Substitute the values for a, b, and c into b2 – 4ac to determine the discriminant. Which quadratic equations will have two real number solutions? (The related quadratic function will have two x-intercepts.) Check all that apply.

The margin of error at a 99% confidence level is 8.36.

The margin of error at a 99% confidence level based on a larger sample of 275 observations is 4.14.

a. Yes, the condition that X−X− is normally distributed is satisfied for a sample size of 69 by the central limit theorem.

b. The margin of error at a 99% confidence level can be computed using the formula:

Margin of error = z* (sigma / sqrt(n))

where z* is the z-score corresponding to a 99% confidence level, sigma is the known standard deviation, and n is the sample size.

The z-score for a 99% confidence level is 2.576 (from the z table).

Substituting the given values, we get:

Margin of error = 2.576 * (27.5 / sqrt(69)) = 8.36

c. The margin of error at a 99% confidence level based on a larger sample of 275 observations can be computed using the same formula:

Margin of error = z* (sigma / sqrt(n))

where z* is the z-score corresponding to a 99% confidence level, sigma is the known standard deviation, and n is the sample size.

The z-score for a 99% confidence level is still 2.576 (from the z table).

Substituting the given values, we get:

Margin of error = 2.576 * (27.5 / sqrt(275)) = 4.14

d. The margin of error is inversely proportional to the square root of the sample size. As the sample size increases, the margin of error decreases. Therefore, the margin of error with n = 275 will be smaller than the margin of error with n = 69, leading to a narrower confidence interval.

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Answer:

Answer C, Arthur will pay about $918 less in interest if he chooses the 3-year loan.

Step-by-step explanation:

(370.53 x 12) x 3 = 13,339.08

(237.61 x 12) x 5 = 14,256.60

14,256.60 - 13,339.08 = 917.58 (then round up)

6) m<ABC = m<ABK + m<CBK

157° = (4x + 10) + (14x +3)

157° = 18x + 13

x = 8°

m<CBK = 14(8°) + 3

m<CBK = 115°

7) am not sure, i think b

Mr. Wilson's order of 12 bars of Minty Morning soap will weigh 1.44 kilograms.

To find out how many kilograms Mr. Wilson's order will weigh, we need to convert the weight of the soap bars from grams to kilograms.

First, we need to determine the total weight of the 12 bars of soap by multiplying the weight of each bar (120 grams) by the number of bars ordered (12):

12 x 120 grams = 1,440 grams

Next, we need to convert the weight from grams to kilograms by dividing by 1,000 (since there are 1,000 grams in a kilogram):

1,440 grams ÷ 1,000 = 1.44 kilograms

Therefore, Mr. Wilson's order of 12 bars of Minty Morning soap will weigh 1.44 kilograms.

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Me das mas información porfavor?

Answer:

\(\bold{\dfrac{6}{7}}\)

Step-by-step explanation:

Given ratio is:

8 gal to \(9\frac{1}3\) gal

To find:

Ratio in Lowest form with whole numbers in numerator and denominator.

Solution:

First of all, let us convert \(9\frac{1}3\) to simple \(\frac{p}{q}\) form:

Formula:

\(a\dfrac{b}{c} = \dfrac{a\times c+b}c\)

Using the formula, we get:

\(9\dfrac{1}{3} = \dfrac{9\times 3+1}{3} = \dfrac{28}{3}\)

Now, let us have a look at the ratio:

\(8 : \dfrac{28}{3}\)

Any ratio, \(p:q\) can be written as \(\frac{p}{q}\).

Writing given ratio as per above:

\(\dfrac{8}{\dfrac{28}{3}}\\\Rightarrow \dfrac{8 \times 3}{28}\\\Rightarrow \dfrac{2\times 3}{7}\\\Rightarrow \bold{\dfrac{6}{7}}\)

Therefore, the answer is

\(\bold{\dfrac{6}{7}}\)

The correct statement is option (B) the market for paper is growing faster than the market for all other

The given statement is

Paper production accounts for approximately 40 percent of the world's industrial use of wood, and the market for paper is growing faster than it is for all major wood products.

The first option is a sentence that in the question but its not conveying the proper meaning of the given statement. Option C, D and E is not saying about the paper market, therefore it is not conveying the correct meaning of the statement

Hence, the correct statement is option (B) the market for paper is growing faster than the market for all other

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Based on the above, the capacity of a 5-liter tin is about  500 cm³.

