A bag of M&M's has 6 red, 3 green, 8 blue, and 5 yellow M&M's. What is the probability of randomly picking: (give answer as a reduced fraction) 1) a yellow? 2) a blue or green? 3) an orange?

Answer: y-intercept is 12

Step-by-step explanation:

y = mx +b

m = slope

b = y-intercept

y | = | x | + | b

f(x) | = | 4x | + | 12

b = y-intercept

We are given the following set of equations,

\(2x-6y=12 \\ -x+3y=1\)

and asked to determine whether they are parallel, perpendicular or neither. We first need to alter each equation and put into slope-intercept form, \(y=mx+b\) (m=slope/rate of change, b=y-intercept). Then we can follow the following basic guidelines,

\(\Rrightarrow\) Lines that are parallel will have slopes that are equal (\(m =m\)) .

\(\Rrightarrow\) Lines that are perpendicular will have slopes that are reciprocal, opposite signs (\(m \rightarrow -\frac{1}{m}\)).

\(\Rrightarrow\) Lines that are neither will have slopes that are NOT equal (\(m_{1} \neq m_{2}\)).

Taking the first equation, \(2x-6y=12\), and putting it in slope-int form.

\(\Longrightarrow2x-6y=12\)

\(\Longrightarrow-6y=12-2x\)

\(\Longrightarrow y=\frac{12}{-6} -\frac{2}{-6} x\)

\(\Longrightarrow y=-2+\frac{1}{3} x\)

\(\Longrightarrow y=\frac{1}{3} x -2\)

The slope of line 1 is \(\frac{1}{3}\).

Now taking the second equation, \(-x+3y=1\), and putting it in slope-int form.

\(\Longrightarrow -x+3y=1\)

\(\Longrightarrow 3y=1+x\)

\(\Longrightarrow y=\frac{1}{3} +\frac{x}{3}\)

\(\Longrightarrow y=\frac{1}{3}x +\frac{1}{3}\)

The slope of line 2 is \(\frac{1}{3}\).

Since the slopes of each line are equal, than the lines are parallel.

Answer:

165 minutes

Step-by-step explanation:

To solve for the number of minutes that Joaquin played for, we can use this expression:

(let 'a' represent how much time passed from the time Joaquin started playing basketball until the time he arrived at home)

Subtracting 1:10 from each side:

1:10 - 1:10 cancels out to 0, while 3:35 - 1:10 is equal to 2:25.

So, the expression is now:

So, 2 hours and 25 minutes passed.

If we know that 1 hour is equivalent to 60 minutes, we can use this expression to solve for however many minutes are in 2 hours:

Now we need to add on the number of minutes and the time it took him to get home:

Therefore, 165 minutes passed from the time Joaquin started playing basketball until the time he arrived at home.

Answer:

A

Step-by-step explanation:

Using proportions, considering the relation between the height and the shadow, it is found that the cell phone tower is 50 feet.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

When the shadow is of 8 feet, the height is of 10 feet. What is the height when the shadow is of 40 feet? The rule of three is:

8 feet - 10 feet

40 feet - h feet

Applying cross multiplication:

8h = 10 x 40

Simplifying by 8:

h = 10 x 5 = 50 feet.

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Answer:

A. $35,095.2

B. $4,995.2

Explanation:

The total amount paid to the bank can be calculated as the monthly payment multiplied by the number of months in the course of the loan. So, it is equal to:

Total = $584.92 x 5 years x 12 months

Total = $35,095.2

On the other hand, the total finance charge paid to the bank can be calculated as the total amount paid to the bank less the initial cost of the car, so:

$35,095.2 - $30,100 = $4,995.2

Therefore, the answers are:

A. $35,095.2

B. $4,995.2

Answer:

n=6 , n=-2

Step-by-step explanation:

\(n^{2}-4n-12=0\)

Factorise to give:

\((n-6)(n+2)\)

Set first one to equal 0:

\(n-6=0\)

\(n=6\)

Set second one to equal 0:

\(n+2=0\)

\(n=-2\)

Reason for 2 solutions:

All quadratics can have a maximum of 2 solutions like this one or a minimum of 0.

The solution(s) is the point where the graph crosses the x-axis

The image below shows the graph of the equation:

\(n^{2}-4n-12\)

When y=0:

It intercepts the x-axis at 6 and -2 giving why n has 2 solutions

Answer:

\( \frac{1}{9 - 4i} \)

I'm not sure

It looks like the limit you want to compute is

\(\displaystyle L = \lim_{x\to0}\left(\frac x{\tan(x)}\right)^{\cot^2(x)}\)

Rewrite the limand with an exponential and logarithm:

\(\left(\dfrac{x}{\tan(x)}\right)^{\cot^2(x)} = \exp\left(\cot^2(x) \ln\left(\dfrac{x}{\tan(x)}\right)\right) = \exp\left(\dfrac{\ln\left(\dfrac{x}{\tan(x)}\right)}{\tan^2(x)}\right)\)

Now, since the exponential function is continuous at 0, we can write

\(\displaystyle L = \lim_{x\to0} \exp\left(\dfrac{\ln\left(\dfrac{x}{\tan(x)}\right)}{\tan^2(x)}\right) = \exp\left(\lim_{x\to0}\dfrac{\ln\left(\dfrac{x}{\tan(x)}\right)}{\tan^2(x)}\right)\)

Let M denote the remaining limit.

