57 plus what equals 86

Answer:

20

Step-by-step explanation:

hope it right not the best with counting

£270 will be allocated to the first person and £135 will be allocated to the second person.

Ratio is a mathematical expression that is used to compare two or more quantities in relation to each other. It is usually expressed as a fraction or a decimal. Ratios are used to compare values, trends, and proportions. Ratios are essential for understanding the relationship between numbers and for making informed decisions. Ratios are often used in business, finance, economics, and other areas to measure performance and risk.

This is calculated by multiplying the total amount of £405 by the ratio 2:3.
The first person's ratio is 2 out of 5 and the second person's ratio is 3 out of 5.

Therefore, 2/5 of £405 is £270 and 3/5 of £405 is £135.

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Simple algebra.

When we convert this to an equation we get: 0.2% of something is equal to 1 unit.

So here's the equation: \(0.02x = 1\)

After we transpose \(0.02\), the equation become: \(x = \frac{1}{0.02}\).

Divide \(1\) with \(0.02\) and you get \(50\).

So the length of the original bar is \(50\) cm. :D

Answer:

2x-18

Step-by-step explanation:

The distributive property has you mulitply the outside number by the inside numbers. 2 multiplied by x is 2x, and 2 multiplied by 9 is 18. We keep the subtraction symbol, this gives us 2x-18.

It could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

The most accurate interpretation of the given confidence interval is as follows:

We are 95% confident that the true difference in mean wait time between Facility A and Facility B falls within the range of 0.32 minutes to 1.47 minutes.

This means that if we were to repeat the study multiple times and calculate a new confidence interval each time, we would expect that approximately 95% of those intervals would contain the true difference in mean wait time between the two facilities.

Furthermore, based on the observed data and the calculated confidence interval, we can conclude that the difference in mean wait time between Facility A and Facility B is likely to be positive, with Facility B having a higher mean wait time than Facility A. However, we cannot say with certainty that the true difference is exactly within this specific range; it could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

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The probability that consumers in this group have a daily discretionary spending of $80 or less is 0.15 or 15%.

Given information:

Mean daily discretionary spending = $136

Uniform probability density function: f(x) = 0.00625 for a ≤ x ≤ b

We need to find the probability that consumers in this group have a daily discretionary spending of $80 or less.

Let's first find the values of a and b:

We know that the probability density function of a uniform distribution is given by:

f(x) = 1 / (b - a) for a ≤ x ≤ b

Since f(x) = 0.00625 for a ≤ x ≤ b, we have:

0.00625 = 1 / (b - a)

b - a = 1 / 0.00625

b - a = 160

We also know that the mean daily discretionary spending is $136. Therefore, we can find the midpoint of the distribution as:

Midpoint = (a + b) / 2 = (b + a) / 2 = 136

Solving the above two equations simultaneously, we get:

a = 56 and b = 216

Now, we need to find the probability that consumers in this group have a daily discretionary spending of $80 or less. This can be represented mathematically as:

P(X ≤ 80) = ∫[56, 80] f(x) dx

Using the uniform probability density function, we get:

P(X ≤ 80) = ∫[56, 80] 0.00625 dx

P(X ≤ 80) = 0.00625 * (80 - 56)

P(X ≤ 80) = 0.15

Therefore, the probability that consumers in this group have a daily discretionary spending of $80 or less is 0.15 or 15%.

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a. The bank can initially lend out $15.00.

b. The money in the economy changes by $20.00.

c. The money multiplier is 4.

d. Eventually, $80.00 will be created by the banking system from Jon's $20.00.

Let us analyze each section separately:

a. To calculate the amount of money the bank can initially lend out, we need to determine the bank's reserves.

Given that the bank keeps 25% of its money in reserves, we can find the reserves by multiplying the deposit amount by 0.25.

In this case, the deposit amount is $20.00, so the reserves would be $20.00 * 0.25 = $5.00. The remaining amount, $20.00 - $5.00 = $15.00, is the money that the bank can initially lend out.

b. When Jon deposits the $20.00 bill into the bank, the money in the economy remains unchanged because the physical currency is converted into a bank deposit. Therefore, there is no change in the total money supply in the economy.

c. The money multiplier determines the overall increase in the money supply as a result of fractional reserve banking. In this case, the reserve requirement is 25%, which means that the bank can lend out 75% of the deposited amount.

The formula to calculate the money multiplier is 1 / reserve requirement. Substituting the value, we get 1 / 0.25 = 4.

