Please find the Sine, Cosine, and Tangent

Answer:

The maximum amount of money that should be spent on housing each month is $522.

The maximum amount of money that should be spent on transportation each month is $290.

The maximum amount of money that should be spent on food each month is $246.50.

The maximum amount of money that should be spent on entertainment each month is $116.

Answer:

$522

Step-by-step explanation:

The maximum amount of money that should be spent on housing each month is $522.

The maximum amount of money that should be spent on transportation each month is $290.

The maximum amount of money that should be spent on food each month is $246.50.

The maximum amount of money that should be spent on entertainment each month is $116.

Answer:

[tex]\sqrt{274}[/tex]

Step-by-step explanation:

Given [tex]z_1=-8+3i,\ z_2=7-4i.[/tex]

1. Find the difference [tex]z_1-z_2:[/tex]

[tex]z=z_1-z_2=-8+3i-(7-4i)=-8+3i-7+4i=(-8-7)+(3i+4i)=-15+7i.[/tex]

This complex number has real part [tex]Rez=-15[/tex] and imaginary part [tex]Imz=7.[/tex]

2. The modulus of complex number z is

[tex]|z|=\sqrt{Re^2z+Im^2z}=\sqrt{(-15)^2+7^2}=\sqrt{225+49}=\sqrt{274}.[/tex]

The distance between [tex]z_1\ \text{and}\ z_2[/tex] is:

                        16.5529 units

We know that the difference between two complex numbers:

[tex]z_1=a_1+ib_1\ \text{and}\ z_2=a_2+ib_2[/tex] is given by:

[tex]|z_1-z_2|=|(a_1+ib_1)-(a_2+ib_2)|\\\\i.e.\\\\|z_1-z_2|=|(a_1-a_2)+i(b_1-b_2)|\\\\|z_1-z_2|=\sqrt{(a_1-a_2)^2+(b_1-b_2)^2}[/tex]

Here we have:

[tex]z_1=-8+3i\ \text{and}\ z_2=7-4i[/tex]

i.e.

[tex]a_1=-8\ ,\ b_1=3,\ a_2=7\ \text{and}\ b_2=-4[/tex]

i.e. we have:

[tex]|z_1-z_2|=\sqrt{(-8-7)^2+(3-(-4))^2}\\\\|z_1-z_2|=\sqrt{15^2+7^2}\\\\|z_1-z_2|=\sqrt{225+49}\\\\|z_1-z_2|=\sqrt{274}\\\\|z_1-z_2|=16.5529[/tex]

Answer:

18.1 million

Step-by-step explanation:

12.1 - 4.9 = 7.2 million increase in 6 years

7.2 / 6 = increase of 1.2 million a year

1.2 x 5 years = 6 million

12.1 million + 6 million = sales of 18.1 million in 2001

Based on linear growth from 1990 to 1996, ABC Electronics can expect total sales of approximately $18.1 million in 2001.

To predict sales for ABC Electronics in 2001 based on a linear growth pattern from 1990 to 1996, we first calculate the annual increase in sales over that period. In 1990, sales were $4.9 million and in 1996, sales were $12.1 million. This is an increase of $12.1 million - $4.9 million = $7.2 million over 6 years, which gives us an annual increase of $7.2 million / 6 years = $1.2 million per year.

Since we're assuming linear growth, we can extend this annual increase to predict sales for subsequent years. From 1996 to 2001 is 5 years, so we calculate the expected sales for 2001 by adding 5 times the annual increase to the 1996 sales figures: $12.1 million + (5 × $1.2 million) = $12.1 million + $6.0 million = $18.1 million.

Therefore, we can expect ABC Electronics to have total sales of approximately $18.1 million in the year 2001 if the linear growth trend continues.

Answer:

9W + 72

Step-by-step explanation:

using the distributive property, you would multiply both the w and the 8 by 9 to obtain 9*w and 9*8. 9*w + 9*8 = 9w + 72.

