. You and your friend are playing the following game: two dice are rolled; if the total showing is
divisible by 3, you pay your friend $6. How much should he pay you when the total is not divisible
by 3 if you want to make the game fair? A fair game is one in which your expected winnings are
$0.

Answer:

1. A. Factor and use the zero-product property; x = 0, -16

   B. Use the quadratic formula; y=-3-√11, -3+√11

   C. Take the square root of each side; x = -6, 6

   D. Complete the square; p= -2(√3 + 1). 2(√3 - 1)

2. A. Downward; coefficient of x² is negative

    B. Above; k is positive

Step-by-step explanation:

1. A. x² = –16x

Factor and use the zero-product property

[tex]\begin{array}{rcl}x^{2} & = & -16x\\x^{2} + 16x & = & 0\\x(x + 16) & = &0\\x = \mathbf{0} & & x+ 16 = 0\\& & x = \mathbf{-16}\\\end{array}[/tex]

B. y² + 6y – 2 = 0

Use the quadratic formula

a = 1; b = 6; y = -2

[tex]\begin{array}{rcl}y & = & \dfrac{-b\pm\sqrt{b^2-4ac}}{2a} \\\\ & = & \dfrac{-6\pm\sqrt{6^2-4\times1\times(-2)}}{2\times1} \\\\ & = & \dfrac{-6\pm\sqrt{36+8}}{2} \\\\ & = & \dfrac{-6\pm\sqrt{44}}{2} \\\\ & = & \dfrac{-6\pm2\sqrt{11}}{2} \\\\ & = & -3\pm\sqrt{11}\\y=\mathbf{-3-\sqrt{11}} & &y= \mathbf{-3+\sqrt{11}}\\\end{array}[/tex]

C. 2a² = 72

Take the square root of each side.

[tex]\begin{array}{rcl}2a^{2} & = & 72\\a^{2} & = & 36\\a & = & \pm 6\\a= \mathbf{-6} & & a = \mathbf{6}\\\end{array}[/tex]

D. p² + 4p = 8

Complete the square.

[tex]\begin{array}{rcl}p^{2} + 4p & = & 8\\p^{2} + 4p + 4 & = & 12\\(p + 2)^{2}& = & 12\\p + 2& = & \pm \sqrt{12}\\& = & \pm 2\sqrt{3}\\p + 2 = -2\sqrt{3} & & p +2=-2\sqrt{3}\\p = -2 - 2\sqrt{3} & & p = -2 +2\sqrt{3}\\p= \mathbf{-2(\sqrt{3}+1)} & & p= \mathbf{2(\sqrt{3}-1)}\\\end{array}[/tex]

2. y = –2x² + 3x + 4

a = -2; b = 3; c = 4

A. Direction of opening

The parabola opens downward because the coefficient of x² is negative.

B. Vertex

The vertex form of a parabola is

y = a(x - h)² + k

where (h, k) are coordinates of the vertex.

The vertex will be above. on, or below the x-axis if k is positive, zero, or negative.

[tex]\begin{array}{rcl}k& = & \dfrac{4ac-b^{2}}{2a}\\\\& = & \dfrac{4\times(-2) \times 4 - 3^{2}}{2\times4}\\\\& = & \dfrac{-32 - 9}{-8}\\\\& = & \dfrac{-41}{-8}\\\\& > &\mathbf{0}\\\end{array}[/tex]

The vertex is above the x-axis because k is positive.  

The graph below shows that your parabola opens downward and the vertex is above the x-axis.

Use the slope formula to find slope m. y2-y1/x2-x1

m=2/5

Answer:i would say A i think

Step-by-step explanation:

Answer:

y = 4x (? See parentheses in explanation)

Step-by-step explanation:

First, change this equation to slope-intercept form.

Then, look at the slope and that is the slope of the parallel line.

(I don't know if the line is supposed to pass through a specific point, but if it does, then use point-slope form.)

Answer:

There are an infinite number of solutions to this queston, but you can find an answer by writing:  

8x+2y = k   ;  where k is any number but 12.

Step-by-step explanation:

Answer:

36 is the answer........

Answer:

36

Step-by-step explanation:

You can use the bus stop method on this

540 how many 15 goes in it =36

Answer:

The frequency of the note a perfect fifth below C4 is;

B- 174.42 Hz

Step-by-step explanation:

Here we note that to get the "perfect fifth" of a musical note  we have to play a not that is either 1.5 above or 1.5 below the note to which we reference. Therefore to get the frequency of the note a perfect fifth below C4 which is about 261.63 Hz, we have

1.5 × Frequency of note Y = Frequency of C4

1.5 × Y = 261.63

Therefore, Y = 261.63/1.5 = 174.42 Hz.

The frequency of the note a perfect fifth below C4 is 174.42 Hz

The perfect fifth is a musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.

For the perfect fifth of a musical note,

we have to play a not that is either 1.5 above or 1.5 below the note to which we refer.

Therefore to get the frequency of the note a perfect fifth below C4 which is about 261.63 Hz,

We have

[tex]1.5 \times Frequency of note Y = Frequency of C4[/tex]

[tex]1.5 \times Y = 261.63[/tex]

divide both sides by 1.5

Y = 261.63/1.5 = 174.42 Hz.

Therefore we get, the frequency of the note a perfect fifth below C4 is  174.42 Hz.

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Answer: Your sister is not correct. You can determine how far the overhang should extend by dividing 8 by [tex]tan(70\°)[/tex]

Step-by-step explanation:

The complete exercise is attached.

Observe the picture attached. You can identify that the angle A and the angle B are congruent (which means that they have equal measure).

Let be "CB" is the length in feet that the overhang should be in order to keep the Sun out when it is at its highest point in the sky.

You need to use the following Trigonometric Identity:

[tex]tan\alpha =\frac{opposite}{adjacent}[/tex]

You can notice that, in this case:

[tex]\alpha =70\°\\\\opposite=8\ ft\\\\adjacent=CB[/tex]

Knowing these values you can substitute them into  [tex]tan\alpha =\frac{opposite}{adjacent}[/tex] and then solve for "CB" in orde to find its value.

You get:

[tex]tan(70\°)=\frac{8}{CB}\\\\CB*tan(70\°)=8\\\\CB=\frac{8}{tan(70\°)}\\\\CB=2.91[/tex]

Therefore, your sisteter is not correct.

Answer:

Your sister is not correct. You can determine how far the overhang should extend by dividing 8.

Step-by-step explanation:

You can determine how far the overhang should extend by dividing

Observe the picture attached. You can identify that the angle A and the angle B are congruent (which means that they have equal measure).

Let be "CB" is the length in feet that the overhang should be in order to keep the Sun out when it is at its highest point in the sky.

You need to use the following Trigonometric Identity:

You can notice that, in this case:

Knowing these values you can substitute them into   and then solve for "CB" in orde to find its value.

Therefore, your sisteter is not correct.

Answer:

The probability that the first block will be green and the second will be yellow is  [tex]\frac{1}{9}[/tex]  or 0.111.

Step-by-step explanation:

We are given that a bag contains 5 yellow blocks, 2 green blocks and 3 blue blocks.

Also, we choose one block and then another block without putting the first one back in the bag.

Firstly, as we know that Probability of any event is given by ;

           Probability of an event  =  [tex]\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}[/tex]  

SO, Probability that the first block will be green =  [tex]\frac{\text{Number of green blocks}}{\text{Total blocks in the bag}}[/tex]

Here, Number of green blocks = 2

Total number of blocks in bag = 5 yellow + 2 green + 3 blue = 10 blocks

So, Probability that the first block will be green  =  [tex]\frac{2}{10}[/tex]

Similarly, Probability that the second block will be yellow =  

                               [tex]\frac{\text{Number of yellow blocks}}{\text{Total number of remaining blocks in the bag}}[/tex]

Here, Number of yellow blocks = 5

Total number of remaining blocks in bag = 10 - 1 = 9 blocks  {because we haven't put the block back after choosing the first}

So, Probability that the second block will be yellow  =  [tex]\frac{5}{9}[/tex]

Now, Probability that the first block will be green and the second will be yellow  =  [tex]\frac{2}{10} \times \frac{5}{9}[/tex]

            =  [tex]\frac{1}{9}[/tex]  = 0.111

Hence, the required probability is 0.111.

Answer:

[tex]d = \sqrt{3} * a = \sqrt{3} * 5 = 8.7[/tex]

Step-by-step explanation:

plz give brainliest

Answer:

$63.54

Step-by-step explanation:

If something is 35% off you pay 65% of the price

115*.65= 74.75

same thing again but with 15% and multiplying by .85

74.75*.85=63.54

Answer:

C. 14

Step-by-step explanation:

2 shirts in each pile x 7 piles of shirts = 14 shirts in total

2 x 7 = 14

Final answer:

To determine how many shirts Mark folded, multiply the number of shirts per pile (2) by the number of piles (7), which equals 14 shirts.

