A C=26
9 units
1.8 units

In 11.56 years the given amount of $ 900 will be double.

The interest charged on a loan or deposit is known as compound interest which depends on both the principal amount and rate of interest.

The formula  used for

where P = Principal amount

r = Rate of interest in decimal

n = Number of compounds per year  

t = Time period  

Here from the given data,

Principal amount, p = $ 900

Rate of interest, r = 6% = 6/100 = 0.06

Number of compounds, n = 12    [ ∵ compounded mothly ]

Here we need to find the time period

Assume that after 'n' years the amount will be doubled i.e $ 1800

From the given problem,

Amount, A = 900(1+0.06/12)¹²ⁿ        

= 900(1+0.06/12)¹²ⁿ

= 900(1 + 0.005)¹²ⁿ

= 900 (1.005)¹²ⁿ  

As we assumed after 'n' years the amount is $ 1800

=> 900 (1.005)¹²ⁿ = 1800  

=> (1.005)¹²ⁿ = 2    

Apply to log on both sides

=> log (1.005)¹²ⁿ = log 2

=> 12n log(1.005) = log 2

=> 12n = log 2/log(1.005)

[ use calculator for log (1.005) and log 2]

=> 12n = 0.301029996/ 0.00216606176  

=> 12n = 138.975722

=>  n =  11.5813102

=>   n = 11.56  

Therefore,

In 11.56 years the given amount of $ 900 will be double.

Learn more about Compound interest at

brainly.com/question/26457073

#SPJ4

Angle θ with 0∘ < θ < 360∘ that has the same: sine as 30°:∅= degrees

cosine as 30°:∅= degrees are 150 and 330 degrees.

What is trigonometric function?

Trigonometric functions are referred to as Circular Functions may be merely outlined because the functions of an angle of a triangle

Main Body:

We have to find an angle θ with 0° < θ < 360° that has the same:

(a) sin(30∘)

We know that sin(θ) is positive in 2nd quadrant and in the 2nd quadrant θ lies between 90∘ and 180∘.

sin(30∘)=sin(180∘−30∘)

[∵sin(180∘−θ)=sin(θ)]=sin(150∘)

Thus:

sin as 30∘:θ=150 degrees

(b) cos(30∘)

We know that cos(θ) is positive in the 4th quadrant and in the 4th quadrant θ lies between 270∘ and 360∘.

cos(30∘)=cos(360∘−30∘)

[∵cos(360∘−θ)=cos(θ)]=cos(330∘)

Thus:cos as 30∘

:θ=330 degrees

To know more about trigonometric function , visit:

https://brainly.com/question/1143565

#SPJ1

The part (a) is not correct i.e. The slope is 3, which indicates that a mouse's weight should increase by about 3 grams for each additional millimeter of tail length.

What is Regression analysis ?

Regression analysis is the process of determining how one or more variables and the outcome variable relate to one another. Risk factors, co-founders, and the outcome variable are all referred to as predictors or independent variables. The result variable is sometimes referred to as the dependent or response variable. Regression analysis displays the dependent variable as "y" and the independent variables as "x".

Given, tail length = (3 × weight) + 20

(a) Here, The slope is 3 which indicates that a mouse's length is the sum of 3 times the weight and 20. So, the statement is not correct.

(b) If weight is 38 gm, then

    tail length = 38 × 3 + 20

                     = 114 + 20 = 134mm.

So, the statement is correct.

(c) We've  tail length = (3 × weight) + 20

we can see that the relationship between the two is positive because when the weight is increased, the tail length also increases.

So, the given statement is correct.

(d) The slope is 3 when the tail length is being measured in millimeters.

Now, If we measure it in centimeter = 3/10 = 0.3 cm

∵ 1 mm = 1/10 cm.

So, the given statement is correct.

(e) when a mouse has weight of 29 grams and tail length of 100 mm.

    When the weight is 29 grams, it should have tail length as :

             tail length = 29 × 3 + 20

                              = 107 mm.

  but, tail length is given as 100 mm.

So, the residual for the mouse is -7 i.e. (100 - 107)

Hence, The given statement is correct.

Learn more about Regression analysis from the link given below:

https://brainly.com/question/25987747

#SPJ4

By setting up the equation, we get the system of linear equations are

9x + 7y = 77

3x + 5y = 49

solving these equation Cost to rent a chair = $1.75

cost to rent a table = $8.75

A system of linear equations is a collection of one or more linear equations involving the same variables.

There are several methods for solving systems of linear equations, including:

Graphing: One way to solve a system of linear equations is to graph each equation on the same set of axes and look for the point of intersection. This method is useful when you want to visualize the solution, but it can be time-consuming if you have a large system of equations.

