Out of 1,000 tickets in a raffle, one ticket will win a $710 prize. The rest will win nothing. If you have a ticket, what is the expected payoff?

Answer:

The height of the rocket after 3 seconds is 63 feet.

Step-by-step explanation:

The path of a model rocket is represented by:

[tex]h(t)=-t^2+20t+12[/tex]

where [tex]h(t)[/tex] represents the height in feet of rocket and [tex]t[/tex] represents time in seconds.

To find the height of the model rocket after 3 seconds from launch.

Solution:

In order to find the  height of the model rocket after 3 seconds from launch, we will plugin [tex]t=3[/tex] in the given function of path of rocket.

Thus, we have

[tex]h(3)=-(3)^2+20(3)+12[/tex]

[tex]h(3)=-9+60+12[/tex]

[tex]h(3)=63[/tex]

Thus, height of the rocket after 3 seconds is 63 feet.

∛128

Divide 128 by 2 to get 64

Now you have: ∛(64 *2)

Rewrite 64 as 4³

Now you have:

∛(4³ *2)

Pull Terms out of the radical to get the final answer:

4∛2

Answer:

-17

Step-by-step explanation:

28 - 45 = -17$ in her account

The integer will represent the amount of money in Alaina’s account is -17 dollars.

Given that, Alaina has $28 in her account. She wants to purchase a pair of shoes that costs $45.

To subtract two integers, rewrite the subtraction expression as the first number plus the opposite of the second number.

Now, 28-45=-17

Therefore, the integer will represent the amount of money in Alaina’s account is -17 dollars.

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The value of x when y = 9 is x = 2 or x = -2

Solution:

Given that value of y varies inversely as the square of x, and y=4, when x=3.

Therefore the initial statement is:

[tex]y \propto \frac{1}{x^{2}}[/tex]

To convert to an equation, multiply by k, the constant  of variation

[tex]y = k \times \frac{1}{x^2}[/tex]

[tex]y = \frac{k}{x^2}[/tex]  --- eqn 1

Given that,

y = 4 when x = 3

Now find value of k

[tex]4 = \frac{k}{3^2}\\\\4 \times 9 = k\\\\k = 36[/tex]

Find the value of x when y = 9

x = ?

y = 9

From eqn 1,

[tex]9 = \frac{k}{x^2}\\\\9 = \frac{36}{x^2}\\\\x^2 = 4\\\\x = \pm 2[/tex]

Thus value of x is found

Final answer:

To find the value of x when y=9 for a scenario where y varies inversely as the square of x, and given y=4 when x=3, we first determine the constant of variation and then solve for x, resulting in x=2.

Explanation:

The student's question concerns an inverse variation where the value of y varies inversely as the square of x, with an initial condition that when x=3, y=4. To find the value of x when y=9, we recall that an inverse variation can be expressed as y = k/x², where k is a constant. Using the given condition, we can solve for k: 4 = k/3², leading to k = 36. To find x when y=9, we set up the equation 9 = 36/x² and solve for x, yielding x = 2.

Answer:

10 rectangles can fit in the square that has one side 10 cm long.

Step-by-step explanation:

Given:

Rectangle 5 cm multiply 2 cm .

Square that has one side 10cm long.

Now, to find the number of rectangle that can fits in the square.

So, for getting the number of rectangle we need to get the area first:

Area of rectangle as given 5 cm multiply 2 cm :

[tex]5\ cm\times 2\ cm=10\ cm^2[/tex]

Then the area of square as given side is 10 cm:

Area of square = (side)²

[tex]Area\ of\ square=10^2[/tex]

[tex]Area\ of\ square=100\ cm^2[/tex]

Now, for getting the number of rectangle we divide the area of square by area of rectangle:

Number of rectangle = Area of square ÷ Area of rectangle

[tex]Number\ of\ rectangle=100\ cm^2\div 10\ cm^2[/tex]

[tex]Number\ of\ rectangle=10.[/tex]

Therefore, 10 rectangles can fit in the square that has one side 10 cm long.

                               Question # 1 Solution

Answer:

32≤x≤48 is the best estimate for the amount of money, x, that Erika has to pay to get to her destination. Hence, option D is correct.

Step-by-step Explanation:

Information Fetching and Solution Steps

As Erika estimates that she is 200 to 300 miles away from her destination, and car travels 25 miles per gallon of gas. So,

        i.e 200/25 = 8 gallons.

        As cost of each gallon being $4.00.

