Dana is planning the school picnic and needs to decide what food vendor to
use. She asks 750 students whether they would rather have a taco truck or a
fruit smoothie cart. The results of the survey are shown in the table.
Taco truck Fruit smoothles Total
Eighth-graders 180
120
300
Ninth-graders
110
90
200
Total
290
210
500
What is the relative frequency of eighth-graders who want fruit smoothies?
A. 0.36
B. 0.24
C. 0.22
D. 0.12

Answer:

The probability of rolling an even number would be [tex]\frac{1}{2}[/tex] or 50%.

Step-by-step explanation:

A standard number cube has 6 sides that features numbers 1 to 6 on each side. Since there are three even numbers (2, 4, 6) total on the sides of the number cube, that means the theoretical probability of rolling an even number would be [tex]\frac{3}{6}[/tex], which simplifies to [tex]\frac{1}{2}[/tex] or 50%.

Answer:

It's C :D

Step-by-step explanation:

Answer:

x = 20 units

Step-by-step explanation:

∆KJL is a 30° - 60° - 90° triangle which means that side opposite of 30° is x, side opposite of 60° is x√3, and side opposite of 90° is 2x.

Since side opposite of 90° is 40√2 which is 2x and x is the side opposite of 30° (JL).

2x = 40√2 → 2x ÷ 2 = 40√2 ÷ 2 → x = 20√2.

∆JML is a 45° - 45° - 90° triangle which means that sides opposite of 45° are x and 90° is x√2.

Since side JL is also the side opposite of 90° and the sides opposite of 45° are the value x,

20√2 = x√2 → 20√2 ÷ √2 = x√2 ÷ √2 → 20 = x →

x = 20.

9514 1404 393

Answer:

  M R T V B K

Step-by-step explanation:

From left to right the solutions are ...

__

B: equating expressions for y

  -2x = x -3   ⇒   3 = 3x   ⇒   x = 1

R: given

  x = -2

V: filling in for y

  4x +5(2) = 10   ⇒   x = 0

T: subtracting the first from twice the second

  2(3x +y) -(-3x +2y) = 2(0) -9   ⇒   9x = -9   ⇒   x = -1

K: adding the two equations

  (2x +y) +(3x -y) = (7) +(3)   ⇒   5x = 10   ⇒   x = 2

M: equating expressions for y

  x -2 = 1/3x -6   ⇒   2/3x = -4   ⇒   x = -6

__

The solutions in order least to greatest are ...

  -6 (M), -2 (R), -1 (T), 0 (V), 1 (B), 2(K)

The passcode is MRTVBK.

_____

Additional comment

In several cases, there are variables and constants on both sides of the equal sign. The solution method is to identify the smallest variable coefficient, and add the opposite of that term. Also added at the same time is the opposite of the constant term on the other side of the equal sign. The net effect is to put the variable on one side and the constant on the other side. Then the equation is divided by the coefficient of the variable.

For example, in the first equation, -2x is the variable term with the smallest coefficient. -3 is the constant on the other side of the equation. To get from the initial expression to the next, we add 2x+3 to both sides of the equation.

Answer:

do you have an attatchment or guide i can use to answer this?

Step-by-step explanation:

Transposing a,

[tex]d + a = h \\ a = h - d[/tex]

Answer:

C; D; E

Step-by-step explanation:

✔️Angles in a straight line = 180°

Therefore, m<5 + m<6 = 180° is correct.

✔️Exterior angle of a triangle = the sum of the opposite interior angels based on the exterior angle theorem of a triangle.

Therefore,

m<2 + m<3 = m<6 is correct.

✔️The sum of m<2 + m<3 + m<5 = 180° is correct. This is true based on the sum of triangle theorem.

Answer:

Bella is largely mistaken.

Step-by-step explanation:

What she described equals 90

Answer:

[tex]\frac{7}{9}[/tex] of a mile per hour

0.77777778 of a mile per hour

Step-by-step explanation:

[tex]\frac{y}{14} :\frac{1}{18}[/tex]

y · 18 = 1 · 14

18y = 14

18y ÷ 18 = 14 ÷ 18

[tex]y=\frac{7}{9}[/tex]

Answer: 1.28571428571

Step-by-step explanation: You divide the hours by miles

Answer:

G

Step-by-step explanation:

it is the correct answer

Answer:

Look at the image and

H. 30%

Step-by-step explanation:

