Isabella uses one-foot cubical blocks to build a rectangular fort that is 12 feet long, 10 feet wide, and 5 feet high. The floor and the four walls are all one foot thick. How many blocks does the fort contain?

Answer:

In the year 2019 the number of new cars purchased will reach 15,000.

Step-by-step explanation:

t = 0 corresponds to the number of new cars purchased in 1998. If that is so, we can determine t ( time ) by making our quadratic equation here equal to 15,000 - considering that we want the year the number of cars reaches this value. t here is only the number of years to reach 15,000 cars, so we would have to add that value to 1998, to see the year that the cars will reach 15,000.

The " set up " should look like the following quadratic equation -

20t² + 135t + 3050 = 15,000 - Isolate 0 on one side,

20t² + 135t - 11950 = 0 - From here on let us solve using the quadratic equation formula,

[tex]t=\frac{-135+\sqrt{135^2-4\cdot \:20\left(-11950\right)}}{2\cdot \:20}:\quad \frac{-27+\sqrt{38969}}{8}[/tex],

[tex]t=\frac{-135-\sqrt{135^2-4\cdot \:20\left(-11950\right)}}{2\cdot \:20}:\quad -\frac{27+\sqrt{38969}}{8}[/tex] ... now as you can see we have two solutions, but time can't be negative, and hence our solution is the first one - about 21.3 years. 1998 + 21.3 = ( About ) The year 2019. Therefore, in the year 2019 the number of new cars purchased will reach 15,000.

Answer:

2019

Step-by-step explanation:

first you should change the statement into quadratic equation and replace c with 15000.

c=20t^2+135t+3050.

15000=20t^2+135t+3050

15000-3050=20t^2+135t

11950=20t^2+135t. then write the equation in standard quadratic form.

20t^2+135t-11950=0. after this you got 4 ways of solving the quadratic equation but I am just gone using quadratic formula:

-b+ - √b^2-4ac. a,b and C stand for the

2a. the coefficients

-135+ - √((135)^2-4(20)(-11950))

2(20)

-135+ - √(974225))

)) 40

-135 - 987 or -135+ 987

40. 40

-1122/40. or 852/40

- 28.05 or. 21.3

in this case we have to answer but time cannot be negative we take value 21.3(it is the approximate value)

so we add 21.3 to 1998 to find the year

>>21.3 + 1998 = 2019.3 but we write it as 2019 instead of 2019.3

Answer:

Step-by-step explanation:

A ratio is a comparison of two numbers. A ratio can be written using a colon, 8:12 , or as a fraction 8/12 . A rate is a comparison of two quantities which can have different units. For example 8 miles per 4 hours is a rate.

Answer:

sure

Step-by-step explanation:    

I am bob and I work at a restaurant. I notice at 4 and 6 am 2 people come into the restaurant and at 7 and 8 pm 2 people come, but at 9 and 10 pm 8 people come in. So I graph the data and i find out that the graph is skewed to the right as most of the data points are more to the right/positive part of the graph

Answer:

Mr. Wilson invested $ 2,000 in the 12% simple interest account and $ 6,000 in the 6% simple interest account.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Amount of the investment = $ 8,000  

Interest rate of the first account= 6% simple  

Interest rate of the second account= 12% simple  

Interest of the accounts in a year = $ 600  

2. How much did he invest in each account?

For answering the question, we will use the following equation:  

x = Amount invested in the first account  

8,000 - x = Amount invested in the second account  

0.06x + 0.12 * (8,000 - x) = 600

0.06x + 960 - 0.12x = 600

-0.06x = 600 - 960 (Subtracting 960 at both sides)

-0.06x = -360

x = -360/-0.06

x = 6,000 ⇒ 8,000 - x = 2,000  

Mr. Wilson invested $ 2,000 in the 12% simple interest account and $ 6,000 in the 6% simple interest account.

Answer:

the smallest possible perimeter is 6

Step-by-step explanation:

since the smallest possible prime number is 2 it would make since if each side is 2 which makes the smallest perimeter possible. i really hope this helped :)

Answer:

6

Step-by-step explanation:

the smallest possible number will be 2.

2 inches/centimeters of each 3 sides of the triangle

Answer:

[tex]x=-1[/tex]

Step-by-step explanation:

[tex]\frac{6x+1}{3}+1=\frac{x-3}{6}[/tex]

To make things simple, multiply everything by the LCM of the denominator. In this case, the LCM of 3 and 6 is 6.

