10. If you invest $2000 at 6% compounded monthly, how long will it take the account to double in
value?

First, you have to locate the point (1,3)

Next, from that point, you have to locate the next one. To do that, you need the slope, which in this case is 3. So, from (1,3) you have to move 1 unit to the right and 3 units up, reaching the point (2, 6). Finally, you draw the line that passes through these two points

Answer:

[tex] \sf x=-1.25 [/tex]

[tex]\sf--------------------------------------------------------------------- [/tex]

Step-by-step explanation:

4x = -5

Divide both sides by 4 to single out the variable

4x/4 = -5/4

x = -1.25

6x - 9y - 7x + -6y

To simplify the expression add the like terms

The like terms are the terms which have the same variable and same degree

6x, -7x are like terms

-9y, -6y are like terms

So let us add them

(6x + -7x) + (-9y + -6y)

6 + -7 = -1

6x + -7x = -x

-9 + - 6 = -15

-9y + -6y = -15y

(6x + -7x) + (-9y + -6y) = -x + -15y

Remember (+)

The value of

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

g(n) = n² − 4, h(n) = n − 5

g(n).h(n)

= (n² − 4).(n-5)

= n³ - 5n² - 4n + 20

and, g(x) = 4x + 4, f(x) = x³ − 1

(gof)(x)

=g(f(x))

=g(x³-1)

= 4(x³-1) + 4

= 4x³ - 4 + 4

= 4x³

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Okay, here we heve this:

We need to combine like terms in the following equation:

The amount Rebecca has put into fixed savings each month to cover her annual expenses for life insurance, auto insurance and real estate taxes is $ 194.

Given that:-

Amount invested in life insurance = $ 255

Number of payments in life insurance = 4

Amount invested in real estate taxes = $ 455.35

Number of payments in real estate taxes  = 2

Amount invested in auto insurance = $ 66.21

Number of payments in auto insurance = 6

We have to find the amount Rebecca has put into fixed savings each month to cover her annual expenses for life insurance, auto insurance and real estate taxes.

Hence,

Total amount put by Rebecca in a year = 255*4 + 455.35*2 + 66.21*6 = 1020 + 910.70 + 397.26 = $ 2,327.96

Amount put by Rebecca in a month = 2327.96/12 =  $ 193.997 ≈ $ 194

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The given expression is

We just have to multiply.

Here, we want to complete the table

To do this, we consider points on the plot

From what we have;

We are told that a graph of an exponential function does not cross the x-axis and thus, y cannot be zero

When x =0, y = 1

When x = 1, y = 2

when x = 2, y = 4

The y-intercept is the value of y when x = 0; it is the point at which the graph crosses the y-axis

What we have here is that wehn x = 0, y = 1

Hence, 1 is the y-intercept

Now, let us take a look at the end behavior

We can obtain this from the graph;

As x moves towards infinity, the y value moves towards infinity too as evident from the upward curve of the graph

As x moves toward negative infinity, y moves closer to zero

tan (Q) = opposite/ adjacent

tan (55º) = PR/ 4.9

________________________

1.43 = PR/ 4.9

PR= 1.4* 4.9 = 6.9

Answer

6.9

______________________________________

Can you see the updates?

Do you have any questions regarding the solution?

____________________

PR= tan (55)* 4.9 = 6.997925 ≅ 7

_________________________________

The amount of money that Johnny makes now = $282,508.38

Annual payment is the type of payment that is done every 12 month and by the end of the year.

The initial annual payment received by Johnny= $111,180

The new career pays the rate of 154.1% more that is;

( 154.2% of $111,180 ) + $111,180 Which is;

= (154.1/100 × 111,180) + $111,180

= (17,132,838/100) + $111,180

= $ 171,328.38 + $111,180

= $282,508.38.

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Explanation

where x is the number of days since the start of the job

and f(x) is the rate of change

Step 1

a)find the total expenditure if the job takes 12 days

so, as x represents the number of days, just replace and calculate

let x= 12

so

a) 51.1

Step 2

now, let's find the total spent on the job from the 10 to 20th day

a) find the x value ( number of days since the job started)

x= 20 days-10dys= 10

so

x= 10

Since the equation is y=3/8x and x is equal to 44/3, we have

A 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is 0.503 < p < 0.397.

In the given question,

We have to construct a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone.

A 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is

..............< p <...............

We have to construct the 90% confidence interval.

From the given question we know that among 240 cell phone owners aged 18 - 24 surveyed, 108 said their phone was an android phone.

So the total number of cell phone owners aged 18 - 24 is 240.

So n=240

From them 108 have an android phone.