To be able to convert the capacity of a 5-liter tin to its volume in cm³, One need to use the conversion factor that is, 1 liter is equivalent to 100 cm³.

So, to be able to calculate the volume of a 5-liter tin in cm³, one have to multiply the capacity (5 liters) by the conversion factor (100 cm³/liter):

Volume in cm³ = 5 liters x 1000 cm³/liter

                           = 500 cm³

Therefore, the capacity of a 5-liter tin is about  500 cm³.

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See full text below

Convert the capacity of a 5 litre tin to its volume in cm³.1litre is equivalent to 100cm³

The monthly payment for the 20-year mortgage on the farming operation is approximately $5,118.42. and The new monthly payment would be approximately $5,901.25, but refinancing would result in higher costs overall

To calculate the monthly payment for a 20-year mortgage on a farming operation in Gates County, NC, we can use the formula for calculating the monthly mortgage payment:

\(M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)\)

Where:

M is the monthly payment

P is the principal amount (loan amount)

r is the monthly interest rate

n is the total number of monthly payments

Given:

Loan amount (P) = $900,000 - 10% down payment = $810,000

Interest rate (r) = 5% per annum = 5% / 12 months = 0.4167% per month

Total number of monthly payments (n) = 20 years * 12 months = 240 months

Substituting these values into the formula:

\(M = $810,000 * (0.004167 * (1 + 0.004167)^240) / ((1 + 0.004167)^240 - 1)\)

Calculating the monthly payment:

M ≈ $5,118.42

Therefore, the monthly payment for the 20-year mortgage on the farming operation is approximately $5,118.42.

Now, let's consider the situation where the interest rates drop to 4% after five years. We need to calculate the new monthly payment for the 15-year mortgage.

Loan amount (P) for the new mortgage = $810,000 remaining balance after five years

Interest rate (r) = 4% per annum = 4% / 12 months = 0.3333% per month

Total number of monthly payments (n) = 15 years * 12 months = 180 months

To determine if refinancing is beneficial, we need to compare the savings in monthly payments with the cost of refinancing.

To calculate the new payment, we use the same formula:

\(M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)\)

\(M = $810,000 * (0.003333 * (1 + 0.003333)^180) / ((1 + 0.003333)^180 - 1)\)

Calculating the new monthly payment:

M ≈ $5,901.25

To determine if refinancing is beneficial, we compare the savings in monthly payments:

Monthly savings = $5,118.42 - $5,901.25 ≈ -$782.83

However, there is also a cost associated with refinancing, which is a $2,000 fee plus 1 point ($810,000 * 1% = $8,100) financed by the bank.

Total refinancing cost = $2,000 + $8,100 = $10,100

Considering the negative monthly savings and the cost of refinancing, it is not advisable to refinance in this scenario.

The new monthly payment would be approximately $5,901.25, but refinancing would result in higher costs overall. Therefore, it is not recommended to refinance in this case.

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Answer:

n = -7

Step-by-step explanation:

to solve for a variable (in this case it's n) we have to isolate it. we do this by moving like terms on one side of the equation.

-53 = 3 + 8n

- 3    -3

since we are subtracting 3 on the right side, we also have to subtract it on the left side.

-56 = 8n

we divide both sides by 8

n = -7

Answer:

a = r + d - c

Step-by-step explanation:

a + c = r + d

You want a alone on the left side. c is being added to a.

To get rid of the c, you must subtract c from the left side, but the rule of equations is that you must do the same operation to both sides of the equation. We subtract c from both sides of the equation.

a + c - c = r + d - c

c - c = 0, so the c is eliminated from the left side.

We now have

a + 0 = r + d - c

a = r + d - c

Answer:

a = r + d - c

Step-by-step explanation:

All we do is transpose c to the other side to isolate a.

Match each quotient of the complex numbers accordingly as shown below.

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1. The real part of a complex number is represented by a, while the imaginary part is represented by bi.