[tex]6(\frac{6x+1}{3}+1) =6(\frac{x-3}{6}) \\6(\frac{6x+1}{3})+6(1)=(x-3) \\ 2(6x+1)+6=x-3[/tex]

Now, simplify and solve for x:

[tex]12x+2+6=x-3\\12x+8=x-3\\11x+8=-3\\11x=-11\\x=-1[/tex]

Answer:

where are the statements...

mention the statements first

I'm assuming you meant to say P(A) = 3/5 and P(B|A) = 8/9.

If so, then we multiply the probabilities to get P(A and B)

P(A and B) = P(A)*P(B|A)

P(A and B) = (3/5)*(8/9)

P(A and B) = (3*8)/(5*9)

P(A and B) = 8/(5*3)

P(A and B) = 8/15

Answer:

x = y+7

x = y -1

Step-by-step explanation:

Variable x is 7 more than variable y

is means equals

x = y+7

Variable x is also 1 less than y

x = y -1

Answer:

The length of the diagonal of the trunk is 56.356011 inches

Step-by-step explanation:

According to the given data we have the following:

height of the trunk= 26 inches

length of the trunk= 50 inches

According to the Pythagorean theorem, to calculate the length of the diagonal of the trunk we would have to calculate the following formula:

length of the diagonal of the trunk=√(height of the trunk∧2+length of the trunk∧2)

Therefore, length of the diagonal of the trunk=√(26∧2+50∧2)

length of the diagonal of the trunk=√3176

length of the diagonal of the trunk=56.356011

The length of the diagonal of the trunk is 56.356011 inches

Answer:

( x + y )² = 32

Step-by-step explanation:

So far, I can tell that your calculations are incorrect. ( x + y )² is indeed x² + 2xy + y², which you can prove right by expanding the expression ( x + y )( x + y ). You simply swapped the positioning in this second step, and decided that the addition of x² + y² is x²y², but that is incorrect. You can't combine the two terms unless you multiply the two.

We should just be left with the expanded expression x² + y² + 2xy. Given that x² + y² = 17, and xy = 7.5, let's substitute and solve for the value of the expression.

17 + 2( 7.5 ) = 17 + 15 = 32,

( x + y )² = 32

Answer:

the other person is correct

Step-by-step explanation:

Answer:

2560

Step-by-step explanation:

Answer:

2,560

Step-by-step explanation:

To find the total, we need to use the number of options for all 4 of the categories. Once we have those number, we just need to multiply them to find the total number of possibilities. This is called the Fundamental Counting Principle.

8 x 8 x 8 x 5 = 2560

Hope this helps!! ;)

Answer:

Fraction- 12/20 or 3/5

Percentage- 60%

Decimal-0.6

Step-by-step explanation: Add 8 and 12 together and that’s your denominator and top is 12 because those are many consonants there are. So the fraction is 12/ 20 an you can simplify it. Then you can change it into a decimal and percentage.

Answer:

67,108,864 or 4^13

Step-by-step explanation:

4^6*4^7=4^13 you basically just add the exponents since the base is the same.

Since these two powers have the same base of 4, you can multiply

them together by simply adding their exponents to get 4¹³.

This idea is called the product rule.

A common mistake in this problem would be to multiply

the bases together and give an answer of 16¹³.

It's important to understand however that the 4's in this problem can't

be multiplied together because they're not coefficients, they're bases.

When applying your exponent rules, your base will never change.

Answer:

Step-by-step explanation:

area of shaded region = 3168/7 - 55 = 397.5cm^2 (app)= 0.397cm^2 ( since we have to round to nearest hundredth

Answer:

The answer is

Step-by-step explanation:

To find the area of the shaded area first find the area of both the rectangle and the circle and subtract the smaller one from the larger one.

that's

For the rectangle

Area of rectangle = length × width

From the question

length = 5cm

width = 11 cm

So we have

Area of rectangle = 5cm × 11cm = 55cm²

For the circle

Area of a circle = πr²

where r is the radius

From the question

r = 12 cm

Area of circle = π (12)²

= 144π

= 452.40 cm²

Area of shaded figure

Since the area of the rectangle is smaller than that of the circle we subtract the area of the rectangle from the circle

That's

452.40 cm² - 55cm²

= 397.40 cm² to the nearest hundredth

Hope this helps you

Answer:

The speed of plane = 40 m/s

The speed of the wind = 300 m/s

Step-by-step explanation:

Let the speed of the plane = Y

And the speed of the wind = X

If the plane then travel 340 miles per hour with the wind, that means the plane and the wind are moving in the same direction. Therefore,

X + Y = 340 ..... ( 1 )

Also, 260 miles per hour against the wind. That is, the plane is moving opposite to the direction of the wind. Therefore,

X - Y = 260 ..... ( 2 )

Solve the two equations simultaneously by addition. That will eliminate Y

X + Y = 340

X - Y = 260

2X = 600

X = 600/2

X = 300 m/s

Substitutes X in equation (1)

300 + Y = 340

Make Y the subject of formula by collecting the like terms

Y = 340 - 300

Y = 40 m/s

Therefore, the speed of the plane is 40 m/s. While the speed of the wind is 300 m/s.

