For the quadratic equation 2x² - 6x + 7 = 0, enter the correct values of a, b, and c.
X =
-b ± √√b² - 4ac
2a

The variance and standard deviation of the frequency distribution data are;

The variance, s² = 14

The standard deviation, s ≈ 3.742

A frequency distribution displays the number of data within a specified interval.

The steps to find the variance and the standard deviation of the grouped data are as follows;

The midpoints of the class intervals are found as follows;

Class interval [tex]{}[/tex]       Midpoint

1 - 3                  [tex]{}[/tex]        2

4 - 6                  [tex]{}[/tex]       5

7 - 9                  [tex]{}[/tex]       8

10 - 12                      11

13 - 15                  [tex]{}[/tex]    14

19 - 21                  [tex]{}[/tex]    20

The mean is then found as follows;

(2×1 + 5×9 + 8×25 + 11×35 + 14×17 + 17×10 + 20×3)/(1+9+25+35+17+10+3)

The variance can then be found as follows;

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Answer:

6.6 x 10^6

Step-by-step explanation:

The equivalent fractions of 7/11 are 14/22, 21/33, 28/44 and 35/55

There are infinitely many numbers equivalent to 7/11

since 7/11 is a fraction that can be simplified in different ways.

We can multiply the numerator and denominator with the same number to get the equivalent fractions

7/11×2/2 = 14/22

7/11×3/3= 21/33

7/11×4/4 =28/44

7/11×5/5 =35/55

Hence, the equivalent fractions of 7/11 are 14/22, 21/33, 28/44 and 35/55

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The equivalent value of the expression is A = four thousand two hundred and A = 4,200

Given data ,

Let the expression be represented as A

Now , the value of A is

A = four thousand two hundred

On simplifying the equation , we get

A = 4,200

And , when we write "four thousand two hundred," it is written in word form

Hence , the equation is A = 4,200

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Answer:

Step-by-step explanation:

its 123 jd

Step-by-step explanation:

Answer and Explanation:

The set contains 13 elements here, so the total number of subsets can be calculated as 213=8192 2 13 = 8192 .

Answer:

588π

Step-by-step explanation:

Volume of cylinder = π r ² h

=  π (7)² (12)

= 588π

Explanation, step-by-step

You would need two angles to know the lines are parallel

Answer:

The length of the belt needed to go around the drive wheel and the vat is approximately 79.6 feet. This is calculated by using the circumference formula C = 2πr where r is the radius of the wheel (5 feet) and the radius of the vat (9 feet). The total circumference is then 2 x 3.14 x (5 + 9) = 79.6 feet.

Answer:

79.6 feet.

Step-by-step exp

2 x 3.14 x (5 + 9) = 79.6 feet.

The required scale factor for the dilation of segment AB to create segment A'B' is 2.

If the length of the original segment AB is 5 units and the length of the dilated segment A'B' is 10 units, the scale factor can be calculated as follows:

Scale factor = Length of A'B' / Length of AB

Scale factor = 10 / 5

Scale factor = 2

Therefore, the correct scale factor for the dilation of segment AB to create segment A'B' is 2.

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The actual width of the soccer field is 60 yards.

Given, the scale of the drawing is 1 inch : 5 yards.

The width of the soccer field in the drawing is 12 inches.

So, the actual width of the soccer field can be found by multiplying the width in the drawing by the scale factor:

Actual width = Width in drawing x Scale factor

The scale factor is 5 yards per inch, so we can write:

Actual width = 12 inches x 5 yards per inch

Actual width = 60 yards

Therefore, the actual width of the soccer field is 60 yards.

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The amount of money Gillians owes for student loans is $12,250

How to determine this

When Gillians net worth = $90,500

House(Current value) = $87,900

Checking account = $950

Credit- card = -$2,650

Automobile(current value) = $10,300

Student loans = ?

Investment = $5,000

Personal loans = 1,200

Savings account = $2,450

To calculate the money Gillians Owen owes student loans

Let x represent the student loans

$90,500 = $87,900 + $950 - $2,650 + $10,300 + x + $5,000 - $1,200 + $2,450

$90,500 = $102,750 + x

Collect like terms

x = $90,500 - $102,750

x = 12,250

Therefore, the money Gillians owes student loans is $12,250

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Answer: The last one is the right one

Step-by-step explanation:

So first solve for n

1/2n+3<5

1/2n<2, multiple by 2 on both sides to remove fraction

n<4

the circle will be at 4, and since n<4, n is less than 4, so your line must also be less that 4.

The line of the best fit that models the data is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The graph

To draw a line to model the data is to draw the line of best fit

A good line of best fit would have equal number of points on either sides

To plot the graph, we draw a line that divides the points on the graph evenly

This line when drawn on the scattered points divided the points approximately evenly

Hence, the line of the model is attached

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The solution for w is given by the natural logarithm of 88 divided by 3x, all raised to the power of 1/5.

Exponential functions are always increasing or decreasing, depending on the sign of the base "a".

The graph of an exponential function has a characteristic shape that depends on the base "a". When "a" is greater than 1, the graph is an increasing curve that becomes steeper as x increases; when "a" is between 0 and 1, the graph is a decreasing curve that approaches the x-axis as x increases.

Starting with the equation:

[tex]-3xe^{(5w)} = -88[/tex]

We can first isolate the exponential term by dividing both sides by -3x:

[tex]e^{(5w)} = \dfrac{88 }{ (3x)}[/tex]

Then, taking the natural logarithm of both sides, we get:

[tex]5w = ln(\dfrac{88} { 3x})[/tex]

Finally, dividing both sides by 5, we obtain the solution for w:

[tex]w = (\dfrac{1}{5}) ln(\dfrac{88} { 3x})[/tex]

Therefore, the solution for w is given by the natural logarithm of 88 divided by 3x, all raised to the power of 1/5.