This works because if you have 9 of (w+8), you have 9 w's and 9 8's. Adding these up is simply multiplying 9 by w (since there are 9 w's) and 9 by 8 (since there are 9 8's).

Answer:

I’m patty’s urge in 9W + 8

Step-by-step explanation:

I just got the question right on Edge!

Answer:

The second one that starts with 3

Step-by-step explanation:

To know if it's a function , check all the domains and make sure there are no repeating ones, if there is a repeating domain , it's not a function

Answer:

y-determinant = 2

Step-by-step explanation:

Given the following system of equation:

Let's represent it using a matrix:

[tex]\left[\begin{array}{ccc}1&2\\1&-3\end{array}\right] = \left[\begin{array}{ccc}5\\7\end{array}\right][/tex]

The y‐numerator determinant is formed by taking the constant terms from the system and placing them in the y‐coefficient positions and retaining the x‐coefficients. Then:

[tex]\left[\begin{array}{ccc}1&5\\1&7\end{array}\right] [/tex]

y-determinant = (1)(7) - (5)(1) = 2.

Therefore, the y-determinant = 2

Answer:

7(x + 2)

Step-by-step explanation:

7x + 14 =

7 can be factored out of each term.

= 7 * x + 7 * 2

= 7(x + 2)

Answer:

3/1

Step-by-step explanation:

think in this question we have to find the ratio .

Question:

There are 9 tennis balls in 3 cans. What is the RATIO of number of tennis balls to number of cans?

Solution:

Given:

Number of tennis ball= 9

Number of cans = 3

Ratio of number of tennis balls to number of cans= tennis ball : cans

= 9/3 = 3/1

Hence, Ratio of number of tennis balls to number of cans= tennis ball : cans= 3:1

==================================================================

Hope this will help you....

Answer:

2A/b =h

Step-by-step explanation:

A = 1/2bh

Multiply each side by 2

2*A = 2*1/2bh

2A = bh

Divide each side by b

2A/b = bh/b

2A/b =h

Answer:

The probability that Mario will randomly catch the right goldfish on the first 5 attempts = 0.069

Step-by-step explanation:

From geometric distribution.

If the probability of success on each trial = P,

then the probability that the Nth trial is the first success

                    Pr (X = N) = [tex](1 - P)^{N - 1}[/tex] P

Now,

        P = [tex]\frac{1}{70}[/tex]

        Maximum attempt = 5

Probability that Mario will randomly catch the right goldfish on the first 5 attempts

= [tex]\frac{1}{70}[/tex] + [tex](1 - \frac{1}{70} )^{1}[/tex] [tex]\frac{1}{70}[/tex] + [tex](1 - \frac{1}{70} )^{2}[/tex] [tex]\frac{1}{70}[/tex] + [tex](1 - \frac{1}{70} )^{3}[/tex] [tex]\frac{1}{70}[/tex] + [tex](1 - \frac{1}{70} )^{4}[/tex] [tex]\frac{1}{70}[/tex]

= [tex]\frac{1}{70}[/tex] + [tex]\frac{69}{70}[/tex] [tex]\frac{1}{70}[/tex] + [tex](\frac{69}{70} )^{2}[/tex] [tex]\frac{1}{70}[/tex] + [tex](\frac{69}{70} )^{3}[/tex] [tex]\frac{1}{70}[/tex] + [tex](\frac{69}{70} )^{4}[/tex] [tex]\frac{1}{70}[/tex]

= 0.069

Answer: 1. A) 0.14

2. C) 46%

3. D) 86%

4. B) 0.513

5. A) 0.003

6. C) 0.069

7. C) 0.25%

8. D) 0.03

9. C) 71%

10. A) 10%

Step-by-step explanation: 100% :)

Answer:

The total pennies in Russell's collection dated after 2000 is 800

Step-by-step explanation:

Given

Total Pennies: 1,200

Pennies before 1980: 25%

Pennies between 1980 and 2000: 35%

Required

Number of pennies in Russell’s collection are dated after 2000

Let P1 represent pennies dated before 1980

Let P2 represent pennies dated between 1980 and 2000

Let P3 represent pennies dated after 2000

To calculate the number of pennies dated after 2,000. you have to understand that his total collection of pennies is 100%

This means that

P1 + P2 + P3 = 100%

Where P1 = 25% and P2 = 35%.