Substitution: The substitution method involves solving one of the equations for one of the variables and substituting this expression into the other equation. This will result in an equation with only one variable, which you can then solve.

Elimination: The elimination method involves adding or subtracting the equations in such a way that one of the variables is eliminated. This will result in an equation with only one variable, which you can then solve.

etc.

To solve the system of equations 9x + 7y = 77 and 3x + 5y = 49, you can use the substitution method.

First, solve the first equation for y:

9x + 7y = 77

7y = -9x + 77

y = (-9/7)x + 11

Now substitute this expression for y into the second equation:

3x + 5((-9/7)x + 5(11) = 49

3x - (45/7)x + 55 = 49

solving for x :

x = 1.75

Now substitute this value for x back into the first equation to find y:

y = 8.75

To learn more about substitution method visit:

https://brainly.com/question/14619835

#SPJ1

The explicit formula for the geometric sequence 6, -24, 96, ... is

Every term in a geometric series is obtained by multiplying the term before it by the same number called the common ratio

The common ratio is denoted by the number r. It can be calculated by dividing any term in the sequence by the term before it.

For the given sequence the first term is a = 6

The common ratio is solved as follows

a * r  = second term

6 * r = -24

r = -24/6

r = -4

check

-24 * -4 = 96 correct

The nth term of a geometric sequence

= ar^(n - 1)

= a * -4^(n - 1)

checking for the third term

= a * -4^(n - 1)

= 6 * -4^(3 - 1)

= 6 * -4^(2)

= 6 * 16

= 96

Learn more about geometric sequence at:

https://brainly.com/question/1509142

#SPJ1

Answer:

y = 3x + 2

y = 1/2 x -1

Step-by-step explanation:

The slope intercept form of a line is

y = mx + b  You substitute in the slope for m and the y intercept for b

Answer:

Step-by-step explanation: 270

Answer:

goes from(6,0),(10,1),(14,2) in +ve

Answer: 1.49 x [tex]10^{-5}[/tex]

Step-by-step explanation:

The amount invested in Sock Y is - $126,000 and the Beta of the portfolio is 1.636.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Data provided in the question:

Total amount to be invested = $140000

Stock                          X       Y

Expected return       14%     10%

Beta                          1.42     1.18

Expected return of portfolio = 17.6%

Now,

let the weight invested n stock X be W

therefore,

Weight of Stock Y = 1 - W

thus,

( W × 14% ) + (1 - w) × 10% = 17.6 %

14W + 10% - 10W = 17.6%

4W = 7.6

W = 1.9

Therefore,

weight of Y = 1 - 1.9 = -0.9

Amount investment in Sock Y = Total amount to be invested × Weight

= 140,000 × ( - 0.9 )

= - $126,000 i.e short Y

Beta of portfolio = ∑ (Beta × Weight)

Beta of portfolio= [ 1.42 × 1.9 ] + [ 1.18 × (-0.9) ]

Beta of portfolio= 2.698 - 1.062

Beta of portfolio= 1.636

To know more about an expression follow

https://brainly.com/question/17328622

#SPJ1

The exponential function that contains the points (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20) is y = 4.002 · [tex]e^{1.609\cdot x}[/tex].

In this problem we must determine the exponential function that contains the points (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20), whose formula is described below:

y = A · [tex]e^{B\cdot x}[/tex]

Where:

If we know that (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20), then the values of constants are:

4 / 5 = A · [tex]e^{-B}[/tex]

20 = A · [tex]e^{B}[/tex]

If we divide the latter expression by the former, then:

25 = [tex]e^{2\cdot B}[/tex]

㏑ 25 = 2 · B

B = (1 / 2) · ㏑ 25

B ≈ 1.609

And the value of A is:

A = 20 / [tex]e^{1.609}[/tex]

A ≈ 4.002

The exponential function is y = 4.002 · [tex]e^{1.609\cdot x}[/tex].

To learn more on exponential functions: https://brainly.com/question/11487261

#SPJ1

Answer:

100°

Step-by-step explanation:

180°- 80°= 100°

The angles are supplementary, meaning that they have to add up to 180.

Hope this helps!!! :)

Answer:

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

The difference of the functions is:

The difference between functions is positive, therefore it is a vertical shift up by 2 units.

The value of x in simplest radical form is x = [tex]\sqrt{17}[/tex]

Explain Pythagoras theorem.

The Pythagorean Theorem (also known as the Pythagorean Theorem) is an important topic in mathematics that describes the relationship between the sides of a right triangle. The sides of a right triangle are also called Pythagorean numbers.

The Pythagorean theorem is basically used to find unknown side lengths and triangle angles. Using this theorem, we can derive the formulas for the base, perpendicular and hypotenuse.