Answer:

22ft^2

Step-by-step explanation:

I am not sure if this is the correct answer since there were no numbers to the question you wrote out.

Answer:

A, D and E

Step-by-step explanation:

Option B is an inequality while Option C is an Equation. However, Rest of the options are expressions because they don't have any equality (=) sign or any inequality (<,>,≥,≤). So, they are expressions.

Answer:

i. [tex]Total\ Income = Rs\ 16,100[/tex]

ii. [tex]Monthly\ Sales = Rs\ 1,500,000[/tex]

Step-by-step explanation:

Given

[tex]Salary = Rs\ 12,500[/tex]

Commission = 0.5% of Monthly Sales

Calculating his total income is total sales is  Rs 720,000

[tex]Total\ Income = Salary + Commission[/tex]

Substitute (0.5% of Monthly Sales) for Commission

[tex]Total\ Income = Salary + (0.5\%\ of\ Monthly\ Sales)[/tex]

Substitute Rs 720,000 for Monthly Sales and Rs 12,500 for Salary

[tex]Total\ Income = Rs\ 12,500 + 0.5\%\ of\ Rs\ 720,000[/tex]

[tex]Total\ Income = Rs\ 12,500 + 0.5\%\ * Rs\ 720,000[/tex]

Convert % to decimal

[tex]Total\ Income = Rs\ 12,500 + 0.005\ * Rs\ 720,000[/tex]

[tex]Total\ Income = Rs\ 12,500 + Rs\ 3,600[/tex]

[tex]Total\ Income = Rs\ 16,100[/tex]

Calculating his total sales if total income = Rs 20,000

Recall that;

[tex]Total\ Income = Salary + Commission[/tex]

Substitute Rs 20,000 for Total Income; Rs 12,500 for Salary and (0.5% of Monthly Sales) for Commission

[tex]Rs\ 20,000 = Rs\ 12,500 + 0.5\%\ of\ Monthly\ Sales[/tex]

Subtract Rs 12,500 from both sides

[tex]Rs\ 20,000 - Rs\ 12,500 = Rs\ 12,500 - Rs\ 12,500 + 0.5\%\ of\ Monthly\ Sales[/tex]

[tex]Rs\ 7,500 = 0.5\%\ of\ Monthly\ Sales[/tex]

[tex]Rs\ 7,500 = 0.5\%\ *\ Monthly\ Sales[/tex]

Divide both sides by 0.5%

[tex]\frac{Rs\ 7,500}{0.5\%} = \frac{0.5\%\ *\ Monthly\ Sales}{0.5\%}[/tex]

[tex]\frac{Rs\ 7,500}{0.5\%} = Monthly\ Sales[/tex]

Convert % to decimal

[tex]\frac{Rs\ 7,500}{0.5\%} = Monthly\ Sales[/tex]

[tex]\frac{Rs\ 7,500}{0.005} = Monthly\ Sales[/tex]

[tex]Rs\ 1,500,000 = Monthly\ Sales[/tex]

[tex]Monthly\ Sales = Rs\ 1,500,000[/tex]

Answer:

144 units

Step-by-step explanation:

3x + 8 + 4x + 10 = 8x

7x + 18 = 8x

8x - 7x = 18

x = 18

8x is length of BC

8 × 18 is length of BC

144 units

Answer:

What is the length of segment BC?

144 units

explanation:

<3

Answer:

Expected win = $15.17 to the nearest cent.

Step-by-step explanation:

Expected win = (1/6)*(1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2) = 15.167  or $15.17 to the nearest cent.

The positive expected value means that Monica wins 1.17 dollars on average for each roll.

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

Explanation:

The sample space is {1,2,3,4,5,6} to represent the outcomes of the die.

Of that list, {2,3,5} are prime numbers. Note that 1 is not a prime number. It's not composite either. So Monica will lose money when she rolls a 1. If she rolls {4,6} then she wins 0 dollars.

