An engineer fitted a straight line to the following data using the method of Least Squares: 1 2 3 4 5 6 7 3.20 4.475.585.66 7.61 8.65 10.02 The correlation coefficient between x and y is r = 0.9884, t

Answer:

Growth rate = 4.08%

Step-by-step explanation:

Rate of interest 'i' for the growth in the cost of the house,

i = \((\frac{\text{Final amount}}{\text{Initial amount}})^{\frac{1}{n}}-1\)

Here 'n' = Duration or time (in years)

i = \((\frac{560000}{320000})^{\frac{1}{14}}-1\)

i = \((\frac{7}{4})^{\frac{1}{14}}-1\)

i = 1.0408 - 1

i = 0.0408

i = 4.08%

Therefore, growth rate for this period is 4.08%.

Answer:

20%

Step-by-step explanation:

The largest number 60 and 40 can be divided by is 20. When we divide both numbers by 20, we get the new reduced ratio as follows: 3:2. To summarize, the ratio 60:40 reduced as much as possible is 3:2.

Answer:

100-500

Step-by-step explanation:

Both sides of a triangle cannot be shorter than the remaining side.  Thus, the side must be less than 500 units.  With the same rule, the side must be greater or equal to 100 units, as if it was less, then 200 + 99 < 300.

The compound inequality for the range of the possible lengths for the third side will be 100- 500.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The meaning of inequality is to say that two things are NOT equal. One of the things may be less than, greater than, less than or equal to, or greater than or equal to the other things.

Given:

side lengths of 200 units and 300 units.

The largest value of the third side will be

200+300=500

and, the smallest value will be

300-200=100

Hence, 100<X<500

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Answer:

l = 40 m

Step-by-step explanation:

The formula for area of a rectangle is

A = lw, where

Step 1:  Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):

360 = 9l

Step 2:  Divide both sides by 9 to solve for l

(360 = 9l) / 9

40 m = l

Optional Step 3:  We can check our answers by checking that the product of 40 and 9 is 360

40 * 9 = 360

360 = 360

The Fermi level corresponds to the energy where the probability of occupation is 50% at absolute zero temperature.

The actual position of the Fermi level in a specific material can be influenced by various factors, such as the density of states and the doping level.

In the context of physics and semiconductor materials,

The Fermi level refers to the energy level in a material ,

That has a 50% probability of being occupied by an electron at absolute zero temperature (0 Kelvin or -273.15 degrees Celsius).

The given statement suggests that the probability of a state being empty at energy Ev - kT

where k is the Boltzmann constant and T is the temperature is equal to,

The probability of a state being filled at energy Ev - 3kT.

This implies that the energy difference between the two states is 2kT.

Assuming that Ev is the energy of the Fermi level, we can conclude that the Fermi level is located at energy Ev - 2kT.

The Fermi level is shifted by an energy equal to 2kT from the energy at which the probability of occupation changes from empty to filled.

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Answer:

The solutions of the compound inequality is 5 ≤ x  ≤ 6

Step-by-step explanation:

A compound inequality is two or more inequalities joined. For its resolution, each inequality must be solved separately. In the case of 15 ≤ 2x + 5 ≤ 17, you have:

Inequality (A) 15 ≤ 2x + 5 and Inequality (B) 2x + 5 ≤ 17

The solution of the inequalities consists of finding the value that the unknown x must take for the inequality to be fulfilled, passing all the terms with x to one member (for example to the first member), and all the numbers (terms without x) to the other member through the opposite operation (The opposite operation to addition is subtraction and vice versa, and the opposite operation to multiplication is division and vice versa). In this case, solving the inequalities:

Inequality (A) 15 ≤ 2x + 5

15 - 5 ≤ 2x

10 ≤ 2x

10÷2 ≤ x

5 ≤ x

Inequality (B) 2x + 5 ≤ 17

2x ≤ 17 -5

2x ≤ 12

x ≤ 12÷2

x ≤ 6

The solution of a compound inequality are all the solutions that have in  common the two inequalities. Graphically, it is as if they were two graphs that overlap.

So, in this case the solutions of the compound inequality is 5 ≤ x  ≤ 6

In the image you can see the solution to the compound inequality.

For an event based on order by sam for ham and coffee with different probabilities, then the probability that he will order neither ham nor coffee is equals to the 0.07.

