use the method of example 9.5.10 to answer the following questions. (a) how many 14-bit strings contain exactly six 1's? the number of 14-bit strings that contain exactly six 1's equals the number of ways to choose the positions for the 1's in the string, namely, . (b) how many 14-bit strings contain at least eleven 1's? (c) how many 14-bit strings contain at least one 1? (d) how many 14-bit strings contain at most one 1?

Answer:

Simplify- 12y + 20.  Factor- 4(−3y+5)

Step-by-step explanation:

Simplify- 12y + 20.

Let's answer: Simplify

4 + −5y + (−2) (3.5y) + (−2) (−8)

= 4+ −5y + −7y + 16

Combine Term:

4+ −5y + −7y + 16

( −5y +− 7y ) + ( 4 + 16 )

Our answer: −12y + 20

Let's answer: Factor

Factor- 4 −5y −2 ( 3.5y −8 )

−12y + 20

Our answer: 4 ( −3y +5 )

Answer:

Step-by-step explanation:

1234=454665-5656=56-5

The square root of 13 is 3.6055512755. The next whole number is 4.

The value of the t score for a 95% confidence interval for degree of freedom 16 will be 2.120.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The confidence interval = 95%

And, Size of sample = 17

Now,

Since, The confidence interval = 95%

And, Size of sample (n) = 17

Hence, The degree of freedom (n - 1) = 16

Thus, The value of the t score for a 95% confidence interval for degree of freedom 16 will be 2.120.

Therefore, The value of the t score for a 95% confidence interval for degree of freedom 16 will be 2.120.

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Answer:

11.5 & 25.5

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The value of expression (a + b + c + d) is 20

Consider given equations x + y = 4       ........(1)

and 3xy = 4        .........(2)

The solutions of given equations are of the form \($x = \frac{a \pm b\sqrt{c}}{d}$\)

where a, b, c, and d are positive integers and the expression is completely simplified.

From equation (2),

y = 4/3x

Substitute above value of y in equation (1),

x + y = 4

x + (4/3x) = 4

3x² + 4 = 12x

3x² - 12x + 4 = 0

After solving above quadratic equation we get,

\(x=\frac{6\pm 2\sqrt{6} }{6}\)

Comapring this solution with \($x = \frac{a \pm b\sqrt{c}}{d}$\) we get,

a = 6, b = 2, c = 6 and d = 6

Now we find the value of expression (a + b + c + d)

a + b + c + d

= 6 + 2 + 6 + 6

= 20

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Answer:

\(\sqrt[8]{197^{7} }\)

Step-by-step explanation:

\(\sqrt[8]{197^{7} }\)

Total number of pencils and pens bought by Henry = 35.

What is the unitary method of problem solving?
The unitary technique, in its most basic form, is used to calculate the value of a single unit from a specified multiple. The unitary approach can be used to complete it. Additionally, after determining the value of a single unit, we can multiply that value by the number of units needed to determine the value of the additional units. The concept of ratio and proportion is mostly applied using this way.

Given, for every 3 pencils, number of pens bought = 2
Therefore, every 1 pencil, number of pens bought = 2/3
Thus, for 21 pencils, number of pens bought = (2/3)*21 = 14
Therefore, total number of pencils and pens bought by Henry = 21 + 14 = 35.

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Answer:

A. 35 deg

Step-by-step explanation:

Use the exterior angle measure theorem.

The measure of the exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

60 + x = 95

x = 35

Answer:

ya about 1 billion

Dang that's a lot

Answer:

Step-by-step explanation:

Given the complex expression, (3 + i)(1+2i) we are to expand it in the form a+bi as shown;

(3 + i)(1+2i)

= 3(1)+3(2i)+1(i)+i(2i)

= 3 + 6i + i + 2i²

= 3 + 71 + 2i²

According to complex notation i² = -1

;Substitute

= 3+7i+2(-1)

= 3 + 7i - 2

= 1 + 7i

Comparing 1+7i with a + bi

a = 1 and b = 7

The values of a and b are 1 and 7 respectively and this can be determined by using the arithmetic operations.

Given :

Expression -- (3 + i)(1+2i)

The following steps can be used to determine the values of 'a' and 'b':

Step 1 - Write the given expression.

= (3 + i)(1+2i)

Step 2 - Multiply 3 by (1 + 2i) and multiply i by (1 + 2i) in the above expression.