Using Pythagoras theorem in both the triangles,

Find the hypotenuse in above triangle

[tex]h^2=P^2+B^2[/tex]

[tex]h^2=4+4=8[/tex]

h = [tex]2\sqrt{2}[/tex]

Now, using Pythagoras theorem in below triangle,

[tex]h^2=P^2+B^2[/tex]

[tex]5^2 = x^{2} + 8[/tex]

25 = [tex]x^{2}[/tex] + 8

[tex]x^{2}[/tex] = 25 - 8 = 17

x = [tex]\sqrt{17}[/tex]

Therefore, x = [tex]\sqrt{17}[/tex]

To learn more about Pythagoras theorem from the given link.

https://brainly.com/question/343682

#SPJ1

To decide whether to use the normal or the Student’s t distribution, for an x distribution that is mound-shaped:

Use the normal distribution if the standard deviation is known. Use the Student's t - distribution when the standard deviation is not known.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution.

It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution is depicted graphically as a bell curve.

For small sample numbers or unidentified variances, population parameters are estimated using a form of probability function called a t-distribution.

Hence t-distribution is suitable when the variance which is standard deviation squared is unknown

Learn more about t-distribution at:

https://brainly.com/question/16959076

#SPJ1

The units digit of the double factorial notation is the units digit of the product of all the even integers from 2 to 8, which is 8! The units digit of 8! is 8, so the answer is 8.

Factorials are mathematical operations symbolized by an exclamation point following a number. To find the factorial of a number, such as 5, write it down as 5! then multiply it by all the positive integers less than 5, including 1. Therefore, 5! is equivalent to 5 x 4 x 3 x 2 x 1, or 120. Factorials are frequently employed in mathematical equations and computations, especially in probability and statistics, where they are used to calculate the number of combinations or permutations that may be made from a given collection of numbers or variables. For example, if you had 5 distinct objects and want to determine how many various combinations , you used the factorial of 5.

To learn more about factorials, visit:

https://brainly.com/question/1216161

#SPJ4

Answer:

x > 24 goes to the bottom

x < 24 goes to the 3rd slot

x ≤ 24 goes to the 1st slot

x ≥ 24 goes to the 2nd slot

Step-by-step explanation:

Hope this helps.

The coordinate of the vertices of △A'B'C' are A'(3,6), B'(9,-3), and C'(-12, 6). Since the scale factor is 3.

What is coordinate of a point?

The coordinates are a pair of numbers that, using the horizontal and vertical lines, precisely pinpoint a point's location on a cartesian plane. typically represented by (x, y), the point's x and y values on a graph.

The coordinate of △ABC are A(1,2), B(3,-1) and C(-4,2).

The scale factor is k = 3.

The x-coordinate of A is 1.

The y-coordinate of A is 2.

The x-coordinate of B is 3.

The y-coordinate of B is -1.

The x-coordinate of C is -4.

The y-coordinate of C is 2.

To find the vertices of △A'B'C', multiplying x-coordinate and y-coordinate by 3.

The x-coordinate of A' is 1 × 3 = 3.

The y-coordinate of A' is 2 × 3 = 6.

The x-coordinate of B' is 3 × 3= 9.

The y-coordinate of B' is -1 × 3 = -3.

The x-coordinate of C' is -4 × 3 = -12.

The y-coordinate of C' is 2 × 3 = 6.

To learn more about dilate, click on below link:

https://brainly.com/question/24276109

#SPJ1

The relation between a and r is 2r

According to the given information

a varies directly with r

a = 8

r = 4

a is directly proportional to r

a ∝ r

a = k r

where k is constant of proportionality

k =  [tex]\frac{a}{r}[/tex]

k = [tex]\frac{8}{4}[/tex]

k = 2

so,

a = k r

putting the value of k in the above equation

we get

a = 2r

The relation between a and r is 2r

To know more about Constant of proportionality

https://brainly.com/question/18707816

#SPJ1

Answer:

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

Given  number is 71830.

The last part:  830 is same on both lines.

We need to represent 71000 in different way, instead of 7 ten thousands and 1 thousands we have 6 ten thousands then we need:

It is 11 thousands.

Answer:

11,000 (or) 11 thousands

Step-by-step explanation:

Now we have to,

→ find the missing number.

→ Let the number be x.

Forming the equation,

→ 60,000 + x + 800 + 30 = 71,830

Then the value of x will be,

→ 60,000 + x + 800 + 30 = 71,830

→ x + 60,830 = 71,830

→ x = 71,830 - 60,830

→ [ x = 11,000 ]

Hence, the value of x is 11,000.