Explanation:

The question asks us to calculate the total number of shirts Mark folded if he put 2 shirts in each pile and there are 7 piles of shirts.

To find the total number of shirts, we need to multiply the number of shirts per pile by the number of piles. So, the calculation is as follows:

Determine the number of shirts per pile: 2 shirts.

Determine the total number of piles: 7 piles.

Multiply the number of shirts per pile by the number of piles: 2 shirts x7 piles = 14 shirts.

Therefore, Mark folded a total of 14 shirts.

Answer:

48

Step-by-step explanation:

Final answer:

The possible side lengths for a cubic aquarium that can hold between 4096 cubic inches and 8000 cubic inches of water are between 16 inches and 20 inches.

Explanation:

To find the possible side lengths of an aquarium in the shape of a cube that holds between 4096 cubic inches and 8000 cubic inches of water, you need to find the cube root of each volume since the volume of a cube is V = s³, where s is the side length.

For the minimum volume (4096 cubic inches):
[tex]\sqrt[3]{4096}[/tex] = 16 inches.

For the maximum volume (8000 cubic inches):

[tex]\sqrt[3]{8000}[/tex] = 20 inches.

Hence, the side lengths of the aquarium must be between 16 inches and 20 inches.

Answer:

20%

Step-by-step explanation:

14/70x100=20%

Step-by-step explanation:

The concert organizers estimate people will attend if it is not raining = 19000

If its raining people will attend = 4000

On the day of the​ concert, meteorologists predict a 90​% chance of rain.

This means 10 % chance of not raining

The expected number of people = 90% (4000) + 10% (19000)

   = 360 + 1900

  = 2260

The expected number of people who will attend this concert = 2260

Answer:

B: 50% chance

Step-by-step explanation:

50/50 chance of happening is an equal chance

Answer:

no its B

Step-by-step explanation:

Because you have a 50 50 % chance

Answer:

c = 27/40.

Step-by-step explanation:

1/8 + c = 4/5

1/8 - 1/8 + c = 4/5 - 1/8

c = 4/5 - 1/8

c = 32/40 - 5/40

c = 27/40.

Answer:

If it is asking for the order of the letters, it would be: Δ J H E

Explanation:

You have to put the letters in the same order that they were on the first triangle.

Hope this helps!!  :)

Answer:

yes

Step-by-step explanation:

n

Answer:

C: 56

Step-by-step explanation:

Hi there,

To find the least common multipul (LCM) of 8 and 14, you can list off the multipules of each, and see what they have in common.

Multiples of 8:

8, 116, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112

Multiples of 14:

14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182

When you list off the multipules of both numbers, they have 56, and 112, in common. The problem is asking for the least common multiple the answer is 56.

Hope this helps!

- Emily

Answer:

3:4

Step-by-step explanation:

Before we start to deal with the ratio, we need all lengths in the same units.

The width is 18 inches.

The height is 2 feet.

Let's convert the height to inches. Then we will have both dimensions in the same units, inches.

2 ft * (12 in.)/ft = 24 in.

Now we have:

width = 18 in.

height = 24 in.

ratio of width to height = 18 in. to 24 in. = 18/24 = 3/4 = 3:4

Answer:

I believe the correct answer is C, sorry for the late answer/response, but I believe this is the right answer. Have a nice day

Step-by-step explanation:

:)

Final answer:

The quotient of the polynomial division (3x³ - x² - x - 1) ÷ (x - 1) is 3x² + 2x + 1 using synthetic division.

Explanation:

To find the quotient of (3x³ - x² - x - 1) ÷ (x -1), we can use polynomial long division or synthetic division. In this case, the coefficient in front of x in the divisor (x - 1) is 1, so we can use synthetic division directly.

Set up the synthetic division by writing the coefficients of the dividend, which are 3, -1, -1, and -1, and the zero of the divisor, which in this case is +1. Carry out the synthetic division process to get the quotient.

The result of the synthetic division gives us the coefficients of the quotient, which are the coefficients for the powers of x in the quotient polynomial, starting from one degree less than the original polynomial because we are dividing by a first-degree polynomial.

The remainder, if there is one, would be the constant at the end or the remainder over the divisor.

The quotient of the polynomial division is (3x² + 2x + 1) with no remainder.

