x from the set {4 , 5, 6, 7} makes the equation 4(8 - x) = 8 true.

We know that,

A group of well defined objects is referred to as a set. Only on the basis of simplicity are the objects of a set considered to be distinct.

A family or collection of sets are common names for a group of sets.

So,

The set has 4 numbers by substituting the numbers we get to know if the equation is true or false.

Take the equation,

4(8 - x) = 8

If x = 4,

4(8 - 4) = 8

4 × 4 = 8

16 ≠ 8

Now, If x = 5,

4(8 - 5) = 8

4 × 3 = 8

12 ≠ 8

Now, If x = 6,

4(8 - 6) = 8

4 × 2 = 8

8 = 8

And, If x = 7,

4(8 - 7) = 8

4 × 1 = 8

4 ≠ 8

Therefore, Option-C is correct that is number 6.

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Answer:

2,562,300 Litres per year (Pls forgive me if I'm wrong, I was doing this quickly during class.)

Step-by-step explanation:

(Forgive the first part of the PDF, the answer is on the second page.)

-Hope this helped.

An informal proof uses specific examples to show that a conjecture is true.

An informal proof is a proof that is written in plain language and is intended to be read by someone who is familiar with the subject matter but not necessarily trained in mathematical rigor or logic. These proofs are usually less formal than formal proofs but are still valid and are often used in textbooks, journals, and other publications.

The main difference between formal and informal proofs is that formal proofs rely on a strict set of rules and symbols, while informal proofs use more everyday language and examples. Informal proofs are often easier to understand than formal proofs because they are written in a more conversational tone and use everyday language and examples that most people are familiar with.

Informal proofs typically use specific examples to show that a conjecture is true. These examples are often drawn from real-world situations or other areas of mathematics and are used to illustrate the key concepts involved in the proof.

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Answer:

Since Manish hit the target 25 - 5 = 20 times, he earned 15 * 20 = ₹ 300. Since he missed 5 times, he lost 5 * 5 = ₹ 25, therefore, he only earned 300 - 25 = ₹ 275.

Answer:

Manish hit the target=25-5=20times

He he earned=15×20=₹300

Since he missed 5 times he lost 5×5=₹25

Therefore,he only earned 300-25=₹275

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Answer:

No solution

Step-by-step explanation:

-2x + 3 + x > -x - 1

-2x + x + x > -1 - 3

0 > -4

There is no solution for this inequality

Answer: -4/5

Step-by-step explanation:

Any positive number/fraction multiplied by -1 will become negative

ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following division

Now we carry out the operation and we have:

We divide the quotients of the higher degree terms of the numerator and the divisor

Then we multiply this quotient by the denominator

Now, we subtract this value from the numerator and we have

Therefore the final result would be

The required confidence interval for the population mean is  (6.296 , 7.104).

A confidence interval for a populace mean gives potential qualities the genuine populace mean will accompany a specific degree of certainty.

Standard deviation(S) = 1.9, Mean(x) = 6.7,  CL = 0.95 , n = 85

Then, α = 0.05

\(Z_{\alpha /2}\\\) = \(Z_{0.25}\)  = -1.96

Margin of error (E) = \(Z_{0.25}\\\) ×S/√85

E = -1.96×1.9/9.21 = 0.404

Then lower level = x-E = 6.7-0.404 = 6.296

Upper level = 6.7+0.404 = 7.104

Thus, required interval is (6.296 , 7.104)

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Step-by-step explanation:

1,

It is found that m divided by n is equal  to 8/7.

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.

Thus, if 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.

Division, thus, can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.

Thus,  a/ b = a divided in b equal parts.

If n divided by m equals 7/8, then m divided by n equal.

n / m = 7/8

Then m/n = 8/7

Therefore,  m divided by n is equal  to 8/7.

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Answer:

B

Step-by-step explanation:

Circumference is 3.14*d

Where d is the diameter.

3.14*8000

= 25120

The Earth has a circumference of 25120 miles approximately.

Answer:

B. 25,120 miles.

Step-by-step explanation:

Circumference = π * diameter

= 3.14 * 8000

= 25,120 miles.

Answer:

g(-3) = 18

Step-by-step explanation:

The equation is given so plug in -3 into x

g(-3) = -5(-3) + 3

g(-3) = 15 + 3     here you multiple -5 by -3 and since they're both negatives it cancels out and the product becomes positive.

g = 18                 now just simplify by adding the numbers

Answer:

A

Step-by-step explanation:

If we evaluate 3/x at x=1, we get 3/1 = 3.

The only one that showed that is graph A, and we can further check by evaluating other points, such as when x = 1/2, y = 6, and that's shown on graph A.

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Graph A, correctly represents the function y = x/3.

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

From the table of y = 3/x,

The value of (x, y) are (0.5, 6), (1, 3), (2, 1.5), (3, 1) and (4, 0.75).

Now, Observe graphs A, B, and C.

Graph A, when x = 0.5, y = 6, when x = 1 y = 3 so graph A matches with our table.

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1.The equivalent algebraic expression becomes: y(x + 5) + 2(x + 5)

2.The common factor in the two terms is (x + 5). Both terms have (x + 5) as a factor.

