If linear correlation between two variable is negative, what can be said about the slope of the regression line

The approximate value of e^-0.01 is 0.99

Given :

we use linear approximation to estimate the given number

[tex]e^{-0.01}[/tex]

For linear approximation we use equation

[tex]L(x)=f(a)+f'(a)(x-a)[/tex]

Lets assume some value for 'a' that is close to -0.01

Lets assume a=0

[tex]f(x)=e^x\\f(0)=e^0\\f'(x)=e^x\\f'(0)=e^0[/tex]

Lets plug in all the values

[tex]L(x)=f(a)+f'(a)(x-a)\\L(x)=e^0+e^0(x-0)\\L(x)=1+1(x-0)\\L(x)=1+1x[/tex]

Now we estimate e^-0.01

the value of x is -0.01

[tex]L(x)=1+x\\L(-0.01)=1-0.01\\L(-0.01)=0.99[/tex]

The approximate value is 0.99

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To estimate the value of e^−0.01 using linear approximation or differentials, we can use the fact that the derivative of e^x is e^x. Specifically, we can linearize the function at a point close to x = -0.01 and use the linear equation to estimate the value of e^−0.01.

To estimate the value of e^−0.01 using linear approximation or differentials, we can use the fact that the derivative of e^x is e^x.

Specifically, we can linearize the function at a point close to x = -0.01 and use the linear equation to estimate the value of e^−0.01.

Let's use the point x = 0 as our approximation point.

The linear equation is given by y = f'(a)(x - a) + f(a), where y represents the value of e^x, f'(a) represents the derivative of e^a at x = a, and f(a) represents the value of e^a at x = a.

Since the derivative of e^x is simply e^x, we have f'(0) = e^0 = 1.

Plugging in the values, we get y = 1(x - 0) + e^0 = x + 1. Therefore, substituting x = -0.01 into the equation, we estimate that e^−0.01 ≈ -0.01 + 1 = 0.99.

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The units listed in order of increasing length are: inch, centimeter, foot, yard, meter, hectometer, kilometer, mile.

To list the given units in order of increasing length, we need to understand both the metric and customary systems of measurement commonly used. The metric system is primarily used in the world and includes units like the meter, centimeter, and kilometer. The U.S. customary units include the inch, foot, yard, and mile. Here's the list from smallest to largest:

Inch (1 inch is approximately 2.54 centimeters)

Centimeter (1 centimeter is 1/100 meter)

Foot (1 foot is 12 inches)

Yard (1 yard is 3 feet)

Meter (1 meter is slightly more than 3 feet; 100 centimeters)

Hectometer (1 hectometer is 100 meters)

Kilometer (1 kilometer is 1000 meters)

Mile (1 mile is 5280 feet or approximately 1.609 kilometers

Since bank charges are deductions from the bank statement balance, the correct answer is:

B. a deduction from the balance per bank statement.

When reconciling a bank statement with the company's books, bank charges are typically deducted from the balance per bank statement.

Let's break down the process:

1. Balance per bank statement: This is the ending balance reported by the bank on the statement.

2. Additions to the bank statement balance: These are items such as deposits in transit (deposits made but not yet recorded by the bank), interest earned, or other credits.

3. Deductions from the bank statement balance: These are items such as outstanding checks (checks issued by the company but not yet cleared by the bank), bank fees or charges, and NSF (non-sufficient funds) fees.

Answer:

The length of the wire in millimeters is 9 × 10² mm.

Step-by-step explanation:

1 meter is equal to 1000 millimeters. This is the ratio that we use to convert a length in meters to one in millimeters. A scientist is working with 0.9 m of gold wire. We will use a conversion fraction to express this number in millimeters.

0.9 m × (1000 mm/ 1 m) = 900 mm = 9 × 10² mm (we round off to 1 significant figure)

The length of the wire in millimeters is 9 × 10² mm.

Answer:

  25

Step-by-step explanation:

0.36 × (a number) = 9

9/0.36 = (a number) = 25 . . . . . divide by the coefficient of the variable

The number is 25.

Answer: 47.5 miles per hour

Step-by-step explanation:

We know that ,

[tex]\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]

Given : The distance to the friend’s house is 276.45 miles. It takes the family 5.82 hours to complete the trip.

i.e. Distance = 276.45 miles

Time = 5.82 hours

Then, the rate(speed) for the family’s trip in miles per hour will be :-

[tex]\text{Speed}=\dfrac{276.45}{5.82}=47.5\text{ miles per hour}[/tex]

Hence, the rate for the family’s trip = 47.5 miles per hour

There are 1,152 different ways that five people can be hired for different positions in the company.

