Please help me with this homework

Answer:

Step-by-step explanation:

Circumference = π × diameter

3.14 = π

3,14 × 12 = 37.68 cm

Answer:

Step-by-step explanation:

Answer:

  23.6 years

Step-by-step explanation:

Given that a population is described by y = 82700e^(-0.00036t), you want to know the value of t when the population is 82000.

Substitute the given number for y and solve for t:

  82000 = 82700e^(-0.00036t)

  820/827 = e^-0.00036t . . . . . . . . . . divide by 82700, simplify

  ln(820/827) = -0.00036t . . . . . . . . take natural logs

  t = ln(820/827)/-0.00036 ≈ 23.6 . . . . . divide by the coefficient of t

It will take approximately 23.6 years.

__

Additional comment

The problem statement tells us y₀ is 82700, so we used that in the given equation.

It's a bit odd that the population is reported in thousands of thousands. It could be described as 82.7 million, declinding to 82 million.

Answer:

Let x be Kiran's speed from Tortula to Cactus.

The time it took her to drive from Tortula to Cactus is 250/x.

The time it took her to drive from Cactus to Dry Junction is 360/(x+10).

The total time of the trip is 250/x + 360/(x+10) = 11.

Multiplying both sides of the equation by x(x+10), we get:

250x + 360 = 11x^2 + 110x

11x^2 - 140x + 360 = 0

Factoring the equation, we get:

(x-12)(x-30) = 0

Therefore, x = 12 or x = 30.

Since x is the speed, it must be a positive number. Therefore, x = 12.

Kiran's speed from Tortula to Cactus was 12 mph.

Step-by-step explanation:

The difference between the summations of these two sequence is zero.

To compute the difference between the summation of (1 + 3n) from n = 0 to 4 and the summation of (3i - 5) from i = 2 to 6, we can first evaluate each summation individually and then subtract the result of the second summation from the first.

The summation of (1 + 3n) from n = 0 to 4 can be written as:

∑(1 + 3n) = (1 + 3(0)) + (1 + 3(1)) + (1 + 3(2)) + (1 + 3(3)) + (1 + 3(4))

= 1 + 4 + 7 + 10 + 13

= 35

Similarly, the summation of (3i - 5) from i = 2 to 6 can be written as:

∑(3i - 5) = (3(2) - 5) + (3(3) - 5) + (3(4) - 5) + (3(5) - 5) + (3(6) - 5)

= 1 + 4 + 7 + 10 + 13

= 35

Therefore, the difference between the two summations is:

∑(1 + 3n) - ∑(3i - 5) = 35 - 35 = 0

This means that the sum of the first sequence is equal to the sum of the second sequence.

Correct Question :

What is difference between Σ(1+3n) from n = 0 to 4 and Σ(3i-5) from i = 2 to 6.

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Almost 1.79 million population out of 44.7 million population is aged 65 or above.

It is given that in 2015, there were 44.7 million people in Ukraine. 4% of the population were aged 65 or above.

Assume that the population with age 65 or over in 2015 be {x}. Then, we can write that -

{x} = 4% of 44.7

{x} = (4/100) x 44.7

{x} = 1/25 x 44.7

{x} = 1.79 million

Therefore, almost 1.79 million population out of 44.7 million population is aged 65 or above.

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To construct a 98% confidence interval for the mean of repeated measurements of the weight, we can use the formula:

Confidence interval = mean ± (t-value) x (standard error)

where the standard error is the standard deviation of the sample divided by the square root of the sample size, and the t-value is based on the degrees of freedom (n-1) and the desired level of confidence. Since we are given the sample mean, standard deviation, and sample size, we can plug in the values and solve for the confidence interval and margin of error.

First, we need to calculate the standard error:

Standard error = standard deviation / √n

Standard error = 0.020 gram / √40

Standard error = 0.00316 gram

Next, we need to find the t-value for a 98% confidence interval with 39 degrees of freedom. We can use a t-distribution table or calculator to find the t-value, which is approximately 2.423.

