Jack splits 28 muffins among 4 baskets. He puts the same number of muffins in each basket.

How many muffins are in each basket?

77a)

[tex]y=0.5x-2\implies y=\cfrac{x}{2}-2\implies \stackrel{x-intercept}{0=\cfrac{x}{2}-2} \\\\\\ 2=\cfrac{x}{2}\implies 4=x\qquad \qquad \boxed{(4~~,~~0)} \\\\\\ \stackrel{y-intercept}{y=0.5(0)-2}\implies y=-2\qquad \qquad \boxed{(0~~,~~-2)}[/tex]

77b)

[tex]y=-0.4x+2\implies y=-\cfrac{4x}{10}+2\implies y=\cfrac{2x}{5}+2 \implies \stackrel{x-intercept}{0=\cfrac{2x}{5}+2} \\\\\\ -2=\cfrac{2x}{5}\implies -10=2x\implies \cfrac{-10}{2}=x\implies -5=x~\hfill \boxed{(-5~~,~~0)} \\\\\\ \stackrel{y-intercept}{y=-0.4(0)+2}\implies y=2\qquad \qquad \boxed{(0~~,~~2)}[/tex]

Answer:

It would be 8 cups of flour.

Answer:

8 cups

Step-by-step explanation:

If the angles are equal, then, x = 9.

Simplification of expressions means rewriting the same algebraic expression with no like terms and in a compact manner.

Given are two angles, 3x -8° and 2x + 1°, simplifying by equating them,

3x -8° = 2x + 1°

x = 9

Hence, If the angles are equal, then, x = 9.

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Answer:

a. x = [tex]\frac{1}{12}[/tex]

b. [tex]\frac{1}{4}[/tex] = 1x

c. 3x = [tex]\frac{3}{3}[/tex]

d. x = [tex]\frac{1}{20}[/tex]

e. x = [tex]\frac{10}{3}[/tex]

Answer:

  y = √(5x+34)

Step-by-step explanation:

The regression formula that matches a square root function to these points can be worked out by a suitable calculator. The attachments shows the points are matched exactly by the function ...

  y = √(5x+34)

__

If you would like to work this by hand, you can put the (x, y) point values into the proposed equation and see what the coefficients need to be:

  y = √(ax +b)

  7 = √(3a +b)   ⇒   49 = 3a +b

  8 = √(6a +b)   ⇒   64 = 6a +b

Subtracting the first equation from the second, gives ...

  (64) -(49) = (6a +b) -(3a +b)

  15 = 3a   ⇒   a = 5

  49 = 3(5) +b   ⇒   b = 34

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{40\% of 59}}{\left( \cfrac{40}{100} \right)59}\implies 23.6~\hfill \underset{sale~price}{\stackrel{59~~ - ~~23.6}{35.4}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{8\% of 35.4}}{\left( \cfrac{8}{100} \right)35.4}\implies 2.832~\hspace{10em}\underset{\textit{sale price plus tax}}{\stackrel{35.4~~ + ~~2.832}{\approx 38.23}}[/tex]

Answer: 86 + 7.5 = 93.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Initial function is

Changed function is

This is best explained when graphed. See below to confirm the correct option

f(x+8)

So

x² is changed to (x+8)²

Change in x

It will shift 8 units left

Option B

Answer:

9/4 seconds

Step-by-step explanation:

Plug 13 into the equation

13=94-16t^2

subtract 94

-81=-16t^2

divide by -1

81=16t^2

take the square root of both sides

9=4t

divide by 4

t=9/4

Answer:

Step-by-step explanation:

The sides of a triangle measure 6, 8 and 10 cm. What is the area of the triangle?

from the data it is a right triangle, 10 cm is the hypotenuse

so

1/2 (6 * 8) =

1/2 * 48 =

24 units²

Solution:

Note that:

Let's substitute x as 2 to find out y.

Let's substitute x as 4 to find out y.