In this question, we need to determine the number of different ways that five people can be hired for different positions in a company.

Given that the first position must be filled by an accounting major, the second position by an economics major, and the third position by a marketing major, we have 4 choices for the first position, 2 choices for the second position, and 3 choices for the third position.

For the last two positions, any major can be hired, so we have 9 choices for the fourth position and 8 choices for the fifth position.

To find the total number of ways, we multiply all the choices together: 4 * 2 * 3 * 9 * 8 = 1,152.

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The number sequence alternates between 1 and multiples of 5. The pattern of the multiples of 5 increases by a factor of 5 each time, next number in the sequence being 500.

The sequence shown is 1, 4, 1, 20, 1, 100, 1.
To find the next number in this sequence, we can observe that the sequence of numbers (not including the 1's) is increasing by a factor of 5 each time =(4, 20, 100, ...).
Since 100 =5*20, to find the next number after the last 1, we need to multiply 100 * 5.

So, the next number after the last 1 would be 100* 5 = 500.

Answer:

Step-by-step explanation:

bs

An equation with zeroes at r1 and r2 factors to (x-r1)(x-r2).

double root at r1 just means (x-r1)^2

We have given that,

enter a quadratic polynomial which has zeros at 11 and 3

A quadratic polynomial is a second-degree polynomial where the value of the highest degree term is equal to 2. The general form of a quadratic equation is given ax^2+bx+C=0

1. f(x)=(x-11)(x-3)

2. f(x)=(x-(-2))(x-6) or f(x)=(x+2)(x-6)

3. f(x)=(x-(-6))^2 or f(x)=(x+6)^2

if you wanted an expanded form

1. f(x)=x²-14x+33

2. f(x)=x²-4x-12

3. f(x)=x²+12x+36

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Dimensions of the room with area of 456 square feet is 19 feet by 24 feet.

To solve for the dimensions of a room where the area is 456 square feet and one dimension is 5 feet more than the other, we can set up the following equations:

Let the width be x feet.

Then the length will be (x + 5) feet.

The area of a rectangle is given by the multiplication of its length and width, so the equation to represent the area is x(x + 5) = 456.

Expanding this, we get x2 + 5x - 456 = 0.

This is a quadratic equation which can be factored or solved using the quadratic formula. Factoring gives us (x - 19)(x + 24) = 0.

Since a room cannot have a negative dimension, we take the positive value of x, which is 19 feet.

Therefore, the width of the room is 19 feet, and the length is 19 + 5 = 24 feet.

To determine the original price of Janelle's sneakers, we calculate the inverse of the 15% discount that left her with a final price of $75.65, revealing the original price to be $89.00.

To find the original price of the sneakers that Janelle bought with a 15% discount, we need to understand that the final price after the discount represents 85% of the original price. This is because a 15% discount reduces the original price by 15%, leaving us with 100% - 15% = 85% of the original price. Janelle's sneakers cost her $75.65 after the discount.

Let's denote the original price by x. Therefore, 85% of x is equal to $75.65. We can set up an equation to represent this relationship:
0.85x = $75.65

To find x, we divide both sides of the equation by 0.85:
X = $75.65 / 0.85
x = $89.00

Thus, the original price of the sneakers was $89.00 before the 15% discount.

To find the x-intercepts of the parabola given its vertex and y-intercept, we can first determine the equation of the parabola. Then, we set y equal to zero and solve for x. In this case, the x-intercepts are 0 and -6.

The x-intercepts of a parabola can be found by setting the y-coordinate to zero and solving for x. The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) is the vertex. In this case, the vertex is (-3, -18), so the equation of the parabola is y = a(x + 3)^2 - 18. Since the y-intercept is at (0, 0), we can substitute these values into the equation to solve for a. Plugging in the values gives: 0 = a(0 + 3)^2 - 18. Solving for a, we get a = 2. Therefore, the equation of the parabola is y = 2(x + 3)^2 - 18. To find the x-intercepts, we set y equal to zero and solve for x: 0 = 2(x + 3)^2 - 18. Simplifying, we have 2(x + 3)^2 = 18. Dividing both sides by 2 gives (x + 3)^2 = 9. Taking the square root of both sides, we get x + 3 = ±3. Solving for x gives the x-intercepts as x = 0 and x = -6.

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