= 3 + 6i + i + 2(i\(\times\)i)

Step 3 - The value of i\(\times\)i = -1. So put the value (i\(\times\)i) in the above expression.

= 3 + 6i + i - 2

Step 4 - Add 6i and i in the above expression.

= 3 + 7i -2

Step 5 - Subtract 2 from 3 in the above expression.

= 1 + 7i

Step 6 - Compare the above expression to a+bi.

a = 1

b = 7

So, the values of a and b are 1 and 7 respectively.

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Answer:

16

Step-by-step explanation:

18-7=11 2+3=5. 11+5=16

according to BODMAS rule

18 - 7 × 5

18 - 35

-17

The smallest measurement used in the apothecary system for volume is the minim.

The apothecary system is an outdated system of measurements primarily used in pharmacy and medicine. It includes various units for measuring volume, weight, and other quantities.

In the apothecary system, the minim is the smallest unit of measurement for volume. It is equivalent to approximately 0.0616 milliliters.

The minim is a small unit of measurement and is typically used for precise dosing of liquids in the apothecary system. It is commonly used in pharmaceutical compounding and in the preparation of medications.

However, it's important to note that the apothecary system is no longer widely used in modern healthcare practices. The metric system, with units such as milliliters and liters, has become the standard for measuring volume in most countries.

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Zaid picked 6 and 1-eighth kilograms of peaches, which is equivalent to 49/8 kilograms.

Let's call the amount of peaches Zaid's sister picked "x" kilograms. We know that Zaid picked 3-eighths kilogram more than his sister, which can be written as: 49/8 = x + 3/8
To solve for "x," we can subtract 3/8 from both sides: 49/8 - 3/8 = x
Simplifying the left side: 46/8 = x
Reducing the fraction: 23/4 = x
So Zaid's sister picked 23/4 kilograms of peaches, or 5 and 3/4 kilograms.

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Zaid's sister picked 5 and 3-quarters kilograms of peaches.

The question involves a scenario where Zaid has picked 6 and 1-eighth kilograms of peaches, which is 3-eighths of a kilogram more than the weight of the peaches his sister picked.

To find out how many kilograms Zaid’s sister picked, we subtract 3-eighths of a kilogram from Zaid's total weight of peaches, because that is the extra amount Zaid picked compared to his sister.

So, Zaid's sister picked 6 kilograms minus 1-quarter kilogram, which is 5 and 3-quarters kilograms of peaches.

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Parallelograms are quadrilaterals with parallel and congruent opposite sides

The value of the variable is 30

The given parameters are:

RZ = 6x + 9

SW = 13x - 12

From the parallelogram, we have the following relationship between lengths RZ and SW

\(SW =2 * RZ\)

So, we have:

\(13x - 12 = 2 * (6x + 9)\)

Open brackets

\(13x - 12 = 12x + 18\)

Collect like terms

\(13x - 12x = 12 + 18\)

\(x = 30\)

Hence, the value of the variable is 30

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Answer:

The fraction representing the number of bad oranges can be written as 6/30. This fraction can be simplified by dividing both the numerator and the denominator by 2, which gives us 3/15. This fraction is already in its lowest terms, so 3/15 is the final answer.

Step-by-step explanation:

0.007 kg

\(1000\ grams=1\ kg\\ 7\ grams=0.007\ kg\\ Check\ conversion\)

I hope this helps you

:)

Answer:

p = 1/3

Step-by-step explanation:

Total days in April = 30

Two digit odd days = 10

p =10/30

p = 1/3

Answer:

if the odd number is 2 then it will be 2/4 that would be the probability.

The Z-score for the observation of a sample mean of 3.6 pounds is 2.5.

The probability of obtaining a sample mean of 3.4 pounds or larger is 0.4207.

A) To find the Z-score for a sample mean of 3.6 pounds with a sample size of 25, we use the formula:

Z = (x - μ) / (σ / sqrt(n))

where:

x = Sample mean

μ = Population mean

σ = Population standard deviation

n = Sample size

Substituting the values, we have:

Z = (3.6 - 3.2) / (0.8 / sqrt(25))

Z = 0.4 / (0.8 / 5)

Z = 0.4 / 0.16

Z ≈ 2.5

B) To find the probability of obtaining a sample mean of 3.4 pounds or larger with a sample size of 64, calculate the area under the standard normal distribution curve to the right of the Z-score.

