3 new books and 8 used books what is the ratio

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1200\\ P=\textit{original amount deposited}\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}\)

\(1200 = P\left(1+\frac{0.07}{12}\right)^{12\cdot 15} \implies 1200=P\left( \frac{1207}{1200} \right)^{180} \\\\\\ \cfrac{1200}{ ~~ \left( \frac{1207}{1200} \right)^{180} ~~ }=P\implies 421.21\approx P\)

Answer:

3.

\( \frac{28}{3} \)

Step-by-step explanation:

number 1 equals 8 1/5

number 2 equals 5

number 3 equals 9 1/3

The variable y is directly proportional to x, which is the definition of direct variation.

The intersection of two perpendicular lines, the x-axis and the y-axis, results in a 2D plane known as a coordinate plane. In geometry, a coordinate system is a method for calculating the positions of the points using one or more integers or coordinates.

The graph that represents a function with direct variation is a coordinate plane with a line passing through (0, 0) and some other point that is not the origin.

Out of the given options, the graph that represents a function with direct variation is the coordinate plane with a line passing through (negative 4, 0) and (0, negative 2).

This is because the equation of this line can be written in the form y = mx, where m is the slope of the line. In this case, the slope is:

m = (0 - (-2)) / (-4 - 0) = 1/2

So the equation of the line is y = (1/2)x - 2, which is in the form of y = kx, where k = 1/2. This means that y is directly proportional to x, which is the definition of direct variation.

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Answer:  12x4= 48 so 48

Step-by-step explanation:

Answer:

follow me and I will answer it

Answer:

This expression has no roots.

Step-by-step explanation:

Using the discriminant: b² - 4ac, we get:

2² - 4 × 3 × 1

= 4 - 12

= -8

So this equation has no real solutions.  Let's prove that by trying to solve for x:

3x² + 2x + 1 = 0

9x² + 6x + 3 = 0

9x² + 6x + 1 = -2

(3x + 1)² = -2

3x + 1 = i√2

3x = -1 ± i√2

x = (-1 ± i√2) / 3

The only solutions available then are indeed complex.

This expression has no roots. the discriminant of the equation is -8.

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Using the discriminant: b² - 4ac, we get:

2² - 4 × 3 × 1

= 4 - 12

= -8

So this equation has no real solutions.  Let's prove that by trying to solve for x:

3x² + 2x + 1 = 0

9x² + 6x + 3 = 0

9x² + 6x + 1 = -2

(3x + 1)² = -2

3x + 1 = i√2

3x = -1 ± i√2

x = (-1 ± i√2) / 3

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Answer:

6/5

Step-by-step explanation:

5x + 14 = 20

Subtract 14 from 20

5x = 6

Divide both sides by 5

x = 6/5

Observe the given probability density function (PDF) carefully.

The function is constant and spans from x=0 to x=2.

The probability of the random variable lying in an interval is given by the area under the PDF corresponding to that interval.

Since the total probability is always unity in the entire domain of the PDF. The total area of the rectangle must be unity.

Let 'c' be the height of the rectangle, then equating the total area to unity,

Now that we know the height of the rectangle is 0.5, so the probability that the value of random variable X is at least 1.28 is equal to the area under the curve beyond x = 1.28,

Answer:

3.93

Step-by-step explanation:

the circle is 3.14 area plus the bottom .79 area = 3.93

Answer:

95% of the data would lie between the two standard deviation range.

Step-by-step explanation:

Answer:11.50

Step-by-step explanation:

Answer:

16.9

Step-by-step explanation:

We can use a proportion also in this case

51.6 : 23 = 38 : NO

NO = (38 x 23)/51.6 = 16.9

Answer:

D

Step-by-step explanation:

A and D are both equidistant from the x- axis, that is

A is 3 units above the x- axis and D is 3 units below the x- axis

then the x- axis is the line of symmetry

Answer: K=23

Step-by-step explanation:

Answer:

k=9

Step-by-step explanation:

4k+44 because you distribute the 4 to the parenthesis

new equation: 4k+44-2=6

add 2 to 6 which would be 8 because you have to get k by itself

4k+44=8 subtract 44 from 8

-36=4k

divide by four

k=-9

if the equation is really 4(k+11)--2=6

do the same first steps so 4k+44

but the -2 would become positive cuz of the double negative

so:

4k+44+2=6

4k+46=6

subtract 46 from 6

4k=-40

divide -40 by 4

k=-10

The company should invest in 69.06 units of labor and 67.47 units of capital to maximize production output given the budget constraint.

We have,

We want to maximize the production output

P = L^0.8 K^0.2

subject to the constraint 10L + 20K = 2700.

We can solve for K in terms of L from the constraint equation:

10L + 20K = 2700

20K = 2700 - 10L

K = (2700 - 10L) / 20

K = 135 - 0.5L

Substitute this expression for K into the production function:

P = L^0.8 K^0.2

P = L^0.8 (135 - 0.5L)^0.2

We want to maximize P with respect to L.

Taking the derivative of P with respect to L:

dP/dL = 0.8L^-0.2 (135 - 0.5L)^0.2 + 0.2L^0.8 (135 - 0.5L)^-0.8 (-0.5)

dP/dL = 0.16(135 - 0.5L)^0.2 L^-0.2 - 0.1(135 - 0.5L)^-0.8 L^0.8

Setting dP/dL equal to zero and solving for L:

\(0.16 (135 - 0.5L)^{0.2} L^{-0.2} - 0.1 (135 - 0.5L)^{-0.8} L^{0.8} = 0\)

0.16(135 - 0.5L)^0.2 = 0.1(135 - 0.5L)^-0.8 L^1

1.6(135 - 0.5L) = (135 - 0.5L)^-0.8 L

1.6 = (135 - 0.5L)^-1.8 L^-1

1.6L = (135 - 0.5L)^1.8

1.6L = (135^1.8 - 0.5L)^1.8

1.6L = 2.24474e+15 - 4.52222e+14 L + 1.22313e+13 L^1.8

1.22313e+13 L^1.8 - 4.52222e+14 L + 2.24474e+15 - 1.6L = 0

This equation can be solved numerically using a solver or a graphing calculator.

