The value of a car decreases linearly with time. The car was bought new for $62,000 and had a value of $41,000 after 6 years.

The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm

To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.

The formula for a confidence interval for the population mean (μ) is:

Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

For the first situation:

n = 15

Confidence level is 95% (which corresponds to an alpha level of 0.05)

x = 35 (sample mean)

s = 2.7 (sample standard deviation)

Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.

The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.

Plugging the values into the formula:

Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))

Calculating the confidence interval:

Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)

Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.

For the second situation:

n = 37

Confidence level is 99% (which corresponds to an alpha level of 0.01)

x = 82 (sample mean)

s = 5.9 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.

The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.

Plugging the values into the formula:

Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))

Calculating the confidence interval:

Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)

Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.

For the third situation:

n = 1009

Confidence level is 90% (which corresponds to an alpha level of 0.10)

x = 0.9 (sample mean)

s = 0.04 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.

The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.

Plugging the values into the formula:

Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))

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Answer:

95 mi/hr

Step-by-step explanation:

475/5 = 95

285/3 = 95

Equation (12x² - 6x)(4x - 2) simplifies to 12x(2x - 1)².

We can start by factoring out the greatest common factor from both terms, which is 6x:

(12x² - 6x)(4x - 2) = 6x(2x - 1)(4x - 2)

Next, we can simplify the expression by factoring out the common factor (4x - 2) from the remaining terms (2x - 1):

6x(2x - 1)(4x - 2) = 6x(2x - 1) × 2(2x - 1)

Now we have two factors that are the same, (2x - 1), so we can combine them by multiplying them together:

6x(2x - 1) × 2(2x - 1) = 12x(2x - 1)²

Therefore, (12x² - 6x)(4x - 2) simplifies to 12x(2x - 1)².

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Given question is incomplete, the complete question is below

Assuming that x ≠ 1/2, simplify (12x² - 6x)(4x - 2).

Answer:

Therefore, you need 2600 pounds of 35% supplement and 1300 - 2600 = -1300 pounds of 10% ration.

Step-by-step explanation:

The unknown variable is x, which is the amount of 35% supplement needed. The other expressions are derived from the given information and the fact that the total amount of solution is 1300 pounds.

The equation from the fourth column is:

0.35x + 0.10(1300 - x) = 0.25(1300)

Solving for x, we get:

x = (0.25(1300) - 0.10(1300)) / (0.35 - 0.10) x = 650 / 0.25 x = 2600

Answer:

See explanation

Step-by-step explanation:

We have that;

P(t) = (25t2 + 150t + 100)/(t2 + 6t + 24)

a) rate at which Glen Cove's population is changing with respect to time.

dP/dt = (t^2 + 5t + 40) (50t + 125) - (25t^2 + 125t + 200) (2t + 5)/(t^2 + 5t + 40)^2

dP/dt = 1000t + 3000/(t^2 + 6t + 24)^2

b)  population after 10 years

P(t) = (25t2 + 150t + 100)/(t2 + 6t + 24)

P(t) =(25(10)^2 + 150(10) + 100)/((10^2 + 6(10) + 24)

P(t) = 4100/184

P(t) = 22283

c) when t = 10

dP/dt = 1000t + 3000/(t^2 + 6t + 24)^2

dP/dt = 1000(10) + 3000/(10^2 + 6(10) + 24)^2

dP/dt = 13000/33856

dP/dt = 0.384

The quantity of string he use is 4/15 yd

Fractions are represented as numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing

Given that: He had 4/5 yd of string

Since he uses 1/3 of the string, that means he used 1/3 multiplied by the quantity of the string he has:

1/3 x 4/5 yd = 4/15 yd

Therefore, the amount of string he use is 4/15 yd

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Answer:

13

Step-by-step explanation:

Answer:

.75 pounds= $1.77, 1.25 pounds=$2,95, 2 pounds=$4.72, 2.5 pounds= $5.90

Step-by-step explanation:

multiply each number in the pounds column by 2.36 to get the total cost

.75(2.36)=1.77

1.25(2.36)=2.95

2(2.36)=4.72

2.5(2.36)=5.9

The first debt that Alice would have to pay based on the Stack method would be the third debt. Option C

From the stack method, the debt that Alice would have to pay off first would be the debt that has the highest interest rate.