No. 1

Multiply the numerator and denominator by 3-4i:

1/(3 + 4i) = 1/(3 + 4i)  * (3 - 4i)/(3 - 4i)  

             =  (3 - 4i)/(9 + 16)

             =  (3 - 4i)/25

             =  3/25 - 4/25 i

No. 2

Multiply the numerator and denominator by 3+4i:

1/(3 - 4i) = 1/(3 - 4i)  * (3 + 4i)/(3 + 4i)  

             =  (3 + 4i)/(9 + 16)

             =  (3 + 4i)/25

             =  3/25 + 4/25 i

No. 3

i/i = 1

   = 1 + 0i

No. 4

Multiply the numerator and denominator by 3-4i:

(3 - 4i)/(3 + 4i) = (3 - 4i)/(3 + 4i) * (3 - 4i)/(3 - 4i)

                       = (9 - 24i -16) / (9 + 16)

                       = (-7 - 24i) / 25

                       = -7/25 - 24i/25

No. 5

(3 - 4i)/ 1 = 3 - 4i

No. 6

Multiply the numerator and denominator by 3+4i:

(3 + 4i)/(3 - 4i) = (3 + 4i)/(3 - 4i) * (3 + 4i)/(3 + 4i)

                       = (9 + 24i -16) / (9 + 16)

                       = (-7 + 24i) / 25

                       = -7/25 + 24i/25

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18 lines of symmetry the dome have, after excluding the spire of the dome.

36 ÷ 2 = 18

3 row × 36 windows per row, total windows = 108. 36 of them connects a window with the window across to form 1 line of symmetry.

If two additional identical parts that are arranged in an orderly fashion can be divided from a shape, it is said to be symmetrical. As an illustration, if you are instructed to cut out a "heart" from a piece of paper, you need just fold the paper, draw one-half of the heart at the fold, and then cut it out to discover that the second half exactly matches the first half.

Asymmetrical and symmetrical balances are the two types of balance. The two parts of the thing are precisely identical and balanced in symmetrical balance. The two parts of an asymmetrical balance are not similar; rather, separate things are arranged such that they appear to be balanced.

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An equation that matches the table include the following: y = x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 5)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1.

At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 1(x - 0)

y - 5 = x

y = x + 5

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Answer:

Step-by-step explanation:

Answer:

your answer is A, C, B

Step-by-step explanation:

I did the assignment.

Answer:

the answer is:

Step-by-step explanation:

1. A

2. C

3. B

Answer:

I mean, I think it varies by house and by location but a general range would be:

Min: 64 *F

Max: 74 *F

Answer:

Step-by-step explanation:

Ok since they haven't specifically told use what the four consecutive numbers is we gotta use

X, x+1, x+2, x+3

Then you collect the like terms and sum them up

x+x+x+x+ 1 + 2 + 3 =278

4x+6=278

4x=272

Then you simplify

4x/4= 272/4

x=68

Now that you know what x is then the four consecutive numbers are 68, 69, 70, 71.

Adiosss

But the way I think I know do you have exams tomorrow??

let me know if this is wrong

He had saved 127 pictures originally

Parameters:

Pictures saved = 13

Pictures deleted = 32

New total number of pictures = 108

Let old total number of pictures = x

Then

x + 13 - 32 = 108

x - 19 = 108

x = 108 + 19

= 127

He had saved 127 pictures originally

Answer:

£780

Step-by-step explanation:

as its a decrease

we subtract 35 from 100 to get 65

we then divide 65 by 100

to get 0.65

then we do 0.65*1200

to get the answer of $780

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%. The sale price of the bed is $780.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that the normal price of a bed is $1200. Therefore, the sale price of the bed is,

Sale Price = $1200 × (100% - 35%)

                 = $1200 × 65%

                 = $780

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a) the electric oven takes longer to cook the meat than the microwave oven, and that the difference in cooking times will increase with larger weights.

b)a joint of meat that takes about 2 hours to cook in an electric oven weighs approximately 1.29 kg.

c) The answer to part a seems sensible, as the formula for the electric oven predicts longer cooking times than the formula for the microwave oven.

The definition of an equation is the claim that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can contain variables, constants, operations, and functions.

a) The two formulae for cooking times are:

(66 x weight in kg) + (35 x time in an electric oven

Microwave oven time = (26 x weight in kg) + 15

We can compare the two formulae by looking at their coefficients and constants.  This suggests that the electric oven takes longer to cook the meat than the microwave oven, and that the difference in cooking times will increase with larger weights.

b) (66 x weight in kg) + (35 x time in an electric oven

2 x 60 = (66 x weight in kg) + 35

120 - 35 = 66 x weight in kg

85 = 66 x weight in kg

weight in kg = 85 / 66

weight in kg ≈ 1.29

So, a joint of meat that takes about 2 hours to cook in an electric oven weighs approximately 1.29 kg.