        So, 8 × 4 = 32$ is the amount she needed to make 200 miles.

        i.e 300/25 = 12 gallons.

        As cost of each gallon being $4.00.

        So, 12 × 4 = 48$ is the amount she needed to make 300 miles.

From the above calculation, we observe that 32$ and 48$ is the best estimate between 200 miles and 300 miles.

Therefore, 32≤x≤48 is the best estimate for the amount of money, x, that Erika has to pay to get to her destination. Hence, option D is correct.

                                   Question # 2 Solution

Answer:

Consultant B offers the cheapest price for a five hour session.

Hence, B. Consultant B is the correct option.

Step-by-step Explanation:

Analyzing the offer price of Consultant A, B and C for a Five hour session:

So, for five hour session, Consultant A is offering the price:

$160 + $75 + $75 + $75 + $75 = $460

So, for five hour session, Consultant B is offering the price:

$90 + $90 + $90 + $90 + $90 = 450 US$

So, for five hour session, Consultant C is offering the price:

$140 + $80 + $80 + $80 + $80 = $460

Comparing the price offers of Consultant A, B and C

So, by comparing the price offers of Consultant A, B and C, we determine that:

So, from this comparison, we conclude that Consultant B offers the cheapest price for a five hour session.

Hence, B. Consultant B is the correct option.

                             Question # 3 Solution

Answer:

They spent 4 nights at the hotel. Hence, option B is correct.

Step-by-step Explanation:

To determine:

how many nights did they stay at the hotel?

Information Fetching and Solution Steps

As the total amount they spent = $1,200

As $75 is the service charges as Jessica and Ashely purchased full room service for every night.

Per night charges = hotel chargers + service charges

Per night charges = $225 + $75 ⇒ $300

So, total nights will be calculated as:

Total nights = total amount they spent ÷ Per night charges

Total nights = $1,200 ÷ $300 ⇒ 4 nights

Therefore, they spent 4 nights at the hotel. Hence, option B is correct.

                                 Question # 4 Solution

Answer:

Hence, |h − 57.5| ≤ 7.5 is the absolute values which best represents this restriction, where ( h ) represents height. Hence, option A is correct.

Information Fetching and Solution Steps

Let us take the equation of following absolute value:

|h − 57.5| ≤ 7.5

We know h − 57.5 ≤ and h − 57.5 ≥ −50

h − 57.5 ≤ 7.5         (Condition 1)

h − 57.5 + 57.5 ≤ 7.5 + 57.5      (Add 57.5 to both sides)

h ≤ 65

h − 57.5 ≥ −7.5         (Condition 2)

h − 57.5 + 57.5 ≥ −7.5 + 57.5     (Add 57.5 to both sides)

h ≥ 50

So, h ≤ 65 and h ≥ 50

Solution Graph is also attached as shown in attached figure a.

Hence, |h − 57.5| ≤ 7.5 is the absolute values which best represents this restriction, where ( h ) represents height. Hence, option A is correct.

Using same methodology we observe that all other options B, C, and D brings wrong values which is as follows:

Hence, from all discussion, we conclude that |h − 57.5| ≤ 7.5 is the absolute values which best represents this restriction, where ( h ) represents height, as it brings h ≤ 65 and h ≥ 50. Hence, option A is correct.

Keywords: inequality, graph solution, absolute value

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Answer:

[tex]8b^2+7b-1=(b+1)(8b-1)[/tex]

The missing factor is: [tex](8b-1)[/tex]

Step-by-step explanation:

Given expression:

[tex]8b^2+7b-1=(b+1)(_-)[/tex]

To find the missing factor of the given expression.

Solution:

In order to factor the given term, we will split the middle term into two terms such that the product of the two terms is equal to the product of the first and last term of the expression.

The product of first and last term for the expression is = [tex](8b^2)(-1)=-8b^2[/tex]

The middle term = [tex]7b[/tex] which can be split into  [tex](8b-b)[/tex] as their product = [tex]-8b^2[/tex]

Thus, the expression can be rewritten as:

⇒ [tex]8b^2+8b-b-1[/tex]

We will factor in pairs by taking GCF.

⇒ [tex]8b(b+1)-1(b+1)[/tex]

Factoring the whole expression by taking the common factor.

⇒ [tex](b+1)(8b-1)[/tex]

Thus, the missing factor is: [tex](8b-1)[/tex]

Answer:

0.072

Step-by-step explanation:

3/4 percent of the number 9.6 is 0.072.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, 3/4% of 9.6.