The amount of 150 dollars would then be added to the debt that has the second highest rate.

Hence the amount of debt that would be paid off first would be the first debt based on the stack method.

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Answer:

.11+.2=.31, so yes that is correct

Step-by-step explanation:

Answer: look at the picture and I can’t solve y for you.

Step-by-step explanation: Hope this help :D

Answer:

51

Step-by-step explanation:

range = highest number - lowest number

54 - 3 = 51

Answer:

Option B is correct.

A mild skew in the stemplot of the raw data is the statement that makes the confidence interval obtained the most invalid.

Step-by-step explanation:

The conditions necessary for the calculated confidence interval to be valid is that the sample to be used must have been obtained using random sampling techniques with each variable independent from one another and it should be obtained from a population distribution that is normal or almost normal.

Examining the statements given to check which one of them makes the confidence interval the most invalid.

a. the presence of a clear outlier in the raw data

Only one outlier in the raw data doesn't mean that the raw data is still not almost normal. The entire distribution can still be normal with the outlier the only exception. So only one clear outlier doesn't do enough to invalidate the confidence interval obtained.

b. mild skew in the stemplot of the raw data

A mild skew in the stemplot of the raw data translates to a distribution that deviates from normality. Although, the fact that the skew in the distribution of raw data was stressed to be 'mild' indicates that the distribution can still be almost normal and still give a confidence interval that works, but of the 3 options provided, this is the one that most invalidates any confidence interval that might be obtained using these given statements.

c. not knowing the population standard deviation.

This is the least severe option, as long as the conditions given above have been satisfied, if the population distribution isn't known, the critical value that is needed to estimate the confidence interval is simply obtained from the t-distribution. The z-distribution is used when the population standard deviation is known or when the population standard deviation is not known, but the sample size is large enough to replicate the population.

So, the t-distribution ensures that we still obtain a valid enough confidence interval.

Hope this Helps!!!

The reason that the point (3, 5) is not a solution to the given inequality is given below.

We are given that;

y > 2x + 1

Now,

The inequality y > 2x + 1 can be graphed by first graphing the boundary line y = 2x + 1. Since the inequality is strict (y >), we draw a dashed line to indicate that points on the line are not solutions to the inequality. Then, we shade the region above the line to indicate all points that satisfy the inequality.

If we have (3,5) as a point, we can see that it lies on the boundary line

y = 2x + 1.

Since the inequality is strict (y >), points on this line are not solutions to the inequality

Therefore, by the inequality the answer will be given above.

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Horizontal changes are often the opposite of what you'd expect to see in the formula.

12:

To shrink/compress horizontally by a factor of 2/3, you need \(g(x) = f(\frac{3}{2}x)\).

Notice we have the reciprocal inside of the function notation.

13:

To translate left 5 units, you have \(g(x) = f( x+5 )\).

Notice we have the opposite sign inside of the function notation.

Answer:

Supplementary angles - d ... 4. The complement of an angle of t° is an angle of_70-7_º mais. 5. If 4 1 and 22 are ... Linear Pair Postulate - If two angles form a linear pair, then they are supplementary. 1. 2 ... LA and Z B are complementary.

Step-by-step explanation:

The value of x is 13, then the measure of angle ∠B will be 121 degrees. Then the correct option is D.

Angle is the space between the line or the surface that meets.  And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.

Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.

The angle ∠A and ∠B form a linear pair.

If ∠A = (6x – 19) and ∠B = (11x – 22).