The solution is L = 69.06 units of labor.

To find the corresponding value of K, we can use the constraint equation:

10L + 20K = 2700

20K = 2700 - 10L

K = (2700 - 10(69.06)) / 20

K = 67.47 units of capital

Therefore,

The company should invest in 69.06 units of labor and 67.47 units of capital to maximize production output given the budget constraint.

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Answer:

130° and 310°

Step-by-step explanation:

the bearing of A from B is the measure of the clockwise angle from a north line at B to A

the angle at B and A are same- side interior angles and sum to 180°

angle at B = 180° - 50° = 130°

the bearing of A from B is then 130°

the bearing of B from A is the measure of the clockwise angle from the north line at A to B

the complete angle about A = 360° then clockwise angle from north line at A to B is

360° - 50° = 310°

the bearing of B from A is 310°

Answer:

x intercept: (-8,0)

y intercept: (0,2)

Answer:

• (a)It costs $77.50 to buy five tickets.

• (b)You can by 8 tickets with $130.

Explanation:

The cost (in dollars) of buying x tickets to the orchestra is given by the formula:

(a)When the number of tickets, x=5

It costs $77.50 to buy five tickets.

(b)When the cost, C(x)=$130

You can by 8 tickets with $130.

Answer:

x = 3√10

Step-by-step explanation:

We can find the value of x by using Euclidean theorem

x^2 = 9 × 10

x^2 = 90

x = 3√10

Answer:

x=-1,y=0

Step-by-step explanation:

-10y+9x=-9

10y+5x=-5

14x=-14

x=-1

-10y-9=-9

y=0

Answer:

4\(y^{\frac{3}{2} }\)

Step-by-step explanation:

using the rule of exponents/ radicals

\(\sqrt[n]{a^{m} }\) = \(a^{\frac{m}{n} }\)

then

4 \(\sqrt{y^{3} }\)

= 4\(y^{\frac{3}{2} }\)

Answer:

If 20 is 100% then 20 divided by 4 equals 5 so 20 lbs. - 5 lbs. = 15 lbs. the baker has 15 pounds of sugar left.

Step-by-step explanation:

This is a wonderfully easy problem. So, you start off by dividing the pounds of sugar by the denominator which is 4. So:

20 / 4 = ?

Then you that product and multiply it by the numerator, which is 3 in this case and you get your answer.

Thanks!

Answer: 12 men would be needed to repair the same road in 3 1/3 hrs. Inverse proportion because usually in work,food and time its inversly proportional.

8 hours --> 5 men

1 hour --> 5*8 = 40 men

3 1/3 hours --> 40/ (3 1/3) men

                  --> 12 men

Answer:

0

Step-by-step explanation:

Use discramnt formula

\(b {}^{2} - 4ac\)

Where 6 is a, 11 is b and 9 is c

\(11 {}^{2} - 4(6)(9) \)

\(121 - 216 = - 95\)

Since the discramnt is negative, there are no real solutions and it will only produce imaginary solutions

Answer:

6

Step-by-step explanation:

4

Answer:

The answer is C

Step-by-step explanation:

Assuming this is a fair coin, the theoretical probability of the coin going on one side, let's say heads, is 50%, or 0.5. So what's the chance the coin lands head 5 times? To do this we do 0.5^5 OR 0.5*0.5*0.5*0.5*0.5. Both of these answers equal 0.03125. So C is the Answer. Hope this helps :D

The surface area of the pyramid is 300 square inches.

The surface area of a square pyramid can be calculated by:

The area of the square base is

10 inches * 10 inches = 100 square inches.

Based on the given parameters:

The area of each triangular face is:

(10 inches * 10 inches) / 2 = 50 square inches.

So, the total surface area of the pyramid is:

100 square inches + 4 * 50 square inches = 300 square inches.

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The equation of the perpendicular line passing through (0, -1) is y = -9x - 1.

To find the equation of a line that is perpendicular to the given line y = (1/9)x + 2 and passes through the point (0, -1), we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other.

The given line has a slope of 1/9. To find the slope of the perpendicular line, we take the negative reciprocal of 1/9, which is -9.

Using the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept, we can substitute the slope and the coordinates of the given point (0, -1) into the equation.

y = -9x + b

Since the line passes through the point (0, -1), we can substitute the x-coordinate as 0 and the y-coordinate as -1 into the equation:

-1 = -9(0) + b

-1 = b

Therefore, the y-intercept (b) of the perpendicular line is -1.

Putting it all together, the equation of the line that passes through (0, -1) and is perpendicular to y = (1/9)x + 2 is:

y = -9x - 1

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Answer: y

=

2

x

−

2

,  

(

−

2

,

7

)

Step-by-step explanation:

(

2

(

7

)

−

2

)

−

(

2

(

−

2

)

−

2

)

(

7

)

−

(

−

2

)

Answer:

3a + 3b

Step-by-step explanation:

The distributive property of multiplication over addition is

a(b + c) = ab + ac

Here we have

3(a + b)

We apply the distributive property and get

3 × a + 3 × b

which simplifies to

3a + 3b