What is the lateral area of the rectangular prism? Round the answer to the nearest whole number. Assume the 4 m × 8 m rectangles on the left and right are the bases. The diagram is not drawn to scale.

Answer:

  B) x = 2, y = 1

Step-by-step explanation:

Add the two equations to eliminate the x-variable.

  (x +3y) +(-x +6y) = (5) +(4)

  9y = 9 . . . . . . .simplify

  y = 1 . . . . . . . . divide by 9

You can substitute this value into either equation to find x.

  x + 3(1) = 5

  x = 2 . . . . . . . . subtract 3

The solution is (x, y) = (2, 1).

Answer:

B) x=2, y=1

Step-by-step explanation:

x+3y=5

-x+6y=4

solve the equation

x=5-3y

-x+6y=4

substitute the value of x into an equation

-1(5-3y)+6y=4

multiply numbers in parenthesis by -1

-5-3y+6y=4

put -5 as positive and add 5 to 4 and put -3y as positive and add to 6y.

9y=9

divide both sides by 9

y=1

substitute the value of y into an equation

x=5-3•1

multiply 3 to 1

x= 5-3

subtract 5 to 3

x=2

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

x=2

y=1

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

Answer:

-7 is the real part

5i is the imaginary part

Step-by-step explanation:

z = -7 + 5i

i is the imaginary number

-7 is the real part

5i is the imaginary part

Answer:

The real part of the complex number is -7

The imaginary part of the complex number is 5

Answer:

1. independent variable

2. dependent variable

3. control group

Step-by-step explanation:

Independent variables are the factors in the experiment that are being modified to discover some sort of result.

Dependent variables are those that change because of the independent variable; they're also the ones that are measured in the experiment.

The control group is a group that undergoes the same exact procedure as the experimental group(s) do, but without the independent variable; it is to make sure that the different results aren't due to environmental factors.

Here, because Hannah is changing the amount of fertilizer in the plants (none or a specific amount), the presence of fertilizer is the independent variable. Since the heights of the plants will likely change due to the presence of fertilizer, height is the dependent variable. And, finally, the pots without fertilizer undergo the same procedure but without the independent variable, or the fertilizer, so it's the control group.

Hope this helps!

Answer:

The presence of fertilizer in the soil is the independent variable

The height of the tomato plants is the dependent variable

The pots without fertilizer form the control group

Step-by-step explanation:

She has divided the pots into 2 groups of 10 each:

1) experimental group

2) control group

She can decide the amount of fertiliser so that's an independent variable

What's she's observing are the heights which she can't control so heights is the dependent variable

Answer: 1 1/4

Step-by-step explanation:

Solving the fraction parts

3/8 + 7/8 = 10/8

Reducing the fraction part, 10/8

10/8= 5/4

Simplifying the fraction part, 5/4

5/4= 1 1/4

Answer:

10/8

Step-by-step explanation:

You add 7/8 + 3/8 and that equals 10/8

I hope that's helpful

Answer:

The answer is The MAD of set 1 is 5 less than the MAD of set 2.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

54mm

Step-by-step explanation:

50, 50, 52,53, 54, 55, 55, 55, 57

Answer:

Santiago earns 8.7 $ from each sold shirt

Step-by-step explanation:

1). 45 % of 6 is = 6 * 0.45 = 2.7 $

2). 6 $ + 45 % of 6 = 6 + 2.7 = 8.7 $ - Answer

Answer:

There is a relationship between the variables, because as the number of apples increases, the weight of the apples also increases.

Step-by-step explanation:

Answer:the answer is: increases

Step-by-step explanation:

Answer:

limit is 2.

Step-by-step explanation:

f(x) = 10x + 2  for x< 0   ,

f(x) = |2 - x|  for x>=0

get x close to 0

lim  10x + 2  x-->0-  = 2

lim  |2 - x|   x-->0+ =  2

Answer:

I think it would be 4/5 of a chance?

Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

Answer:

1/3 2/6

Step-by-step explanation:

Answer:

2/6 and 1/3

Step-by-step explanation:

Answer:

56.7% to one decimal place

Step-by-step explanation:

30 students

13 are boys

30-13=17

17 are girls

As a decimal 0.5667

As a percentage 56.67%

56.7% to one decimal place

Answer:

C

Step-by-step explanation:

In order to be a function, all of the graphs need to pass the vertical line test

Vertical line test- Only one point per vertical line, if there are more than one, it is not a function

C is the only one that has more than one point at a vertical line

The answer is c. If there are 2 points in a vertical line, it is not a function.

Answer:

The Sun's diameter is [tex]1.075\times 10^2[/tex] times the Earth's diameter.  

Step-by-step explanation:

We are given the following in the question:

Sun's diameter = 860,000 miles

Earth's diameter = 8000 miles

Comparison of Sun's and Earth's diameter:

[tex]\dfrac{\text{Sun's Diameter}}{\text{Earth's Diameter}}\\\\=\dfrac{860000}{8000}\\\\=\dfrac{8.6\times 10^{5}}{8\times 10^3}\\\\=1.075\times 10^2[/tex]

Thus, the Sun's diameter is [tex]1.075\times 10^2[/tex] times the Earth's diameter.

Answer:

Length = 12yards

Width = 14yards

Sum = 26yards

Step-by-step explanation:

Let assume the play ground is rectangular in form.

Area of a rectangle = length × width

Given area of the playground = 168yd²

If the width of the playground is 2yd longer than its length, then:

W = L+2

Substituting W = L+2 into the formula above we have:

A = L × (L+2)

A = L²+2L

168 = L²+2L

L²+2L-168 = 0

L²+14L-12L-168 = 0

L(L+14)-12(L+14) = 0

(L-12)(L+14) = 0

L-12 = 0 and L+14 =0

L = 12 and -14

Taking the positive length, L = 12yards

If Length = 12yards

W = L+2

W = 12+2

Width = 14yards

Sum of the length and width will be:

L+W= 12+14

= 26yards

Answer:

The length  of playground is 12 yd

The width of playground is 14 yd

The sum of the length and width of playground is 26 yd

Step-by-step explanation:

The area, A of the playground is given as 168 yd²

The formula for the area of the playground is given as follows;

Area, A of playground = Length, L × Width, W

The Width =  length  + 2 yd or W  = L + 2

Therefore, A = L × (L + 2)

A = L² + 2·L

Where we have A = 168 yd², we have the area equation presented as follows

168 = L² + 2·L or

L² + 2·L - 168 = 0

Factorizing the above equation gives

L = 12 or L = -14 we note that the appropriate solution is L = 12 yd

Therefore W = L + 2 = 12 + 2 = 14 yd

The length  of playground = 12 yd

The width of playground = 14 yd

The sum of the length and width of playground = 12 + 14 = 26 yd.

Answer:

$14,030.48

Step-by-step explanation:

We can use the following formula to solve:

[tex]A=P(1-r)^t[/tex]

P = principal value

r = rate (decimal)

t = time (years)

First, lets change 7.3% into a decimal:

7.3% -> [tex]\frac{7.3}{100}[/tex] -> 0.073

Next, plug in the values:

[tex]A=19,000(1-0.073)^4[/tex]

[tex]A=14,030.48[/tex]

The value will be $14,030.48

Answer: m<D = 80º

Step-by-step explanation:

Since we know triangle ABC is congruent to triangle EDC, the angle 60º can be know for angle ACB. Triangles have a interior total of 180, so 40+60 is 100. Subtract 100 from 180 to get your angle of B. Since the triangles are similar we know that B=D so D=80º

Answer: 169.6

Step-by-step explanation:

The lateral area of a triangular pyramid is calculated by finding the area of each of the pyramid's three triangular faces and adding them together. This process is simplified if the pyramid is equilateral.

To calculate the lateral area of a triangular pyramid, you start by finding the area of each of the three triangular faces (the base is not included). If the pyramid has equal sides (an equilateral triangular pyramid), the process is simplified. The area of a single triangle face is found using the formula 0.5*base*height. Then simply multiply this by 3 since there are three faces. If the pyramid doesn't have equal sides, you will need to calculate the area of each face separately and then add them together to find the total lateral area.

