A cereal company packages their granola in cylindrical containers that have a diameter of 20 cm and a height of 17. 4 cm. Approximately how much granola will a container hold?

Answer: True False True true

Step-by-step explanation:

Answer:

true

false

true

true

Step-by-step explanation:

The farmer has 90 meters of fencing available to create a rectangular garden in the middle of an open field. The solution depends on how the farmer decides to allocate the fencing among the length and width.

To maximize the area of the rectangular garden, the farmer needs to determine the dimensions that will utilize the given 90 meters of fencing most effectively. Let's assume the length of the garden is L and the width is W. For a rectangular shape, the perimeter is given by P = 2L + 2W. Since the farmer has 90 meters of fencing, we can write the equation as 2L + 2W = 90. To maximize the area, we need to solve for L and W. Since the perimeter is fixed, the longer one side becomes, the shorter the other side needs to be. The solution depends on how the farmer decides to allocate the fencing among the length and width.

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Answer: Choice B

The initial amount in the account.

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

Reason:

x is the number of years

x = 0 is the starting point. Let's plug that in to find...

\(y = 982(1.07)^x\\\\y = 982(1.07)^0\\\\y = 982(1)\\\\y = 982\\\\\)

At the start, Sammy has $982 in the bank.

Side note: The 1.07 means the account is growing by 7% each year.

There are two terms in the given expression 5xy²+ 35xy².

What is meant by term?

Terms comprise expressions. A term may be a constant, a variable, or a combination of variables and constants.

What is an example of a term?

It could be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase. Single-word examples: A single phrase is 3x.

There are two terms in the equation 5xyA ^2 + 35xyA^2 that is separated by an arithmetic operator +.

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Answer:

4.65 British pound sterling

Step-by-step explanation:

\(7.50*0.62 = 4.65\)

7.5 U.S. dollars = 4.65 British pound sterling

Answer:

b) arithmetic

Step-by-step explanation:

Knowledge Needed

c and d are not valid sequence types.

Geometric Sequences are when the values of terms are found by multiplying the previous term's value by the same number.

Example:

1, 2, 4, 8, 16

x2

2, 6, 18, 54, 162

x3

20, 10, 5, 2.5, 1.25

x0.5

Arithmetic Sequences are when the values of terms are found by adding the previous term's value by the same number.

Example:

5, 6, 7, 8

+1

7, 19, 31, 43

+12

9, 6, 3, 0

-3

Question

Examine the sequence. From viewing the first 2 terms, we know that it can either be a geometric sequence that multiplies by 11/3 every time the term increases or an arithmetic sequence that adds 8 every time the term increases.

Looking at the 2nd and 3rd term, we know it is an arithmetic sequence because 19 is not equal to 11 times 11/3.

Answer:

b is 3 pythagorean theorem

Step-by-step explanation:

Answer:

your answer for B is 3

Step-by-step explanation:

this is easy its a Pythagorean Triple (with triples u dont have to do much work all u have to do is know ur Triples and its that easy)

so the Triples are

p.s you might want to write these down for the future

so if we look at this picture of the triangle we can tell its a 3,4,5 triple

and there is one missing side which is 3.

The given conditions are:The weight of women follows normal distribution with a mean of 178.1lb and a standard deviation of 49.2lb.The ejection seats of military aircraft are designed for men weighing between 135.5lb and 205lb.

The probability of women having weights between 135.5lb and 205lb is to be found.Using the normal distribution formula, the standardized score for 135.5lb and 205lb can be calculated.z = (X - μ) / σz₁ = (135.5 - 178.1) / 49.2z₁ = -0.8674z₂ = (205 - 178.1) / 49.2z₂ = 0.5480The z-tables show that 0.8078 lies between the two values of z₁ and z₂. Therefore, the probability of women having weights between 135.5lb and 205lb is 0.8078 or 80.78%. The percentage of women that have weights between those limits is 80.78%.Therefore, option B. No, the percentage of women who are excluded, which is equal to the probability found previously, shows that very few women are excluded is the correct answer.Long answer:From the given information, it is given that the weights of women are normally distributed with a mean of 178.1lb and a standard deviation of 49.2lb.