We have \(\dfrac x{\tan(x)}\to1\) as \(x\to0\), so \(\ln\left(\dfrac x{\tan(x)}\right)\to0\) and \(\tan^2(x)\to0\). Apply L'Hopital's rule:

\(\displaystyle M = \lim_{x\to0}\dfrac{\ln\left(\dfrac{x}{\tan(x)}\right)}{\tan^2(x)} \\\\ M = \lim_{x\to0}\dfrac{\dfrac{\tan(x)-x\sec^2(x)}{\tan^2(x)}\times\dfrac{\tan(x)}{x}}{2\tan(x)\sec^2(x)}\)

Simplify and rewrite this in terms of sin and cos :

\(\displaystyle M = \lim_{x\to0} \dfrac{\dfrac{\tan(x)-x\sec^2(x)}{\tan^2(x)}\times\dfrac{\tan(x)}{x}}{2\tan(x)\sec^2(x)} \\\\ M= \lim_{x\to0}\dfrac{\sin(x)\cos^3(x) - x\cos^2(x)}{2x\sin^2(x)}\)

As \(x\to0\), we get another 0/0 indeterminate form. Apply L'Hopital's rule again:

\(\displaystyle M = \lim_{x\to0} \frac{\sin(x)\cos^3(x) - x\cos^2(x)}{2x\sin^2(x)} \\\\ M = \lim_{x\to0} \frac{\cos^4(x) - 3\sin^2(x)\cos^2(x) - \cos^2(x) + 2x\cos(x)\sin(x)}{2\sin^2(x)+4x\sin(x)\cos(x)}\)

Recall the double angle identity for sin:

sin(2x) = 2 sin(x) cos(x)

Also, in the numerator we have

cos⁴(x) - cos²(x) = cos²(x) (cos²(x) - 1) = - cos²(x) sin²(x) = -1/4 sin²(2x)

So we can simplify M as

\(\displaystyle M = \lim_{x\to0} \frac{x\sin(2x) - \sin^2(2x)}{2\sin^2(x)+2x\sin(2x)}\)

This again yields 0/0. Apply L'Hopital's rule again:

\(\displaystyle M = \lim_{x\to0} \frac{\sin(2x)+2x\cos(2x)-4\sin(2x)\cos(2x)}{2\sin(2x)+4x\cos(2x)+4\sin(x)\cos(x)} \\\\ M = \lim_{x\to0} \frac{\sin(2x) + 2x\cos(2x) - 2\sin(4x)}{4\sin(2x)+4x\cos(2x)}\)

Once again, this gives 0/0. Apply L'Hopital's rule one last time:

\(\displaystyle M = \lim_{x\to0}\frac{2\cos(2x)+2\cos(2x)-4x\sin(2x)-8\cos(4x)}{8\cos(2x)+4\cos(2x)-8x\sin(2x)} \\\\ M = \lim_{x\to0} \frac{4\cos(2x)-4x\sin(2x)-8\cos(4x)}{12\cos(2x)-8x\sin(2x)}\)

Now as \(x\to0\), the terms containing x and sin(nx) all go to 0, and we're left with

\(M = \dfrac{4-8}{12} = -\dfrac13\)

Then the original limit is

\(L = \exp(M) = e^{-1/3} = \boxed{\dfrac1{\sqrt[3]{e}}}\)

Answer:

3

Step-by-step explanation:

this is what I think

\(\huge\text{Hey there!}\)

\(\large\text{All you have to do is COMBINE your LIKE TERMS}\)

\(\large\text{5w + 10w}\)

\(\large\text{(5w + 10w) = 15w}\)

\(\boxed{\boxed{\large\text{Answer: \bf{15w}}}}\huge\checkmark\)

\(\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\):)

Given problem;

   Inequality equation;

               \(\frac{x}{16}\)   <   6

Before we solve, let us first translate this problem.

It simply states that for what value(s) of x will the expression be less than 6.

To find this value, we can simply carry out the normal mathematical simplification.

Simply multiply both sides by 16 to reduce the fraction;

      16  x (\(\frac{x}{16}\))   <  6 x 16

 On the left hand side, 16 will cancel out;

                   x <  96

Any value for which x is less than 96 will make the solution of this problem less than 6.

For example, 95;

                       \(\frac{95}{16}\)  = 5.93

This value is less than 6

Answer:

10 + x/6

Step-by-step explanation:

10 + x/6 represents this phrase

Answer:

8 and 9

Step-by-step explanation

Answer:

5

Step-by-step explanation:

Just grap any two consecutive terms in the sequence. lets say -55 and -50

-50-(-55) = 5

you can check this by picking two other terms

Answer:

The graph is constant from (-oo,-2)U(4,oo).

The graph is increasing from (-2,4).

The graph never decreases.