Then we have

                  ∠A + ∠B = 180°

(6x – 19) + (11x – 22) = 180

                    17x – 41 = 180

                            17x = 221

                               x = 13

The value of x is 13, then the measure of angle ∠B will be

∠B = (11 × 13 – 22)

∠B = 143 – 22

∠B = 121

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Answer:

the answer is 30

Step-by-step explanation:

hope it helps

The solution of the equation 2(x + 1) = 6(x – 1), is the value of x = 2.

To solve an equation means to find what the value of the variable of the equation would be that would make the equation true if the value of the variable is plugged into the equation.

The necessary steps taken to find the value of x in the equation, 2(x + 1) = 6(x – 1) are explained below:

2(x + 1) = 6(x – 1) [given]

Apply the distributive property

2x + 2 = 6x - 6

Combine like terms

2x - 6x = -2 - 6

-4x = -8

Divide both sides by -4

-4x/-4 = -8/-4

x = 2

The value of x is 2. To check the solution, plug in the value of x back into the equation:

2(2 + 1) = 6(2 – 1)

2(3) = 6(1)

6 = 6 [true]

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The total surface area of the doghouse is 1452 ft²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The dog house has many surfaces including the roofs . The total surface area is the sum of all the area of the surfaces.

area of the roof part = 2( 13×11) + 2( 12× 10)×1/2

= 286 + 720

= 1006 ft²

surface area of the building

= 2( lb + lh + bh) -bh

= 2( 10× 11 + 10×8 + 11×8) - 10×11

= 2( 110+80+88)-110

= 2( 278) -110

= 556 -110

= 446ft²

The total surface area = 1006 + 446

= 1452 ft²

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Rounding to the nearest hundredth, the area is approximately 151.976 cm².

The formula for the area of a sector is:

A = (θ/360) x πr²

where θ is the central angle in degrees, r is the radius, and π is pi (3.14).

Plugging in the given values, we get:

A = (144/360) x 3.14 x 11^2

A = 0.4 x 3.14 x 121

A = 151.976

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The length of the diagonal is the square root of 29.

What is the diagonal?

A diagonal is a line segment connecting the opposite vertices (or corners) of a polygon. In other words, a diagonal is a line segment connecting two non-adjacent vertices of a polygon.

The longest diagonal in a box is the diagonal that runs from one corner of the box to the opposite corner, passing through the center of the box.

To find the length of this diagonal, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the diagonal is the hypotenuse of a right triangle whose legs are the three dimensions of the box. So, we have:

diagonal² = length² + width² + height²

Plugging in the given values, we get:

diagonal² = 2² + 3² + 4²

diagonal² = 4 + 9 + 16

diagonal² = 29

Therefore, the length of the diagonal is the square root of 29.

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Answer:

Step-by-step explanation:

Answer:

2462.4 square inches

Step-by-step explanation:

we know the shorted side of the wall is 36 inches so we divide 2.5 to 36 to see how much bigger the actual wall is to the scale

36/2.5= 14.4

The actual wall is 14.4 times bigger than the scale

14.4 x 4.75= 68.4

68.4 x 36= 2462.4 inches

Answer:

The value of x in 15x=3, is 1/5 or 0.2

Answer:

\(\huge \boxed{2}\)

Step-by-step explanation:

\(8^\frac{1}{3}\)

Apply rule : \(a^\frac{1}{3}=\sqrt[3]{a}\)

\(8^\frac{1}{3}=\sqrt[3]{8}\)

8 is a perfect cube. Evaluate the cube root of 8.

\(\sqrt[3]{8}=2\)

Answer:

Radical expression

\( \sqrt[3]{2} \)

Evaluation

\( {8}^{ \frac{1}{3} } = 2\)

Step-by-step explanation:

8^(⅓) = ³√8

=³√(2×2×2)

=³√(2³)

= 2

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Answer:

6

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

9b⁶c⁵

Step 2 Identify

Our largest degree is the variable raised to the highest exponent.

b⁶ > c⁵

Therefore our degree is 6.

Step-by-step explanation:

most likley