So x=108

Estimation of sample proportion([tex]\hat p[/tex]) = x/n

Now putting the value

Estimation of sample proportion([tex]\hat p[/tex]) = 108/240

Estimation of sample proportion([tex]\hat p[/tex]) = 0.45

Now the construct a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone

C.I. = [tex](\hat p \pm z_{\alpha /2}\sqrt\frac{\hat p(1-\hat p)}{n}})[/tex]

As we know that

[tex]\hat p=0.45[/tex]

Now finding the value of [tex]z_{\alpha /2}[/tex]

We have to find the 90% confidence interval. We can write 90% as 90/100 = 0.90

So [tex]\alpha[/tex] = 1-0.90

So [tex]z_{\alpha /2}=z_{0.10 /2}[/tex]

[tex]z_{\alpha /2}=z_{0.05}[/tex]

From the standard z table

[tex]z_{0.05}[/tex] = 1.645

Now putting the value in the

C.I. =  [tex](\hat p \pm z_{\alpha /2}\sqrt\frac{\hat p(1-\hat p)}{n}})[/tex]

C.I. = [tex](0.45 \pm 1.645{\sqrt\frac{0.45(1-0.45)}{240}})[/tex]

Simplifying

C.I. = [tex](0.45 \pm 1.645{\sqrt\frac{0.45\times0.55}{240}})[/tex]

C.I. = [tex](0.45 \pm 1.645{\sqrt\frac{0.2475}{240}})[/tex]

C.I. = [tex](0.45 \pm 1.645\sqrt{0.001031})[/tex]

C.I. = [tex](0.45 \pm 1.645\times0.0321)[/tex]

C.I. = [tex](0.45 \pm 0.053)[/tex]

We can write it as

C.I. = {(0.45+0.053),(0.45-0.053)}

C.I. = (0.503,0.397)

Hence, a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is

0.503 < p < 0.397.

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He needs 2/3 cup of sugar . But he can only find 1/2 cup measures.

The average of a set is computed as follows:

In this case,

The polynomial function of least degree with only real coefficients will be;  y = x³ - 8 · x² + 22 · x - 20.

Algebraic expressions called polynomials include constants and indeterminates. Polynomials can be thought of as a type of mathematics.

The statement indicates that the polynomial has  real coefficients having zeros 3 and 1 - 32 and a lead coefficient of 1.

By algebra of quadratic equations, equations with real coefficients with complex roots are α + i β and α - i β. Then we get;

y = 1 · (x - 3) · (x - 3 - i) · (x - 3 + i)

y = (x - 3) · [x² - 3 · x - i · x - 3 · x + i · x + (3 + i) · (3 - i)]

y = (x - 3) · (x² - 6 · x + 9 - i²)

y = (x - 3) · (x² - 6 · x + 10)

y = x³ - 6 · x² + 10 · x - 2 · x² + 12 · x - 20

y = x³ - 8 · x² + 22 · x - 20

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Answer:

[tex]p(x)=x^3-5x^2+16x-30[/tex]

Step-by-step explanation:

Given information:

For any complex number  [tex]z = a+bi[/tex] , the complex conjugate of the number is defined as  [tex]z^*=a-bi[/tex].  

If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.

Therefore, if p(x) is a polynomial with real coefficients, and (1 - 3i) is a root of p(x)=0, then its complex conjugate (1 + 3i) is also a root of p(x)=0.

Therefore, the polynomial in factored form is:

[tex]p(x)=a(x-3)(x-(1-3i))(x-(1+3i))[/tex]

As the leading coefficient is 1, then a = 1:

[tex]p(x)=(x-3)(x-(1-3i))(x-(1+3i))[/tex]

Expand the polynomial:

[tex]\implies p(x)=(x-3)(x-(1-3i))(x-(1+3i))[/tex]

[tex]\implies p(x)=(x-3)(x-1+3i)(x-1-3i)[/tex]

[tex]\implies p(x)=(x-3)(x^2-x-3xi-x+1+3i+3ix-3i-9i^2)[/tex]

[tex]\implies p(x)=(x-3)(x^2-x-x-3xi+3ix+1+3i-3i-9i^2)[/tex]

[tex]\implies p(x)=(x-3)(x^2-2x+1-9(-1))[/tex]

[tex]\implies p(x)=(x-3)(x^2-2x+10)[/tex]

[tex]\implies p(x)=x^3-2x^2+10x-3x^2+6x-30[/tex]

[tex]\implies p(x)=x^3-2x^2-3x^2+10x+6x-30[/tex]

[tex]\implies p(x)=x^3-5x^2+16x-30[/tex]

The boy goes to school by bus for 1 3/4km, then he walks 1/3 km.

