Take 4x + 2 from 8x + 5.

4x + 3
4x - 3
-4x - 3

The amount of money which you must invest today is equal to $68,517.85.

Mathematically, the present value of an investment can be calculated by using this formula:

Present Value, PV = FV/(1 + r)^t

Given the following data:

Time, t = 9 years.

Future value, FA = $190,000.

Interest rate, r = 12% = 0.12.

Substituting the given parameters into the formula, we have;

PV = 190,000/(1 + 0.12)^9

PV = 190,000/(1.12)^9

PV = 190,000/2.7730

PV = $68,517.85.

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Answer:

385

Step-by-step explanation:

Mean = 402.5.

Variance = 77,556.3

Standard deviation = 278.5

See attachment for the complete table.

The mean of a data is the sum of all data values divided by the number of data values we have in the data set.

Variance is calculated by finding the sum of the squares of the deviations from the mean, find the average, then find the average.

The standard deviation = the square root of variance.

The mean of the data given would be: 402.5.

402.5 is subtracted from each of the data points to get the deviations which are squared.

It is the sum of the deviations that gives us 310,225.2.

To find the variance, divide 310,225.2 by the number of data values which is 4.

Variance = 310,225.2/4

Variance = 77,556.3

Standard deviation = √77,556.3

Standard deviation = 278.5

The complete table containing the missing values is given in the image attached below.

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Answer: 13

Step-by-step explanation:

4x+3y=-5 solve x :    

4x = -3y + -5           | -3y

1x = -0.75y + -1.25  | : 4

-3x + 7y = 13 solve x :

-3x + 7y = 13              | -7y

-3x = -7y = 13             | : (-3)

Equalization Method Solution: -0.75y+-1.25=2.333y+-4.333

-0, 75y - 1,25 = 2,333y - 4, 333 solve y:

-0, 75y - 1,25 = 2,333y -4, 333    | -2,333y

-3, 083y - 1,25 = -4,333               | + 1, 25

-3. 083y = -3,088                         | : (-3, 083)

y = 1

Plug y = 1 into the equation 4x + 3y = -5 :

4x + 3 · 1           | Multiply 3 with 1

4x + 3 = -5        | -3

4x = -8              | : 4

x = -2

So the solution is:

y = 1, x = -2

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The number of students who applied at most two universities is 26 students.

The population of students in a class = 60 students

Number of students who applied for Addis Ababa University = 30 students

Number of students who applied for Bahir Dar University = 25 students

Number of students who applied for Wachemo University = 24 students

Number of students who applied for Addis and Bahir = 11 students

Number of students who applied for Addis and Wachemo = 6 students

Number of students who applied for Wachemo and Bahir = 9 students

The number of students who applied at most two universities is 26 (11+ 6 + 9).

Thus, the number of students who applied at most two universities is 26.

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5√2 · 9√6

Simplify.

5 × 9 √ 2 x 6 ⇒ Multiply 2 × 6.

5 × 9 √12

Simplify √12 to 2√3.

5 × 9 × 2√3 ⇔ Multiply

90√3

Therefore, the correct alternative is option "B".

The simplified form of the given expression is 90√3. Therefore, the correct answer is option B.

The given expression is 5√2·9√6.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Here, 5×9×√2×√6

= 45√12

= 45√4×3

= 90√3

Therefore, the correct answer is option B.

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The length of the semi-major axis of the ellipse is 7.

What is the semi-major axis of an ellipse?

The semi-major axis of an ellipse is the half of the longest diameter passing through its vertex and focus.

The general equation of an ellipse is :

⇒ x²/a²+y²/b²=1, where a is the semi-major axis and b, is the semi-minor axis

x²/49+y²/36=1

x²/(7²)+y²/(6²)=1

x²/a²+y²/b²=1

a=7

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The cost of hiring a car for 2 days in 2013 is Rs. 316.8

The cost for hiring a car for 2 days in 2018 was Rs. 264 which was 20% more than in 2013.