The weights of ejection seats are designed for men whose weight is between 135.5lb and 205lb.To find out how many women can fit the criteria of ejection seats, we need to calculate the probability that a woman will weigh between 135.5lb and 205lb.Using the z-score formula,z = (X - μ) / σwhere X is the value of weight, μ is the mean weight, and σ is the standard deviation of the weight of women.Using the formula for the lower weight range,z₁ = (135.5 - 178.1) / 49.2z₁ = -0.8674Using the formula for the upper weight range,z₂ = (205 - 178.1) / 49.2z₂ = 0.5480Now we can look at the standard normal distribution table to find the probability of a random variable having a value between these two values of z.In other words, we need to find P(z₁ < z < z₂). P(z₁ < z < z₂) is the probability that a woman weighs between 135.5lb and 205lb.We get this probability from the standard normal distribution table. We look up the z-score -0.8674 in the table, which gives us 0.1928. Then we look up the z-score 0.5480 in the table, which gives us 0.7086. The probability between these two z-scores is 0.7086 - 0.1928 = 0.5158. Therefore, the probability that a woman weighs between 135.5lb and 205lb is 0.5158 or 51.58%.

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Zelda can swim at a speed of 75 meters per minute in still water and the rate of the water current is 25 meters per minute.

Let's call Zelda's speed in still water "s" and the rate of the water current "c".

When swimming upstream, Zelda's speed relative to the ground is s - c. When swimming downstream, her speed relative to the ground is s + c.

We're told that Zelda can swim 50 meters per minute upstream, so we can write the equation:

s - c = 50

We're also told that she can swim twice as fast downstream, so:

s + c = 2(50) = 100

Now we have two equations with two variables. We can solve for s by adding the two equations together:

s - c = 50

s + c = 100

(s - c) + (s + c) = 50 + 100

2s = 150

s = 75

So Zelda can swim at a speed of 75 meters per minute in still water.

To find the rate of the water current, we can substitute s = 75 into either of the two equations we wrote earlier. Let's use the first one:

s - c = 50

75 - c = 50

c = 25

So the rate of the water current is 25 meters per minute.

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The 95% confidence interval for the proportion of all Californians who considered moving out of state is (0.504, 0.530). We can be 95% confident that the true proportion of all Californians who considered moving out of state lies between 50.4% and 53.0%.

The UC Berkeley Institute of Governmental Studies conducted a poll in 2019 with 4,527 respondents in California, where 51.7% of them reported considering moving out of the state. The objective is to calculate a 95% confidence interval for the proportion of all Californians who considered moving out of state, given the sample size and proportion.

B. The formula to calculate the confidence interval for a proportion is:

CI = p^ ± z* √[(p^(1-p^))/n]

Where p^ is the sample proportion, n is the sample size, and z* is the critical value of the standard normal distribution for the desired confidence level. For a 95% confidence level, z* = 1.96.

Substituting the given values into the formula, we get:

CI = 0.517 ± 1.96 * √[(0.517*(1-0.517))/4527]

CI = 0.517 ± 0.013

The 95% confidence interval for the proportion of all Californians who considered moving out of state is (0.504, 0.530). Therefore, we can be 95% confident that the true proportion of all Californians who considered moving out of state lies between 50.4% and 53.0%.

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This is an example of systematic sampling, where every nth item is selected for testing throughout the production day.

In this case, every 100th product produced is selected for quality control testing. Systematic sampling is a statistical technique used in survey methodology that involves choosing components from an ordered sampling frame. An equiprobability approach is the most typical type of systematic sampling.

This method treats the list's evolution in a cyclical manner, returning to the top after it has been completed. The sampling process begins by randomly choosing one element from the list, after which every subsequent element in the frame is chosen, where k is the sampling interval (sometimes referred to as the skip).

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Answer:

Al evento entraron 82 adultos y 18 menores de edad.