[tex]\frac{100}{y}: \frac{300}{390}[/tex]

y · 300 = 100 · 390

300y = 39000

300y ÷ 300 = 39000 ÷ 300

y = 130

130% - 100% = 30%

Answer:

y(t) = 720e^0.3466t

y = 2036.6288

Step-by-step explanation:

The exponential relation :

y = Ae^kt

A = initial value ; y = final value ; r ; k = exponential rate, t = time

At t = 0

y = 720e^0 ; y = 720

At t = 2 ; y = 720e^2k

1440 = 720e^2k

1440/720 = e^2k

2 = e^2k

Take the In of both sides

0.6931471 = 2k

k = 0.6931471 / 2

k = 0.3466

Hence, equation becomes :

y = 720e^0.3466t

After 3 hours ;

t = 3

y = 720e^0.3466*3

y = 720e^1.0398

y = 720 * 2.8286512

y = 2036.6288

Answer:

−6x^2+7x+1

Step-by-step explanation:

1)(7x+8x-4)=15x−4

2)15x-4-(6x^2+8x-5)=−6x2+7x+1

Answer:

the 1st option is false; there is no 'addition' sign

Step-by-step explanation:

Answer:

78.54 inches squared

Step-by-step explanation:

A=πr^2

π·5^2

Have a good day :)

Answer:

450

Step-by-step explanation:

6% = 0.06

0.06x = 27

Divide both sides by 0.06

x = 450

Answer:

a) A = 8000(1 + .06/4)^4t

b) $9,564.95

Step-by-step explanation:

b) A = 8000(1 + .06/4)^12

Answer:

Option D

Step-by-step explanation:

Equation of the piecewise function,

f(x) = -x² + 2x  for x ≤ -3

        [tex]2(\frac{1}{3})^{2x}[/tex] for -3 < x < 4

         [tex]\frac{2x-5}{x-7}[/tex] for x ≥ 4

For x = -3,

f(x) = -x² + 2x

f(-3) = -(-3)² + 2(-3)

       = -9 - 6

       = -15

For x = -1

f(x) = [tex]2(\frac{1}{3})^{2x}[/tex]

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

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

      = [tex]2\times 3^2[/tex]

      = 18

For x = 4

f(x) = [tex]\frac{2x-5}{x-7}[/tex]

f(4) = [tex]\frac{2(4)-5}{4-7}[/tex]

     = [tex]\frac{3}{-3}[/tex]

     = -1

Therefore, f(-3) + 2f(-1) + f(4) = -15 + 2(18) - (-1)

                                              = -15 + 36 + 1

                                              = 22

Option D will be the correct option.

Answer:

D

Step-by-step explanation:

You have the opposite side given and the adjacent side. That means you will use the tangent.

Tan(theta) = opposite / adjacent

opposite = 6

adjacent = 3.5

Tan(theta) = 6 / 3.5

Tan(theta) = 1.714

Tan-1(1.714) = 59.74

when you get an answer over 1 from the division, you know that the angle is over 45 degrees.

Answer:

14mph

Step-by-step explanation:

First, lets find how many 16s can go into 60.

We can find this by doing 60 / 16 = 3.75

Then we need to find his average speed. We can find this by doing

18.4 * 3.75 = 69

To find how much he exceeded the speed limit, we will subtract 55 from 69

69 - 55 = 14

Therefore, Femi's average speed exceeded the speed limit by 14mph.

Answer:

[tex]Pr(Head) = \frac{2}{3}[/tex]

Step-by-step explanation:

The right parameters are:

[tex]Head = 12[/tex]

[tex]Toss = 18[/tex] (not 10)

Required

[tex]Pr(Head)[/tex]

The experimental probability of Head is:

[tex]Pr(Head) = \frac{Head}{Toss}[/tex]

This gives

[tex]Pr(Head) = \frac{12}{18}[/tex]

Simplify

[tex]Pr(Head) = \frac{2}{3}[/tex]

Answer: x = 10 OR x = 4.

Step-by-step explanation: If x = 10 or 4 then the last step of the equation will always be multiplying by 0 which equates to 0 as well.

if x = 10

(10-10)(10-4) -> (0)(6) -> 0 x 6 = 0

if x = 4

(4-10)(4-4) -> (-6)(0) -> -6 x 0 = 0

Answer:

[tex]x = 10 \: and \: 4[/tex]

Step-by-step explanation:

Hope it is helpful....

Answer:

Step-by-step explanation:

Let the equation of the function is,

y = mx + b

Here, m = slope of the function

b = y-intercept

y-intercept of function is the y-value of a point where x = 0.