Substituting the values into the formula, we get:

Confidence interval = 10.230 ± (2.423)(0.00316)

Confidence interval = 10.230 ± 0.00766

Rounding to three decimal places, the 98% confidence interval for the mean weight is (10.222, 10.238) grams. The margin of error is half the width of the confidence interval, which is 0.00766/2 = 0.00383 grams

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 13200\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years \end{cases}[/tex]

[tex]13200 = 7000\left(1+\frac{0.055}{12}\right)^{12\cdot t} \implies \cfrac{13200}{7000}=\left(1+\frac{0.055}{12}\right)^{12t}[/tex]

[tex]\cfrac{66}{35}=\left(\frac{12+0.055}{12}\right)^{12t}\implies \cfrac{66}{35}=\left(\frac{12.055}{12}\right)^{12t}\implies \log\left( \cfrac{66}{35} \right)=\log\left[ \left(\frac{12.055}{12}\right)^{12t} \right] \\\\\\ \log\left( \cfrac{66}{35} \right)=t\log\left[ \left(\frac{12.055}{12}\right)^{12} \right]\implies \cfrac{\log\left( \frac{66}{35} \right)}{\log\left[ \left(\frac{12.055}{12}\right)^{12} \right]}=t\implies \boxed{11.56\approx t}[/tex]

Step-by-step explanation:

The volume of a cone is given by the formula:

V = (1/3)πr^2h

where r is the radius of the base and h is the height of the cone.

In this case, the cone has a height of 14 cm and a base radius of 4/2 cm, which is equal to 2 cm. Therefore, the volume of the entire cone is:

V = (1/3)π(2 cm)^2(14 cm) = (4/3)π(28 cm^3) = 37.333... cm^3

To find the volume of water that is exactly half the volume of the cone, we need to divide the volume of the cone by 2:

V_water = (1/2)V = (1/2)(37.333...) cm^3 = 18.666... cm^3

To calculate the height of the water in the cone, we can use the formula:

V_water = (1/3)πr^2h

where h is the height of the water.

We know the volume of water (18.666... cm^3) and the radius of the base (2 cm), so we can rearrange the formula to solve for h:

h = 3V_water / (πr^2) = 3(18.666...) / (π(2 cm)^2) ≈ 2.366 cm

Therefore, the height of the water in the cone is approximately 2.366 cm.

The mean would be inappropriate as a measure of central location for data in option D: number of pages in textbooks on statistics, that has extreme outliers or is skewed.

Out of the options given, the number of pages in textbooks on statistics could potentially have extreme outliers, such as a textbook with significantly more pages than the rest of the sample. Therefore, the mean may not be the most appropriate measure of central location for this type of data. A better measure might be the median, which is less affected by extreme values.

In contrast, the mean would be an appropriate measure of central location for the incomes of lawyers, ages of adults at a senior citizen center, and marital status of college students at a particular university, as these data sets are less likely to have extreme outliers or be heavily skewed.

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Complete question:

the mean, as a measure of central location, would be inappropriate for which one of the following? multiple choice

incomes of lawyers

ages of adults at a senior citizen center

marital status of college students at a particular university

number of pages in textbooks on statistics

Graham's Law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. So, for two gases A and B, the ratio of their rates of diffusion (rA/rB) can be expressed as: rA/rB = √(MB/MA).

In the Graham's Law experiment, the ratio of rates should have been calculated by dividing the rate of effusion/diffusion of gas A by the rate of effusion/diffusion of gas B.

The ratio of rates should ideally be equal to the square root of the reciprocal of the molar masses of the gases being compared. However, there may be differences due to experimental error, variations in temperature, pressure, and other factors that may affect the results. To account for these differences, it is important to repeat the experiment multiple times and take the average of the results.

Additionally, it may be necessary to adjust the experimental conditions to minimize any sources of error and ensure accurate measurements.

To determine the ratio of rates for the Graham's Law experiment, you can follow these steps:

1. Identify the two gases involved in the experiment and their molar masses.
2. Calculate the square root of the inverse molar masses for each gas.
3. Divide the result for the lighter gas by the result for the heavier gas.