3. The polynomial can be expressed as a product of two binomials: (x + 5)(y + 2)

Let's start by factoring out the common factors from each group:

From the first group (xy + 5y), we can factor out y, which gives us y(x + 5).

From the second group (2x + 10), we can factor out 2, which gives us 2(x + 5).

So, the equivalent algebraic expression becomes:

y(x + 5) + 2(x + 5)

The common factor in the two terms is (x + 5). Both terms have (x + 5) as a factor.

Now, using the distributive property, we can factor out (x + 5) from both terms:

y(x + 5) + 2(x + 5) = (x + 5)(y + 2)

The polynomial can be expressed as a product of two binomials: (x + 5)(y + 2).

In this factored form, we can see that we have two binomial expressions multiplied together. The first binomial (x + 5) represents the common factor, and the second binomial (y + 2) represents the remaining terms after factoring out the common factor.

Overall, the factoring process involved identifying the common factor, using the distributive property to factor it out, and expressing the polynomial as a product of two binomials. This factored form can be useful in further simplification, solving equations, or analyzing the polynomial's behavior

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Check the picture below.

Make sure your calculator is in Degree mode.

Answer:  The slope-intercept form is y = -2x + 10

Step-by-step explanation:

Step 1: The y-intercept is the point where x=0, so that is (0,10)

Step 2: Use the points (-2,14) and (-1,12) to find the slope

Slope (m) = ΔY/ΔX = -2/1 = -2

Step 3: The slope-intercept form is:

y = mx+b

y = (step 2 value) x + (step 1 value)

y = -2x+10

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The solutions for the given conditions are;

a)Twenty people are to be divided into two teams with ten players on each team, this can be done in 184756 ways.

(b)Thirty-five discrete math students are to be divided into seven discussion groups, each consisting of five students, this can be done in \(\frac{35!}{(5!)^7}\)

Here we are given two different cases where we can solve both cases using Combinations.

(a) Twenty people are to be divided into two teams with ten players on each team, this can be done in;

⇒ ²⁰ C ₁₀ * ¹⁰ C ₁₀

= \(\frac{20!}{10! *(20-10)!}\) * 1

= 184,756

(b) Thirty-five discrete math students are to be divided into seven discussion groups, each consisting of five students, this can be done in;

⇒ ³⁵ C ₅ * ³⁰ C ₅ * ²⁵ C ₅ * ²⁰ C ₅ * ¹⁵ C ₅ * ¹⁰ C ₅ * ⁵ C ₅

= \(\frac{35!}{5!(35-5)!}*\frac{30!}{5!(30-5)!}*\frac{25!}{5!(25-5)!}*\frac{20!}{5!(20-5)!}*\frac{15!}{5!(15-5)!}*\frac{10!}{5!(10-5)!}*1\)

= \(\frac{35!}{(5!)^7}\)

Hence;

(a)Twenty people are to be divided into two teams with ten players on each team, this can be done in 184756 ways.

(b)Thirty-five discrete math students are to be divided into seven discussion groups, each consisting of five students, this can be done in \(\frac{35!}{(5!)^7}\)

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a) P = 0.04*0.35 + 0.13*0.3 + 0.075*0.35 = 0.07925

b) P = 0.04*0.35/0.07925 = 0.17666

are  the probability that a randomly selected automobile manufactured by the company will have a defective microprocessor

Probability = number of paths to success. A total number of possible outcomes. For example, the probability of flipping a coin and getting heads is ½. This is because there is one way to get heads and the total number of possible outcomes is 2 (heads or tails). We write P(heads) = ½.

Probability is a measure of the likelihood that an event will occur. Many events cannot be predicted with complete certainty. We can only predict the probability that an event will occur. H. Possibility of using it.

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Answer:

its option E

Step-by-step explanation:

We can use the bank reconciliation statement to find out the correct amount of July bank disbursements. Let's go through each reconciling item one by one:1. Bank error disbursement for 57 recorded twice in July- This means that the bank recorded a disbursement of 57 dollars twice in their records. This would cause the bank balance to decrease by 57 dollars more than it should have. So, we need to add back 57 dollars to the disbursements in the bank statement.2. July NSF check of 59 recorded by the bank as a disbursement and by the books as a negative receipt - This means that the bank recorded the check as a disbursement but it was not cleared due to insufficient funds. The books recorded it as a negative receipt to reflect this fact. So, we need to subtract 59 dollars from the disbursements in the bank statement.3. NSF check of 54 recorded by the bank as an August disbursement - This means that the bank recorded the check as a disbursement in August but it was actually written in July. So, we need to subtract 54 dollars from the disbursements in the bank statement.Let's start with the June 30 balance of 80 dollars.Adding July receipts of 5200 dollars gives us a total of 5280 dollars.Subtracting the reconciling item 1 of 57 dollars gives us 5223 dollars.Adding reconciling item 2 of 59 dollars gives us 5282 dollars.Subtracting reconciling item 3 of 54 dollars gives us a final amount of 5228 dollars.Therefore, the correct amount of July bank disbursements is $5228.Option e. $270 is not the correct answer.  