So, we're solving for P3

By substituting, P1 = 25% and P2 = 35%, we have

25% + 35% + P3 = 100%

60% + P3 = 100%

Make P3 the subject of formula

P3 = 100% - 60%

P3 = 40%

The quantity of pennies dated after 2,000 is then calculated by P3 * Total.

i.e. 40% * 2000

= 0.4 * 2000

= 800

Hence, the total pennies in Russell's collection dated after 2000 is 800

Answer: p = 6

Step-by-step explanation:

HI !

 px + 3y - ( p-3)=0

a₁ = p , b₁ = 3 , c₁ = - (p-3)

=====================

12x + py - p=0

a₂ = 12  , b₂ = p , c₂ = -p

since , the equations have infinite solutions , 

a₁/a₂ = b₁/b₂ = c₁/c₂

p/12 = 3/p =  p-3/p

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

p/12 = 3/p

cross multiply ,

p² = 36

p = √36

 p = 6

for the value of p = 6 , the equations will have infinitely many solutions

Answer:

[tex]\dfrac{12}{x-7},[/tex]

[tex]x\neq 7,\ x\neq -3.[/tex]

Step-by-step explanation:

Consider the expression

[tex]\dfrac{12x+36}{x^2-4x-21}.[/tex]

1. The numerator can be factored as

[tex]12x+36=12(x+3).[/tex]

2. The denominator [tex]x^2-4x-21[/tex] has the discriminant

[tex]D=(-4)^2-4\cdot (-21)\cdot 1=16+84=100.[/tex]

Then

[tex]x_{1,2}=\dfrac{-(-4)\pm \sqrt{100}}{2\cdot 1}=\dfrac{4\pm 10}{2}=7,\ -3.[/tex]

Then

[tex]x^2-4x-21=(x-7)(x+3).[/tex]

Note that restrictions on the variable x are [tex]x\neq 7,\ x\neq -3.[/tex]

3. Simplify the fraction:

[tex]\dfrac{12x+36}{x^2-4x-21}=\dfrac{12(x+3)}{(x-7)(x+3)}=\dfrac{12}{x-7}.[/tex]

Final answer:

Jim can rent the car for a maximum of 4 whole days with his budget of $115, as the inequality 21d + 0.10(250) <= 115 reveals that he doesn't have enough funds to cover the fifth day.

Explanation:

To determine the maximum number of days Jim can rent a car, we can set up an inequality. The cost per day to rent the car is $21.00, and he will be charged $0.10 for every mile he drives. Jim will travel 250 miles in total. Jim has a budget of $115.00 to spend.

Let d represent the number of days Jim can rent the car for. The inequality would be:

21d + 0.10(250) ≤ 115

To solve for d, you would perform the following steps:

Solving the inequality:

21d ≤ 90

d ≤ 90 / 21

d ≤ 4.2857

Since Jim can only rent the car for a whole number of days, the maximum number of days he can rent the car is 4 days.

Therefore, Jim's belief that he can rent the car for a maximum of 5 whole days is incorrect because he does not have sufficient funds for the fifth day.

1. The answer is A.

Based on the line plot, we can see that Sandy drank 12 juice boxes on October 12th. Each X on the plot represents 2 juice boxes, and there are 6 of them, meaning she drank 12. October 2nd has 1 X, meaning she drank 2 that day.

2. The answer is A.

On a graph, the point (1, 3) would mean that 1 is on the x-axis, and 3 is on the y-axis. Therefore, point B is correct because it is 1 space to the right, and 3 spaces up from the origin.