Using a Z-table, the area to the right of a Z-score of 0.2 is approximately 0.4207.

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The area of kite ABCD is equal to half the product of the sum of its diagonals and the height between them.

Since kite ABCD is divided into two triangles by its diagonals, we can find the area of the kite by finding the sum of the areas of these two triangles.

Let AC and BD be the diagonals of the kite, intersecting at point E. Then triangle ABE and triangle CDE are the two triangles formed by the diagonals.

The area of a triangle can be found using the formula: Area = (base x height) / 2

For triangle ABE, the base is AB and the height is the distance from E to the line containing AB. Similarly, for triangle CDE, the base is CD and the height is the distance from E to the line containing CD.

Since the diagonals of a kite are perpendicular and bisect each other, the distance from E to the line containing AB is the same as the distance from E to the line containing CD.

Therefore, the heights of the two triangles are equal.

So, we can find the area of ABCD as follows:

Area of ABCD = Area of triangle ABE + Area of triangle CDE

= (AB x height)/2 + (CD x height)/2

= (AB + CD) x height / 2

Therefore, the area of kite ABCD is equal to half the product of the sum of its diagonals and the height between them.

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when the price is equal to the market equilibrium price, total surplus is maximized.

What is surplus?

Making the most of society's well-being is a desired goal for an economic system. Do free markets perform that? Buyers must profit from their purchases, and sellers must profit from their sales, in order to provide an answer. Consumer surplus is the difference between the price consumers are willing to pay and the price they actually pay for a commodity or service. When individuals buy something, they typically pay less than they would have otherwise. Similar to producers, sellers might command a higher price for a good than it costs them to make it; this is known as producer surplus because it occurs when the cost of production is less than the price at which the good is sold.

Consumer Surplus = Willingness to Pay Price − Market Price

Producer Surplus = Market Selling Price − Economic Cost

Total Surplus = Consumer Surplus + Producer Surplus

Only the most effective producers will be able to produce a product for less than the market price in highly competitive markets. Therefore, only those vendors will create a good.

Therefore, when the price is equal to the market equilibrium price, total surplus is maximized.

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Step-by-step explanation:

4 /5x+6y=15

4/5x+6y-15=0

4x+30y-75=0

Answer:        All whole numbers are rational numbers

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a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.

b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25

c) The probability that between one and three students show up = 0.7

d) The probability that the professor shows up = 0.20

First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.

x        p(x)

0       0.20

1       0.25

2       0.30

3       0.15

4       0.10

The probability histogram of this data is shown below.

The probability that at least two students show up would be,

P(x ≥ 2) = p(2) + p(3) + p(4)

P(x ≥ 2) = 0.30 + 0.15 + 0.10

P(x ≥ 2) = 0.55

Now the probbability that more than two students show up:

P(x > 2) = p(3) + p(4)

P(x > 2) = 0.15 + 0.10

P(x > 2) = 0.25

The probability that between one and three students show up would be:

P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)

P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15

P(1 ≤ x ≤ 3) = 0.7

And the probability that the professor shows up would be: p = 0.20

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Answer:

9) C: x=4, y=2rt3

10) A: XY/YZ

11) A: XY/XZ

Step-by-step explanation:

9 - that is a 30, 60, 90 triangle so the ratios will be a, root3a, 2a

10 - tan = opposite / adjacent

11 - cos = adjacent/hypotenuse

Answer:

9. (c)

10. (a)

11. (a)

................

Given: A team of 3 employees is preparing 20 reports. Mary takes 30 minutes to complete a report. Matt takes 45 minutes to complete a report.

All reports are completed in 4 1/2 hours. To Find: How long does it take the third team member to complete a report?Solution: Let the third employee takes x minutes to complete a report work done by Mary in 1 minute = 1/30Work done by Matt in 1 minute = 1/45Work done by the third employee in 1 minute = 1/x Total work done by all three in 1 minute = 1/30 + 1/45 + 1/x (As all are working together) a Total number of reports to be prepared = 20Therefore, total work = 20Now,

we know that all reports are completed in 4 1/2 hours = 9/2 hours∴ Total time = 9/2 x 60 = 270 minutes according to the problem statement, Total work = Total time x Total work done by all three in 1 minute20 = 270 (1/30 + 1/45 + 1/x)Solving the above equation for x, we get :x = 90 minutes therefore, it takes the third team member 90 minutes to complete a report.