Final answer:

Option B is correct.

Solution:

We know that:

[tex]\bullet \ \ \tex\text{Area of triangle:} = \frac{1}{2} \times \tex\text{Base} \times \tex\text{Height}[/tex]

Let the base of the triangle be 11 yd. If we extend the base, it will allow us to find the height of the triangle, which is 8 yd.

Using the formula:

[tex]\bullet \ \ \tex\text{Area of triangle:} = \frac{1}{2} \times 11 \times 8[/tex]

Now, let's simplify.

[tex]\bullet \ \ \tex\text{Area of triangle:} = \frac{1}{2} \times 11 \times 8[/tex]

[tex]\bullet \ \ \tex\text{Area of triangle:} = 11 \times 4[/tex]

[tex]\boxed{\bold{\tex\text{Area of triangle:} = 44 \ \tex\text{yd}^{2}}}[/tex]

The events of rainfall and having a full moon on a given date are illustrations of probability

The probability that there will be rainfall and a full moon on that date is 0.0049

From the question, we have the following parameters

P(A) = 1/7 --- the probability that it rains

P(B) = 1/29 --- the probability of having a full moon

So, the probability that is rains and there is a full moon on a given day is:

[tex]p = \frac 17 * \frac 1{29}[/tex]

Simplify

[tex]p = 0.0049[/tex]

Hence, the probability that there will be rainfall and a full moon on that date is 0.0049

Read more about probability at:

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Answer:

13.33

Step-by-step explanation:

Write the equation for an inverse variation

⇒ y = k/x

Where x is degrees and y is minutes

Substitute 20 and 20 for x and y

⇒ 20 = k/20

Multiply both sides by 20 to solve k

⇒ 20 × 20 = 20 × k/20

⇒ k = 400

After solving for k, write an equation for the inverse variation

⇒ y = 400/x

Substitute 30 for x

⇒ y = 400/30

⇒ y = 40/3

⇒ y = 13.3333333333

⇒ y = 13.33

[RevyBreeze]

Answer

A.) As the number of years increased, the population increased.

Answer:

about 42 the not rounded is 41.6

Answer:

60

Step-by-step explanation:

Multiply to find that the answer is: 41.6

To estimate, simply round the numbers before multiplying. That would be thirty percent of 200. The answer is 60. This is close to 41.6 and is a reasonable estimate.

Answer:

4n ≤ 32

/4      /4

n ≤ 8, he could run less than 8 or just 8 laps,

so possible laps:

1, 2, 3, 4, 5, 6, 7, or 8 laps he could've ran.

Answer:

The discount is $18.20 which changes the price of the jeans to $27.30.

Answer:

384sqrt3

Step-by-step explanation:

The formula for the area of a hexagon is A = 3sqrt3 times s^2 /2

Plug in s = 16 to get A = 3sqrt3 times 16^2 (256) / 2

3sqrt3 times 256 is 768sqrt3

You divide that by 2 to get 384sqrt3

Answer:

Vertical Asymptote at: x = - 1.5

Slanted Asymptote at: y = -x  9/2

Step-by-step explanation:

See image (I HAVE NO IDEA IF YOUR SUPPOSED TO GIVE THE SLANTED ASYMPTOTE. THE PROBLEM ONLY SAYS VERTICAL AND HORIZONTAL ONLY, SO I GUESS ONLY DRAW THE GREEN LINE, NOT THE PURPLE ONE!)

So only draw the x = - 1.5 line that is green!