Now, 0.75% of 9.6

= 0.0075×9.6

= 0.072

Therefore, 3/4 percent of the number 9.6 is 0.072.

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Answer:

16 cm

Step-by-step explanation:

Let the width be x

The length will be 3 x since the length is three times the width

Perimeter=2(l+w) where l is length and w is width

By substituting 128 cm for perimeter, x for w and 3 x for l then

128=2(3x+x)

128=8x

[tex]x=\frac {128}{8}=16[/tex]

Therefore, the width is 16 cm, the width is 16*3=48 cm

The correct answer is:

The greatest possible width for the rectangle, with length three times, is 16 cm, ensuring the perimeter doesn't exceed 128 cm.

Let's denote:

- Width of the rectangle as [tex]\( w \)[/tex] cm

- Length of the rectangle as [tex]\( 3w \)[/tex] cm (since it is three times the width)

The perimeter of a rectangle is given by:

[tex]\[ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) \][/tex]

Given the perimeter is at most 128 cm, we can write:

[tex]\[ 2 \times (3w + w) \leq 128 \][/tex]

Now, let's solve for [tex]\( w \)[/tex]:

[tex]\[ 2 \times (3w + w) \leq 128 \]\[ 2 \times 4w \leq 128 \]\[ 8w \leq 128 \]\[ w \leq \frac{128}{8} \]\[ w \leq 16 \][/tex]

So, the width of the rectangle must be less than or equal to 16 cm. Therefore, the greatest possible value for the width is 16 cm.

Answer:

your answer is option A

Answer:

A is the correct answer... ten hundreths thousandths

βrainliest pleaseeeeeeeeeeeee

Answer: 1,602 Crayons with old labels that the company has in stock

Step-by-step explanation:

The total is 2,776 and 1,174 of the total have new labels so you would have to subtract 1,174 from 2,776. Your welcome

Answer:

The fraction taken from 17 is [tex]$ \frac{16}{3}$[/tex].

Step-by-step explanation:

Let the fraction that is taken from 17 be 'a'.

Writing the given statement mathematically, we would have:

[tex]$ 17 - a = \frac{17}{3} +  6$[/tex]

⇒ 51 - 3x = 17 + 18

⇒ 51 - 3x = 35

⇒ 3x = 16

⇒ x = [tex]$ \frac{16}{3} $[/tex] is the answer.

The equation that represents the relationship between the remaining balance on Renata's gift card and the number of songs purchased is y = 20 - 1.25x, where x represents the number of songs purchased.

The equation that represents the relationship between the remaining balance on Renata's gift card and the number of songs purchased is y = 20 - 1.25x.

Here's how we get to this equation:

For example, if Renata purchased 16 songs, the equation becomes y = 20 - 1.25(16) = 20 - 20 = 0, which matches the given information that the gift card has a remaining balance of $0 after 16 songs are purchased.

Problem 1

--------------

Work Shown:

For any convex polygon, the sum of the exterior angles is always 360 degrees

Add up all the angles shown, set the sum equal to 360, then solve for v.

9v+(19v-21)+45+(v+48)+7v = 360

36v+72 = 360

36v+72-72 = 360-72

36v = 288

36v/36 = 288/36

v = 8

===============================================

Problem 2

--------------

Explanation:

Segment WU is not an altitude because we have no angle markers to show if WU is perpendicular to VT.

Segment WU is not a median since we dont know if TU = UV or not.

Segment WU is not an angle bisector. If it were an angle bisector, then the two angles marked (33 and 40) should be equal angles. In other words, an angle bisector cuts an angle into two equal halves.

Answer:

3: 6,9,12,15,18,21 and 24.

7: 14,21,28,35,42,49 and 56.

5: 10,15,20,25,30,35 and 40.

9: 18,27,36,45,54,63 and 72

4: 8,12,16,20,24,28 and 32.

Step-by-step explanation:

Given are the number at the beginning of each strings.

We need to write multiples of number on first light of string on rest of lights on the string.

3: [tex]3\times 1= 3 (given)[/tex]

[tex]3\times 2= 6\\3\times 3= 9\\3\times 4= 12\\3\times 5= 15\\3\times 6= 18\\3\times 7= 21\\3\times 8= 24[/tex]

7: [tex]7\times 1= 7 (given)[/tex]

[tex]7\times 2= 14\\7\times 3= 21\\7\times 4= 28\\7\times 5= 35\\7\times 6= 42\\7\times 7= 49\\7\times 8= 56[/tex]

5: [tex]5\times 1= 5 (given)[/tex]

[tex]5\times 2= 10\\5\times 3= 15\\5\times 4= 20\\5\times 5= 25\\5\times 6= 30\\5\times 7= 35\\5\times 8= 40[/tex]

9: [tex]9\times 1= 9 (given)[/tex]

[tex]9\times 2= 18\\9\times 3= 27\\9\times 4= 36\\9\times 5= 45\\9\times 6= 54\\9\times 7= 63\\9\times 8= 72[/tex]

4: [tex]4\times 1= 4 (given)[/tex]

[tex]4\times 2= 8\\4\times 3= 12\\4\times 4= 16\\4\times 5= 20\\4\times 6= 24\\4\times 7= 28\\4\times 8= 32[/tex]

Answer:

y=-3x+14

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-4-26)/(6-(-4))

m=-30/(6+4)

m=-30/10

m=-3

y-y1=m(x-x1)

y-26=-3(x-(-4))

y-26=-3(x+4)

y=-3x-12+26

y=-3x+14

Solution: [tex]\frac{12}{13}[/tex]. The cosine of an acute angle of a right triangle is the adjacent side divided by the hypotenuse.

Answer:

The total cost to make 3 widgets is $64.

Step-by-step explanation:

As cost is give by quadratic function such as [tex]c(x) = ax^2 + bx + d[/tex]

As it costs $29 to produce 2 widgets. So,

[tex]c(2) = a(2)^2 + b(2) + d[/tex]

[tex]29= 4a+2b+d ....[A][/tex]

As it costs $115 to produce 4 widgets. So,

[tex]c(4) = a(4)^2 + b(4) + d[/tex]

[tex]115= 16a+4b+d ....[B][/tex]

As it costs $757 to produce 10 widgets. So,

[tex]c(10) = a(10)^2 + b(10) + d[/tex]

[tex]757= 100a+10b+d ....[C][/tex]

In order to find the values of a, b, c and d, we have to equations [A], [B] and [C]

Subtracting Equation [A] from [B] and [B] from [C]

 12a + 2b = 86  ........[D]

 84a + 6b = 642  ........[E]

Multiplying Equation [D] by 3 and subtracting from [E]

84a + 6b + 3(12a + 2b) = 642 - 86

48a = 384

a = 8

Putting value of a = 8 in equation [D]

12(8) + 2b = 86

96 + 2b = 86

2b = -10

b = -5

Substituting the value of a = 8 and b = -5 in Equation [A].

29= 4a+2b+d

29 = 4(8) + 2(-5) + d

29 = 32 - 10 + d

d = 29 + 10 - 32

d = 7

The required form of equation can be obtained by substituting a = 8, b = -5 and d = 7 in the cost equation. So,

[tex]c(x) = 8x^2 - 5x + 7[/tex] is the required form of equation.

Therefore, the total cost to make 3 widgets will be:

Putting x = 3 in [tex]c(x) = 8x^2 - 5x + 7[/tex]

[tex]c(3) = 8(3)^2 - 5(3) + 7[/tex]

[tex]c(3) = 72 - 15 + 7[/tex]

[tex]c(3) = 64[/tex]

Hence, the total cost to make 3 widgets is $64.

Keywords: quadratic equation, cost

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Answer:

279J is the total amount of gravitational potential  energy gained by the box.

Step-by-step explanation:

Note: As you missed to add the diagram. So, I found and have attached the diagram as shown in figure a which is attached below, based on which I am answering your question. Hopefully, it would help understand the concept.

The energy stored in an object near the surface of the Earth due of its state in a gravitational field is termed as Gravitational potential energy.

The formula to get gravitational potential energy: [tex]Ep_}=mgh[/tex]

Here,

m = mass of the object normally measured in kg

g =  gravitational acceleration having constant value as 9.8 m/s²

h = height in m

As from the diagram a, we observe that object carries 155-newton force and at point B, the height is 1.80 m, as shown in figure a.

So,

      F = 155 N

      h = 1.80 m

From F = mg, we can get the mass of  object

       F = mg        ∵ g =  gravitational acceleration

      m = F/g

      m = 155/9.8 ⇒ m = 15.81

The gravitational potential energy is measured in joule which is abbreviated as 'J'.

