Please help with this postulate. :)

The walkway is 11 feet 6 inches long.

To find the length of the walkway, we need to add the lengths of the two boards.

The first board is 6 feet 11 inches long, which can be written as 6 + 11/12 feet using the fact that there are 12 inches in a foot.

The second board is 5 feet 7 inches long, which can be written as 5 + 7/12 feet.

Now we can add the lengths of the two boards:

6 + 11/12 feet + 5 + 7/12 feet

= 11 + 6/12 feet

=11 + 1/2 feet

Therefore, the walkway is 11 feet 6 inches long.

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Answer: 64

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

please mark as brainlyest

Answer:

a) \(\mu -3\sigma= 7.14 -3*0.7= 5.04\)

\(\mu +3\sigma= 7.14 -3*0.7= 9.24\)

b) \( z=\frac{7.8-7.14}{0.7}=0.943\)

Using the normal approximation we can assume that this value 7.8 is approximately 1 deviation above the mean so then the percentage of values above is (100-68)/2 = 16%

c) \( z=\frac{5.7-7.14}{0.7}=-2.06\)

\( z=\frac{9.2-7.14}{0.7}=2.94\)

So we want to find approximately the % between 2 deviation below the mean and 3 deviation above the mean. For the % below two deviations from the mean we have (100-95)/2= 2.5% and for the % above 3 deviations from the mean we got (100-99.7)/2= 0.15% so then the percentage desired would be (100-2.5-0.15)% = 97.35%

Step-by-step explanation:

Let X the random variable that represent the times for the mile run of a population, and for this case we know the distribution for X is given by:

\(X \sim N(7.14,0.7)\)  

Where \(\mu=7.14\) and \(\sigma=0.7\)

We can use the z score to find how many deviation we are from the mean with this formula:

\(z=\frac{x-\mu}{\sigma}\)

Part a

From the empirical rule we know that we have 99.7% of the data within 3 deviations from the mean and we can calculate the range like this:

\(\mu -3\sigma= 7.14 -3*0.7= 5.04\)

\(\mu +3\sigma= 7.14 -3*0.7= 9.24\)

Part b

We can use the z score and we got:

\( z=\frac{7.8-7.14}{0.7}=0.943\)

Using the normal approximation we can assume that this value 7.8 is approximately 1 deviation above the mean so then the percentage of values above is (100-68)/2 = 16%

Part c

We can use the z score formula and we got:

\( z=\frac{5.7-7.14}{0.7}=-2.06\)

\( z=\frac{9.2-7.14}{0.7}=2.94\)

So we want to find approximately the % between 2 deviation below the mean and 3 deviation above the mean. For the % below two deviations from the mean we have (100-95)/2= 2.5% and for the % above 3 deviations from the mean we got (100-99.7)/2= 0.15% so then the percentage desired would be (100-2.5-0.15)% = 97.35%

Answer:

The mean of the sampling distribution of sample means would be of 23.4 pounds.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

What would be the mean of the sampling distribution of sample means?

By the Central Limit Theorem, the population mean, that is, of 23.4 pounds.

Step-by-step explanation:

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Answer:

18,060

Step-by-step explanation:

0.86 kilometers is the same as 860 meters. If he swam 860 meters a day for twenty-one days, (860 times 21) he'd end up with 18,060 meters in total.

(That's about 722 1/2 lengths of a pool, but you didn't need to know that :P )

The value of the equation that defines the function is f(x) = 3(5/3)ˣ

From the question, we have the following parameters that can be used in our computation:

(0, 3) and (1, 5)

An exponential function is represented s

y = abˣ

Where,

a = y when x = 0

So, we have

y = 3bˣ

Using the other point, we have

3b = 5

This gives

b = 5/3

So, we have

f(x) = 3(5/3)ˣ

Hence, the equation defining f is f(x) = 3(5/3)ˣ

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Answer:

69344 is the area but I don't know how large the ice is so I can not tell you how much ice. Is there any more to the question?

Step-by-step explanation:

So sorry but the volume is V≈2.67×105

Answer:

113°F is the highest temperature and -67° is the lowest temperature.

Step-by-step explanation:

(45°C × 9/5) + 32 = 113°F

(-55°C × 9/5) + 32 = -67°F

Answer:

200 pounds

Step-by-step explanation:

4 televisions weigh 160 pounds

1 television weigh 40 punds

5 televisions weigh 200 pounds

Answer:

Logically 200 lbs

Step-by-step explanation:

160/4 = 40

1TV = 40 lbs

40 * 5 = 200

200lbs...