3. The answer is C.

If the coordinate we're looking for is (4, 0) then on a graph you would move 4 spaces to the right, and 0 spaces up or down. Therefore, point B is the correct choice.

Answer: 81, 27, 9, 3, 1, 1/3

There are six terms listed. The first five are whole numbers and the sixth term is a fraction.

==============================================

Explanation:

The equation t1 = 81 means that the first term "t" is 81. The second term is t2 = 27 because we multiply 1/3 by 81, or divide 81 over 3, and we end up with 81/3 = 27 as the second term.

We know to multiply by 1/3 because of the equation tn = (1/3)*t_(n-1) where the "n-1" portion is smaller than 't'. We can write it like this[tex]t_n = \frac{1}{3}*t_{n-1}[/tex]

To get the next term, we multiply by 1/3 again: 27*(1/3) = 27/3 = 9 giving us the third term

And repeat until we have six terms

9*(1/3) = 9/3 = 3 is the fourth term

3*(1/3) = 3/3 = 1 is the fifth term

1*(1/3) = 1/3 is the sixth term

So that is how I got the first six terms to be 81, 27, 9, 3, 1, 1/3

The side measure of the largest-sized square tile will be 4 in.

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.

Given that, The top of a stepping stone  is 24 inches by 20 inches.

GCF of 24 and 20 = 4

Hence, The side measure of the largest-sized square tile will be 4 in.

For more references on GCF, click;

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Answer:

[tex]y = 140000(1.04)^{x}[/tex]; 262 000

Step-by-step explanation:

The general formula for an exponential function is

[tex]y = a(b)^{x}[/tex]

a = 140 000; b = 1.04; x = 16

[tex]y = 140000(1.04)^{x}[/tex]

y = 140 000(1.04)¹⁶

y = 140 000 × 1.873

y = 262 000

The graph below shows the population growth over time.

Final answer:

An exponential function to model the population growth is P(t) = P_0 * e^{rt}, where the initial population P_0 is 140,000, the rate of growth r is 0.04, and the time t is 16 years. The population after 16 years is calculated by P(16) = 140,000 * e^{0.64}.

Explanation:

To model the population growth, we can use the formula for exponential growth which is P(t) = P_0 e^{rt}, where:

P(t) is the future population after time t,

P_0 is the initial population size,

e is the base of natural logarithms (approximately equal to 2.71828),

r is the rate of growth (expressed as a decimal), and

t is the time in years.

In the given situation, the initial population P_0 is 140,000, the growth rate r is 4% per year which is 0.04 when expressed as a decimal, and the time period t is 16 years. Plugging these values into the formula:

P(16) = 140,000 * e^{0.04 * 16}

To calculate the future population after 16 years, solve the equation:

P(16) = 140,000 * e^{0.64}

Using a calculator to compute e^{0.64}, and then multiplying by 140,000, we obtain the future population.

Answer:

x =56.4 degrees

Step-by-step explanation:

For right triangles, we know that the sin x = opposite/ hypotenuse

sin x = 20/24

Taking the arcsin of each side

arcsin (sin x) = arcsin (20/24)

x = 56.44269024 degrees

To the nearest tenth

x =56.4 degrees

Answer:

i squared + 5

Step-by-step explanation:

Answer:

$16

Step-by-step explanation:

A dozen is equal to 12 eggs. In order to find the amount for 50 eggs, we need to find the unit rate. In this problem, we can assume that each of the eggs cost the same amount.  Therefore, we can divide 3.84 by 12 to get the amount of one egg.

3.84/12= 0.32

Now that we have found the unit rate, we simply have to multiply it by 50 to get the cost. To explain why we do this, I will set it up as a proportion.

3.84/1 = ?/50

In order to get the equivalent amount you must multiply by 50.  

0.32 x 50= 16

Therefore, the answer is $16

The cost of 50 eggs is $16.