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Answer:

7 inches

Step-by-step explanation:

Height : Diameter

14 : 6

H : 3

H/14 = 3/6

H = 14 × 3/6

H = 7

Answer:

7 inches

Step-by-step explanation:

Answer:

Her account balance after 3 years is $4,246.71

Step-by-step explanation:

In this question, we are tasked with calculating what Hannah's account balance will be after 3 years and the error she made in her calculations

Mathematically, to calculate the account balance after 3 years, we use the formula for the compound interest as follows.

Mathematically, the amount A earned on a compound interest is calculated as

A = P[tex](1+r/n)^{nt}[/tex]

where A is the account balance after the number of years which is what we want to know

P is the initial amount invested which is $4000

r is the interest rate which is 2%(2/100 = 0.02) according to the question

n is the number of times interest is compounded per year which is 4(quarterly means every 3 months)

t is the number of years which is 3

We plug the values into the question;

A = 4000(1 + 0.02/4)^(3)(4)

A = 4000(1+0.005)^12

A = 4000(1.005)^12

A = $4,246.71

P.S ; I do not see Hannah's calculation and as such I cannot spot where she made the error in her calculations

Final answer:

Hannah made a calculation error; the correct balance after 3 years at 2% interest compounded quarterly on a $4000 investment is approximately $4248.71.

Explanation:

The student has incorrectly calculated the future value of a $4000 investment at 2% interest, compounded quarterly. The accurate calculation involves using the compound interest formula:

P = P0 (1 + r/n)nt

Where:

P is the future value of the investment.

P0 is the principal amount ($4000).

r is the annual interest rate (2%, or 0.02).

n is the number of times interest is compounded per year (4, since it is quarterly).

t is the time the money is invested for (3 years).

Plugging in the values we get:

P = $4000 (1 + 0.02/4)4*3

After solving, we get P = $4000 * (1 + 0.005)12 ≈ $4000 * 1.061677812

Hence, the account balance after 3 years would be approximately $4248.71, not $4244.83 as Hannah initially thought.

Answer:

Gregoire is correct; the diameter is a chord that passes through the center of the sphere.

Step-by-step explanation:

A sphere is a geometrical shape formed from a circle. Some of its parts are: diameter, center, radius circumference, etc.

The center of a sphere is a point at its middle. The diameter is a straight line, e.g a chord, that is drawn from one point on the circumference of a sphere to another point and passes through its center. While radius is a line that is from the center of the sphere to a point on its circumference.

A diameter is twice of a radius, so that:

                            Radius = [tex]\frac{Diameter}{2}[/tex]

⇒                        Diameter = 2 × Radius

Therefore with respect to the question, Gregoire is correct because a diameter is a chord that passes through the center of the sphere.

Answer:

a

Step-by-step explanation:

Given:

The given expression is [tex]\frac{b^{-2}}{a b^{-3}}[/tex]

Let us assume that [tex]a \neq 0, b \neq 0[/tex]

We need to determine an expression that is equivalent to the expression [tex]\frac{b^{-2}}{a b^{-3}}[/tex]

Equivalent expression:

The equivalent expression can be determined by solving the given expression.

Hence, applying the exponent rule, [tex]\frac{x^{a}}{x^{b}}=x^{a-b}[/tex]

Thus, we get;

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

Subtracting the numbers, we get;

[tex]\frac{b^{-2}}{a b^{-3}}=\frac{b}{a}[/tex]

Thus, the equivalent expression is [tex]\frac{b}{a}[/tex]

Hence, Option D is the correct answer.

Answer:

d

Step-by-step explanation:

The theoretical probability of 3 students from your school being selected as contestants out of 9 possible contestant spots is 0.28

Explanation:

School students = 40

Total people = 130

Total contestant spot = 9

Probability of 3 contestant from school = ?

