Oscar and Carla deposit $1,000.00 into a savings account which earns 10% interest compounded annually. They want to use the money in the account to go on a trip in 2 years. How much will they be able to spend?

Answer:

41.54

Step-by-step explanation:

Answer:

ux = 78

s= 0.8485

P ( z>0.33)  = 0.3707

Step-by-step explanation:

According to central limit theorem the mean of the population is equal to the mean of the sample and the standard deviation is found by dividing the standard deviation of the population with the square root of the sample size

Thus

ux = u= 78

σ= 6

s= σ/√n= 6/√50= 6/7.07106= 0.8485

We find the z score

Z= X- u / σ

z= 80-78/6

z= 2/6= 1/3=0.333

P ( z>0.33) = 1 - P(z=0.33)

                  = 1- 0.6293

                     = 0.3707

We see in the figure that the blue area represents the area greater than z= 0.333 or area greater than 1/3.

The probability of z= 0.33 from the table is 0.6293

We find the probability of area greater than 0.33 by subtracting from 1 .

Answer:

$26.98

Step-by-step explanation:

1. You have the following information given in the problem above:

- Lou filled the tank with gas that cost ​$3.80 per gallon.

-   Lou​'s car had 5.9 gallons in the 13​-gallon tank.

2. Therefore, if he filled the tank, you can calculate the total amount of money Lou spent, by subtracting 13 gallons and 5.9 gallons and multiplying the result by ​$3.80.

Answer:

26.98

Step-by-step explanation: 5.3 * 3.8 = 26.98

Answer:

81.82%

Step-by-step explanation:

cuz meth

Answer:

81.82

Step-by Step

In order to round to the nearest thousand, you simply have to move the decimal point to the RIGHT. Hope it helps!

                     ~Happy holidays

Answer:

6) b(3a^4-5c³)

7) 3x³yz(2x+5y)

8) 4a²b²c³(2bc-3a)

9) 4xy(2y+7z-1)

10) 2mn(5n²+2m-3n)

Step-by-step explanation:

6) Factor out the b and you get b(3a^4-5c³)

7) Factor out the 3x³yz and you get 3x³yz(2x+5y)

8) Factor out the 4a²b³c³ and you get 4a²b²c³(2bc-3a)

9) Factor out the 4xy and you get 4xy(2y+7z-1)

10) Factor out the 2mn and you get 2mn(5n²+2m-3n)

Answer: True

Step-by-step explanation:

The function is even and negative. A negative function opens down. With this information, the statement is true: the function opens down.

Answer:

True

Step-by-step explanation:

Given a parabola in vertex form

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

• If a > 0 then the graph opens up

• If a < 0 then the graph opens down

Given

f(x) = - (x + 3)² + 2 ← in vertex form

with a = - 1 < 0 then graph opens down is True

Answer:

Options (2) and (3)

Step-by-step explanation:

Let, [tex]\sqrt{-8+8i\sqrt{3}}=(a+bi)[/tex]

[tex](\sqrt{-8+8i\sqrt{3}})^2=(a+bi)^2[/tex]

-8 + 8i√3 = a² + b²i² + 2abi

-8 + 8i√3 = a² - b² + 2abi

By comparing both the sides of the equation,

a² - b² = -8 -------(1)

2ab = 8√3

ab = 4√3 ----------(2)

a = [tex]\frac{4\sqrt{3}}{b}[/tex]

By substituting the value of a in equation (1),

[tex](\frac{4\sqrt{3}}{b})^2-b^2=-8[/tex]

[tex]\frac{48}{b^2}-b^2=-8[/tex]

48 - b⁴ = -8b²

b⁴ - 8b² - 48 = 0

b⁴ - 12b² + 4b² - 48 = 0

b²(b² - 12) + 4(b² - 12) = 0

(b² + 4)(b² - 12) = 0

b² + 4 = 0 ⇒ b = ±√-4

                     b = ± 2i

b² - 12 = 0 ⇒ b = ±2√3

Since, a = [tex]\frac{4\sqrt{3}}{b}[/tex]

For b = ±2i,

a = [tex]\frac{4\sqrt{3}}{\pm2i}[/tex]

  = [tex]\pm\frac{2i\sqrt{3}}{(-1)}[/tex]

  = [tex]\mp 2i\sqrt{3}[/tex]

But a is real therefore, a ≠ ±2i√3.