Graham's Law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. So, for two gases A and B, the ratio of their rates of diffusion (rA/rB) can be expressed as:
rA/rB = √(MB/MA)

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By using the formed equation we can conclude that, there are 36 students in John's homeroom.

What is equation?

In mathematics, an equation is a statement that shows the equality of two expressions. An equation usually contains one or more variables, which are unknown values that can be solved for using mathematical operations.

Let's use x to represent the total number of students in John's homeroom.

According to the problem, 1/3 of the students walk to school and 1/4 come by car. That means:

(1/3)x + (1/4)x = number of students who don't come by school bus

(1/3)x + (1/4)x = total number of students - number of students who come by school bus

(1/3)x + (1/4)x = x - 15

To solve for x, we can combine the fractions:

(4/12)x + (3/12)x = x - 15

(7/12)x = x - 15

Next, we can isolate x on one side of the equation:

(7/12)x - x = -15

(-5/12)x = -15

x = (-15)/(-5/12)

x = 36

Therefore, there are 36 students in John's homeroom.

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Let s be the length of an edge of the cube. Then, by the Pythagorean theorem, we have:

s^2 + s^2 = (10 cm)^2

2s^2 = 100 cm^2

s^2 = 50 cm^2

s = sqrt(50) cm

Also, by the Pythagorean theorem, we have:

s^2 + s^2 + s^2 = (150 cm)^2

3s^2 = 22500 cm^2

s^2 = 7500 cm^2

s = sqrt(7500) cm

Therefore, the length of an edge of the cube is:

s ≈ 86.6 cm (rounded to the nearest tenth)

Answer:

Let's use the Pythagorean theorem to solve this problem.

If the diagonal of a face measures 10 cm, then we know that the edge of the cube is given by:

edge = 10/√2

Simplifying this expression, we get:

edge = 5√2

Now, we can use the diagonal of the cube to find the length of an edge. If the diagonal of the cube measures 150 cm, then we have:

edge√3 = 150

Substituting the expression we found for the edge, we get:

5√6 = 150/√3

Simplifying this expression, we get:

edge ≈ 19.2 cm

Rounding to the nearest tenth, we get the final answer:

The length of an edge of the cube is approximately 19.2 centimeters.

mark me brilliant

Figure (a) have similar triangles, while figure (b) do not; and the length and the width of the rectangle are 12 cm and 9 cm,

Figure (a)

The similar triangles in this figure are

ABC and AED

This is because:

The triangles have similar corresponding sides and congruent angles

Also, ABC is divided by 3 to get AED

So, we have

x = 15/3 = 5

y = 10/3

Figure (b)

The triangles in this figure are not similar triangles

We have

Area = 108

Width : Length = 3 : 4

So, we have

Width = 3/4Length

The area is

Area = Length * Width

Area = Length * 3/4Length

Length * 3/4Length = 108

3/4Length² = 108

Length² = 144

Length = 12

Recall that

Width = 3/4Length

Width = 3/4 * 12

Width = 9

Hence, the length and the width of the rectangle are 12 cm and 9 cm, respectively

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Trailing zeroes are significant in numbers that have a decimal point, but they are not significant in numbers that do not have a decimal point.

Trailing zeroes can have different levels of significance depending on whether the number has a decimal point or not. In a number without a decimal point, trailing zeroes are generally not significant.

For example, the number 1,200 could also be written as 1,200.0 or 1,200.00, but the additional zeroes do not change the value of the number and are therefore not significant.

On the other hand, in a number with a decimal point, trailing zeroes may be significant.

For example, the number 3.50 has two significant figures because the zeroes after the decimal point indicate that the measurement was taken to the nearest hundredth. Removing the zeroes would change the value and accuracy of the number.

Therefore, it is important to consider the context and purpose of the number when determining the significance of trailing zeroes.

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The options showing the front elevation of each prism are given as follows:

a) Prism X: Option B.

b) Prism Y: Option E.

The front elevation of a prism is defined as how we can see the prism looking at the front of it's shape.

Looking at the front of prism X, on the orange section, we see it as a right triangle pointing to the right, hence it is represented by option B.