Hope i helped :)

To increase usability in a spreadsheet, you can use comments, descriptive labels, and data validation.

To increase usability in a spreadsheet, you can utilize the following techniques:

1. Comments: Comments allow you to add explanatory notes or instructions within cells. They can provide additional context or clarify the purpose of certain data or formulas. Users can view comments by hovering over the respective cell, making it helpful for collaboration and documentation.

2. Descriptive Labels: Instead of relying solely on cell references or generic labels, use descriptive labels that clearly indicate the purpose of each column, row, or range of cells. This approach enhances readability and makes it easier for users to understand the data and navigate through the spreadsheet.

3. Data Validation: Implement data validation rules to ensure the accuracy and integrity of the data entered into the spreadsheet. Data validation allows you to define constraints or conditions for input, such as numeric ranges, predefined lists, or specific text formats. It helps prevent errors and assists users in entering valid data.

4. Formatting: Properly formatting the cells, columns, and rows can greatly enhance usability. Use consistent formatting for similar types of data, apply color schemes or conditional formatting to highlight important information or trends, and adjust the column widths and row heights to optimize readability.

5. Sheet Organization: Organize the spreadsheet by using multiple sheets if needed. Group related information on separate sheets, and provide clear sheet names that reflect the content or purpose of each sheet. This helps users locate and navigate to specific sections or data within the spreadsheet.

6. Clear Instructions or Documentation: Provide clear instructions or documentation either within the spreadsheet or as separate documentation. Explain the purpose of the spreadsheet, any specific procedures or workflows, and how to interpret the data or use any embedded formulas or macros. This helps users understand the spreadsheet's functionality and ensures consistent usage.

7. Error Handling: Implement error handling mechanisms to provide informative error messages or alerts when users input incorrect or incompatible data. Clear error messages guide users in correcting their input and reduce frustration when dealing with potential errors.

By incorporating comments, descriptive labels, data validation, formatting, sheet organization, clear instructions/documentation, and error handling, you can significantly enhance the usability of your spreadsheet and make it more user-friendly for both yourself and others who interact with it.

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Answer:

e = 5

Step-by-step explanation:

Answer:

394 miles.

(its hard to explain but you need to spit 1356 and add 284 to one half)

Answer:

820

Step-by-step explanation:

Let us call the trip back x. The trip back is 284 miles smaller than the trip back, so our equation can be:

x + x + 284 = 1356

2x + 284 = 1356

2x = 1072

x = 536

The we do 536 + 284 because the trip there was 284 miles longer, so that is 820

Answer:

10

Step-by-step explanation:

24-14=10

Do these equations backwards to find the answer you are looking for.

Answer:

10+14=24

24-14=10

Answer is 10

Using Baye's theorem,  the probability that a randomly selected job applicant who tests positive is a drug user is approximately 0.2332, or 23.32%

Let's define the events:

A: Applicant is a drug user

B: Applicant tests positive

We are given the following information:

P(A) = 0.09 (probability that a potential hire is a drug user)

P(B|A) = 0.77 (sensitivity or true positive rate)

P(B|A') = 0.25 (complement of sensitivity, false negative rate)

P(A') = 1 - P(A) = 1 - 0.09 = 0.91 (probability that a potential hire is not a drug user)

P(B|A') = 0.75 (specificity or true negative rate)

We need to find P(A|B), which is the probability that the applicant is a drug user given that they tested positive.

According to Bayes' theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)

To calculate P(B), we can use the law of total probability:

P(B) = P(B|A) * P(A) + P(B|A') * P(A')

Substituting the given values:

P(B) = (0.77 * 0.09) + (0.25 * 0.91) = 0.0693 + 0.2275 = 0.2968

Now we can calculate P(A|B):

P(A|B) = (0.77 * 0.09) / 0.2968 = 0.0693 / 0.2968 ≈ 0.2332

Therefore, the probability that a randomly selected job applicant who tests positive is a drug user is approximately 0.2332, or 23.32%.

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The probability of getting exactly one face card is 0.72.

According to the questions two cards are drawn from a deck.

Since, we know that

Total number of cards in a deck = 52

Total number of face cards =  3 × 4 = 12

So, the number of ways of selecting 2 cards from a deck = \(^{52} C_{2}\)

And, the total number of ways of  getting exactly one face cards

= \(^{12} C_{1} \times ^{40} C_{1}\)  + \(^{40} C_{1} \times ^{12} C_{1}\)

= 2\(^{40} C_{1} \times ^{12} C_{1}\)

Therefore, the probability of getting exactly one face card

= \(\frac{2(^{40} C_{1} \times ^{12} C_{1})}{^{52C_{2} } }\)

\(= \frac{2(\frac{40 \times 39!}{1!\times 39!} \frac{12\times 11!}{11!}) }{\frac{52\times 51\times 50!}{2!\times50!} }\)

\(= \frac{2(40\times 12)}{26\times 51}\)

\(=\frac{2\times 480}{1326}\)

= 0.72

Hence, the probability of getting exactly one face card is 0.72.

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