We have sam is a regular customer at joe's diner. Let us consider two events be defined as A: sam will order ham

B: sam will order coffee

Now, the probability that sam will order ham, P( A) = 0.8

The probability that sam will order coffee, P( B) = 0.65

We have to determine the probability that he will order neither ham nor coffee.

Probability is chances of occurrence of an event. It is calculated by dividing the favourable response to total possible outcomes. Probability value always lies between 0 to 1. Apply probability law P( will order ham ) + P( will not order ham) = 1

=> Probability that sam will not order ham

\(P( \bar A ) \) = 1 - 0.8 = 0.2

Probability that sam will not order coffee,

\(P( \bar A ) \)= 1 - 0.65 = 0.35

Now, as we see both events A and B are independent events so, there corresponding also independent. Therefore, Probability that he will order neither ham nor coffee, \( P( \bar A ∩ \bar B) \)

\(= P( \bar A) P(\bar B) \)

= 0.2 × 0.35 = 0.07

Hence, required probability is 0.07.

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The race horse's speed is approximately 256 furlongs per fortnight.

To determine the race horse's speed in furlongs per fortnight, we need to convert both the distance and time units to their respective values.

1 furlong is equal to 180 yards, so the horse's speed in yards per second (7 yards/second) can be converted to furlongs per second:

Speed in furlongs per second = (7 yards/second) / (180 yards/furlong) = 7/180 furlongs/second

Next, we need to convert the time from seconds to fortnights. Since a fortnight is a time period of two weeks, and there are 7 days in a week, a fortnight consists of 14 days:

Time in seconds per fortnight = (14 days/fortnight) * (24 hours/day) * (60 minutes/hour) * (60 seconds/minute) = 1,209,600 seconds/fortnight

Finally, we can calculate the horse's speed in furlongs per fortnight by multiplying the speed in furlongs per second by the time in seconds per fortnight:

Speed in furlongs per fortnight = (7/180 furlongs/second) * (1,209,600 seconds/fortnight) = 46,080/180 furlongs/fortnight ≈ 256 furlongs/fortnight

The race horse's speed is approximately 256 furlongs per fortnight.

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Answer:

Step-by-step explanation:

45 total hair bands

Answer:

3/2

Step-by-step explanation:

Given y = 2x + 5, let's rewrite the equation in terms of x;

y = 2x + 5 => Bring 5 to the other side

2x = y - 5 => Divide either side by 2

x = (y - 5)/2

If we want to take the inverse, simply swap the variable's positions...

We have y = (x - 5)/2

Now let's determine f^-1(8), substituting for "y" provided y is our inverse, f^-1

f^-1(8) = (8 - 5)/2 = 3/2

Solution: 3/2

Answer:

What? Retype the question below and ill answer it, but this isnt answerable.

Step-by-step explanation:

What is \redD{\text{A}}Astart color #e84d39, start text, A, end text, end color #e84d39 rounded to the nearest ten? What is \redD{\text{A}}Astart color #e84d39, start text, A, end text, end color #e84d39 rounded to the nearest hundred?

Like what kind of language is this ;--;

Answer:

3 : 7

Step-by-step explanation:

Ratios are Proportinalised Numbers that we can use to compare number of units relative to the other value.

Eg. 3 : 15 = 1 : 5

Given Information from the Question:

15 Child Tickets : 35 Adult Tickets

Now we reduce them to simplest form.

(15 ÷ 5) : (35 ÷ 5) = 3 : 7.

Therefore the ratio of Child Tickets to Adult Tickets is 3 : 7.

Answer:

Step-by-step explanation:

Side = 9 cm

Volume of cube = side³

                           = 9³

                           = 9 * 9 *9

                           = 729 cubic cm

Answer:

0.000729 \(m^{3}\)

Step-by-step explanation:

Before solving, make sure to know what is being asked. The question is asking for the answer in cubic meters (\(m^{3}\)), but the given is in cm. Let's convert 9 cm to meter first.

Take note that 1 cm is 0.01 meter, so:

9 cm is 0.09 meter

Next, remember the formula for the volume of a cube: V = \(a^{3}\), where V is equal to volume and \(a^{3}\) refers to the side of the cube multiplied three times.

V = 0.09 m x 0.09 m x 0.09 m

V = 0.000729 \(m^{3}\)

Answer: 7.33980582 x 10^0

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. The sign of the exponent will depend on the direction you are moving the decimal.

