What are the solutions of 15<5(4m+7)?

Answer: 38 divided by 8 which would equal 4.75 or 4 3/4 feet each day.

Step-by-step explanation: You divide the amount of total feet by the amount of days it took.

The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.

A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.

if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.

We have to determine the decrease in diameter of the bar due to the applied load.

Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.

Length of the bar, L = 10 in

Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²

Stress produced by the applied load,σ = P/A

= 80,000/0.4418

= 181163.5 psi

Young's modulus of elasticity, E = 10,000 ksi

Poisson's ratio, ν = 0.3

The longitudinal strain produced in the bar, ɛ = σ/E

= 181163.5/10,000,000

= 0.01811635

The lateral strain produced in the bar, υ = νɛ

= 0.3 × 0.01811635

= 0.005434905'

The decrease in diameter of the bar due to the applied load, ∆d/d = -υ

= -0.005434905∆d

= -0.005434905d

The final diameter of the bar,

d - ∆d = d + 0.005434905d

= 1.005434905d

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The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

We have,

Let's analyze each of the given statements to determine whether they are identities:

tan x = sin x / cos x:

This is an identity.

It is known as the fundamental identity of trigonometry, as it holds true for all values of x (except when cos x is equal to 0).

tan x cos x = sin x:

This is not an identity.

It is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

cos x = tan x sin x:

This is not an identity.

Similar to the previous statement, it is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

sin x / tan x = cos x:

This is an identity.

It can be derived from the fundamental identity by dividing both sides by cos x, resulting in sin x / cos x = cos x / cos x, which simplifies to sin x / tan x = cos x.

Thus,

The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

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In 10,000 independent tosses of a coin and the coin landed on heads 5800 times, is it reasonable to assume that the coin is not fair and may be biased towards heads.

In order to determine if the coin is fair or not, we need to calculate the probability of getting 5800 or more heads in 10,000 tosses assuming the coin is fair.

The probability of getting a head on any one toss of a fair coin is 0.5. The number of heads in 10,000 tosses is a binomial random variable with parameters n=10,000 and p=0.5. We can use the normal approximation to the binomial distribution to calculate the probability of getting 5800 or more heads.

The mean of the binomial distribution is np = 5000 and the standard deviation is sqrt(np(1-p)) = 50.

We can standardize the variable X = number of heads in 10,000 tosses by subtracting the mean and dividing by the standard deviation:

Z = (X - 5000) / 50

The probability of getting 5800 or more heads can be calculated as:

P(X >= 5800) = P(Z >= (5800-5000)/50)

Using a standard normal table or calculator, we find that P(Z >= 1.6) = 0.0548.

This means that the probability of getting 5800 or more heads in 10,000 tosses assuming the coin is fair is only 0.0548, which is quite low.

Therefore, it is reasonable to conclude that the coin is not fair and may be biased towards heads.

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Answer:

It shows how much variable is affected by one another.

Step-by-step explanation:

Answer:

There is a negative correlation in the data set.

Step-by-step explanation:

I hope this helps you! :D

Answer:

the median is 8

Step-by-step explanation:

hope this helps!

2,5,6,7,8,10,11,12,14

Answer:

8

Step-by-step explanation:

Rearrange to 2 5 6 7 8 10 11 12 14 in ascending order

Take the center number

we need 27 ounces of the 11% alcohol solution and 9 ounces of the 23% alcohol solution to obtain 36 ounces of a 14% solution.

Let x be the number of ounces of the 11% alcohol solution, and y be the number of ounces of the 23% alcohol solution. Then we have:

x + y = 36 (total amount of solution)

0.11x + 0.23y = 0.14(36) (total amount of alcohol)

Simplifying the second equation, we get:

0.11x + 0.23y = 5.04

Multiplying the first equation by 0.11 and subtracting from the second equation, we get:

0.12y = 1.08

y = 9

Substituting y = 9 into the first equation, we get:

x + 9 = 36

x = 27

what is numbers?

In mathematics, numbers are abstract concepts used for counting, measuring, and comparing quantities. There are several types of numbers, including natural numbers, integers, rational numbers, irrational numbers, and real numbers. Numbers are used in various mathematical operations, such as addition, subtraction, multiplication, and division, and are a fundamental concept in mathematics.

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1- SHM stands for Simple Harmonic Motion.

In SHM, an object oscillates back and forth about an equilibrium position, with a motion that can be described by a sinusoidal function. The symbols commonly used in SHM are:

y: Displacement from the equilibrium position

t: Time

k: Spring constant or restoring force constant

m: Mass of the object

c₁ and c₂: Constants determined by initial conditions

2- Hooke's law relates the force exerted by a spring to the displacement of the object attached to it. It is represented by the second-order differential equation my" + ky = 0, where m is the mass of the object and k is the spring constant. The solution to this equation is given as y = c₁ cos(√(k/m) * t) + c₂ sin(√(k/m) * t). To determine the values of c₁ and c₂, initial conditions are needed.