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The surface area of a three dimensional shape is the total area of all of the faces. To find the surface area of a shape, we find the area of each face and add them together. E.g. The measurements here are in centimetres so the surface area is measured in square centimetres ( c m 2 ) (cm^2) (cm2).

The function pairs that are inverses are:

C) f(x) = 5x - 3 and g(x) = (x + 3)/5

To determine if two functions are inverses, we need to check if applying one function and then the other function will return the original input.

Let's go through each option:

A) f(x) = -2x and g(x) = (1/2)x

To check if they are inverses, we can apply function f(g(x)) and see if it returns x:

f(g(x)) = f((1/2)x) = -2(1/2)x = -x

Since f(g(x)) = -x ≠ x, these functions are not inverses.

B) f(x) = 4x² and g(x) = √x

To check if they are inverses, we can apply function f(g(x)) and see if it returns x:

f(g(x)) = f(√x) = 4(√x)² = 4x

Since f(g(x)) = 4x = x, these functions are not inverses.

C) f(x) = 5x - 3 and g(x) = (x + 3)/5

To check if they are inverses, we can apply function f(g(x)) and see if it returns x:

f(g(x)) = f((x + 3)/5) = 5((x + 3)/5) - 3 = x + 3 - 3 = x

Since f(g(x)) = x, these functions are inverses.

D) f(x) = x² - 16 and g(x) = x - 4

To check if they are inverses, we can apply function f(g(x)) and see if it returns x:

f(g(x)) = f(x - 4) = (x - 4)² - 16 = x² - 8x + 16 - 16 = x² - 8x

Since f(g(x)) = x² - 8x ≠ x, these functions are not inverses.

Based on the analysis above, the function pairs that are inverses are:

C) f(x) = 5x - 3 and g(x) = (x + 3)/5

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The complete question:

Which of the following function pairs are inverses?

A) f(r) = -2x and g(x) = (1/2)x

B) f() = 4x² and g(x) = √x.

C) f(x) = 5x - 3 and g(x) = (x + 3)/5

D) f(x) =x² - 16 and g(x) = x - 4

There are three dots in the greatest height recorded.

We have,

From the table,

We see that,

The greatest height is 75 inches.

The lowest height is 62 inches.

Now,

If we make a line plot with dots above the height as:

*                                      *

*          *        *        *        *

*          *        *        *        *

62     66     68     72     75

Thus,

There are three dots in the greatest height recorded.

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Answer:

--------------------

The function y = x² - 5 is the translation of the parent function y = x² down by 5 units.

Since the parent function is y = x², it is a parabola that has its vertex at the origin and opens up as its coefficient is positive.

Looking at the answer choices, we see option A is the correct one.

Other options are incorrect:

Answer:

To have a D/E ratio of 1.6, Oceanic Luxury Vessels, Inc. would need to sell debt securities.

First, we need to calculate the market value of the company's equity.

Market value of equity = Number of shares outstanding × Market price per share

Market value of equity = 5,000,000 × $38

Market value of equity = $190,000,000

Next, we can calculate the current debt-to-equity (D/E) ratio of the company:

Current D/E ratio = Total debt / Total equity

Total debt = Number of bonds outstanding × Bond price per bond × Par value

Total debt = 75,000 × 1.02 × $1,000

Total debt = $76,500,000

Current D/E ratio = $76,500,000 / $190,000,000

Current D/E ratio = 0.403

To achieve a D/E ratio of 1.6, the company would need to increase its total debt by a factor of 1.6/0.403 = 3.97.

New total debt = 3.97 × $76,500,000

New total debt = $304,305,000

To calculate the amount of debt securities the company would need to sell, we can subtract the current total debt from the new total debt:

Amount of debt to be sold = $304,305,000 - $76,500,000

Amount of debt to be sold = $227,805,000

Therefore, the company would need to sell debt securities worth $227.8 million to achieve a D/E ratio of 1.6.

The correct answer is C. Debt; $248.5 million.

Answer: Infinity

Step-by-step explanation: Since 0 doesn't have a measurable amount of times it can go into 28 the answer is infinity.

Answer:

{0,2,3,4,8}

Step-by-step explanation:

The probability that the first person will be seated at a plastic table is 0.8

From the question, we have the following parameters that can be used in our computation:

Plastic tables = 12

Composite tables = 3

Using the above as a guide, we have the following:

Total tables = 12 + 3

Evaluate the sum

Total tables = 15

So, we have the probability to be

P = Plastic tables/Total tables

Substitute the known values in the above equation, so, we have the following representation

P = 12/15

Evaluate

P = 0.8

Hence, the probability that the first person will be seated at a plastic table is 0.8

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Answer:

1761 ft²

Step-by-step explanation:

The shape of the attic is a triangular prism.

It has 5 faces: The bases are 2 faces that are congruent triangles. The other 3 faces are rectangles, 2 of which are congruent.

surface area = area of the bases + area of 3 rectangles

surface area = 2 × area of triangle + 2 × area of rectangle + area of other rectangle

surface area = 2 × (1/2)bh + 2 × length × width + LENGTH × WIDTH

surface area = 2 × (1/2)(15 ft)(15 ft) + 2(15 ft)(30 ft) + (21.2 ft)(30 ft)

surface area = 225 ft² + 900 ft² + 636 ft²

surface area = 1761 ft²