Answer: 90 minutes.

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Let's represent the third team member as t. Mary takes 30 minutes to complete a report, while Matt takes 45 minutes to complete a report.

Thus, it takes the third team member 3 hours to complete a report.

Therefore, we can use the information given to form an equation. We are given that the team is preparing 20 reports, so:

30 minutes/report × M reports + 45 minutes/report × N reports + T minutes/report × O reports = 4.5 hours

To make the equation simpler, let the unit conversion 4.5 hours to minutes:

4.5 hours × 60 minutes/hour = 270 minutes

Thus:

30M + 45N + TO = 270

O= 20 - M - N

From the third team member: TO = T × 20

Therefore:

30M + 45N + T × 20 = 270

Solving for T:

30M + 45N + 20T = 270

T = (270 - 30M - 45N)/20

We know that there are only three members in the team, and that M and N have already been defined, so we can substitute these values:

T = (270 - 30(20) - 45(0))/20

T = 3

Thus, the time taken by the third team member is 3 hours to complete a report.

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The pieces of cloth are beyond the standard at 0.05 level of significance.

We can use a one-sample t-test to determine if the mean length of the 35 pieces of cloth is significantly different from the standard length of 3.25 meters.

The null hypothesis is that the mean length of the cloth pieces is equal to the standard length:

H0: μ = 3.25

The alternative hypothesis is that the mean length of the cloth pieces is greater than the standard length:

Ha: μ > 3.25

We can calculate the test statistic as:

t = (x - μ) / (s / √n)

where x is the sample mean length, μ is the population mean length (3.25 meters), s is the sample standard deviation (0.52 meters), and n is the sample size (35).

Plugging in the values, we get:

t = (3.52 - 3.25) / (0.52 / √35) = 3.81

Using a t-table with 34 degrees of freedom (n-1), and a significance level of 0.05 (one-tailed test), the critical t-value is 1.690.

Since our calculated t-value (3.81) is greater than the critical t-value (1.690), we reject the null hypothesis and conclude that the mean length of the 35 pieces of cloth is significantly greater than the standard length at the 0.05 level of significance.

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The fraction equivalent to 1/4 is 2/8.

To find fractions that are equivalent to 1/4, we need to identify fractions with the same value but different numerators and denominators. Let's examine the given options:

a) 2/5: This fraction is not equivalent to 1/4 since the numerator is different.

b) 2/8: This fraction is equivalent to 1/4. By simplifying 2/8, we can divide both the numerator and denominator by 2 to get 1/4.

c) 3/12: This fraction is not equivalent to 1/4 since the numerator and denominator are different.

d) 2/8: This fraction is equivalent to 1/4. Just like in option b, simplifying 2/8 gives us 1/4.

Therefore, both options b) and d) are equivalent fractions to 1/4. The fraction 2/8 is the correct answer, representing the same value as 1/4 but with different numerators and denominators.

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If the tens digit of a two-digit number is one more than the units digit and the number itself is 6 times the sum of the digits, then the solution is a two-digit number 54.

Let's assume that the units digit of the two-digit number is x. According to the problem statement, the tens digit is one more than the units digit, which means that the tens digit is x + 1. Therefore, the two-digit number can be expressed as 10(x+1) + x, which simplifies to 11x + 10.

The problem also states that the number is 6 times the sum of its digits. The sum of the digits is x + (x + 1) = 2x + 1. Therefore, we can set up an equation:

11x + 10 = 6(2x + 1)

Simplifying the equation, we get:

11x + 10 = 12x + 6

Subtracting 11x from both sides, we get:

10 = x + 6

Subtracting 6 from both sides, we get:

x = 4

Therefore, the units digit is 4, and the tens digit is one more than that, which is 5. The two-digit number is 54. We can check that this is indeed 6 times the sum of its digits:

54 = 6(4 + 5)

54 = 6(9)

54 = 54

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Answer:

18 ≤ x + 6 ≤ 34

Step-by-step explanation:

Separate this problem into 2 scenarios:

The number of bags still needed plus the 6 bags they currently have cannot be more than 34.

This can be described as the inequality x + 6 ≤ 34.

The number of bags still needed plus the 6 bags needs to be greater than or equal to 18.

This can be described as the inequality x + 6 ≥ 18

Now combine these inequalities to get the answer: 18 ≤ x + 6 ≤ 34