Therefore, the money multiplier is 4.

d. To calculate the amount of money created by the banking system, we multiply the initial deposit by the money multiplier. In this case, Jon's initial deposit is $20.00, and the money multiplier is 4.

So, $20.00 * 4 = $80.00 will be created by the banking system from Jon's $20.00 deposit.

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Answer:

i think about $3.80

Step-by-step explanation:

Thus, the general solution of the given differential equation `2y′ y = 5t²` is `y = Ke^(5t³/6)` where `K` is a constant of integration.

The general solution of the given differential equation `2y′ y = 5t²` and using it to determine how solutions behave as t is discussed below:Solving the differential equation:

Separating the variables of the differential equation `2y′ y = 5t²` we get:dy/y = (5/2)t² dtIntegrating both sides, we have:ln|y| = (5/6) t³ + C1

Taking the exponential of both sides, we get:y = Ke^(5t³/6) , where K = ± e^(C1) is a constant of integration.

The general solution of the given differential equation is given by `y = Ke^(5t³/6)` where `K` is a constant of integration.

How solutions behave as `t`:When `t → ∞` (i.e., as t grows large), `e^(5t³/6) → ∞`. So solutions of the given differential equation `y′ y = 5t²` grow exponentially as `t → ∞`.

When `t → -∞` (i.e., as t gets very negative), `e^(5t³/6) → 0`. So solutions of the given differential equation `y′ y = 5t²` approach `y = 0` as `t → -∞`.

Thus, the general solution of the given differential equation `2y′ y = 5t²` is `y = Ke^(5t³/6)` where `K` is a constant of integration.

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(a) Based on a continuous compounding interest rate of 6.74%, Choice 2 would be preferred.

(b) The interest rate that would make both choices equally lucrative can be found using logarithmic equations.

(a) To determine which investment option is preferred, we need to calculate the future value of each choice using continuous compounding. Choice 1 has three separate payments at different times, while Choice 2 has three equal yearly payments.

Using the continuous compounding formula, the future value of Choice 1 is:

FV1 = $2500 * e^(0.0674 * 0) + $3000 * e^(0.0674 * 1) + $3560 * e^(0.0674 * 2)

The future value of Choice 2 is:

FV2 = $3000 * e^(0.0674 * 0) + $3000 * e^(0.0674 * 1) + $3000 * e^(0.0674 * 2)

By evaluating these expressions, we can compare the future values and determine that Choice 2 would be preferred.

(b) To find the interest rate that would make both choices equally lucrative, we need to solve the equation:

$2500 * e^(rt) + $3000 * e^(r(t+1)) + $3560 * e^(r(t+2)) = $3000 * e^(rt) + $3000 * e^(r(t+1)) + $3000 * e^(r(t+2))

This equation can be simplified and rearranged to isolate the interest rate 'r'. However, since the question asks for an exact answer using a logarithm, we can solve the equation by taking the natural logarithm of both sides. The resulting equation can then be solved for 'r'.

The exact interest rate that would make both choices equally lucrative can be obtained by solving the logarithmic equation.

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Answer:

multiply you 2 numbers first then you multiply the other numbers use calculator

a. Yes, the estimate of age based on 500 plots is influenced by sampling error.

Sampling error occurs because the sample is only a portion of the entire population, and the sample may not perfectly represent the whole population.

Therefore, the estimate of the mean age derived from the sample might deviate from the true mean age of the entire population.

b. If the investigators had used a sample of only 100 plots instead of 500, the sampling error of the estimate of mean age would likely increase. As the sample size decreases, the likelihood of the sample representing the whole population accurately decreases as well.

Consequently, the deviation between the sample means age and the true population mean age would likely be larger, leading to a higher sampling error.

Sampling error refers to the difference or discrepancy between a sample's characteristics and the corresponding characteristics of the entire population from which the sample was drawn. It arises due to the fact that a sample is only a subset of the population, and the sample may not perfectly represent the whole population. Sampling error can impact the accuracy of statistical inferences and conclusions drawn from the sample, such as estimates of mean, variance, or correlation.

As the sample size decreases, the likelihood of the sample representing the whole population accurately decreases as well, leading to higher sampling error.

Therefore, minimizing sampling error is crucial in ensuring the validity and reliability of research findings.

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Step-by-step explanation:

2x + 7 = 27 OR 3 + 3x = 30.