For any single roll, the probability of landing on that value is 1/6

Multiply 1/6 by each winning amount. Then add up the products

(1/6)*(-3) + (1/6)*(2) + (1/6)*(3) + (1/6)*(0) + (1/6)*(5) + (1/6)*(0)

-3/6 + 2/6 + 3/6 + 5/6

(-3+2+3+5)/6

7/6

1.17 approximately

Monica will get about 1.17 dollars per roll on average. She only loses money on average if the expected value was negative.

Answer:

A = 27π

P =

Step-by-step explanation:

Well if it follows the same proportions as a square then the dotted line is 6 cm.

                                                      Triangle                                                                

So the area of a triangle is b*h / 2

b = 6

h = 6

6*6 = 36

36 / 2 = 18

A = 18cm^2

So to find the missing side or c we do 6^2 + 6^2 = c^2,

36 + 36 = c^2

72 = c^2

≅8

6 + 6 + 8

= 20cm

                                                       Half circle                                                                  

Now the area of a semicircle is,

pi r^2 / 2

So if the diameter is 6 then the radius is 3.

So we do 3*3 = 9

9 * pi = 9π^2

Perimeter: 6π

____________________________________________________________

Thus,

the area is 27π and the perimeter 26π.

Hope this helps :)

Answer:

$810 total raised

Step-by-step explanation:

Charley:

12 * $18 = $216

Maria:

15 * $18 = $270

Paul:

18 * $18 = $324

Total:

$324 + $270 + $216 = $810

Answer:

pls appreciate my efforts by markinf my answer as the brainliest......

Step-by-step explanation:

Charley raised = 12 *18 =$216

Maria raised =15*18 = $270

Paul raised = 18*18 = $ 324

total amount raised = $ 810

Answer: the elementary 45

Step-by-step explanation: if you need anything else let me know

Answer:

x² + -6x = -13

Step-by-step explanation:

8x² - 48x = -104

x² - 6x = -13

The quadratic equation can be written as x² + (- 6x) = - 13

Quadratic equations are algebraic expressions which the highest value of x in its second degree. It is usually expressed in the form: ax² + bx + c

From the given information, the objective is to simplify the quadratic equation in terms of ax² + bx + c  

∴

Given that:

We need to divide through by (8)

Learn more about quadratic equations here:

https://brainly.com/question/1214333

Answer:

1) 0.1504

2) 0.432

Step-by-step explanation:

1) The given information are;

The proportion of the morning appointments that are with elderly patients = 60%

The number of patients in the appointments  = 10 patients

The proportion of the morning appointments that are with non-elderly patients = 100 - 60 = 40%

The binomial probability distribution is given as follows;

[tex]P(X = r) = \dbinom{n}{r}p^{r}\left (1-p \right )^{n-r}[/tex]

[tex]P(X = 0) = \dbinom{10}{0}0.6^{0}\left (1-0.6 \right )^{10}[/tex] = 0.000105

[tex]P(X = 1) = \dbinom{10}{1}0.6^{1}\left (1-0.6 \right )^{9}[/tex] = 0.0016

[tex]P(X = 2) = \dbinom{10}{2}0.6^{2}\left (1-0.6 \right )^{8}[/tex]= 0.01062

[tex]P(X = 3) = \dbinom{10}{3}0.6^{3}\left (1-0.6 \right )^{7}[/tex]= 0.0425

The probability that the first four patients are elderly is 0.000105 + 0.0016 + 0.1062 + 0.0425 = 0.1504

2) The probability that exactly 2 out of 3 morning patients are elderly patient is given as follows

[tex]P(X = 2) = \dbinom{3}{2}0.6^{2}\left (1-0.6 \right )^{1}[/tex]= 0.432

Answer:

Step-by-step explpointsanation:

Answer:

option c (31)

Step-by-step explanation:

Answer:

Option B.

Step-by-step explanation:

Note: The function f(x) is not in correct format it must be [tex]f(x)=3^x[/tex].

It is given that two different plants that grow each month at different rates are represented by the functions f(x) and g(x).

Let as consider the two functions,

[tex]f(x)=3^x[/tex]

[tex]g(x)=5x+12[/tex]

Now, table of values is

Month(x)        [tex]f(x)=3^x[/tex]           [tex]g(x)=5x+12[/tex]

    1                      3                          17

    2                     9                         22

    3                     27                        27

    4                     81                        32

From the above table it is clear that in first and second month the height of the f(x) plant is less than of g(x).

In month 3, heights are equal.

In month 4, height of the f(x) plant exceed that of the g(x) plant.

Therefore, the correct option is B.

Answer:

Step-by-step explanation:

Mary received 726 votes.