Use the following prompt to answer the next 6 questions. Suppose we want to test the color distribution claim on the M&M’s website that a bag of plain M&M’s is made up of 10% blue, 10% orange, 10% green, 20% red, 20% yellow, and 30% brown. We select a sample of 400 plain M&M’s and found the following: Color Blue Orange Green Red Yellow Brown Frequency 30 48 55 66 70 131 Is there evidence to doubt the color distribution claimed by the website? Use ????=0.05

Answer:

1. no solution 2. has one solution

Step-by-step explanation:

first you must find the discriminant of each quadratic also remember

if the discriminant is positive  b^{2}-4ac> 0, then the quadratic equation has two solutions.

if the discriminant is equal  b^{2}-4ac= 0, then the quadratic equation has one solution.

if the discriminant is negative  b^{2}-4ac< 0, then the quadratic equation has no solution.

1. the discriminant is [tex]\sqrt{b^2-4ac}[/tex] and when you plug in the numbers you get -55 which is less than 0

2. the discriminant is 0 so there is one solution

Answer:

1. has no real roots, no solutions (unless you can have imaginary solutions)

2. touches the x axis in one point, so one solution

Step-by-step explanation:

Answer:

300 minutes

2:00 p.m

Step-by-step explanation:

Given the following:

Time taken to mark a script :

Mrs Kanja = 5mins

Miss Kanene = 4mins

Mrs Nyaga = 12 mins

Number of scripts = 160

Start time = 9:00 a.m

Rate at which each of them mark:

Mrs Kanja = t / 5

Miss Kanene = t/4

Mrs Nyaga = t/12

Combined rate :

t/5 + t/4 + t/12 = 160

(12t + 15t + 5t) / 60 = 160

32t / 60 = 160

32t = 160 * 60

32t = 9600

t = 9600 / 32

t = 300 minutes

300 minutes = 300/60 = 5hrs

9:00 a.m + 5 hours = 2:00 p.m

1. (a) 0 = x² + 4x - 12 (Switch Sides)

x² + 4x - 12 = 0 (Factor Expression)

(x - 2)(x + 6) = 0 (Apply the Zero Factor Principle)

x = 2, and x = - 6

x - intercept : (2, 0) and ( - 6, 0)

(b) y = (0)² + 4(0) - 12 (Simplify)

y = 0 + 4 * 0 - 12 = 0 + 0 - 12 = - 12

y - intercept : (0, - 12)

(c) Our vertex belongs to an upward facing parabola, and hence it will be a minimum, of ( - 2, - 16).

2. Seth's solution is not accurate. He did the calculations accurately, and ended up with x = 3 and x = - 2. However he forgot to substitute those values back into the equations y = x² + 3x - 5 and y = 4x + 1, solving for the y values. Instead of being ( - 2, 0) and (3, 0) it should have been (3, 13), ( - 2, - 7)...

y = (3)² + 3(3) - 5 = 9 + 9 - 5 = 18 - 5 = 13,

y = 4( - 2) + 1 = - 8 + 1 = - 7

Hence we get the solutions (3, 13) and ( - 2, - 7).

Answer:

100, 101, 102, 103, 104

Step-by-step explanation:

Basically, if the units (or ones, it's the same thing) digit of the first number is 0, the units digit of the second number should be 1, then 2, and so on. Therefore, one possible list of numbers is as follows: 100, 101, 102, 103, 104.

Answer:

129.5 Square feet is the correct answer.

Step-by-step explanation:

I am a 100% SURE of that.

Hope this helps....

Have a nice day!!!!

The length of the side can be both 5 and 9.

An Isosceles Triangle is a triangle that has two equal sides.

The length of the sides of an isosceles triangle is given as 5 and 9

To determine the third side, the property of Triangle Inequality will be used

According to the property, the sum of any pair of a triangle’s sides is always greater than the third side.

If the third side is 5 then

5+5 > 9

10 >9

true

if the third side is 9 then

5+9 > 9

14>9

Therefore, the length of the side can be both 5 and 9.

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Answer:

son2: 5

son1: 10

Step-by-step explanation:

2x (son1) + x (son2) + 35 (mother) + 3 (years)*3 (people) = 59

3x = 15

x = 5

The age of each boy at present will be 2 years and 3 years.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Let the age of the sons will be x and y.

A mother who is 35 years old has two sons, one of whom is twice as old as the other. Then the equation will be

x = 2y

In 3 years, the sum of all their ages will be 59 years. Then the equation will be

x + y + x + 1 + y + 1 + x + 2 + y + 2 + 35 = 59

Simplify the equation, we have

3x + 3y + 41 = 59

      6y + 3y = 59 – 41

              9y = 18

                y = 2

Then the value of x will be

x = 2y

x = 2(2)

x = 4

Thus, the age of each boy at present will be 2 years and 3 years.

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Answer:

Kindly check explanation

Step-by-step explanation:

SMALL SIZE :

AMOUNT OF LIQUID = 250 milliliters

Sales price = $4.50

Cost per milliliter :

Sales price / amount of liquid

$4.50 / 250 = $0.018

MEDIUM SIZE :

AMOUNT OF LIQUID = 500 milliliters

Sales price = $9.95

Cost per milliliter :

Sales price / amount of liquid

$9.95 / 500 = $0.0199

= $0.020 ( 3 decimal places)

LARGE SIZE :

AMOUNT OF LIQUID = 1 LITRE = 1000 milliliters

Sales price = $16.95

Cost per milliliter :

Sales price / amount of liquid

$16.95 / 500 = $0.0199

= $0.01695

= $0.017 ( 3 decimal places)

A) LARGE < SMALL < MEDIUM

B) LEAST EXPENSIVE WAY TO BUY 1500 milliliters of green cleaner :

1 large size + 2 small sizes

$16.95 + 2($4.50)

$16.95 + $9.00

= $25.95

C.) MOST EXPENSIVE WAY TO BUY 1500 milliliters of green cleaner :

3 medium sizes

3 * ($9.95)

$29.85

Answer:

156.6 m²

Step-by-step explanation:

To find the surface area of this pyramid, we need to find the area of the base and the sides.

The base triangle has a length of 9 and a height of 7.8. So:

[tex]\frac{bh}{2} = \frac{9\cdot7.8}{2} = \frac{70.2}{2} = 35.1[/tex]

Now, the length of the sides are 9 and the height is 9. So:

[tex]\frac{9\cdot9}{2} = \frac{81}{2} = 40.5[/tex]

Since there are 3 identical sides:

[tex]40.5\cdot3=121.5[/tex]

Add the values:

[tex]121.5+35.1=156.6[/tex]

Hope this helped!

Answer:

( 6,6) is outside

Step-by-step explanation:

(x - 2)^2 + (y - 1)^2 = 25

This is of the form

(x - h)^2 + (y - k)^2 = r^2

where ( h,k) is the center and r is the radius

(x - 2)^2 + (y - 1)^2 = 5^2

The center is at ( 2,1) and the radius is 5

P(0,5), Q(2,2) R(5,-2), and S(6,6)

Adding the radius to the y coordinate gives us 6 so the only point with a y coordinate on the circle is ( 2,6)

( 6,6) is outside the circle

Answer: 280 tons

Step-by-step explanation: divide all at tons/pound which accumulated to 280 tons

Answer: 10 ships

Step-by-step explanation:

Answer:

Number of 50sen coins  =  13

Step-by-step explanation:

Let the number of 50sen coins be = x

Let the number of 20sen coins be  = y

Total coins  = 20

x + y = 20 ----------------------(i)

Value of 50sen coins = 0.50*x = 0.50x

Value of 20sen coins = 0.20 *y = 0.20y

Total value = RM 6.10

0.5x + 0.2y = 6.10 -------------------(ii)

Multiply (i) by (-0.5) and then add the equations. So, x will be eliminated and we can find the value of y

(i) * (-0.5)      -0.5x - 0.5y = -10

(ii)                  0.5x  + 0.2y = 6.10 { add and now x will be eliminated}

                              - 0.3y = -3.90

Divide both sides by (-0.3)

y = -3.90/-0.3

y = 13

Plug in the value of y in equation (i)

x + 13 = 20

Subtract 13 from both sides

x = 20 -13

x = 7

Number of 50sen coins  =  13

Answer:

the number of 50sen coins:

x = 7

Step-by-step explanation:

Taking the number of 50sen coins as x

50(x)

∴ the number of 20sen coins is 20-x (as total no. of coins are 20)

20(20-x)

total amount = 6.10RM = 610sen

equating:

50x + 20(20-x) = 610

50x + 400-20x = 610

50x - 20x = 610-400

30x = 210

x = 210/30 = 7

Therefore, the number of 50sen coins is 7

20sen coins is 20-7= 13.

verification=

50*7 + 20*13 = 610

310 + 260 = 610

610sen = 610sen

6.10RM = 6.10RM

L.H.S = R.H.S

hence, verified.

Answer:

(x+1)(x+1)(2x−5)(x^2−4x+5)

Step-by-step explanation:

2x^5−9x^4+6x^3+22x^2−20x−25

2x^5−9x^4+6x^3+22x^2−20x−25

=(x+1)(x+1)(2x−5)(x2−4x+5)

Answer:

-14

Step-by-step explanation:

5-y=19

collect all the like terms on one side

-y=19-5

when 5 moves over the the other side of the equation it becomes a negative

-y=14

divide both sides by a negative sign

y=-14

Answer:

24 square units

Step-by-step explanation:

Use the formula for area of a parallelogram to solve.  The base is 6 units, and the height is 4 units.

A = bh

A = (6)(4)

A = 24 square units

The area of the parallelogram is 24 square units.

Answer:

240 mL.

Step-by-step explanation:

The following data were obtained from the question:

Ratio of Flour = 5

Ratio of brown sugar = 3

Ratio of chocolate = 4

Total volume = 720 mL

Next, we shall determine the total ratio. This can be obtained as follow:

Total ratio = ratio of flour + ratio of brown sugar + ratio of chocolate

Total ratio = 5 + 3 + 4

Total ratio = 12

Finally, we shall determine the volume of the chocolate chips in the mixture as shown below:

Volume of chocolate chips = ratio of chocolate /total ratio x total volume

Ratio of chocolate = 4

Total ratio = 12

Total volume = 720 mL

Volume of chocolate chips =..?

Volume of chocolate chips = ratio of chocolate /total ratio x total volume

Volume of chocolate chip = 4/12 x 720

Volume of chocolate chip = 240 mL

Therefore, the volume of the chocolate chips in the mixture is 240 mL.

Answer:

Each team will get 3 eggs

Step-by-step explanation:

First determine the number of eggs

7 * 12 = 84 eggs

Then divide by the number of teams

84/26 =3 with 6 left over

Each team will get 3 eggs

Answer:

False

Step-by-step explanation:

A > B means A is greater than B, so A is not more than B is false.

Answer:

0.25%

Step-by-step explanation:

Rate of commission

= (commission*100)/cost of land

=( 20000*100)/8000000

= 2000000/8000000

=2/8

= 0.25%

Answer:

12 inches

Step-by-step explanation:

A=1/2bh

30=1/2b5

(30*2)/5=b

B=12

Answer:

200 ft^2

Step-by-step explanation:

The surface area of the pyramid is the sum of the area of the base and the areas of the 4 congruent triangular sides.

SA = LW + 4 * bh/2

SA = 10 ft * 10 ft + 4 * (10 ft)(5 ft)/2

SA = 100 ft^2 + 2(50 ft^2)

SA = 200 ft^2

(P.S. It's impossible to make a pyramid with these dimensions.)

Answer:

[tex]\boxed{\sf 200 \ feet^2}[/tex]

Step-by-step explanation:

The 3D shape is a square-based pyramid.

The surface area of a square-based pyramid is given as:

[tex]\sf SA=2 \times (base \ length) \times (slant \ height) + (base \ length)^2[/tex]

Plug in the values.

[tex]\sf SA=2 \times 10 \times 5 + 10^2[/tex]

[tex]\sf SA=100 + 100[/tex]

[tex]\sf SA=200[/tex]

Answer:

[tex]\Large \boxed{\mathrm{Option \ 2}}[/tex]

Step-by-step explanation:

[tex]2x^2 =16[/tex]

The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is x, so divide both sides by 2 before applying the square root property.