Microwave oven time = (26 x weight in kg) + 15

Microwave oven time = (26 x 1.29) + 15

Microwave oven time ≈ 48.34 minutes

Therefore, a 1.29 kg joint of meat would take about 48 minutes to cook in a microwave oven.

c) The answer to part a seems sensible, as the formula for the electric oven predicts longer cooking times than the formula for the microwave oven.

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The specific average rate of change, you need the temperature values and the corresponding time intervals during which the temperature is decreasing or increasing.

Average rate of change during a decreasing interval:

If the temperature is decreasing over an interval, you need two temperature values: the temperature at the beginning of the interval (T1) and the temperature at the end of the interval (T2). The average rate of change can be calculated using the formula:

Average rate of change = (T2 - T1) / (time interval)

Here, "time interval" represents the duration of the interval during which the temperature is decreasing. The result will be a negative value since the temperature is decreasing.

Average rate of change during an increasing interval:

If the temperature is increasing over an interval, you again need two temperature values: the temperature at the beginning of the interval (T1) and the temperature at the end of the interval (T2). The average rate of change can be calculated using the same formula:

Average rate of change = (T2 - T1) / (time interval)

In this case, the result will be a positive value since the temperature is increasing.

To calculate the specific average rate of change, you need the temperature values and the corresponding time intervals during which the temperature is decreasing or increasing.

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According to the 90° clockwise rotation, the new coordinate of the quadrilateral D' is (3, -2)

Quadrilateral

Quadrilateral refers a closed shape and a type of polygon that has four sides, four vertices and four angles.

If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’.

Here we need to find the coordinate of D'.

In order to find the new coordinates, first we have to identify the current coordinates of the quadrilateral.

While we looking into the graph, we have identify the point of

A (0,0), B(-4, 3), C(1,5) and D(2,3)

Now, we have to use the rule of clockwise 90° rotation, states that to rotate the figure 90 degrees clockwise about a point, every point(x , y) will rotate to (y, -x).

According to this rule, the new coordinates are written as,

A(0,0) = A'(0,0)

B'(-4,3) = B'(-3,-4)

C(1,5) = C'(5, -1)

D(2,3) = D' (3, -2)

Therefore, the new coordinate of D' is (3, -2).

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Answer:

b * 2 < 300

Step-by-step explanation:

The mathematical sentence that expresses the information is 2b>300.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We have,

Emily have 300 books.

If Frank were to double the number of books then he have

= 2b books

So, the number of Frank have after doubling have greater books than Emily .

Then, the inequality can be framed as

2b > 300

b>150.

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Given the trigonometry equation expressed as;

We are to simplify for the value(s) of 'x"

Recall from trigonometry identity that:

Substitute the result into the original equation to have:

Solve for the value of "x"

The general solution to the given trigonometry function is:

If a: b = 1: 3 and b: c= 6: 5, then a: b: c = 2: 6: 5

It is given that a:b = 1:3, so let

a = x .....(i)

b = 3x .....(ii)

where x => some number

Also, it is given that b:c= 6:5, so let

b = 6y .....(iii)

c = 5y .....(iv)

where y => some number

Now, from equations (ii) and (iii),

b = 3x

b = 6y

This implies that

3x = 6y

=> x = 2y .....(v)

Using equation (v) in equation (i), we get

a = x

=> a = 2y .....(vi)

Using equations (vi), (iii) and (vi), we can say

a = 2y

b = 6y

c = 5y

a : b : c

=> (2y) : (6y) : (5y)

=> 2 : 6 : 5

Therefore, a: b: c = 2 : 6 : 5

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If one angle in an isosceles triangle is 90 degrees then the measure of each angle of an isosceles triangle will be 45 degrees

What is an isosceles triangle ?

A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that have the same length.

If the sides AB and AC of a triangle ABC are equal, then the triangle ABC is an isosceles triangle with B = C. "If the two sides of a triangle are congruent, then the angle opposite to them is likewise congruent," states the theorem that characterizes the isosceles triangle.

Since this triangle's two sides are equal, the base of the triangle is the side that is not equal.

As we know that in an isosceles triangle set of two angles are equal

And

we also know that sum of all the angles of a triangle is 180 degrees

So, According to the question

90 degrees + other angles =180 degrees

other angles = 90 degrees

one angle = 90/2

one angle = 45 degree  

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Answer:

1880

Step-by-step explanation:

Answer:

cylinder to cone = 3:1

sphere to cylinder = 4r:3h

cone to sphere = h:4r

hemisphere to cylinder = 2r:3h

Step-by-step explanation: