Write the equation of a line passing through the point (6, 4) that is parallel to the line 2x + 3y = 9.

The integer in the set S:{−24, 2, 20, 35} that will make the inequality five-sixths m minus five is less than one-half m plus 3 false is 35

Inequalities are created through the connection of two expressions. It should be noted that the expressions in inequality aren't always equal. Inequalities imply that the expressions are not equal. They are denoted by the symbols ≥  <  >   ≤.

In this case, based on the information we will replace m with 35. This will be illustrated thus:

= 5/6(35 - 5) < 1/2(35 + 3)

= 5/6(30) < 1/2(38)

= 25 < 19

In this case, 25 isn't less than 19. Therefore, 35 is the correct integer.

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The capital is £430,600.

Define capital.

The money that a company has on hand to support both its current operations and potential expansion is known as capital. One source of funding for it is the earnings from its operations. When calculating a company's capital worth, all of the company's physical assets and financial assets would be included (minus its liabilities).

The capital account—also referred to as the capital and financial account—records the net flow of investment transactions into an economy and is used in macroeconomics and international finance.

Solution Explained:

Given, Assets = £451,100 and liabilities = £20,500

Capital = Assets - Liabilities

            = 451100 - 20500
            = £430,600

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The probability that the mean actual weight for the 100 weights is greater than 25.2 is equal to 0.0136%.

In order to determine the probability that the mean actual weight for the 100 weights is greater than 25.2, we would have to calculate the mean and standard deviation.

In a uniform distribution, the mean of a data set can be calculated by using this formula:

Mean, E(x) = [a + b]/2

Where:

Substituting the given parameters into the formula, we have;

Mean, E(x) = [24 + 26]/2

Mean, E(x) = 50/2

Mean, E(x) = 25.

For the standard deviation, we have:

Standard deviation, S(x) = √((b - a)²/12)

Standard deviation, S(x) = √((26 - 24)²/12)

Standard deviation, S(x) = √((2)²/12)

Standard deviation, S(x) = √(4/12)

Standard deviation, S(x) = 0.5774.

For the sample standard deviation, we have:

Standard deviation = S(x)/√n

Standard deviation = 0.5774/√100

Standard deviation = 0.5774/10

Standard deviation = 0.05774.

By applying the central limit theorem, we would determine the z-score as follows:

Z-score = (x - μ)/σ

Z-score = (25.2 - 25)/0.05774

Z-score = 0.2/0.05774

Z-score = 3.64

Therefore, the p-value is equal to 0.000136.

Probability (x > z) = 0.0136%.

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Answer:

k = - 8

Step-by-step explanation:

- 268 = - 6(- 6 - 6k) + 2k ← distribute parenthesis by - 6

- 268 = 36 + 36 k + 2k ( subtract 36 from both sides )

- 304 = 38k ( divide both sides by 38 )

- 8 = k

The horizontal asymptote is y = [tex]\frac{9}{4}[/tex].

Let f(x) = [tex]\frac{9x^{3}-5x-9}{4x^{3}-9x+4}[/tex]

Line y = L is a horizontal asymptote of the function y=f(x), if either [tex]\lim_{x \to \infty} f(x) = L[/tex] or, [tex]\lim_{x \to -\infty} f(x) =L[/tex] and L is finite.

We will calculate limits :

[tex]\lim_{x \to \infty}(\frac{9x^{3}-5x-9}{4x^{3}-9x+4}) = \frac{9}{4}[/tex]

[tex]\lim_{x \to -\infty}(\frac{9x^{3}-5x-9}{4x^{3}-9x+4}) = \frac{9}{4}[/tex]

Hence, horizontal asymptote is y = [tex]\frac{9}{4}[/tex].

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Answer:

Step-by-step explanation:

3x + 3x equals 11x

1) The interest if it is compounded using simple interest is $240

2) The interest if it is compounded annually is $249.73

3) The interest if it is compounded semiannually is $252.325

4) The interest if it is compounded quarterly is $253.650

5) The interest if it is compounded monthly is $254.543

6) The interest if it is compounded daily is $254.978

7) The interest if it is compounded hourly is $254.993

8) The interest if it is compounded every minute is $254.993

9) The interest if it is compounded continuously is $254.993

10) The difference in interest between simple interest and interest compounded continuously is $14.993

Compound interest is the addition of interest to the principal sum of a loan or deposit, or interest on interest plus interest.

Given, P=2000

r=4%

r=4/100

r=0.04

t=3 years

1) Simple interest⇒ A=P(1+rt)

=2000(1+3(0.04)

=2000(1+0.12)

=2240

S.I= 2240-2000

S.I=$240

2) Compound interest(yearly)

1st year= 2000(4/100)=80

2nd year=2080(4/100)=83.2

3rd year=(2080+83.2)(4/100)=86.528

P=2163.2+86.528

P=2249.728

C.I=2249.728-2000

C.I=249.728≈$249.73

3) Compounded semiannually

A= P(1+(R/200))²ⁿ

A=2000(1+(4/200))⁶

A=2000(1.12616)

A=2252.325

C.I= 2252.325-2000

C.I=$252.325

4) Compounded quarterly

A=P(1+(R/400))⁴ⁿ

A=2000(1+(4/400))¹²

A=2253.650

C.I=2253.650-2000

C.I=$253.650

5) Compounded monthly

A=P(1+(R/1200))³⁶

A=2000(1+(4/1200))³⁶

A=2254.543

C.I= 2254.543-2000

C.I=$254.543

6) Compounded daily

A=P(1+(R/36500))³⁶⁵ⁿ

A=2000(1+(4/36500))¹⁰⁹⁵

A=2254.978

C.I=2254.978-2000

C.I=$254.978

7) Compounded hourly

A=P(1+(R/876000))²⁶²⁸⁰

A=P(1+(4/876000))²⁶²⁸⁰

A=2254.993

C.I=2254.993-2000

C.I=$254.993

8) Compounded every minute

A=P(1+(R/52560000))¹⁵⁷⁶⁸⁰⁰

A=P(1+(4/52560000))¹⁵⁷⁶⁸⁰⁰

A=2254.993

C.I=2254.993-2000

C.I=$254.993

9) Compounded continuously

A= [tex]Pe^{rt}[/tex]

A=2000([tex]e^{0.04*3}[/tex])

A=2254.993

C.I=2254.993-2000

C.I=$254.993

10) The difference in interest between simple interest and interest compounded continuously is

254.993-$240=$14.993

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2/3 is the unit rate of the relationship

A unit rate is defined as the rate for one of something. For example, if 10 oranges cost $50, the unit rate will be $50/10 = $5 i.e.  $5 for one orange.

On a linear graph, the unit rate is obtained by calculating the slope of the line. The slope is the change in y divided by the change in x:

Slope = y2-y1 / x2-x1  

Thus, we can any two convenient points on the graph and use it calculate the slope as shown in the attached image:

Slope = y2-y1 / x2-x1

Slope = 6-2 / 9-3 = 4/6 = 2/3

Therefore, the unit rate for this relationship is 2/3. The 2nd option is the answer

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With the help of unitary method it can be found out that Tomás has to buy more 3650 grams of oranges if he wants to reach 5 kg.

It is given to us that -

Tomás first chose a tray with oranges whose label says 1,350 gram

We have to find out more grams of oranges that he should buy if he wants to reach 5 kilogram.

We know that

1 kilogram = 1000 grams

=> 1000 grams = 1 kilogram ----- (1)

By unitary method, we can find out the number of kilograms equivalent to 1350 grams of oranges.

From equation (1), we have

1000 grams = 1 kilogram

=> 1350 grams = (1/1000) * 1350

=> 1350 grams = 1.35 kilograms ----- (2)

Now, from equation (2), we can see that Tomás first chose 1,350 grams of oranges which is equal to 1.35 kilograms of oranges.

This implies that the more kilograms of oranges that Tomás has to buy to reach 5 kilograms is given by -

(5 - 1.35) kilograms

= 3.65 kilograms

From equation (1), we have

1 kilogram = 1000 grams

=> 3.65 kilograms = 3.65 * 1000 grams

=> 3.65 kilograms = 3650 grams.

Thus, by solving through unitary method we find out that Tomás has to buy more 3650 grams of oranges if he wants to reach 5 kg.

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The constant of proportionality between the total cost and the number of songs is 0.72.

The constant of proportionality is the ratio that supplies the variable cost per unit of each song.

Other names for the constant of proportionality include:

Determining the constant of proportionality can help us formulate the total cost equation as y = 0.72x.

Number of Songs    Total Cost    Unit Cost

          13                     $9.36         $0.72 ($9.36/13)

          17                     $12.24        $0.72 ($12.24/17)

         19                     $13.68         $0.72 ($13.68/19)

Check:

y = 0.72x

y = 0.72(13)

y = $9.36

Thus, the constant of proportionality is 0.72, showing that a downloaded song costs $0.72 each.

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By using subtraction, it can be calculated that there were 496 round beads more than heart shaped beads

What is subtraction?

Suppose, there are two numbers and it is required to find out how much one number is bigger than  the other. The operation used for this is subtraction.

The larger number is called minuend and the smaller number is called subtrehend.

Here, subtraction will be used

Number of round glass beads = 675

Number of beads in the shape of heart = 179

Number of more round beads there were = 675 - 179

                                                                      = 496

There were 496 round beads more than glass beads

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If they observes a blood sample with a compound microscope that has a 10x ocular lens and a 40x objective lens. The larger that the blood cells appear under the microscope is: 400x.

Given data:

Blood sample has:

10x ocular lens

40x objective lens

Using this formula to determine how large the blood cells appear

Blood cells = ocular lens × objective lens

Let plug in the formula

Blood cells =  10x × 40x

Blood cells = 400x or 400 times larger

Therefore the blood cells appear 400 times larger.

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400 times larger

The solution for (18x45) divided by 8 = 101.25

Simplify (18x45) divided by 8

Step 1: Rewrite the equation in mathematical terms

we have:

[tex]\frac{18 x 45}{8}[/tex]= [tex]\frac{810}{8}[/tex]

= 101.25

Therefore, the solution for (18x45) divided by 8 = 101.25

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Answer:

huhh

Step-by-step explanation:

Hi im new can u guys tell me how this work pease??

Answer:

Step-by-step explanation:

idek idek

The two quadratic equations are; y = x² + 2·x - 3 and y = -x² - 2·x + 3

Given,

x - intercepts = (−3,0) and (1,0).

The x-intercepts are given by the point at which the y-value of the equation are zero.

Therefore;

The quadratic equation are;

(x + 3)·(x - 1) = 0

x² + 2·x - 3 = 0

Quadratic equations;-

The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).

Here,

The equation can also be written in the form;

(-x - 3)·(x - 1) = 0

-x² - 2·x + 3 = 0

The quadratic equations are;

y = x² + 2·x - 3 and y = -x² - 2·x + 3

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The radius of the circle is 3 units.

The center of the circle lies on the x-axis.

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

The standard equation of a circle is:

[tex]x^{2} +y^{2} +2gx+2fy+c=0[/tex]

Given circle equation:

[tex]x^{2} +y^{2} -2x-8=0[/tex]

on comparing

2gx = -2x

g = -2

2fy = 0

f = 0

Center = (2,0)

radius r = [tex]\sqrt{g^{2}+f^{2}-c }[/tex]

= [tex]\sqrt{9}[/tex]
r = 3 units.

Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

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Answer: 1253.33

Step-by-step explanation:

As per the given information, Tomas divides one program among four people then each person will get fraction of ( 1/ 4) of the original stack if divided equally .

As given in the question,

Number of stacks of program to be divided = 1

Number of friends = 3

Number of people among whom stack of program is to be divided = 4

Let us consider stack of program divided equally

Fraction of stack of program each friend will get = 1 /4

As

( 1 / 4 ) +  ( 1 / 4 ) + ( 1 / 4 ) + ( 1 / 4 )

= ( 1+ 1+ 1+ 1) / 4

= 4/4

= 1

Therefore, for the given information, Tomas divides one program among four people then each person will get fraction of ( 1/ 4) of the original stack if divided equally .

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(7,0); (7,−5) ;(7,3); (7,10);. (7,y)

Step-by-step explanation:

Answer:

The equation x = 7 forms a vertical line which we refer to as undefined. So any points with a x value of 7 will pass through the line.

Step-by-step explanation:

For example, points like (7, 0) (7, 1) (7, 2) are all points that the line x = 7 passes through.

A point is made up of 2 values. An x-value and and a y-value. You simply plug in 7 for the x and any value for y.

Points that are on the line x = 7 include:

(7, 0)

(7, 1)

(7, 2)

(7, 4)

(7, 5)

(7, 6)

The value of 8x ÷ (16+8) ÷ 32 is x/96

The four basic arithmetic operations in Maths, for all real numbers, are:

Addition (Finding the Sum; ‘+’)

Subtraction (Finding the difference; ‘-’)

Multiplication (Finding the product; ‘×’ )

Division (Finding the quotient; ‘÷’)

Discussing about division or quotient

The division is usually denoted by ‘÷‘ and is the inverse of multiplication. It constitutes two terms dividend and divisor.

To simplify

8x÷(16+8)÷32= 8x×1/24×1/32

= x/96

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Answer:

j = 9

Step-by-step explanation:

Given equation,

→ -3(j - 8) + (-6) = -9

Let's solve for the value of j,

→ -3(j - 8) + (-6) = -9

→ -3j + 24 - 6 = -9

→ -3j + 18 = -9

→ -3j = -9 - 18

→ j = (-27)/(-3)

→ [ j = 9 ]

Hence, the value of j is 9.

Answer:

j = -9

Step-by-step explanation:

[tex] - 3(j - 8) + - 6 = - 9 \\ open \: brackets \\ - 3j + 24 + - 6 = - 9 \\ 3j + 24 = - 9 + 6 \\ 3j + 24 = - 3 \\ 3j = - 3 - 24 \\ 3j = - 27 \\ divide \: by \: 3 \\ j = - 9[/tex]

Answer:

19 and 21|

Step-by-step explanation:

a + (a+2) = 40

2a + 2 = 40

2a = 40 - 2

2a = 38

a = 38/2

a = 19

a+2 = 21

Check:

19 + 21 = 40

Answer:

5/48

Step-by-step explanation:

The fraction of people getting cake will be 1/6 of 5/8 thus it will be 5/48.

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

In another word, if we divide two numbers by each other then the upper word is called the numerator, and the lower word is called the denominator.

As per the given,

James shares 5/8 of a cake between 6 people.

Now, 1/6 of 5/8 will be as,

1/6(5/8) = 5/48

Hence "The fraction of people getting cake will be 1/6 of 5/8 thus it will be 5/48".

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The double inequality describing the length of time (in minutes) that Liz spends on her phone each night is 45 ≤ f(x) ≤ 120.

Double inequality is a mathematical expression that has two inequalities.

Double inequality is also known as a compound inequality. because there is more than one inequality in the expression

The form of double inequality is always written as: a ≤ f (x) ≤ b.

This double inequality gives the value of x as more than a and less than b.

The least number of minutes spent by Liz on her phone = 45 minutes

The maximum number of minutes spent by Liz on her phone = 120 minutes

Inequality 1: 45 ≤ f(x)

Inequality 2: f(x) ≤ 120

Thus, this double inequality 45 ≤ f(x) ≤ 120 shows Liz's time on the phone every night.

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The completion of the inventory table is as follows:

Some of the inventory methods that are used in completing the inventory table are:

                                    Units    Unit Cost    Total Cost

Jan. 1      Beg. Inventory  10       $7.00            $70

Apri. 11    Purchases        30     $12.00          $360

May 17    Purchases        40     $13.00          $520

Dec. 5    Purchases        20    $15.00           $300

Total                              100                        $1,250

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Using division operations and based on the rates of production, given, Machine D works the fastest.

The rate of production can be computed using the division operation, which divides the dividend by the divisor, to obtain the quotient (rate).

The rate of production is the number of goods that can be produced during a given period of time.

The rate of production or production rate also refers to the time consumed in the production of a unit of goods or services.

There are, therefore, two ways of determining production rate.  Firstly, we can divide the total production by the hours consumed.

Secondly, the production rate can be computed by dividing the total production time by the number of goods produced.

                           Units          Production     Rate of

                       Produced          Hours      Production

Machine A        10,000               15             667 cups per hour

Machine B       25,000              20           1,250 cups per hour

Machine C       30,000              30           1,000 cups per hour

Machine D       15,000               10            1,500 cups per hour

Thus, using division operation, Machine D produces at the fastest rate than the other three machines.

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                           Units          Production

                       Produced          Hours

Machine A        10,000               15

Machine B       25,000              20

Machine C       30,000              30

Machine D       15,000               10

If the number of different account numbers are possible if repetitions of letters and digits are allowed is:45,697,600,000.

Let assume you have 26 choices for each of the first 4 slots and 10 choices for each of the last 5 slots.

Hence,

Total possibilities = (26× 26× 26×26) × (10×10×10×10×10)

Total possibilities = 26^4 × 10^5

Total possibilities = 456976×100000

Total possibilities = 45,697,600,000

Therefore we can assume that the total possibilities is : 45,697,600,000.

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Answer:

Step-by-step explanation:

Which graph represents the solution set of - 4x - y ≤ - 6?

Answer: 0.000089

Step-by-step explanation: 0.000089 is already in standard form, if you want 0.000089 in the scientific form then that would be...

8.9 x 10⁻⁵