Therefore,

cost of hiring for 2018 = Rs. 264

Therefore,

let

cost of hiring in 2013 = 20%(264) + 264

cost of hiring in 2013 = 20 / 100 × 264 + 264

cost of hiring in 2013 = 1 / 5 × 264 + 264

cost of hiring in 2013 = 264 / 5 + 264

cost of hiring in 2013 = 52.8 + 264

cost of hiring in 2013 = 316.8

Therefore, the cost of hiring a car for 2 days in 2013 is Rs. 316.8.

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In the case above, the value of the overhead rate for the second quarter is $17,640.

Note that:

In the case above, for one to be able to calculate the predetermined overhead rate, a person need to divide the value of the  estimated overhead costs which is $52,500 by that of the estimated direct labor hours .

Predetermined overhead rate=Estimated overhead costs/ estimated direct labor hours

Predetermined overhead rate=$52,500/  12,500

Predetermined overhead rate=$4.20/DLH overhead rate

Hence:  $52,500/ 12,500 =   $4.20/DLH overhead rate.

Since the Overhead that was applied at standard hours was said to be allowed, then:

= $4.2 x 2,400 x 1.75

= $17,640.

Therefore, In the case above, the value of the overhead rate for the second quarter is $17,640.

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Answer:

the answer is 100,008.

Step-by-step explanation:

To convert temperatures in degrees Fahrenheit to Celsius, subtract 32 and multiply by 5556

Answer: 50° F = 10° C

Step-by-step explanation:

Given information

Convert 50° Fahrenheit to Celcius

Given formula

[tex]C~=~\frac{5}{9}~ (F-32)[/tex]

Substitute values into the formula

[tex]C~=~\frac{5}{9}~ (F-32)[/tex]

[tex]C~=~\frac{5}{9}~ ((50)-32)[/tex]

Simplify values in the parenthesis

[tex]C~=~\frac{5}{9}~ (18)[/tex]

Simplify the multiplication

[tex]\Large\boxed{C=10^\circ C}[/tex]

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Answer:

The function h(x) is decreasing on the interval (3, ∞).

Step-by-step explanation:

Please take a look at the attached image.

You will see a graph of the given function h(x) = -2[tex]\sqrt{x-3}[/tex]. The function is decreasing.

The function starts at 3 and starts to go towards negative infinity on the x-axis. Therefore the function is decreasing on the interval (3, ∞).

If ABC and DEF are complementary, then the value of x will be,

90 - ABC = x

90 - 53 = x

x = 37°

Answer:

x=37

Step-by-step explanation:

complementary means when added up they bring 90
so, 53+x=90

x=90-53

x=37

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Answer:

Step-by-step explanation:

C = 2 π r

A = π r²

~~~~~~~~~~~

(1). C = 8 π

Let the length of the arc ADB is "x"

x = ( 8π ÷ 360° ) × 340°

x = [tex]\frac{68}{9} \pi[/tex]

(2). A = 16 π

The area of shaded region is

( 16 π ÷ 360° ) × 340° = [tex]\frac{136}{9} \pi[/tex]

[tex]\bold{Answer} \downarrow[/tex]

[tex]Length\ of\ Arc\ ADB = \large\boxed{\frac{68\pi}{9} }[/tex]

[tex]Area\ of\ shaded\ region= \large\boxed{\frac{136\pi}{9} }[/tex]

Formulas needed:

[tex]Arc\ length=\boxed{2\pi r(\frac{\theta}{360} )}[/tex]

[tex]Area \ of\ a\ sector=\boxed{(\frac{n}{360})\times\pi \times r^2}[/tex]

[tex]Area\ of\ Circle=\boxed {\pi\times r^2}[/tex]

Step-by-step explanation:

First, let's find the arc length:

[tex]Arc\ length=2\pi r(\frac{\theta}{360})[/tex]

[tex]=2\pi (4)(\frac{340}{360})[/tex]

[tex]=2\pi (4)(\frac{17}{18})[/tex]

[tex]=2\pi(\frac{68}{18})[/tex]

[tex]=\frac{136\pi }{18}[/tex]

[tex]\longrightarrow \large\boxed{\frac{68\pi}{9} }[/tex]

Next, let's find the area of the sliver of the circle we just found the arc length of.

[tex]Area \ of\ a\ sector=(\frac{n}{360})\times\pi \times r^2[/tex]

[tex]=(\frac{20}{360} )\times \pi \times 4^2[/tex]

[tex]=(\frac{1}{18})\times \pi \times 16[/tex]

[tex]=\frac{16\pi}{18}[/tex]

[tex]\longrightarrow \frac{8 \pi}{9}[/tex]

Finally, find the area of the entire circle and subtract the sliver area by that.

[tex]Area\ of\ Circle= {\pi\times r^2[/tex]

[tex]=\pi \times 4^2[/tex]

[tex]\longrightarrow16\pi[/tex]

Subtracting the area by the sliver.

[tex]Area\ of\ entire\ circle \ -\ Area\ of\ sliver\ of\ circle[/tex]

[tex]=16\pi -\frac{8\pi}{9}[/tex]

[tex]=\frac{144\pi}{9} -\frac{8\pi }{9}[/tex]

[tex]\longrightarrow \large\boxed{\frac{136\pi}{9} }[/tex]

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

Let's consider the information given:

Let's setup an equation for the cost

             [tex]\hookrightarrow Cost = 30 + 0.3x[/tex]

             [tex]30 + 0.3x = 55.2\\0.3x = 25.2\\x=84[/tex]

Ken must have traveled 84 miles

Answer: 84 miles

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The value of X - Y such that the eight-digit number 7448X24Y is divisible by both 8 and 9 is 7

The eight-digit number is given as:

7448X24Y

Also, from the question

The number is divisible by 8 and 9

When a number is divisible by 8, then the last three digits of that number would be divisible by 8.

When a number is divisible by 9, the sum of the digits of the number would be divisible by 9.

So, we have:

24Y is divisible by 8

The possible value of Y from the above statement is 0

This is so because 240 is divisible by 8

The sum of the digits of the number would be divisible by 9.

This means that:

7 + 4 + 4 + 8 + X + 2 + 4 + Y = 29 + X + Y

Substitute 0 for Y

29 + X + Y = 29 + X + 0

Evaluate the sum

29 + X + Y = 29 + X

36 is divided by 9

So, we have

29 + X = 36

Subtract 29 from both sides of the equation

X = 7

So, we have

X = 7 and Y = 0

X - Y is calculated as:

X - Y = 7 - 0

Evaluate the difference in the above equation

X - Y = 7

Hence, the value of X - Y such that the eight-digit number 7448X24Y is divisible by both 8 and 9 is 7

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Answer:

  (c)  Factor

Step-by-step explanation:

The constituents of a product are its factors.

Dividing a product by one of its factors will not leave a remainder.

__

A term is a constant or product of one or more variables and a constant. For example, -4 and 24xy are both terms.

A multiple is a product with one factor being an integer. For example, 3×1.5 = 4.5 is a multiple of 1.5.

A variable is a symbol for an unknown value. Commonly, a variable is a single letter, but may also be a blank (__) or a question mark (?). Sometimes a word or phrase is used as a variable. For example, ...

  3 + x = 5

  3 + __ = 5

  3 + ? = 5

  3 + (some number) = 5

The limit does not exist. There are infinitely many infinite discontinuities at [tex]x=n\pi[/tex], where [tex]n\in\Bbb N[/tex]. The function oscillates wildly between negative and positive infinity.

The equation of the ellipse in standard form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)

By analytical geometry we know that foci are along the major axis of ellipses and beside the statement we find that such axis is parallel to the x-axis of Cartesian plane. Then, the standard form of the equation of the ellipse is of the following form:

(x - h)² / a² + (y - k)² / b² = 1, where a > b     (1)

Where:

Now, we proceed to find the vertex and the lengths of the semiaxes:

a = 10 units.

b = 8 units.

Vertex

V(x, y) = 0.5 · F₁(x, y) + 0.5 · F₂(x, y)

V(x, y) = 0.5 · (3, 2) + 0.5 · (- 9, 2)

V(x, y) = (1.5, 1) + (- 4.5, 1)

V(x, y) = (- 3, 2)

The equation of the ellipse in standard form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)