3- If the initial conditions are y(0) = 0 and y'(0) = 0, which means the object starts at equilibrium with zero displacement and zero velocity, we can substitute these values into the solution equation and solve for c₁ and c₂. In this case, we find that c₁ = 0 and c₂ = 0.

4- To show that the sum of the solutions c₁ cos(w₀t) and c₂ sin(w₀t) is also a solution of the SHO (Simple Harmonic Oscillator) differential equation, we substitute the sum into the differential equation and demonstrate that it satisfies the equation. By taking the derivatives and substituting, we can show that the sum of the solutions satisfies the equation, thus confirming that it is also a solution.

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Answer:

A vertical line has an undefined slope. So the equation x=−5 has no defined slope and no y-intercept

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

Answer:

ADD/SUBTRACT A QUANTITY TO/FROM ONLY ONE SIDE

And part 2: is No

Step-by-step explanation:

Answer:

None

Step-by-step explanation:

Let's clarify that a radical symbol beside a number means what number squared (or to the power of 2) can give me the number in the symbol.

In this case it would be 4 because

\(4*4=16\)

A method I use is to find the square root is dividing the number in the radical symbol 2 times

First by the original number, and then by the product of the last equation. It will not always work, but it works in some cases like this one.

\(\frac{16}{2} = 8\\ \\\frac{8}{2}=4\\ \\\sqrt{16}=4\)

Second step, multiply 4 by 4, which equals 16.

Since the square root of 16 is 4, you can substitute 4 in the rest of the equations instead of the radical expression.

None of the following equations equal 16, which means none of the following equations if equal to \(\sqrt{16} *4\)

Answer:

Surface area of 5 sides = 51.2 cm²

Step-by-step explanation:

Given:

Side of cube = 3.2 cm

Find:

Surface area of 5 sides

Computation:

Surface area of 5 sides = Surface area of cube - Surface area 1 side

Surface area of 5 sides = 6a² - a²

Surface area of 5 sides = 6(3.2)² - (3.2)²

Surface area of 5 sides = 6(10.24) - 10.24

Surface area of 5 sides = 6a² - a²

Surface area of 5 sides = 61.44 - 10.24

Surface area of 5 sides = 51.2 cm²

The area of painted surfaces is 51.2 square centimeters.

To understand more, check below explanation.

From the given figure,

It is observed that side of block = 3.2cm

And block is cube.

Since, every surface of the block shown will be painted, except for one of the bases.

Area of painted portion is computed as;

                    \(Area=5*a^{2} \\\\Area=5*(3.2)^{2} \\\\Area=51.2cm^{2}\)

Hence, the area of painted surfaces is 51.2 square centimeters.

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Answer:

there is really no way to show but all you have to do is look at the angle across from angle 1 which is angle 4 because it is vertical to angle 1. hope that helps

The regression model shows that BTU rating, energy efficiency ratio, and number of settings have a significant effect on the price of air conditioners. The results make economic sense as higher BTU ratings, higher energy efficiency ratios, and a hypothesis test confirms the positive effect of BTU rating. The null hypothesis that the three variables do not explain a substantial variation in price is rejected.

The regression equation shows that the price of air conditioners is determined by the BTU rating, energy efficiency ratio, and number of settings. The coefficients indicate that as the BTU rating and energy efficiency ratio increase, the price of the air conditioner also increases. Similarly, as the number of settings increases, the price also increases. The R-squared value of 0.84 indicates that 84% of the variation in the price of air conditioners is explained by the three explanatory variables.

Yes, the results make economic sense as it is logical to expect that air conditioners with higher BTU ratings, higher energy efficiency ratios, and more settings will be priced higher.

To test the hypothesis that the BTU rating has no effect on the price of an air conditioner versus that it has a positive effect, we can set up the null and alternative hypotheses as follows:

H0: β2 = 0 (BTU rating has no effect on price)

Ha: β2 > 0 (BTU rating has a positive effect on price)

Using the t-test, with α=5α=5 and the standard error of β2 from the regression output, we can calculate the t-statistic as:

t = (0.023 - 0) / 0.005 = 4.6

The degrees of freedom are n - k - 1 = 19 - 3 - 1 = 15, where n is the sample size and k is the number of explanatory variables. The critical value for a one-tailed t-test with 15 degrees of freedom at α=5α=5 is 1.753. Since the calculated t-statistic of 4.6 is greater than the critical value of 1.753, we reject the null hypothesis and conclude that the BTU rating has a positive effect on the price of an air conditioner.