2x = 27 - 7 OR 3x = 30 - 3

2x = 20 OR 3x = 27

x = 20/2 OR x = 27/3

x = 10 OR x = 9

The probability is 0.2137

Explanation:

Given a particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls involve fax messages, and consider a sample of 25 incoming calls.

The probability that in a sample of 25 incoming calls, exactly 5 of them involve fax messages is calculated as follows;

P(X = 5) = 25C5(0.25)⁵(0.75)²⁰= 53130(0.25)⁵(0.75)²⁰= 0.2137

Therefore, the probability that in a sample of 25 incoming calls, exactly 5 of them involve fax messages is 0.2137.

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Answer:

Go back to -1

Step-by-step explanation:

4 - -5 = -1

Answer:

Use the graph to complete the statements.

The two variables are  

✔ bananas and days

✔ days

✔ bananas

✔ days

✔ bananas

Got it right lol uwu

The statement first "The number of bananas is the independent variable, and the cost in dollars is the dependent variable" is correct.

A line graph is a graph made up of segments of straight lines that connect the depicted data points.

here, we have,

On a coordinate plane, the points (1, 2), (2, 4), (3, 6), (4, 8), and (5, 10) are plotted.

We have:

The line goes through points (1, 0.27) and (2, 0.54).

The x-axis represents the independent variable

The y-axis represents the dependent variable.

Thus, the statement first "The number of bananas is the independent variable, and the cost in dollars is the dependent variable" is correct.

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she worked 3 hours a week

The predicted college gpa be for a student whose current high school

gpa = 3.2 is 2.9718.

In statistics, a scalar response and one or more explanatory factors are modeled using a linear approach called linear regression. Simple linear regression is the scenario in which there is only one explanatory variable; multiple linear regression is the scenario in which there are numerous explanatory variables.

When predicting a variable's value based on the value of another variable, linear regression analysis is utilized. The dependent variable is the one you're trying to forecast. The independent variable is the one that you are utilizing to forecast the value of the other variable.

The linear regression for Y (dependent variable) on X (independent variable) is given by:

Y = a + bX

where,

a be the y-intercept

b be the slope of the line

When the slope is positive (or negative), the regression line is presumed to be increasing, which gives rise to the characteristics for the assumption (or decreasing).

For a = 0.719, b = 0.704, and X = 3.2, the predicted college GPA exists,

Y′ = 0.719 + (0.704 \(*\) 3.2) = 2.9718

Therefore, the predicted college gpa be for a student whose current high school gpa = 3.2 is 2.9718.

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(a) To evaluate (x^2) for the ground state of the Harmonic Oscillator, we need to integrate x^2 multiplied by the square of the absolute value of the wavefunction ψ0(x).

(b) The expectation value of p^2 for the ground state of the Harmonic Oscillator is simply the eigenvalue corresponding to the momentum operator squared.

(c) By calculating the uncertainties in position (Δx) and momentum (Δp) for the ground state, we can verify that their product satisfies Heisenberg's uncertainty principle, Δx · Δp ≥ ħ/2.

(a) In the ground state of the Harmonic Oscillator, the wavefunction is given by \(\psi_0(x) = \frac{1}{\sqrt{\sigma}}e^{-\frac{x^2}{2\sigma^2}}\), where \(\sigma\) is the standard deviation.

To evaluate \((x^2)\), we need to find the expectation value of \(x^2\) with respect to the wavefunction \(\psi_0(x)\). Using the formula for the expectation value, we have:

\((x^2) = \int_{-\infty}^{\infty} x^2 \left|\psi_0(x)\right|^2 dx\)

Substituting the given wavefunction, we have:

\((x^2) = \int_{-\infty}^{\infty} x^2 \frac{1}{\sqrt{\sigma}}e^{-\frac{x^2}{\sigma^2}} dx\)

Evaluating this integral gives us the value of \((x^2)\) for the ground state of the Harmonic Oscillator.

To evaluate \(\sigma_2\), we can simply take the square root of \((x^2)\) and subtract the expectation value of \(x\) squared, \((x)^2\).

(b) To evaluate \((p^2)\), we need to find the expectation value of \(p^2\) with respect to the wavefunction \(\psi_0(x)\). However, in this case, it is clear that the ground state of the Harmonic Oscillator is an eigenstate of the momentum operator, \(p\). Therefore, the expectation value of \(p^2\) for this state will simply be the eigenvalue corresponding to the momentum operator squared.

(c) The Heisenberg's uncertainty principle states that the product of the uncertainties in position and momentum (\(\Delta x\) and \(\Delta p\)) is bounded by a minimum value: \(\Delta x \cdot \Delta p \geq \frac{\hbar}{2}\).