The x variable should be isolated on one side of the equation. The x variable is squared so before performing the square root property where we take the square root of both sides, we divide both sides by 2, then take the square root of both sides.

Dividing both sides by 2.

[tex]\displaystyle \frac{2x^2 }{2} =\frac{16}{2}[/tex]

[tex]x^2 =8[/tex]

Taking the square root of both sides.

[tex]\sqrt{x^2 } =\pm \sqrt{8}[/tex]

[tex]x=\pm 2\sqrt{2}[/tex]

Answer:

Option 2

Step-by-step explanation:

2x² = 16

Since x is completely squared and and 2 isn't , so we need to divide both sides by 2. As to find x , we need to "isolate" x first so that is why we need to get rid of 2 with the x². We'll divide both sides by 2 in order to get rid of 2.

Dividing both sides by 2

=> x² = 8

Now , that is the x is isolated so we'll take square root on both sides

=> x = ±2√2

That's true. Pi is known to be defined as the ratio of the circumference of a circle to its diameter.

Answer:

The equation of the quadratic function shown is;

x^2+ 2x -3

Step-by-step explanation:

Here in this question, we need to know the quadratic equation whose graph was shown.

The key to answering this lies in knowing the roots of the equation.

The roots of the equation are the solution to the quadratic equation and can be seen from the graph at the point where the quadratic equation crosses the x-axis.

The graph crosses the x-axis at two points.

These are at the points x = -3 and x = 1

So what we have are;

x + 3 and x -1

Multiplying both will give us the quadratic equation we are looking for.

(x + 3)(x-1) = x(x -1) + 3(x-1)

= x^2 -x + 3x -3 = x^2 + 2x -3

it is [tex]\pi[/tex]

since period of tangent is $\pi$ ,so the period of reciprocal will also be same

The period for the cotangent function is π radians.

The period for function y = A sin(Bx + C) and y = A cos(Bx + C) is 2π/|B| radians. Frequency is described as the wide variety of cycles completed in one 2d. If the duration of a function is denoted via P and f is its frequency, then –f =1/ P.

The tangent function has period π. f(x)=Atan(Bx−C)+D is a tangent with vertical and/or horizontal stretch/compression and shift. The cotangent function has period π and vertical asymptotes at 0,±π,±2π, The range of cotangent is (−∞,∞), and the function is decreasing at each point in its range.

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Answer:

See explanation

Step-by-step explanation:

If A = 30 = 1/2ab = 1/2(5)(b)

60 = 5b

b = 12

a/b = 5/12

a + b = 5 + 12 = 17

Answer:

See explanation

Step-by-step explanation:

If A = 30 = 1/2ab = 1/2(5)(b)

60 = 5b

b = 12

a/b = 5/12

a + b = 5 + 12 = 17

Answer:

[tex]x = 4[/tex]

Step-by-step explanation:

We can represent each ratio as a fraction, then use the cross products property to find the value of x.

[tex]\frac{3}{12} = \frac{x}{16} \\\\\\16\cdot3=48\\\\48\div12=4[/tex]

Hope this helped!

Answer:

d. -4

Step-by-step explanation:

Let's plug in g

8 - |2(-3.5) - 5|

8 - |-7-5|

8 - |-12|

The absolute value is always positive of any number,

8 - 12

= -4

Answer:

D. -4

Step-by-step explanation:

We are given this expression:

[tex]8-|2g-5|[/tex]

and asked to evaluate when g= -3.5 Therefore, we must substitute -3.5 in for g.

[tex]8-|2(-3.5)-5|[/tex]

First, multiply 2 and -3.5

2 * -3.5 = -7

[tex]8-|-7-5|[/tex]

Next, subtract 5 from -7.

-7-5= -12

[tex]8-|-12|[/tex]

Next, evaluate the absolute value of -12. The absolute value is how far away a number is from 0, and it is always positive. The absolute value of -12 is 12.

[tex]8-12[/tex]

Subtract 12 from 8.

[tex]-4[/tex]

The value of the expression is -4 and D is the correct answer.

Answer:

No

Step-by-step explanation:

No, 16 is not a perfect cube. Perfect cubes are numbers that are the cube of an integer and can also be written in the form x³ where x is an integer. Since 16 cannot be written like that, it is not a perfect cube.