Looking at the front of prism Y, on the orange section, we see it as an isosceles triangle, which is represented by option E.

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The solution of the system of equations y = -(4/3)x + 2 and y = x - 5 is (3, -2)

An equation is an expression that shows the relationship between numbers and variables using mathematical operators.

The first line passes through (0, 2) and (3, -2), hence:

y - 2 = [(-2-2)/(3-0)](x - 0)

y = -(4/3)x + 2

The first line has an equation of y = -(-4/3)x + 2

The second line passes through (5, 0) and (0, -5), hence:

y - 0 = [(-5-0)/(0-5)](x - 5)

y = x - 5

The second line has an equation of y = x - 5

The solution of the equation is (3, -2)

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So the probability that exactly 2 of the 3 selected buttons are black is 15/28 or approximately 0.5357.

To find the probability that exactly 2 out of 3 selected buttons are black, we need to consider all possible ways of selecting 2 black buttons and 1 red button, and then add up their probabilities.

The total number of ways of selecting 3 buttons out of 8 is:

(8 choose 3) = 8! / (3! * 5!) = 56

The number of ways of selecting 2 black buttons out of 5, and 1 red button out of 3 is:

(5 choose 2) * (3 choose 1) = (5! / (2! * 3!)) * (3! / (1! * 2!)) = 30

Therefore, the probability of selecting exactly 2 black buttons out of 5 and 1 red button out of 3 is:

P(2 black, 1 red) = 30 / 56 = 15 / 28

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The sum of lengths of the two diagonals in a rectangle whose dimensions are 5 by 12 units is 26 units.

As, The length of the diagonal of rectangle

d = √l² + w²

d = √12² + 5²

d= √144+ 25

d= 13 unit

Thus, the sum of lengths of the two diagonals in this rectangle is

= 13 + 13

= 26 unit

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Answer:

10m³ + 2m²- 1m - 5

Step-by-step explanation:

Add like terms together. I am busy I wish I could explain but I gtg. Please ask if you have any other questions!

and

Have a great day!!

The test statistic for this hypothesis test is 2.00, which is less than the critical value of ±2.617 at the 0.01 level of significance.

To conduct a hypothesis test, we need to calculate a test statistic. In this case, we will use a t-test since the population standard deviation is unknown and we have a sample size of 160 engines. The test statistic measures how many standard deviations the sample mean is from the hypothesized population mean under the null hypothesis.

The formula for the t-test statistic is:

t = (x - μ) / (s / √n)

where x is the sample mean (7.1 psi), μ is the hypothesized population mean under the null hypothesis (6.9 psi), s is the sample standard deviation (1.0 psi), and n is the sample size (160 engines).

So, plugging in the values we have:

t = (7.1 - 6.9) / (1.0 / √160)

t = 2.00

This means that the sample mean is 2.00 standard deviations away from the hypothesized population mean under the null hypothesis.

To determine if this test statistic is statistically significant at the 0.01 level, we need to compare it to a critical value from the t-distribution with 159 degrees of freedom (df = n-1). The critical value for a two-tailed test at the 0.01 level of significance is ±2.617.

Since our test statistic (2.00) is less than the critical value (-2.617), we fail to reject the null hypothesis. This means that we do not have sufficient evidence to conclude that the valve performs above specifications at the 0.01 level of significance.

Therefore, we fail to reject the null hypothesis and cannot conclude that the valve performs above specifications.

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The person who filled out the deposit slip received $88.79 in cash. The correct answer is option c.

To find out how much cash the person who filled out the deposit slip received, we need to fill in the missing amounts on the slip.

First, we need to calculate the subtotal by adding the amounts of the checks and cash:

Subtotal = 15.00 + 62.44 + 27.83 + 45.75

Subtotal = 151.02

Next, we need to determine the amount of cash received by subtracting the subtotal from the total:

Total = Subtotal - cash received

62.23 = 151.02 - cash received

To solve for cash received, we can subtract the total from the subtotal:

Cash received = Subtotal - total

Cash received = 151.02 - 62.23

Cash received = 88.79

Therefore, correct option is C.