Answer:

degree: linear

terms: binomial

Step-by-step explanation:

The polynomials are :

Solution :

To classify polynomials, we look at the number of terms and the degree of the polynomial.

monomial - 1 term

binomial - 2 terms

trinomial - 3 terms

polynomial - 4 terms or more

first

second  (quadratic)

third

fourth (quartic)

etc.

_________________

[tex]\pmb{3x+12}[/tex] has 2 terms and its highest exponent is 1. Hence it's a binomial.

[tex]\pmb{x^3-8}[/tex] has 2 terms and its highest exponent is 3, hence we have a third-degree binomial.

Answer: 18π units³ or 56.52 units³

Step-by-step explanation: Notice that the figure shown here is a cylinder. To find the volume of a cylinder, start with the formula for the volume of a cylinder which is shown below.

Volume = πr²h

Here, notice that our cylinder has a radius

of 3 units and a height of 2 units.

So we have (π)(3 units)²(2 units).

Start by simplifying the exponent.

(3 units)² is (3 units)(3 units) or 9 units².

So we have (π)(9 units²)(2 units).

Now, (9 units)²(2 units) is 18 units³.

So we have 18π units³.

So the volume of the cylinder shows here is 18π units³.

Remember that π is approximately equal to 22/7 or 3.14. So we can estimate the value of the volume by plugging in 3.14 for π.

So we have (18)(3.14) which is equal to 56.52.

So the value of the volume is approximately 56.52 units³.

Answer:

lower quartile: 163  upper quartile: 184

Step-by-step explanation:

1. put the numbers in order from least to greatest. 97, 163, 169, 175, 184, 199

2. find the median. 172

3. find the median of the first 3 numbers to get your Q1. 163

4. find the median of the last 3 numbers to get your Q3. 184

The ball hits the ground at t=0 or t=3 seconds. The maximum height of the ball is 9 feet. The ball reaches its highest point at t=1.5 seconds.

To find out how long after the kick the ball hits the ground, we need to solve the equation h=-4t^2+12t  for t when h=0. We can set the equation to zero and solve for t by factoring or using the quadratic formula. In this case, you can factor out a t from the equation and solve for t to find that t=0 or t=3.

To find out how high the soccer ball gets, we need to find the maximum height of the ball. The maximum height occurs at the vertex of the parabolic equation. The formula for finding the x-coordinate of the vertex is x = -b/2a. In this case, a = -4 and b = 12, so the x-coordinate of the vertex is x = -12/(2*-4) = 1.5. Substituting this value into the equation, we can find the maximum height by solving for h, which is h = -4*(1.5)^2 + 12*(1.5) = 9 feet.

The soccer ball hits its highest point at the x-coordinate of the vertex. In this case, the highest point occurs at t = 1.5 seconds.

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Answer:

(-6, 7), r=9

Step-by-step explanation:

The opposite of the number next to the x is -6, the opposite of the number next to the y is 7.  The square root of the number on the right (81) is 9, so 9 is the radius.

Answer: A) y=25,   B) y=10  C) y=-5  D)y=-20

Step-by-step explanation:

So whenever you have a question like this just plug in the values.

A) x=0

y= -3x+25 will now turn into y=0+25, so y=25

B) x=5

y= -3x+25 is now y= -15 +25, so y=10

C) x=10

y= -3x+25 is now y= -30+25, so y=-5

D) x=15

y=-3x+25 is now y= -45+25, so y=-20

Answer:

False

Step-by-step explanation:

The image is after pre-image

Height MT of the pyramid will be 8.9 cm

    Given in the question,

Since, diagonals of a rectangle bisect each other, point M will be the midpoint of the diagonal AC.

By applying Pythagoras theorem in right triangle ΔABC,

AC² = AB² + BC²

AC = [tex]\sqrt{AB^2+BC^2}[/tex]

AC = [tex]\sqrt{6^2+7^2}[/tex]

AC = [tex]\sqrt{85}[/tex]

Therefore, AM = [tex]\frac{\sqrt{85} }{2}[/tex]

AM = 4.61 cm

Apply Pythagoras theorem in right triangle ΔAMT,

AT² = AM² + TM²

TM = [tex]\sqrt{AT^2-AM^2}[/tex]

TM = [tex]\sqrt{(10)^2-(4.61)^2}[/tex]

     = [tex]\sqrt{78.7479}[/tex]

     = 8.874

     ≈ 8.9 cm

    Therefore, height MT of the pyramid will be 8.9 cm.

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Answer: 80 degrees

Step-by-step explanation:

A triangle has 180 degrees.

25+75=100

180-100= 80

That means the other angle must equal 80 degrees