Step-by-step explanation:

De acuerdo a la información proporcionada, puedes plantear las siguientes ecuaciones:

x+y=100 (1)

90x+45y=8190 (2), donde:

x es el número de adultos

y es el número de menores de edad

Puedes despejar x en (1):

x=100-y (3)

Después, puedes reemplazar (3) en (2):

90(100-y)+45y=8190

9000-90y+45y=8190

9000-8190=90y-45y

810=45y

y=810/45

y=18

Ahora, puedes reemplazar el valor de y en (3) para encontrar x:

x=100-y

x=100-18

x=82

De acuerdo a esto, la respuesta es que al evento entraron 82 adultos y 18 menores de edad.

The function does not satisfy both properties, we conclude that the function \(t(a) = a^(-1)\) is not a linear transformation.

To determine whether the function\(t(a) = a^(-1)\) involving the n × n matrix a is a linear transformation, we need to check two properties: preservation of addition and preservation of scalar multiplication.

1. Preservation of Addition:

Let A and B be two n × n matrices. We need to check if t(A + B) = t(A) + t(B).

\(t(A + B) = (A + B)^(-1)\)

\(t(A) + t(B) = A^(-1) + B^(-1)\)

For this function to be a linear transformation, t(A + B) must be equal to t(A) + t(B). However, in general,\((A + B)^(-1)\) is not equal to A^(-1) + B^(-1), so the preservation of addition property does not hold.

2. Preservation of Scalar Multiplication:

Let A be an n × n matrix and k be a scalar. We need to check if t(kA) = kt(A).

\(t(kA) = (kA)^(-1) = k^(-1)A^(-1)\)

kt(A) = \(t(kA) = (kA)^(-1) = k^(-1)A^(-1)\)

For this function to be a linear transformation, t(kA) must be equal to kt(A). However, in general, \(k^(-1)A^(-1)\) is not equal to\(kA^(-1),\) so the preservation of scalar multiplication property does not hold.

Since the function does not satisfy both properties, we conclude that the function\(t(a) = a^(-1)\)is not a linear transformation.

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Determine whether the function involving the n × n matrix a is a linear transformation. t: mn,n → mn,n, t(a) = a−1

Given △FGH ~ △LMN,  all the statements that are true are options A, B , C and E

Since the two triangles are similar, their corresponding angles are going to be congruent and the sides would be proportional as well. This makes A correct

Given that FH ~ LN then the second option is correct

Option C is correct due to the definition of singularity

Option E is correct because ∠H ≅ m∠N

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Answer:

its actually 16

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

There are 1,320 ways to give the first three prizes in the race.

What is meant by ways?

Ways often refers to the number of possible arrangements or permutations of a set of objects or events. It can also refer to the number of possible outcomes or solutions to a problem.

According to the given information

The first prize can be given to any of the 12 students. After the first prize has been awarded, there are 11 students left who can be awarded the second prize. Finally, there are 10 students left who can be awarded the third prize. So, the number of ways to award the first three prizes is:

12 x 11 x 10 = 1,320

Therefore, there are 1,320 ways to give the first three prizes in the race.

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Answer:

Divide 63/9=7

7*2= (the number of teachers) 14

There are 14 teachers for 63 students.

Answer:

teachers 2:9 students

63/ 9 = 7

7 X 2 = 14

teachers 14:63 students

there are 14 teachers

Answer:0.6

Step-by-step explanati

Answer:

f(x)= { 3 if -5<x<=-1

Step-by-step explanation:

I followed the exact pattern the domains below were exemplifying. I really hope this helps, have a good rest of your day/ night :)

Answer:

B

Step-by-step explanation:

I say B because 2 divided by 6 is .333333333 and so on and so forth.

Hope this helped!!

Answer:

10 square centimeters

Step-by-step explanation:

The insides of this square is now made up of a 2 by 2 square in the center, surrounded by 4 triangles with bases of 3 units and heights of 1 unit. The formula for the area of a triangle is bh/2, which means that each triangle had an area of 1.5. Multiplying this by 4 and adding the area of the central square, you get a total area of 4+6=10. Hope this helps!

Using the sample space, the probability of rolling an even number with a six-sided dice is 3/6 or 1/2.