Step-by-step explanation:

Take the x values from when the line is constant (not rising or falling), increasing (rising), and decreasing (falling).

oo means infinity

The graph is constant from (-oo,-2)U(4,oo).

The graph is increasing from (-2,4).

The graph never decreases.

Answer: 312.5 miles

Step-by-step explanation:

125/2 = 62.5 per hour x 5 hours = 312.5 miles

Answer:

BC = 4

Step-by-step explanation:

The diagram shows a circle with radius AE and chord BD.

Assuming that the radius bisects the chord, then AE is perpendicular to BD. So the measure of angle ACB is 90°.

This means that triangle ACB is a right triangle, with legs AC and BC, and hypotenuse AB.

The length of the radius is:

\(AE = 3 + 2 = 5\)

As AB is also the radius, AB = 5.

To find the length of BC, use Pythagoras Theorem:

\(AC^2+BC^2=AB^2\)

    \(3^2+BC^2=5^2\)

      \(9+BC^2=25\)

\(9+BC^2-9=25-9\)

           \(BC^2=16\)

        \(\sqrt{BC^2}=\sqrt{16}\)

            \(BC=4\)

Therefore, the length of line segment BC is 4.

The data correlation in the scatter plot above include the following: B. positive.

In Mathematics, a positive correlation is used to described a scenario in which two variables move in the same direction and are in tandem.

This ultimately implies that, a positive correlation exist when two variables have a linear relationship or are in direct proportion. Therefore, when one variable increases, the other variable generally increases, as well.

By critically observing the scatter plot shown in the image attached above, we can reasonably infer and logically deduce that there is a positive correlation between the x-values and y-values because they both increase simultaneously.

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Answer:

21 diamonds.

Step-by-step explanation:

1 bracelet = 7 diamonds

3 bracelet= ? diamonds

All we have to do is multiply 3 by 7 to get the number of diamonds Jen have with three bracelets.

3 x 7 = 21

Answer:

1 bracelet has 7 diamonds, therefore 2 has 14 and 3 has 21 diamonds

Step-by-step explanation:

The cost of 650 bricks which are right rectangular prisms is $1774.5.

What is a rectangular prism?

Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom and four are lateral faces). The prism's faces are all rectangular in shape. There are three sets of identical faces as a result. A rectangular prism is often referred to as a cuboid because of its shape.

The dimensions of the right rectangular prism brick is -

width, w = 7 in

length, l = 3 in

height, h = 3(1/4) in = 3.25 in

Find the volume of the brick -

Volume = w × l × h

Volume = 7 × 3 × 3.25

Volume = 68.25 in³

The volume occupied by 650 bricks is -

V650 = 68.25 × 650

V650 = 44362.5 in³

The cost of cubic inch of brick is $0.04.

The cost of 650 bricks is -

Total cost = 44362.5 in³ × $0.04

Total cost = $1774.5

Therefore, the total cost is obtained as $1774.5.

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Answer:

Value of x = 11 ° , ∠B = 108° ,∠C = 36° ,∠D = 36°

Step-by-step explanation:

Given :

In ΔBCD , BC = BD And ∠B= (13x-35)° , ∠C= (5x-19)° ,∠D=(2x+14)°

To Find :

value of x and ∠D , ∠B and ∠C

Solution:

∵ BC=BD , So ∠C = ∠D

Therefore 5x-19 = 2x+14

3x = 33 , ∴ x=11°

So, ∠B = (13×11) - 35 = 108°

∠C = (5×11)-19 = 36°

∠D= (2×11) +14 =36°

Step-by-step explanation:

anewer is 30 cubic inches.

Answer:

(fog)(x) means that we have the function f(x) evaluated in the function g(x), or f(g(x)).

So, if f(x) = x^3 + 1 and g(x) = x - 2.

we have:

a) (fog)(0) = f(g(0)) = (0 - 2)^3 + 1 = -8 + 1 = -7

b) (gof)(0) = g(f(0)) = (0^3 + 1) - 2 = -1

c)  (fof)(1) = f(f(1)) = (1^3 + 1)^3 + 1 = 2^3 + 1 = 8 + 1 = 9

d) (gog)(1) = g(g(1)) = (1 - 2) - 2 = -1 -2 = -3

Answer:

-4

Step-by-step explanation:

The volume of the cylinder is equal to 300π cubic feet.

What is meant by volume?

Volume is the measure of space within a particular 3D object in mathematics. For instance, a fish tank measures three feet long by one foot wide by two feet high. The volume is calculated by multiplying the length, the breadth, and the height, or 3x1x2, which equals six. The fish tank, therefore, has a 6 cubic foot volume.

It is given that the radius and height of the cone and cylinder are the same.

The volume of the cone is 100π cubic feet.

The volume of a cone is \(\frac{1}{3} \pi r^{2} h=100\pi\)

The volume of a cylinder is \(\pi r^{2}h\).

Therefore the volume of a cylinder is 3 times the volume of a cone with the same radius and height.

Therefore the volume of the cylinder is equal to 300π cubic feet.

To learn more about the volume of the cone and cylinder, refer to the link below:

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