To determine the total distance he traveled you have to add both distances:

To solve this sum, add the fractions first and then add the result to the whole number:

- Add both fractions:

To add both fractions you have to express them using the same denominator first. A common multiple between the denominators "4" and "3" is "12". Multiply the first fraction by 3 and the second by 4 to express them as their equivalent fractions with denominator 12. Then proceed to add them:

The result is 13/12, as you can see the numerator is greater than the denominator, which indicates that this is an improper fraction, i.e. its value is greater than 1. You can write this fraction as a mixed number as follows:

- Solve the division:

The mixed number will have the whole number "1".

- To express the decimal value as a fraction, multiply it by 12

The result is the numerator of the fraction, and the denominator will be 12, so:

And the resulting mixed number is:

Finally, add the remaining whole number from the first sum to determine the distance between his house and the school:

The distance he traveled from home to school is 2 1/12 km.

The pair of complex numbers whose sum is -4 and whose product is 53 is illustrated as -b² - 4b - 53 = 0.

Let the numbers be represented as a and b.

Therefore a + b = -4 .....i

a × b = 53 ........... ii

From equation I, a = -4 - b

Put this into equation ii

ab = 53

(-4 - b)b = 53

-b² - 4b = 53

Equate to 0

-b² - 4b - 53 = 0

The value can be found using the Almighty formula

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If we use the variable t to represent the number of hours skating, the fixed price is $5 and the variable price is $3 per hour, that is, we have a variable cost of 3t.

So the final cost (variable C) is the sum of the fixed and variable costs:

The value of x = 40°

To solve for x, we will use an illustration:

When two lines intersect, the angles opposite each other are vertical angles. Vertical angles are equal.

The angles marked in magenta are equal.

The angle by the right in magenta colour will also be 52°.

The sum of angles in a triangle = 180°

x° + 52° + 88° = 180°

x + 140 = 180

subtract 140 from both sides:

x + 140 - 140 = 180 - 140

x = 40°

You have the following function:

the x coordinate of the vertex is given by:

in this case, a = 2 and b = -4. Replace these values into the previous expression and simplify:

next, replace the previous values of x into the function g(x):

then, the vertex is (1,-18)

In order to graph, calculate another point for any value of x, for instance, for x = 0:

g(0) = 2(0)^2 - 4(0) - 16

Explanation:

To know how much ice pop mixture can each mold hold, we need to calculate the volume of the mold.

The volume of a cone is equal to

Where r is the radius and h is the height of the cone. Replacing r = 2 cm and h = 15 cm, we get:

Therefore, the answer is

A. 20

The scale factor from the drawing to the room is 1 to 30. Then, multiply the dimensions of the drawing by 30 to obtain the real dimensions of the room. Then, use the real values to find the area of the room.

Since the length is labeled 2 inches, the real length of the room is:

Since the width is labeled 4.5 inches, the real with of the room is:

1 foot is equal to 12 inches. Then, divide the dimensions by 12 to find the measurements in feet:

Multiply the width and the length to find the area of the room:

Therefore, to the nearest whole number, the area of the game room is 56ft^2.

In the given right angle triangle BCA : BC = 5, CA = 3 and BA = root 34

From the trignometric ratio of right angle triangle :

The tangent of angle is the ratio of the Adjacent side to the opposite side

In the given triangle, the side opposite to angle A = BC and adjacent side CB

Substitute the value :

The value of tanA = 5/3 or 1.66

We want to know how many brownmies did Fred and his family eat together.

We will call to the total of the brownies by 1. On this case, after Fred ate 1/3 of the brownies, he will have:

This means that he has left 2/3 of the brownies. After his family ate 1/6 of the brownies:

This means they will have left 1/2 of the tray of brownies, and that they ate half of it.

Because we have the same denominator we can do the subtraction

Paul did well the representation of the fractions in the diagram, but the operation that he made as we can see is wrong because the result is 9/10

The arc length can be found through the formula:

then, we can say that r is equal to 4 and the angle is 30°

Answer:

The arc length is approximately equal to 2.09

Given:

Calculate the values for f(x),

The graph of given function is,

shoe box = 1 cubic foot = 1 * 1 * 1

1 Layer: 6 shoe boxes -> Layer lenght = 6 feet, layer depht = 1 foot

Box height = 4 feet

Box volume = 6*4*1 = 24 feet

We know,

1 liter=1000 milliter.

So, millilters in 1/5 liters​ is,

Therefore, there are 200 milliters in 1/5 liters.