For b = ±2√3

a = [tex]\frac{4\sqrt{3}}{\pm 2\sqrt{3}}[/tex]

a = ±2

Therefore, (a + bi) = (2 + 2i√3) and (-2 - 2i√3)

Options (2) and (3) are the correct options.

Answer: b and c

Step-by-step explanation:

Answer:

one part = 20.5

the other part = 61.5

Step-by-step explanation:

let one part = x

let another part = y

(1) create two equations

i) 82 is separated into 2 parts, x and y. it means x plus y equals to 82

x+y = 82

ii) one part is bigger than the other. if x is the bigger part, it is 3 times bigger than y

x = 3y

(2) use substitution method to find the value of x and y

x+y = 82 -------- (1)

x = 3y ---------- (2)

substitute (2) into (1)

x+y = 82

3y+y = 82

4y = 82

y = 82/4

y = 20.5

substitute y = 20.5 into (2)

x = 3y

x = 3(20.5)

x = 61.5

Answer:

A Rational Number can be made by dividing two integers

The cordinate plane can be used to plot points and graph lines

Answer:

1) x=1

2)x=4

Step-by-step explanation:

Solved the equation and checked using calculator

Answer:

she has 15 boxes of pencils

Step-by-step explanation:

if we have 90 total pencils that need to be split into groups of 6, the way to find how many groups there are is by dividing 90/6, which gives you 15 groups or, in this case, 15 boxes. and you can check your work by multiply the 15 boxes by the 6 pencils in each box, which gives you 90 pencils total, so you're all good!

Answer: x = 15/8

Explanation: I used a calculator on a website.

Answer:

15/8

Step-by-step explanation:

Hope this helps: )

Answer:

The percent error is 99%

Step-by-step explanation

Estimated weight of cat = 10 pounds

Actual weight of cat = 1375 pounds

We need to find the percent of error.

The formula used is: [tex]Percent\:Error=\frac{|Estimated\:value-Actual\:Value|}{Actual\:Value}\times 100[/tex]

Putting values and finding percent of error.

[tex]Percent\:Error=\frac{|Estimated\:value-Actual\:Value|}{Actual\:Value}\times 100\\Percent\:Error=\frac{|10-1375|}{1375}\times 100 \\Percent\:Error=\frac{|-1365|}{1375}\times 100 \\Percent\:Error=\frac{1365}{1375}\times 100\\Percent\:Error=0.99\times 100 \\Percet\:Error=99\%[/tex]

So, the percent error is 99%

Step-by-step explanation:

y = -5x² + 2x - 3 and y = -3x - 3.

=> -5x² + 2x - 3 = -3x - 3

=> 5x² - 5x = 0

=> 5x(x - 1) = 0

=> x = 0 or x = 1.

When x = 0, y = -3(0) - 3 = -3.

When x = 1, y = -3(1) - 3 = -6.

The solutions are (0,-3) and (1,-6).