Answer:

(0, 2)

Step-by-step explanation:

We will solve as follows:

*We determine the return as follows:

*First: We determine the total earned after selling:

+Second: We determine the change between the money gained and the money spent buying them:

So, the total return was $3000.

Answer:

2

Step-by-step explanation:

x1, y1. x2, y2

(-2,2) (-4,-2)

Divide y2-y1 and x2-x1:

-2-2÷ -4-(-2)= -4/-2

Simply. (A negative divided by a negative is a positive.)

-4/-2=2

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

interval in minutes = (24.88, 35.12)

Step-by-step explanation:

we can use the following formula:

interval = population mean ± (z · σ)

interval = 30 minutes ± (1.28 · 4 minutes)

interval in minutes = (30 - 5.12), (30 + 5.12) = (24.88, 35.12)

Answer:

5.4%

Hope This Helps!

Answer:

Step-by-step explanation:

Well, since the length of a month can vary in the number of days, this answer can also vary.

For example, February is only 28 days long, while December is 31 days long.

That being said, the average length of all 12 months is 30.436875 days, so if Denny left to another country on June 20th, he would most likely be back   July 19th of July 20th.

I hope this helps!

Answer:

9.4 miles approx.

Step-by-step explanation:

Answer:

9.4 miles to the nearest tenth.

Step-by-step explanation:

This run forms a right angled triangle with legs of 5 and 8 miles.

By Pythagoras:

x^2 = 8^2 + 5^2

x = √(64+25) = √89

x = 9.434 miles

Analysing the Question:

We are given the following equations:

x - y = 4

x + y = 9

writing these equations in slope-intercept form

y = x - 4

y = -x + 9

the general form of the slope-intercept equation is :   y = mx + b (where m is the slope and b is the y-intercept)

Hence, we can say that the for Equation 1:

Slope  = 1

y-intercept = -4

For equation 2:

Slope = -1

y-intercept = 9

Finding if the lines are Perpendicular, parallel or neither

If the slope of the lines is equal, the lines are parallel

If the slope of the lines is the additive inverse (negative) of each other, the lines are perpendicular

Since the slopes of the 2 lines are the additive inverse (negative) of each other, the lines are perpendicular     [slope 1 = 1    , slope 2 = -1]

The z score corresponding to the sample is -6.25

The formula for calculating the z-score is expressed as

z = x- μ/σ

Given the following parameters

x = 22 (sample size)

Mean  μ = 72

standard deviation σ = 8

Substitute

z = 22-72/8

z = -50/8

z = -6.25

Hence the z score corresponding to the sample is -6.25

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The quadratic function for the value of David's investment indicates;

(i) $45,000

(ii) 9.375 months

A quadratic function is a function that can be expressed in the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.

The model of the value of the investment in the bank obtained from the amount of his retirement funds David invested in the bank can be presented as follows;

a = 45 + 75·t - 4·t²

Where;

a = The value of the investment in thousand of dollars after t months

t = The number of months of the investment

(i) The initial amount David invested can be found by plugging in t = 0, in the function for the amount David invested in the bank, as follows;

a = 45 + 75 × 0 - 4 × 0² = 45

The initial amount David invested is; a = $45,000

(ii) The number of months it takes for David investment to reach a maximum value can be found from the quadratic function as follows;

The number of months t(max) at the maximum amount is; t(max) = -75/(2 × (-4)) = 9.375

Therefore, it will take 9.375 months for David's investment to reach a maximum value

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Answer:

I think 180

Step-by-step explanation:

A= a+b/h = 10+20/2 = 60

A=bxh = 6x20 = 120

120+60

The graph of the population equation is on the image at the end.

Here we know that the function p(h) models the population of bacteria as the function of h, the number of hours.

And we can write this as the exponential function:

p(h) = 150*(3)^h

The graph of this will be an exponential that starts at 150 and triples for each increase in the horizontal variable, then the graph of this will be like the one you can see at the end of the answer.

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Three reasons why the other method is not better is because to use drawing program would mean you would need some sort of technology and electricity to use it and some places, like third world countries, do not have access to that, so most probably you would have to resort to paper. Also, drawing programs are based off the skills needed to create geometric figures with a straightedge and compass. And lastly, what if we had no more technology anymore? Then how would we use a drawing program? Drawing programs are only reliable when electricity is located.