To show that the uncertainty product satisfies the uncertainty principle, we need to calculate \(\Delta x\) and \(\Delta p\) for the ground state of the Harmonic Oscillator and verify that their product is greater than or equal to \(\frac{\hbar}{2}\).

If the ground state wavefunction \(\psi_0(x)\) is a Gaussian function, then the uncertainties \(\Delta x\) and \(\Delta p\) can be related to the standard deviation \(\sigma\) as follows:

\(\Delta x = \sigma\)

\(\Delta p = \frac{\hbar}{2\sigma}\)

By substituting these values into the uncertainty product inequality, we can verify that it satisfies the Heisenberg's uncertainty principle.

Regarding the statement \((x) = 0\) and \((p) = 0\) for this problem, it seems incorrect. The ground state of the Harmonic Oscillator does not have zero uncertainties in position or momentum. Both \(\Delta x\) and \(\Delta p\) will have non-zero values.

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Answer: 380 ft

Step-by-step explanation: To find the length in between, you simply subtract the numbers.

1,515 - 1,135 = 380

Therefore, the ladder needs to be extended 380 ft.

$173.68 is the total amount Julio and Marisol still need to sell

Given that Julio and Marisol are selling magazines for a band fundraiser

Julio has sold $150.67 worth, and Marisol has sold $175.65.

We have to find  the total amount they still need to sell to reach the goal of

$500.00

To find the total amount Julio and Marisol still need to sell

we subtract the amount they have already sold from their goal of $500.00.

Total amount they still need to sell = $500.00 - ($150.67 + $175.65)

= $500.00 - $326.32

= $173.68

Therefore, the total amount Julio and Marisol still need to sell is $173.68.

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Step-by-step explanation:

\(area = length \times width \\ = (4x + 3) \times (2x + 2) \\ = ( {8x}^{2} + 8x + 6x + 6) \\ = ( {8x}^{2} + 14x + 6) \: {units}^{2} \)

Answer:

\((8x + 14x + 6)^{2}\)

Step-by-step explanation:

Area of a rectangle is length x breadth

In the given figure, the length is 2x + 2 and breadth is 4x + 3

So, the area would be:-

(2x + 2) (4x + 3)

\(8x^{2}\) + 6x + 8x + 6

So the area would be => \((8x + 14x + 6)^{2}\)

Answer:

the highest amount is heart disease its such high risk to die from it the number would be high.

Step-by-step explanation:

Answer:

397/378=0.971

Step-by-step explanation:

plato/edmentum

A 95% confidence interval for the mean weight level based on a sample is (25.504, 25.67)

We know that, the confidence interval is:

\(\bar{x}\pm z\frac{\sigma}{n}\)

where,

\(\bar{x}\) is the sample mean.

z is the critical value.

n is the sample size.

σ (OR s) is the standard deviation for the population.

In this question, we need to calculate the 95% confidence interval for an experiment that found the sample mean temperature for a certain city in August was 101.82, with a population standard deviation of 1.2

The critical value is z = 1.96

We have been given x¯ = 25.6, σ = 0.6 and n = 150

\(\Rightarrow \bar{x}+ z\frac{\sigma}{\sqrt{n} } \\\\= 25.6+ 1.96\frac{0.6}{\sqrt{150} } \\\\=25.67\)

And

\(\Rightarrow \bar{x}- z\frac{\sigma}{\sqrt{n} } \\\\= 25.6- 1.96\frac{0.6}{\sqrt{150} } \\\\=25.504\)

Required interval is (25.504, 25.67)

Thus, the mean weight level( 25.6 grams) is accurate.

Therefore, a 95% confidence interval for the mean weight level based on a sample is (25.504, 25.67)

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For the given standard deviation the minimum value we would assign is 22.the maximum value we would assign is 88.

To calculate the minimum and maximum values based on the given information, we need to consider the standard deviation and the respective interest rates for the 3-year and 10-year periods.

Given:

S = 26.32 (Initial value)

E = 55 (Expected value)

t = 3 (Years)

Standard deviation = 60% (of the expected value)

3-year interest rate = 2.4%

10-year interest rate = 3.1%

To find the minimum value, we will calculate the value at the end of the 3-year period using the lowest possible growth rate.

Minimum value calculation:

Minimum value = E - (Standard deviation * E) = 55 - (0.6 * 55) = 55 - 33 = 22

Therefore, the minimum value we would assign is 22.