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Using a branch-and-bound algorithm combined with an effective search strategy and an appropriate selection of branching rules you can find the optimal solution for an optimization model with integer decision variables.

Solving an optimization model with integer decision variables requires a branch-and-bound algorithm, which recursively partitions the feasible region into smaller sub-regions until the optimal solution is found or proven to be infeasible. An effective search strategy, such as depth-first or best-first search, is used to explore the sub-regions efficiently.

The selection of branching rules is critical to the performance of the algorithm, as it determines the order in which variables are selected for partitioning. Effective branching rules, such as the most constrained variable or the strongest branching rule, can significantly reduce the number of nodes explored and improve the chance of finding the optimal solution. Additionally, using advanced techniques, such as domain reduction and cutting planes, can further enhance the performance of the algorithm.

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The population is estimated to increase by approximately 38,880 people in 1 day.

To calculate the population increase in 1 day, we first need to convert the birth and death rates to a per-day basis. Since there are 60 seconds in a minute and 60 minutes in an hour, there are 60 x 60 = 3600 seconds in an hour, and 24 x 3600 = 86,400 seconds in a day. Therefore, in a day, the population will increase by: [(9 people/2 seconds) x (86,400 seconds/day) / 2] - [(3 people/2 seconds) x (86,400 seconds/day) / 2] = 38,880 people/day.

We multiply the per-second rates by the number of seconds in a day (divided by 2 since we are counting births and deaths separately) to get the per-day rates. We subtract the death rate from the birth rate to get the net population increase per day.

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The value of z-score concerning for 4.51 is 1.62 under the given condition that the mean of a set of data is -1.82 and its standard deviation is 3.91.

The formula for evaluating a z-score is
z = (x-μ)/σ,
Here
x = raw score,
μ = population mean,
σ = population standard deviation.
For the given  case,  
Mean = -1.82
Standard deviation = 3.91.

To evaluate the z-score for a value of 4.51,
z = (x - μ) / σ
= (4.51 - (-1.82)) / 3.91
= 6.33 / 3.91
= 1.62
The value of z-score is 1.62
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Answer:

He would have 12 rows with 15 chairs in each row.

Step-by-step explanation:

180 divided by 18 is 10

10 plus 5 is 15

180 divided by 15 is 12.

Answer:

A:1/3

Step-by-step explanation:

There are 6 possible outcomes when Sauli rolls the number cube, with each outcome having an equal probability of 1/6. To find the probability of rolling a number greater than 4, we need to count the number of favorable outcomes, which are the numbers 5 and 6.

Therefore, the probability of rolling a number greater than 4 is 2 favorable outcomes out of 6 possible outcomes, which simplifies to 1/3.

So the answer is A. 1/3.

If it takes 48 days for patch to cover entire lake, then it will take (a) 47 days to cover the half of lake.

The patch of Lilypad doubles in size every day, so, we use the exponential growth to represent its size.

Let the initial size of patch be = "P" and

Let the final size of the patch (when it covers the entire lake) be = "L",

So, we have , L = 2⁴⁸ × P,

We have to find out how long it takes for patch to cover half of lake.

Let the size of patch at that point be = "H", where "H" is half the size of L,

Which is written as : H = L/2 = 2⁴⁷ × P,          ...equation(1)

Let the number of days to cover half lake be = "d",

So, we write equation to solve for the number of days it takes for the patch to reach size "H",

⇒ H = [tex]2^{d}[/tex] × P,

Substituting the value of "H" from equation(1),

We get,

⇒ 2⁴⁷ × P = [tex]2^{d}[/tex] × P,

Simplifying further,

We get,

⇒ 2⁴⁷ = [tex]2^{d}[/tex],

Since, the base is same, we can equate the power,

We get,

⇒ d = 47,

Therefore, it takes 47 days for the patch to cover half the lake, Correct option is (a).

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The given question is incomplete, the complete question is

In a lake, there is a patch of Lilypad. Every day, the patch doubles in size, if it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half the lake?

(a) 47 days

(b) 24 days

(c) 12 days

(d) 36 days