Based on the high R-squared value of 0.84, we can conclude that the three explanatory variables (BTU rating, energy efficiency ratio, and number of settings) explain a substantial variation in the prices of air conditioners. Therefore, we would not accept the null hypothesis that these variables have no effect on the price of air conditioners.

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Yes, it is true that if "x" is an optimal solution to a linear programming problem, then it is a vertex of the feasible region.

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The trip will take about 11.93 hours, or approximately 11 hours and 56 minutes.

What is distance?

Distance is the measure of how far apart two objects or locations are from each other. It is usually measured in units such as meters, kilometers, miles, or feet. Distance is a scalar quantity, meaning it has only magnitude and no direction.

To calculate the total time for the trip, we need to take into account the time for driving and the time for lunch.

First, let's calculate the time for driving:

Distance to be covered = 800 miles

Average speed = 70 miles per hour

Time for driving = Distance / Speed

Time for driving = 800 miles / 70 miles per hour

Time for driving = 11.43 hours

So, the driving time is approximately 11.43 hours.

Now, let's add the time for lunch. The stop for lunch is 30 minutes, which is equivalent to 0.5 hours.

Total time for the trip = Time for driving + Time for lunch

Total time for the trip = 11.43 hours + 0.5 hours

Total time for the trip = 11.93 hours

Therefore, the trip will take about 11.93 hours, or approximately 11 hours and 56 minutes.

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Answer:

Step-by-step explanation:

A simple way to calculate the distance between numbers on a number line is to count every number between them. A faster way is to find the distance by taking the absolute value of the difference of those numbers. Absolute value of a number on a number line is its distance from 0 on the number line .

Answer:

17 1/2

Step-by-step explanation:

im sorry if its wrong i feel like that would be the closest but if not im

sorry lol

There are 4 hits and 4 misses in the address sequence 0, 2, 4, 8, 10, 12, 14, 8, 0 using the MRU replacement policy.

LRU replacement policy

There are 5 hits and 3 misses in the address sequence 0, 2, 4, 8, 10, 12, 14, 8, 0 using the LRU replacement policy.

The status of the cache after each address is accessed is as follows:

Address of Memory Block Accessed | Evicted Block | Hit or Miss

--------------------------------|------------|------------

0                              | N/A         | Hit

2                              | N/A         | Hit

4                              | 0           | Miss

8                              | 2           | Hit

10                             | 4           | Miss

12                             | 8           | Hit

14                             | 12          | Miss

8                              | 14          | Hit

0                              | 8           | Hit

4.2 - MRU (most recently used) replacement policy

There are 4 hits and 4 misses in the address sequence 0, 2, 4, 8, 10, 12, 14, 8, 0 using the MRU replacement policy.

The status of the cache after each address is accessed is as follows:

Address of Memory Block Accessed | Evicted Block | Hit or Miss

--------------------------------|------------|------------

0                              | N/A         | Hit

2                              | N/A         | Hit

4                              | 0           | Miss

8                              | 2           | Hit

10                             | 4           | Miss

12                             | 8           | Hit

14                             | 10          | Miss

8                              | 12          | Hit

0                              | 14          | Hit

As you can see, the LRU replacement policy results in 1 fewer miss than the MRU replacement policy. This is because the LRU policy evicts the block that has not been accessed in the longest time, while the MRU policy evicts the block that has been accessed most recently.

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Answer:

show graph

Step-by-step explanation:

Answer:

  the sides are different lengths as shown in the diagram

Step-by-step explanation:

Plotting the three points, you can see by "inspection" that the middle length side (PQ) is longer than the shortest side (QR) and shorter than the longest side (PR). You could use the distance formula to show this, or you can use a scale to measure the drawing.

A triangle with three unequal sides is a scalene triangle. ∆PQR is scalene.

Answer:

\(-6-7\left(c+10\right)=-7c-76\)

Step-by-step explanation:

Given the expression

\(-6\:-\:7\:\left(c+10\right)\)

simplifying the expression

\(-6-7\left(c+10\right)\)

Expanding -7(c + 10) = -7c - 70

\(-6\:-\:7\:\left(c+10\right)=-6-7c-70\)

subtract the numbers: -6 - 70 = -76

                           \(=-7c-76\)

Therefore, we conclude that:

\(-6-7\left(c+10\right)=-7c-76\)

Given:

\(\begin{aligned}&x^2+y^2=16 \\&z=x y\end{aligned}\)

Express 16 as \(4^{2}\): \(x^2+y^2=16\)

\(x^2+y^2=4^2\\x^2+y^2=4^2 \times 1\)

Trignometry,

\(\cos ^2(t)+\sin ^2(t)=1\)

Now, substitute \(\cos ^2(t)+\sin ^2(t)\) for 1:

\(\begin{aligned}&x^2+y^2=4^2 \times 1 \\&x^2+y^2=4^2 \times\left[\cos ^2(t)+\sin ^2(t)\right]\end{aligned}\\x^2+y^2=4^2 \times \cos ^2(t)+4^2 \times \sin ^2(t)\)

Law of indicates:
\(\begin{aligned}&x^2+y^2=[4 \times \cos (t)]^2+[4 \times \sin (t)]^2 \\&x^2+y^2=[4 \cos (t)]^2+[4 \sin (t)]^2\end{aligned}\\x^2=[4 \cos (t)]^2 \text { and } y^2=[4 \sin (t)]^2\)

Taking positive square roots as follows:

\(x=4 \cos (t), y=4 \sin (t)\)

Recall that, z = xy.