Answer:

T=-9

Step-by-step explanation:

Answer:

4 containers orange juice

4 containers pinapple

2 containers cranberry

Step-by-step explanation:

1000 milliliters are in a liter

4 liters orange juice, 4*500 = 2,000

4 liters pinapple, 4*500 = 2,000

2 liters cranberry, 2*500 = 1,000

Total 5 liters

Given :

⠀

To Find :

⠀

Solution :

Perimeter of the plank :

[tex]\: {\qquad \dashrightarrow \sf 2 \times (Length + Breadth) }[/tex]

[tex]\: {\qquad \dashrightarrow \sf{{ 2 \times (300 + 30) \: cm }}}[/tex]

[tex]\: {\qquad \dashrightarrow \sf{{ 2 \times (330) \: cm }}}[/tex]

[tex]\: {\qquad \dashrightarrow \sf{{ 600 \: cm }}}[/tex]

⠀

Area of the plank :

[tex]\: {\qquad \dashrightarrow \sf (Length \times Breadth) }[/tex]

[tex]\: {\qquad \dashrightarrow \sf (330 \times 30) \: {cm}^{2} }[/tex]

[tex]\: {\qquad \dashrightarrow \sf 9 000 \: {cm}^{2} }[/tex]

⠀

Step-by-step explanation:

Given :-

To find :-

Solution :-

Perimeter of rectangular plank = 2(L+W)

putting the values,

perimeter = 2(300+30)cm

⇝660 cm

Area of rectangular plank = L × W

putting the known values ,

Area = 300 × 30 cm²

⇝ 9000cm²

Answer:

100

Step-by-step explanation:

Angle x and the angle equaling 100 are vertical angles.

the 45 degree angle is just there to confuse you

Answer:

Given that measure 2 is 79 degrees, we know it'll be supplementary to angle 1 meaning that that both angle measures 1 and 2 will equal 180 degrees:

79 + x = 180

-79        -79

x = 101, ∠1 = 101°

Angles 2 and 4 are vertical, so they are congruent meaning they measure the same degrees:

if ∠2 = 79, then ∠4 is also equal to 79°

Now that we found the measure of angle 1, we can determine the measure of angle 3 since they are vertical as well, (vertical angles are congruent, meaning they measure the same degrees):

if ∠1 = 101, then ∠3 is also equal to 101°

Answer:

Step-by-step explanation:

First add what you have.

Sum = 5 + 7 +7+8 + x + 5 + 4 +3 + 1 +2

Sum =  x + 42

Now when you divide this by the number of terms, you get

(x + 42) / 10

The answer is 4.5

(x + 42) / 10 = 4.5                 Multiply by 10

x + 42 = 4.5 * 10

x + 42 = 45                           Subtract 42

x = 45  - 42

x = 3

12)

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{4}}}\implies \cfrac{-2}{-8}\implies \cfrac{1}{4}[/tex]

now, I used y₂ - y₁  and x₂ - x₁, is pretty much the same slope the other way.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{\cfrac{1}{4}}(x-\stackrel{x_1}{4}) \\\\\\ y-5=\cfrac{1}{4}x-1\implies y=\cfrac{1}{4}x+4[/tex]

13)

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{0}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-2)}}}\implies \cfrac{-2}{-4+2}\implies \cfrac{-2}{-2}\implies 1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_2=m(x-x_2) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{1}(x-\stackrel{x_1}{(-4)}) \\\\\\ y=1(x+4)\implies y=x+4[/tex]

notice, for the point-slope form, we can use either x₁ , y₁  or x₂ , y₂ , doesn't quite matter, so long we use the corresponding coordinates.

Answer:

M = 20

Step-by-step explanation:

given M is directly proportional to r³ then the equation relating them is

M = kr³ ← k is the constant of proportion

to find k use the condition when r = 4, M = 160 , then

160 = k × 4³ = 64k ( divide both sides by 64 )

[tex]\frac{160}{64}[/tex] = k , then

k = 2.5

M = 2.5r³ ← equation of proportion

when r = 2 , then

M = 2.5 × 2³ = 2.5 × 8 = 20

Answer:

116.663333333 repeating

Step-by-step explanation:

do 349.99 divided by 3

Answer:

6 pounds = 96 ounces

4 pounds = 64 ounces