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Answer:

Step-by-step explanation:

y-4=0(x+8)

y-4=0

y=4

Answer:

i

Step-by-step explanation:

y-4=0(x+8)

y-4=0

y=4

Answer:

$29765.50

Step-by-step explanation:

Median is the middlemost value (or the average of the 2 middlemost value if there are even number of values) in an ascending order.

First, arrange the salary list in an ascending order.

$21,971 , $25,997 , $27,512 , $32,019 , $38,860 , $43,702

As we can see here, there are even number of values (6), so the median will be the average of the 2 middlemost value, which will be:

Median = [tex]\frac{27512 + 32019}{2}[/tex]

= [tex]\frac{59531}{2}[/tex]

= $29765.50

Answer:

$29,765.50 is the median salary

Step-by-step explanation:

To find the median of the following salary list $32,019, $21,971, $27,512, $43,702, $38,860, $25,997

The steps to do this is:

Doing the steps:

This means take the average of $27,512 and $32,019

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Answer 1:

1.23456789 × (10-6) = 4.93827156

Answer 2:

(1.23456789 × 10) - 6 = 6.3456789

Answer 3:

1.23456789 × [tex]10^{-6}[/tex] = 0.000000123456789

Hope this helped! :)

Answer:

yes

Step-by-step explanation:

f the exterior angle of a polygon is given, then the formula to find the interior angle is Interior Angle of a polygon = 180° – Exterior angle of a polygon Method 3: If we know the sum of all the interior angles of a regular polygon, we can obtain the interior angle by dividing the sum by the number of sides

The interquartile range of 48, 26, 31, 50, 38, 40, 42, 34, 44, 36, is: D. 10.

The interquartile range of a data distribution is determined as: upper quartile (Q3) - lower quartile (Q1).

The upper quartile of a data distribution is the center of the second half of a data distribution while the lower quartile is the center of the first half of a data distribution.

Given the data, 48, 26, 31, 50, 38, 40, 42, 34, 44, 36:

Order the data set as, 26, 31, 34, 36, 38, 40, 42, 44, 48, 50

The first half of the data is: 26, 31, 34, 36, 38.

The center is 34.

Lower quartile (Q1) = 34.

The second half of the data is: 40, 42, 44, 48, 50. The center is 44.

Upper quartile (Q3) = 44.

Interquartile range = 44 - 34

Interquartile range = 10

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The statement that a linear equation is an equation whose graph is a straight line is True.

A  linear equation can be defined as an algebraic equation with each term having an exponent and the graphing of the equation results in a straight line.

From the definition, it can be deduced that the statement is True.

Thus, the statement that a linear equation is an equation whose graph is a straight line is True.

The complete question is:

True or false

A linear equation is an equation whose graph is a straight line.

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The required number is 7. The expression formed with the given information is x - 21 = 2(-x).

An expression is the combination of variables, constants, and coefficients.

If two expressions are related by an equal in between them, then that is said to be an equation.

From the given data,

Consider the required number = x

The number is decreased by 21 i.e., x - 21

Twice the opposite of the number = 2(-x)

So, on equating,

x - 21 = 2(-x)

On simplifying,

⇒ x - 21 = -2x

⇒ x + 2x = 21

⇒ 3x = 21

∴ x = 7

Thus, the required number is 7.

Check:

7 - 21 = -14 and 2(-7) = -14.

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The critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881

The scatter plot of the election is added as an attachment

From the scatter plot, we have the following highlights

Start by calculating the degrees of freedom (df) using

df =n - 2

Substitute the known values in the above equation

df = 8 - 2

Evaluate the difference

df = 6

Using the critical value table;

At a degree of freedom of 6 and significance level of 0.01, the critical value is

z = 0.834

From the list of given options, 0.834 is between  -0.881 and 0.881

Hence, the critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881

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Answer:

0

Step-by-step explanation:

We are looking at the change in y over the change is x.  The change is y is always 0 and 0 divided by anything will be zero.

The number of copies sold (x) to date is 463043

The given parameters are:

Copies sold = 42,600

Proportion sold = 9.2% of the number of copies sold to date.

The number of copies sold (x) to date is calculated as:

Copies sold = Proportion * number of copies sold to date

Substitute the known values in the above equation

9.2% * x = 42,600

Divide both sides by 9.2%

x = 463043

Hence, the number of copies sold (x) to date is 463043

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