From the table given,

y-intercept 'b' = 1

Slope of the line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope of the line passing through (2, 6) and (4, 2) will be,

Slope = [tex]\frac{6-2}{2-4}[/tex]

          = [tex]-2[/tex]

Equation of the line will be,

y = -2x + 1

B). Slope of the line = -2

x-intercept of the line (at y = 0),

y = -2x + 1

0 = -2x + 1

x = [tex]\frac{1}{2}[/tex]

y-intercept of the line = 1

y-intercept indicates that the power of the battery was 100% when we turn on the laptop.

C). Equation of the line is,

y = -2x + 1

Here, y = power remaining

x = Hours

For y = 75% ≈ 0.75

0.75 = -2x + 1

0.75 - 1 = -2x

-0.25 = -2x

x = 0.125

Therefore, after 0.125 hours battery power will be 75%.

The slope means that the percentage decrease by 20% each hour, the y intercept means that the battery was 100% at start.

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

Let y represent the percent of battery after x hours.

From the table using the points (0, 1) and (4, 0.2):

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\ \\ y-1=\frac{0.2-1}{4-0}(x-0)\\ \\ y=-0.2x+1[/tex]

At y = 75% (0.75):

0.75 = -0.2x + 1

x = 1.25 hours

The slope means that the percentage decrease by 20% each hour, the y intercept means that the battery was 100% at start.

Find out more on linear equation at: https://brainly.com/question/14323743

Answer:

[tex]110\ in^2[/tex]

Step-by-step explanation:

[tex]1)\ A_1 = b * h_1 = 10 * 8 = 80\ in^2[/tex]

[tex]2)\ A_2 = \frac{b*h_2}{2} = \frac{10*(14-8)}{2} = \frac{10*6}{2} = \frac{60}{2} = 30\ in^2[/tex]

[tex]3)\ A = A_1 + A_2 = 80 + 30\ in^2 = 110\ in^2[/tex]

Answer:

0,5

Step-by-step explanation:

u just need to shorted it

Answer:

1800 m²

Step-by-step explanation:

Since the cost of constructing the path at rs 40 per sq m is rs 13760, if A is the area of the path then we have

rate × area = cost

area = cost/rate = 13760/40 = 344 m²

Now, let L = length of rectangular field and B = breadth of rectangular field. So, its area is A'= LB. Given that L = 2B, A' = 2B × B = 2B².

Also, since the width of the path is 2 m, the inner field has dimensions L - 2 - 2 = L - 4 as length and B - 2 - 2 = B - 4 as breadth since we subtract 2 m from both ends of the each dimension.

So, the inner area is (L - 4)(B - 4) = (2B - 4)(B - 4) = 2B² - 8B - 4B + 16 = 2B² - 12B + 16.

The area of the rectangular field is thus the inner area plus the area of the uniform path

So, 2B² - 12B + 16 + 344

We equate this the the area of the rectangular field. So,

2B² - 12B + 16 + 344 = 2B²

- 12B + 16 + 344 = 2B² - 2B²

- 12B + 360 = 0

- 12B = -360

B = -360/-12

B = 30 m

Since the area of the field A' = 2B²,

A' = 2(30 m)²

= 2(900 m²)

= 1800 m²

5 marbles.

We first need to find how many marbles we have in total.

8 marbles * 5 boys = 40 marbles.

These 40 marbles will now be divided by 8, since we are taking the total amount of marbles we have and separating them into 8 different piles.

40/8 = 5

There will be 5 marbles in each heap.

Answer:

[tex]\displaystyle (-12)^{-\frac{1}{3}}[/tex]

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \frac{1}{\sqrt[3]{-12}}[/tex]

Step 2: Rewrite

Answer:

60[tex]\pi[/tex] m³

Step-by-step explanation:

Use the cone volume formula, V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]

If the diameter is 12 m, the radius will be 6 m.

Plug in the height and radius into the formula, and solve:

V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]

V = [tex]\pi[/tex](6²)[tex]\frac{5}{y}[/tex]

V = [tex]\pi[/tex](36)[tex]\frac{5}{3}[/tex]

V = 60[tex]\pi[/tex]

So, the volume of the cone is 60[tex]\pi[/tex] m³

Answer:

no

Step-by-step explanation:

x²-2x-5=0

a=1

b=-2

c=-5

So also you need to correct the equasion according to the schematic below:

x=(-b+-root(b²-4*a*c))/2*a