The number of combinations of 3 of the 40 students getting a spot = ⁴⁰C₃

The number of combinations of the other audience members filling the other 6 spots = ⁹⁰C₆

The number of 9 contestants with 3 students in them = ⁴⁰C₃ X ⁹⁰C₆

The total number of possible 9 contestants from the audience = ¹³⁰C₉

Probability of the group of contestants having 3 students = [tex]\frac{^4^0C_3 X ^9^0C_6}{^1^3^0C_9}[/tex]

Solving the equation further we get:

Probability of the group of contestants having 3 students = 0.28

Answer:

Step-by-step explanation:

Suppose m = 2 + 6i, and |m+n|=3√10,

The modulus sign means m+n can either be positive or negative as shown.

If it is positive:.2+6i+n = 3√10

n = 3√10-(2+6i)

n = 3√10-2-18√10i

n = (-2+3√10)+√10i

b) Example of the complex number is given as (-2+3√10)+√10i. This is a complex number because it contains the real part and the imaginary part.

Answer:

x^2 - 81

Step-by-step explanation:

There is a formula called the difference of squares, which is

(a+b)(a-b) = a^2 - b^2

Answer: 9x²-81x

Step-by-step explanation:

1. Reorder the terms like this: (9x)• (x-9)

2. Remove unnecessary Parentheses like this: 9x•(x-9)

3. Distribute 9x through the Parentheses like this:

9x would become 9x² (because I combined 9x and 9x which become 9x²)

(x-9) would become -81x (so if you need further explanation I took the (x-9) and made it -9x then multiplied it by the 9x because of distributive property.)

The solution: 9x²-81x

Answer:

5/6

Step-by-step explanation:

Rise over run

y2-y1 / x2-x1

30-15 / 36-18

Hope this helps!

Answer:

He should be very confident

Step-by-step explanation:

He should be very confident because he has a 7 out of 8 chance of getting a small medium or large prize and he has a 1 out of 8chance of getting nothing

The probability that the box selected will win the prize is A = 7/8 = 87.5 %

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability that the box selected will win the prize be A

Now , the total number of boxes = 8

The box which has a big prize = 1

The number of boxes which have medium prize = 3

The number of boxes which have small prizes = 3

So , the total number of boxes with prize = 7 boxes

And , probability that the box selected will win the prize A = total number of boxes with prize / total number of boxes

On simplifying , we get

The probability that the box selected will win the prize A = 7 / 8

The probability that the box selected will win the prize A = 0.875

Hence , the probability is 7/8

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Answer:

Step-by-step explanation:

Fill in the blanks:

a. range

b. median

c. mode

d. mean

1. mean: 5+3+2+6+5+2+5= 15+4+6+3= 28/7= 4

  median: 2,2,3,5,5,5,6: 5

  mode: 5

  range: 6-2= 4

2. 24+12+10+15+10+22+12= 105/7= 15 mean

   10,10,12,12,15,22,24: 12 is the median

    mode: 10, 12

    range: 24-10= 14

3. 14+9+20+5+17+13= 78/6= 13 is the mean

    5,9,13,14,17,20: 13+14= 27/2= 13.5 median

    no mode

    20-5= 15 the range

4. 21+15+16+25+13+18= 108/6= 18 is the mean

  median: 13,15,16,18,21,25: 16+18= 34/2= 17

   no mode

   range: 25-13= 12

5. 10+12+17+18+20+25+31= 133/7= 19 mean

   median: 18

  mode: none

  range: 31-10=21

6. 40+43+46+48+52+53= 282/6= 47

   median: 46+48= 94/2 = 47

   mode: none

   range: 53-40= 13

7. 8+9+10+15+28= 70/5= 14 mean

   median: 10

   mode: none

   range: 28-8= 20

8. 22+32+33+58+85= 230/5= 46 mean

   median: 33

   mode: none

   range: 85-22= 63

9. 17+18+20+24+30+35= 144/6= 24 mean

   median: 24+20= 44/2= 22

   mode: none

   range: 35-17= 18

10. 116+120+125+125+130+140= 756/6=126: mean

    median: 125+125= 250/2= 125

    mode: 125

   range: 140-116= 24