The expression in scientific notation is 7 ×10^5

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

Given that the terms are;

(8.4×10^8) ÷ (1.2×10^3)

Step 1: Divide the numerical parts:

8.4 ÷ 1.2 = 7

Step 2: Subtract the exponents:

10^8 /10^3 = 10^5

Now Putting the numerical part and the exponent together, we get:

7 ×10^5

Hence, the result of the expression in scientific notation is; 7 ×10^5

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\( \sf2x + 3y = - 6 \\ \sf2x + 3 \times 0 = - 6 \\ \sf2x = - 6 \\ \boxed{ \tt x = - 3}\)

Answer: 14/285

Step-by-step explanation:

B = 10

G = 8

T = 18

So its a 8/20 that 1 is a girl but then 2nd its 7/19 and 3rd 6/18 so

8/20 * 7/19 * 6/18 = 14/285

Answer:

decimal: .6

fraction: 3/5

Answer:

2(x + 5)

twice — 2

the sum of an unknown number and 5 — x + 5

The approximate probability that the total score is at least 375 when a fair six-sided die is rolled 100 times is (d) 0.4420.

When a fair six-sided die is rolled, the random variable X represents the outcome. The mean (μX) of X is 3.5, and the standard deviation (σX) is 1.71.

To find the probability that the total score is at least 375 when the die is rolled 100 times, we can use the Central Limit Theorem. According to the theorem, the sum of a large number of independent and identically distributed random variables approximates a normal distribution.

In this case, the sum of the outcomes of 100 rolls of the die follows a normal distribution with a mean of μX multiplied by the number of rolls (100) and a standard deviation of σX multiplied by the square root of the number of rolls (10). Therefore, the approximate probability can be calculated by finding the probability that the sum is greater than or equal to 375.

Using a normal distribution table or a calculator, we can find that the approximate probability is 0.4420, which corresponds to answer (d). This means that there is a 44.20% chance that the total score will be at least 375 when the die is rolled 100 times.

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Answer:

x = 20

Step-by-step explanation:

\(\frac{10}{x}\) = \(\frac{x}{40}\)

We cross-multiply and get

400 = \(x^{2}\)

\(\sqrt{400}\) = \(\sqrt{x^{2} }\)

x = 20

So, the answer is x = 20

The given problem is asking for a test to see if the sample mean is significantly different from 85 at the 0.05 level. To solve the problem, we can use the following formula:$$t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$$where$\bar{x}$ = sample mean$\mu$ = population mean$s$ = sample standard deviation$n

$ = sample sizeTo calculate the t-value, we need to calculate the sample mean and the sample standard deviation. The sample mean is calculated as follows:$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$where $x_i$ is the score of the $i$th student and $n$ is the sample size.

Using the given data, we get:$$\bar

{x} = \frac{78+89+67+85+90+83+81+79}{8}

= 81.125$$The sample standard deviation is calculated as follows:$$

s = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1}}$$Using the given data, we get:$$

s = \sqrt{\frac{(78-81.125)^2+(89-81.125)^2+(67-81.125)^2+(85-81.125)^2+(90-81.125)^2+(83-81.125)^2+(81-81.125)^2+(79-81.125)^2}{8-1}}

= 7.791$$Now we can calculate the t-value as follows:$$

t = \frac{\bar{x} - \mu}{\frac{s}

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The density of glycerin at 60°C is approximately 19.9592 g/cm³.

To find the density of glycerin at 60°C, we can use the volume expansion coefficient and the given density at 20°C.

The formula for volume expansion is:

ΔV = β * V₀ * ΔT

where:

ΔV is the change in volume,

β is the volume expansion coefficient,

V₀ is the initial volume, and

ΔT is the change in temperature.

In this case, we want to find the change in density, so we can rewrite the formula as:

Δρ = -β * ρ₀ * ΔT

where:

Δρ is the change in density,

β is the volume expansion coefficient,

ρ₀ is the initial density, and

ΔT is the change in temperature.

Given:

ρ₀ = 20 g/cm³ (density at 20°C)

β = 5.1 x 10⁻⁴ °C⁻¹ (volume expansion coefficient)

ΔT = 60°C - 20°C = 40°C (change in temperature)

Substituting the values into the formula, we have:

Δρ = - (5.1 x 10⁻⁴ °C⁻¹) * (20 g/cm³) * (40°C)

Calculating the expression:

Δρ = - (5.1 x 10⁻⁴) * (20) * (40) g/cm³

≈ - 0.0408 g/cm³

To find the density at 60°C, we add the change in density to the initial density:

ρ = ρ₀ + Δρ

= 20 g/cm³ + (-0.0408 g/cm³)

≈ 19.9592 g/cm³

Therefore, the density of glycerin at 60°C is approximately 19.9592 g/cm³.