In the given question we have to find the probability of rolling an even number with a six-sided dice.

The sample space of dice through the experiment is

{1,2,3,4,5,6}

The even numbers is {2,4,6}.

The probability of rolling an even number with a six-sided dice is

P(E)=Total number of even outcome/Total number of outcome

P(E)=3/6

P(E)=1/2

Hence, the probability of rolling an even number with a six-sided dice is 3/6 or 1/2.

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Answer:

9(x+3)

Step-by-step explanation:

9x + 27

Taking 9 as the common factor in the 2 terms

=> 9(x) + 9(3)

=> 9(x+3)

In order for a sample of the entire population to be considered representative in public opinion polls, it must correctly and fairly reflect the views of the entire population.

Public opinion surveys are used to collect data and information on the opinions and views of people in a given population. For the results of a survey to be valid and reliable, the sample of people chosen for the survey must be representative of the entire population. This means that the views of those in the sample must accurately and proportionately reflect the views of the whole population.

Public opinion surveys are designed to measure the opinions and views of people in a given population. To ensure the results of the survey are accurate and reliable, the sample of people chosen for the survey must be representative of the entire population. This means that the views of those in the sample must accurately and proportionately reflect the views of the whole population. It is not necessary for the sample to exceed 50% of the targeted population, nor does it need to be based on all registered voters in the population. Therefore, option d. is the correct answer, which states that the sample must be representative in that the views of those in the sample must accurately and proportionately reflect the views of the whole population.

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Answer:

The radius of the hole is 0.24 feet

Step-by-step explanation:

Firstly, we need to convert the miles to feet

Mathematically;

1 mile = 5,280 feet

4.3 miles is thus;

4.3 * 5,280 = 22,704 feet

Mathematically, the volume of a cylinder is;

V = pi * r^2 * h

here, we want to get r

4200 = 3.142 * r^2 * 22,704

r^2 = 4200/(3.142 * 22,704)

r = 0.24 feet

The ratio 6:14 represents the number of cases of black ink to the number of cases of blue ink. This means that for every 6 cases of black ink, there are 14 cases of blue ink. The ratio does not give any information about the total number of cases of ink, only the relative proportions of black ink to blue ink.

The ratio 6:14 represents the number of cases of black ink to the number of cases of blue ink that are being sold at the art supply store. This means that for every 6 cases of black ink that are sold, there are 14 cases of blue ink sold. The ratio does not give any information about the total number of cases of ink that are being sold, only the relative proportions of black ink to blue ink.

For example, if the art supply store is selling a total of 20 cases of ink, the ratio of 6:14 could represent 6 cases of black ink and 14 cases of blue ink, or 12 cases of black ink and 28 cases of blue ink. In both cases, the ratio of black ink to blue ink would be the same, but the total number of cases of ink being sold would be different.

Understanding ratios like 6:14 can be useful for comparing the relative proportions of different quantities, such as the sales of different products or the proportions of different ingredients in a recipe.

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¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)

Proof:

1. ∃x(Fx & Gx) [Premise]

2. Fx & Gx [∃-Elimination, 1]

3. ∃xFx [∃-Introduction, 2]

4. ∃xGx [∃-Introduction, 2]

5. ∃xFx & ∃xGx [Conjunction Introduction, 3 and 4]

6. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx [1-5, Modus Ponens]

ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks)

Proof:

1. ¬ 3x(Px v Qx) [Premise]

2. ¬ Px v ¬ Qx [DeMorgan’s Law, 1]

3. Vx ¬ Px [∀-Introduction, 2]

4. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px [1-3, Modus Ponens]

iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)

Proof:

1. ¬ Vx(Fx → Gx) v 3xFx [Premise]

2. (¬ Vx(Fx → Gx) v 3xFx) → (¬ Vx(Fx → Gx) v Fx) [Implication Introduction]

3. ¬ Vx(Fx → Gx) v Fx [Resolution, 1, 2]

4. (¬ Vx(Fx → Gx) v Fx) → (Fx → Gx) [Implication Introduction]

5. Fx → Gx [Resolution, 3, 4]

6. ¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

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