To find the maximum value, we will calculate the value at the end of the 10-year period using the highest possible growth rate.

Maximum value calculation:

Maximum value = E + (Standard deviation * E) = 55 + (0.6 * 55) = 55 + 33 = 88

Therefore, the maximum value we would assign is 88.

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The aquarium have a length, width and height measuring 6 m each

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

The volume of a cube is the product of its length, width and height. But all the sides are equal, hence:

Volume = length * width * height = length * length * length = length³

A cube aquarium For Five Sea lions has a Volume of 216m³. Hence:

Volume = length³

Substituting:

216 = length³

length = 6 m

The aquarium have a length of 6 m.

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For the given bridge: No of truss nodes = 19

Total uniformly distributed load, W = 48.76 kN/m2

Therefore, nodal load on each truss node = W/No of truss nodes= 48.76 / 19≈ 2.56 kN/m2

Hence, each joint on the bottom chord of the truss will experience 1.28 kN/m nodal load.

Given data: Number of 33.4 meter Truss span = 9

Number of 19.2 meter through girder span = 6

Number of 8.3 meter girder span = 17

Estimated width of bridge = 5 meters

1. List all distributed forces that the truss needs to carry.

For truss bridge, the distributed forces are:

Self-weight of truss

Bridge deck weight

Live loads

Wind loads

Earthquake loads

Temperature stresses

Snow loads

2. Find the total uniformly distributed force over 1m2 of the truss (kN/m2).

Uniformly distributed load = (weight of bridge + weight of structure)/Area of bridge= (W1 + W2)/L1.L2

Where, W1 is the weight of the truss,

W2 is the weight of the deck

L1 is the length of truss

L2 is the width of the bridge

Using the data given:

Weight of truss = weight of girder spans + weight of truss spans

Weight of girder spans = 17 x 8.3 x 25 = 3602.5 kN

Weight of truss spans = 9 x 33.4 x 25 = 7455 kN

Weight of truss = 3602.5 + 7455 = 11057.5 kN

Weight of deck = length x width x unit weight= 33.4 x 9 x 25 = 7507.5 kN

Total uniformly distributed load = (11057.5 + 7507.5)/(33.4 x 9)≈ 48.76 kN/m2

3. Considering the distance between the trusses, find the portion of the structure which is supported by each truss.

The distance between the trusses = total length of truss span / number of truss spans= 33.4 x 9 / 10 = 30.06 m

For the bridge to be stable, it is necessary that the two trusses have a shared center of gravity.

So the portion of structure which is supported by each truss is the same.

4. Convert the UDL to the nodal loads acting on the bottom chord's nodes of the truss.

Each joint takes half of the UDL applied on the member to the left and half of the UDL applied on the member to the right.

Nodal load = UDL x Length of truss span / 2

Let’s assume that W is the total uniformly distributed load over the truss and N is the number of nodes in the truss, then each node will have a nodal load = W/N

Hence, for the given bridge: No of truss nodes = 19

Total uniformly distributed load, W = 48.76 kN/m2

Therefore, nodal load on each truss node = W/No of truss nodes= 48.76 / 19≈ 2.56 kN/m2

Hence, each joint on the bottom chord of the truss will experience 1.28 kN/m nodal load.

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Answer: 8.12

Step-by-step explanation:

In a sample of 8 years, the mean number of years that the mango tree does not give fruit is 4.96, the variance is 1.87, and the standard deviation is 1.37.

The mean, variance, and standard deviation for the number of years that a mango tree does not bear fruit in a sample of 8 different years, given a 38% chance of bearing fruit in a given year, can be calculated using probability theory and statistical formulas.

To begin, we can find the probability of the mango tree not bearing fruit in a given year, which is 1 - 0.38 = 0.62. Using this probability, we can construct a binomial distribution with n = 8 trials and p = 0.62 probability of success (not bearing fruit). The mean (expected value) of the distribution is given by μ = np = 8 x 0.62 = 4.96.

The variance of the distribution is given by the formula σ^2 = np(1-p), which in this case equals 8 x 0.62 x 0.38 = 1.87. Finally, the standard deviation of the distribution is the square root of the variance, which equals sqrt(1.87) = 1.37.

Therefore, the mean number of years that the mango tree does not bear fruit in a sample of 8 years is 4.96, the variance is 1.87, and the standard deviation is 1.37. This means that we can expect the mango tree to bear fruit approximately 3 times in the sample of 8 years.

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