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Answer:

32−4x=12,

25 over x end fraction plus 4 equals 9 ((25)/(x)+ 4 equals 9), and

x over 5 end fraction plus 5 equals 6 ((x)/(5) plus 5 equals 6)

Step-by-step explanation:

hope this help

Answer:

humanism

Step-by-step explanation:

read about it thats how you'll know

Answer:

B.    humanism

Step-by-step explanation:

Cultural Geography of Europe  Quiz on edge.

To determine which method can be used to prove the similarity of the given triangles, use SAS, SSS, and AA.

To determine which method can be used to prove the similarity of the given triangles, let's briefly discuss each method:

a) SAS~ (Side-Angle-Side Similarity): If two sides of a triangle are proportional to two sides of another triangle, and their included angles are congruent, then the triangles are similar.

b) SSS~ (Side-Side-Side Similarity): If all three sides of a triangle are proportional to the corresponding sides of another triangle, then the triangles are similar.

c) AA~ (Angle-Angle Similarity): If two angles of a triangle are congruent to two angles of another triangle, then the triangles are similar.

Unfortunately, I cannot see the given triangles in your question, but based on the provided information, you can use these explanations to determine which method (SAS~, SSS~, or AA~) can be used to prove their similarity. If none of these methods apply, then similarity cannot be proved for the triangles.

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Answer: x = 1

Step-by-step explanation: 4(1-x) = 6(x-1)

 -  4-4x = 6x-6

 -  6x-4x = 6-4

 -  2x = 2

 - x= 1

Answer:

A

Step-by-step explanation:

\(\frac{2}{5} = \frac{4}{10} \\.3=\frac{3}{10} \\5\frac{3}{10} -\frac{4}{10} =4\frac{9}{10}\)

Let's denote the radius of your neighbor's watermelon as r(t), where t is the time in weeks. We know that the thickness of the rind is one-tenth of the radius, so the inner radius of the watermelon (i.e., the radius of the edible part) is 9/10 of the total radius.

The volume of the watermelon can be expressed as the difference between the volumes of the outer sphere and the inner sphere:

V = (4/3)πr(t)^3 - (4/3)π(9/10r(t))^3

= (4/3)πr(t)^3 - (27/1000)πr(t)^3

= (1073/750)πr(t)^3

The rate at which the radius is growing is given by the derivative of r(t) with respect to t:

r'(t) = 20/((4/3)π(1.1r(t))^2)

= 750/221πr(t)^2

We can use this expression to find the rate at which the radius is growing after 5 weeks:

r'(5) = (750/221π)r(5)^2

We don't have enough information to solve for r(5) exactly, but we can use the fact that the rind grows at a constant rate of 20 cubic centimeters a week. The volume of the rind is given by the difference between the volumes of the outer sphere and the inner sphere with radii r(t) and 9/10r(t), respectively:

V_rind = (4/3)πr(t)^3 - (4/3)π(9/10r(t))^3

= (1073/750)πr(t)^3 - (243/1000)πr(t)^3

= (673/750)πr(t)^3

The rate at which the rind is growing is given by the derivative of V_rind with respect to t:

dV_rind/dt = (673/250)πr(t)^2 dr/dt

We know that dV_rind/dt = 20, so we can solve for dr/dt:

dr/dt = 20 / ((673/250)πr(t)^2)

We still don't know the value of r(5), but we can use the fact that the thickness of the rind is one-tenth of the radius to relate the volume of the rind to the radius:

V_rind = (1/10)³ (4/3)πr(t)^3

= (4/3)πr(t)^3/1000

We know that V_rind = 20(5) = 100, so we can solve for r(5):

(4/3)πr(5)^3/1000 = 100

r(5) = 1000(750/221π)^(1/3)

This gives an approximate value of r(5) ≈ 13.825 centimeters. We can use this value to find the rate at which the radius is growing:

r'(5) = (750/221π)r(5)^2

≈ 4.942 centimeters per week

Therefore, after 5 weeks, your neighbor's watermelon has a radius of approximately 13.825 centimeters and is growing at a rate of approximately 4.942 centimeters per week