Answer:

11 buses

Step-by-step explanation:

Divide 42 by 4 to get 10 and a remainder of 2. The 2 students not on the bus need another bus so you need 10+1=11 buses

Answer:

The answer is below

Step-by-step explanation:

A) i)

For Anna initially, she has $0 from making 0 envelopes. After making 400 envelopes she has $20. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (400, 20). Using the equation of a line:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{20-0}{400-0}(x-0)\\\\y=\frac{1}{20} x[/tex]

The table is:

x:   200     400       600     800     1000

y:    10        20          30        40       50

ii)

For Jason initially, he has $0 from making 0 envelopes. For every 250 envelopes he has $10. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (250, 10). Using the equation of a line:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{10-0}{250-0}(x-0)\\\\y=\frac{1}{25} x[/tex]

The table is:

x:   200     400       600     800     1000

y:    8         16           24        32       40

The graph is plotted using geogebra online graphing

b) From the table above we can see that Anna makes more stuffing than Jason.

c) Anna has a savings of $100. Hence this can be represented by the points (0, 100) and (250, 10). Using the equation of a line:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-100=\frac{20-0}{400-100}(x-0)\\\\y=\frac{1}{15} x+100[/tex]

We can see from the graph that there is a y intercept at 100. That is the earnings starts from 100.

The equation of a line is given as y = mx + b, where m is the slope and b is the y intercept (initial value)

For the first graph, the slope is 1/20 and the initial value is 0 while for the second graph the slope is 1/15 and the initial value is 100

D) The line pass through (10, 10) and (100, 40), hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-10=\frac{40-10}{100-10}(x-10)\\\\y-10=\frac{1}{3} (x-10)\\\\y=\frac{1}{3}x+\frac{20}{3}[/tex]

Answer:

Step-by-step explanation:

$220

5 members

220/5

=44

Answer:

A. x = -40

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

-3.5(x + 12) = -2x + 18

Step 2: Solve for x

Answer:

y = -x - 4

General Formulas and Concepts:

Pre-Algebra

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

x + y = -4

Step 2: Rewrite

Find slope-intercept form

Answer:

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

2

Answer:

8 * 10^6

Step-by-step explanation:

The question is asking us to represent the value 8,406,000 in standard. The standard form of an expression is expressed as;

A * 10^n

A is any integer between 1 and 10

n is any integer.

Given the value 8,406,000

8,406,000.

We are going to move the decimal point at the end to first digit value. This point will be shifted 6 times to have;

8,406,000 = 8.6 * 10^6 (Note that n is positive since the value given is greater than 1)

Since we are to express as a single digit times a power of ten, the required answer will be 8 * 10^6

Step-by-step explanation:

For this set there are 8 subsets and 7 proper subsets

the subsets are:

{}

{2}

{4}

{6}

{2,4}

{2,6}

{4,6}

{2,4,6}

Answer is:

29/2 = 14.5

Answer:

Step-by-step explanation:

triangles that are the same are congruent

A) no

B) no

C) yes

D) yes

E) no

Answer:

Probability of choosing two different types of biscuits is  [tex]\frac{31}{90}[/tex].

Step-by-step explanation:

We have 10 biscuits in a tin.

There are 5 digestive, 3 chocolate, 2 ginger.

Steve takes two biscuits at random.

There are three combinations of biscuits.

P(d, c) + P(c,g)+P(d,g)

Let's find probability of each.

P(d,c)= P(d)* p(c)

         = [tex]\frac{5}{10}*\frac{3}{9}[/tex]

Let's simplify it, we get [tex]\frac{1}{6}[/tex]

Like so, for P(c,g)

P(c,g)= P(c) * P(g)

       =[tex]\frac{3}{10}*\frac{2}{9}[/tex]

Let's multiply and simplify, we get [tex]\frac{1}{15}[/tex].

Now, for p(d,g)

P(d, g)= P(d)* p(g)

        =[tex]\frac{5}{10} *\frac{2}{9}[/tex]

Let's simplify and multiply, we get [tex]\frac{1}{9}[/tex].

Now, add them together

[tex]\frac{1}{6} +\frac{1}{15} +\frac{1}{9}[/tex]

Now, find LCD to make the denominators as same and then add them together.

LCD is 90

So, find equivalent fraction of each which has denominator as 90.

[tex]\frac{15}{90}+\frac{6}{90} +\frac{10}{90}[/tex] = [tex]\frac{31}{90}[/tex]