In the following proportions:-

A. [tex]\frac{2}{8} =\frac{3}{12}[/tex]

C. [tex]\\\\\ \frac{25}{10} =\frac{5}{2}[/tex]

D. [tex]\\\\ \frac{3}{4} =\frac{15}{20}[/tex] Are Equal

What are proportion?

A part, share, or quantity that is compared to a total is referred to as a proportion. According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

When two ratios are equal, they are said to be in proportion.For instance, the time it takes a train to go 50 kilometers per hour is equal to the time it needs to travel 250 kilometres in 5 hours. e.g., 250km/5 hours at 50 km/h.

[tex]A) \\\\\frac{2}{8} =\frac{3}{12} =\frac{1}{4}\\\\(B) \\\\\frac{3}{4} \ !=\frac{8}{10}= \frac{4}{5}\\\\\ (C)\\\\\frac{25}{10} =\frac{5}{2}\\\\(D)\\\\ \frac{3}{4} =\frac{15}{20}[/tex]

Learn more about Proportions from the link below

https://brainly.com/question/7096655

#SPJ4

If f(x) = 4x - 5 and g(x) = 6 - 3x then f(x) + g(x) = x + 1.

When the output of one function is given to the input of another function they are called composite functions. In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

We know f(x) + g(x) = (f + g)(x).

Given, f(x) = 4x - 5 and g(x) = 6 - 3x.

∴ f(x) + g(x) = (4x - 5) + (6 - 3x).

f(x) + g(x) = 4x - 3x - 5 + 6.

f(x) + g(x) = x + 1.

learn more about composite functions here :

https://brainly.com/question/20379727

#SPJ1

The number of liters in the tank after 109 seconds is 60.5 liters.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

2.5 liters = 1 minute

2.5 liters = 60 seconds

Multiply 109/60 on both sides.

109/60 x 2.5 liters = 109 seconds

4.5 liters = 109 seconds

This means,

4.5 liters is drained after 109 seconds

Now,

The liters of water in the tank.

= 65 - 4.5

= 60.5 liters

Thus,

There are 60.5 liters in the tank.

Learn more about unit rates here:

https://brainly.com/question/11258929

#SPJ1

The mistake happens when computing 70-64. The result is not 4, but should be 6 instead.

The correct long division is shown below.

This means [tex]\frac{15}{8} = 1.875[/tex] in which you can use your calculator to verify this.

Answer:

√65

Step-by-step explanation:

Compute the Euclidean distance between the following points:

p_1 = (-2, 3) and p_2 = (5, -1)

The Euclidean distance between points (x_1, y_1) and (x_2, y_2) is:

sqrt((x_1 - x_2)^2 + (y_1 - y_2)^2)

Substitute (x_1, y_1) = (-2, 3) and (x_2, y_2) = (5, -1):

= sqrt((-2 - 5)^2 + (--1 + 3)^2)

(-1)^2 = 1:

= sqrt((-2 - 5)^2 + (1 + 3)^2)

-2 - 5 = -(2 + 5):

= sqrt((-(2 + 5))^2 + (3 + 1)^2)

2 + 5 = 7:

= sqrt((-7)^2 + (3 + 1)^2)

Multiply each exponent in -7 by 2:

= sqrt((-1)^2×7^2 + (3 + 1)^2)

7^2 = 49:

= sqrt((-1)^2×49 + (3 + 1)^2)

(-1)^2 = 1:

= sqrt(49 + (3 + 1)^2)

3 + 1 = 4:

= sqrt(49 + 4^2)

4^2 = 16:

= sqrt(49 + 16)

| 1 |

| 4 | 9

+ | 1 | 6

| 6 | 5:

Answer: √65

Answer:

The vendor sold 212 sodas and 34 hot dogs.

Step-by-step explanation:

Subtract 34 from 246 for the number of sodas sold.

Answer:

m= -3

Step-by-step explanation:

5(2m+1)-3m=-16

5(2m)+5(1)-3m= -16

10m+5-3m= -16

7m+5= -16

     -5.   -5

7m= -21

/7.    /7

m= -3

Hopes this helps please mark brainliest

And :-3

process:

5(2m + 1) - 3m = - 16

10m+5-3m=-16

7m=-16-5

m=-21/7

m=-3

Answer:  [tex]y = \frac{-3}{2} x + \frac{5}{2}[/tex]

Given: [tex]3x + 2y = 5[/tex]

We are needed to find the slope-intercept form.

We know that the slope-intercept form of an equation is given by

[tex]y = mc + c[/tex]

[tex]3x + 2y = 5[/tex]

[tex]2y = 5 -3x[/tex]

[tex]2y = -3x + 5[/tex]

[tex]y = \frac{-3}{2} x + \frac{5}{2}[/tex]

Thus, the answer is [tex]y = \frac{-3} {2} x + \frac{5}{2}[/tex]