SO THE ANSWER IS A hope it help :)

I believe that there is a need for students to understand and be able to construct geometric figures using a compass and straightedge.

The compass and straightedge can be used anywhere. The compass and straight edge have been around for lots of years. They are a valuable tool for students in math and in real world applications. The compass and straightedge are portable and handy to use any given time. That is why there is a need for students to understand and be able to construct geometric figures using a compass and straight edge.

The compass and straight edge have been used to accurately create geometric figures for thousands of years. This shows that they are accurate and useful to us. Using technology is less reliable for many reasons. Technology can break, or glitch and shut down, making you lose all your work. You cannot draw on physical objects with an iPad like you could with a pencil or pen. Having a physical copy of things makes things easier to keep track of. Having a blueprint would be better than having a drawing on your phone. You can get another blueprint, but if your phone breaks and that drawing isn't saved, it's gone.

These are only a few reasons why I believe that there is a need for students to understand and be able to construct geometric figures using a compass and straightedge.

Answer:

29°

Step-by-step explanation:

Since this a right triangle and the sum of interior angles in a triangle is 180° We can say

2x + 1 + 5x + 5 = 90°

7x + 6 = 90°

7x = 84°

x = 14 and m<A = 2x + 1 we replace x with the value we found m<A = 14 × 2 + 1 = 29°

Answer:

\(\sf A. \quad -3.5 < -\dfrac{10}{3}\)

Step-by-step explanation:

Convert -3.5 into a fraction:

\(\implies \sf -3.5=-\dfrac{35}{10}=-\dfrac{\diagup\!\!\!\!5 \times 7}{\diagup\!\!\!\!5 \times 2}=-\dfrac{7}{2}\)

Rewrite both fractions so that they have the same denominator:

\(\implies \sf -\dfrac{7}{2}=-\dfrac{7 \times 3}{2 \times 3}=-\dfrac{21}{6}\)

\(\implies \sf -\dfrac{10}{3}=-\dfrac{10 \times 2}{3 \times 2}=-\dfrac{20}{6}\)

\(\textsf{As }\: -\dfrac{21}{6} < -\dfrac{20}{6} \textsf{ then}:\)

\(\sf \implies -3.5 < -\dfrac{10}{3}\)

When proving the properties of logarithms when exponents must be used, the property that is used in all of these is D. \(log_{b} (b^y) = y\)

When proving any property of logarithms that have to do with exponents, one property that should always be used is  \(log_{b} (b^y) = y\).

Expressing y as a product of \(log_{b} (b^y)\) is the most basic property of using exponents on logs because it has both product, quotient, and power rules of logarithms.

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So, each farmer pays the following amounts: The first farmer pays 738.40 euros. The second farmer pays 443.04 euros. The third farmer pays 418.56 euros

Proportion refers to the equality of two ratios. In other words, when two ratios are set equal to each other, they form a proportion. A proportion is typically written in the form of two fractions separated by an equals sign, such as a/b = c/d. Proportions are commonly used in mathematics to solve problems involving ratios and proportions, such as finding missing values or scaling up or down a given quantity.

Here,

To find out how much each farmer pays, we need to determine the proportion of the total rent that each farmer owes based on the number of sheep they have. First, we need to find the total number of sheep:

120 + 72 + 68 = 260

The first farmer has 120 sheep, which is 46.15% of the total number of sheep (120/260). Therefore, the first farmer owes 46.15% of the rent:

0.4615 x 1600 = 738.40 euros

Similarly, the second farmer has 72 sheep, which is 27.69% of the total number of sheep (72/260). Therefore, the second farmer owes 27.69% of the rent:

0.2769 x 1600 = 443.04 euros

The third farmer has 68 sheep, which is 26.15% of the total number of sheep (68/260). Therefore, the third farmer owes 26.15% of the rent:

0.2615 x 1600 = 418.56 euros

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Complete question:

The rent of 1600 euros for a piece of land is divided among three farmers who graze their sheep there. As they do not have the same number of sheep, they decide to pay proportionally according to the number of sheep each has. If the first one has 120 sheep, the second 72, and the third 68. How much does each one pay?

Answer:

074°

Step-by-step explanation:

the bearing of Y from X is the measure of the angle from the north line (N) at X in a clockwise direction to Y , that is ∠ NXY

∠ NXY = 180° - 106° = 74°

the 3- figure bearing of Y from X is 074°

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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