Now, we have:

\(\begin{aligned}&z=4 \cos (t) \times 4 \sin (t) \\&z=16 \cos (t) \cdot \sin (t)\end{aligned}\)

Now, substitute the values:
\(r(t)=x_t i+y_t j+z_t k\)

So, the vector r(t) is: \(r(t)=(4 \cos (t)) i+(4 \sin (t)) i+(16 \cos (t) \cdot \sin (t)) i\)

Therefore, the vector function r(t) is written as: \(r(t)=x_t i+y_t j+z_t k\)

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The product of the slopes of two non-vertical perpendicular lines is always -1.

It is NOT possible for two perpendicular lines to both have a positive slope because the product of two positives is positive. So for the product of the slopes to be -1, one of the slopes must be positive and the other negative.

The definition of perpendicular lines is lines that intersect and at the point of intersection they form a right angle of 90°.

In determining the gradient of two mutually perpendicular when multiplied it will produce the number -1. So the formula used is:

y = mx + c

Meanwhile, the gradient formula is m1 = -1/m2.

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The equation's answer is x = 7.5. 4x - 1 2 = x + 7.

x = 1 is the answer to the problem 3x + 2 = (2x + 13) 3.

a) To solve the equation 4x - 1 ÷ 2 = x + 7, we need to isolate the variable x. Let's follow the steps:

1: Distribute the division operation to the terms inside the parentheses.

  (4x - 1) ÷ 2 = x + 7

2: Divide both sides of the equation by 2 to isolate (4x - 1) on the left side.

  (4x - 1) ÷ 2 = x + 7

  4x - 1 = 2(x + 7)

3: Distribute 2 to terms inside the parentheses.

  4x - 1 = 2x + 14

4: Subtract 2x from both sides of the equation to isolate the x term on one side.

  4x - 1 - 2x = 2x + 14 - 2x

  2x - 1 = 14

5: Add 1 to both sides of the equation to isolate the x term.

  2x - 1 + 1 = 14 + 1

  2x = 15

6: Divide both sides of the equation by 2 to solve for x.

  (2x) ÷ 2 = 15 ÷ 2

  x = 7.5

Therefore, x = 7.5 is the solution to the equation 4x - 1 ÷ 2 = x + 7. However, note that this answer is not an integer, so it may not be valid for certain contexts.

b) To solve the equation 3x + 2 = (2x + 13) ÷ 3, we can follow these steps:

1: Distribute the division operation to the terms inside the parentheses.

  3x + 2 = (2x + 13) ÷ 3

2: Multiply both sides of the equation by 3 to remove the division operation.

  3(3x + 2) = 3((2x + 13) ÷ 3)

  9x + 6 = 2x + 13

3: Subtract 2x from both sides of the equation to isolate the x term.

  9x + 6 - 2x = 2x + 13 - 2x

  7x + 6 = 13

4: Subtract 6 from both sides of the equation.

  7x + 6 - 6 = 13 - 6

  7x = 7

5: Divide both sides of the equation by 7 to solve for x.

  (7x) ÷ 7 = 7 ÷ 7

  x = 1

Hence, x = 1 is the solution to the equation 3x + 2 = (2x + 13) ÷ 3.

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Answer:

8 1/2

Step-by-step explanation:

To find the estimated population growth between 2021 and 2039, we first need to determine how many years have passed since 2000. The population is estimated to grow by 21,000 people between 2021 and 2039.

Since we are looking at the time period between 2021 and 2039, we know that 21 years have passed since 2000. Therefore, we can use the formula for population growth:
P(t) = P(0) + r(t)
Where P(t) is the population at time t, P(0) is the initial population, and r(t) is the rate of growth per year. We can plug in the values we know:
P(t) = 45,000 + 1200t (since the rate of growth is 1200 people per year)
To find the population in 2021, we need to plug in t=21:
P(21) = 45,000 + 1200(21) = 72,600
To find the population in 2039, we need to plug in t=39:
P(39) = 45,000 + 1200(39) = 93,600
Therefore, the estimated population growth between 2021 and 2039 is:
93,600 - 72,600 = 21,000

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