Given that, a dozen eggs cost $3.84.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here, the cost of one egg = 3.84/12

= $0.32

Now, the cost of 50 eggs

= 50 × 0.32

= 16

Therefore, the cost of 50 eggs is $16.

To learn more about the unitary method visit:

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Answer:

40 cm

Step-by-step explanation:

Using the conversion

1 litre = 1000 cm³, then

40 litres = 40 × 1000 = 40000 cm³

The volume ( V) of a cuboid is

V = lbh ( divide both sides by bh )

l = [tex]\frac{V}{bh}[/tex] = [tex]\frac{40000}{50(20)}[/tex] = [tex]\frac{40000}{1000}[/tex] = 40 cm

Length of water tank is 40 cm

Given that;

Capacity of tank = 40 liters

Dimensions of tank = 50cm × 20cm

Find:

Length of water tank

Computation:

Capacity of tank = 40 liters

Capacity of tank = 40 × 1000

Capacity of tank = 40,000 cm³

Length of water tank = 40,000 / [50cm × 20cm]

Length of water tank = 40,000 / 1,000

Length of water tank = 40 cm

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Look at the picture.

[tex]A(3,\ 2)\to A'(2,\ 3)\\\\B(-4,\ 1)\to B(1,\ -4)\\\\C(-3,\ -2)\to C'(-2,\ -3)[/tex]

Answer:

You are going to line up the decimal points to each other and add a zero to the end of the shortest decimal.

3.99+39.9=43.89

Step-by-step explanation:

You are going to take the 3.99 and add that to the 39.9 like normal but you are first going to line up the decimals.

Answer:

The answer is $61.20

Step-by-step explanation:

First you multiply 72 by .15 (which is 15% converted to a decimal), which gives you 10.8. You then subtract 10.8 from 72.

Answer: Her total bill including tip is $51.75

Step-by-step explanation:

Hi, first, we have to multiply the cost of the meal by the tip percentage in decimal form (percentage divided by 100).

Mathematically speaking:

45 x (15/100) = 45 x 0.15 = 6.75 tip amount

Finally, add the amount of the tip to the meal's cost.

45 +6.75 = $51.75

Her total bill including tip is $51.75

Feel free to ask for more if needed or if you did not understand something.

Answer:

840 kg of bamboo in 6 weeks

Step-by-step explanation:

if a panda eats 20 kg of bamboo per day he eats 140 kg of bamboo every week. multiply the amount he eats per week (140) by the amount of weeks (6) and you get 840 kg of bamboo

Answer:

1,848

Step-by-step explanation:

The panda eats 20kg of bamboo per day, and 1 L = 2.2 Ib, so multiplying 20 x 2.2 = 44, and there is 42 days in 6 weeks, so you multiply 44 x 22 = 1,848. I hope this is the correct answer, you're welcome!

Answer: u = -4w + 9

Step-by-step explanation:

u - 5 = -4(w - 1)

u - 5 = -4w + 4

  +5           +5  

u         = -4w + 9

The proper formula to solve the equation u - 5 = -4(w - 1) for w is w = (u + 9) / 4, after rearranging and simplifying the terms of the equation.

The question involves solving a linear equation with variables u and w. Initially, we have the equation u - 5 = -4(w - 1). To solve for w, we need to isolate w on one side of the equation. A statement in the information provided seems to mistakenly give the result of w, which probably arises from a typo or error, stating w = -40 - 5. However, this is incorrect given the initial equation.

Let's start by expanding the right side of the initial equation:

And then rearranging to solve for w:

From this process, we see that the correct formula to isolate and solve for w is w = (u + 9) / 4.

Answer:

X = 73

Step-by-step explanation:

X - 3 = 53 + 17

Add 53 and 17

It gives you 70

Add 3 to boths sides

you get 73 on right side

Cancels out the negative 3 on left side and gives you 73 for final answer

X = 73