The formula to get gravitational potential energy:

[tex]Ep_}=mgh[/tex]

[tex]Ep_}=(15.81)(9.8)(1.80)[/tex]

[tex]Ep_}=278.88J[/tex]  ≈ [tex]279J[/tex]

Therefore, 279J is the total amount of gravitational potential  energy gained by the box.

Keywords: potential energy, force

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Answer:22/18 or 1 4/15

First, you have to find out how many pieces were eaten in all. This could be done with addition. 1/5+1/3= (3/15+5/15)= 8/15

Lastly, you have to find out how much they ate from 15 pieces. This could be done with subtraction. Since 15 is a whole number, the fraction for it would be 15/1. 15/1-8/15=(30/15-8/15)=22/18 or 1 4/15

Answer:

Step-by-step explanation:

he uses 3/4 cup of butter in each batch...and he made 2 1/2 batches..

so he used :

2 1/2 * 3/4 =

5/2 * 3/4 =

15/8 =

1 7/8 cups of butter <====

A 5/3x3/4=1 7/8 because 15/8 is 5/3 x 3/4 = 1 7/8

Answer:

4875

Step-by-step explanation:

100%-84%=16%

16%x=780

x=4875

The solutions for the inequality y > (1/5)x + 3 exist in Quadrants I and II.

The inequality y > (1/5)x + 3 represents a line with a positive slope of 1/5.

The solutions for this inequality exist in the quadrants where y is greater than the value of (1/5)x + 3.

When x is positive and y is positive, the solutions exist in Quadrant I. When x is negative and y is positive, the solutions exist in Quadrant II.

Since the inequality is y > (1/5)x + 3 and not y >= (1/5)x + 3, the solutions do not exist in Quadrant III or IV where y would be negative.

Therefore, the solutions for the inequality y > (1/5)x + 3 exist in Quadrants I and II.

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Answer:

Julie made $3 /hour more than Loren

Step-by-step explanation:

Loren makes 18 /2 = 9 ($9 / hour constant ratio)

Julie: 36 /3 = 12 ($12 / hour)

Julie - Loren = 12 -9 = 3

? in Loren's : 126, 144

? in Julie's : 72, 252

Answer:

1

Step-by-step explanation:

Correct question:  2x2 - 5x - 3 / 4x2 + 12x + 5 divided by 3x2 - 11x + 6 / 6x2 + 11x - 10.

As given: [tex]\frac{(2x^{2}-5x-3) }{(4x^{2}+12x+5 )} \div \frac{(3x^{2} -11x+6)}{(6x^{2}+11x-10) }[/tex]

Solving it by using quadratic equation.

= [tex]\frac{(2x^{2}-6x+1x-3) }{(4x^{2}+10x+2x+5) } \div \frac{(3x^{2}-9x-2x+6 }{(6x^{2}+15x-4x-10) }[/tex]

= [tex]\frac{(2x+1) (x-3)}{(2x+1) (2x+5)} \div \frac{(3x-2) (x-3)}{(2x+5) (3x-2)}[/tex]

To divide fraction take the reciprocal of divisor and multiply the dividend.

= [tex]\frac{(2x+1) (x-3)}{(2x+1) (2x+5)} \times \frac{(2x+5) (3x-2)}{(3x-2) (x-3)}[/tex]

We solve it to get 1 as it cancel fraction on both side.

Answer is 1.

Answer:

First part: C

Second part: 1

Step-by-step explanation:

Answer:

C. Select a number from {1, 2, 3, 4, 5, 6} and a vowel.

Step-by-step explanation:

Let's start this with a simple example: how many messages are possible using one number from {7, 9} and one letter from {a, b}. It will be 4 as 7a, 7b, 9a and  9b. This result can also come by multiplying the number of digits used and number of alphabets used - here number of digits are 2 (they are 7 and 9) and number of alphabets used are 2 (they are 'a' and 'b'). So 2 × 2 = 4.

[NOTE : In this question 7a and a7 are same]

Maximum number of options consists of vowels as letters so we will first find the number of digits needed if vowels are used as letters.

The number of vowels are 5 (they are 'a', 'e', 'i', 'o', 'u').

The number of possible precodes needed = 30

Let the number of digits needed be 'n'.

Then n × 5 = 30

∴ n = 6

Therefore the number of digits needed is 6 which is there in option C. The digits are {1, 2, 3, 4, 5, 6}

Therefore option C is the answer.

Answer:

See image

Step-by-step explanation:

Plato

Answer:

see them bellow

Step-by-step explanation:

Answer:

um whats the question

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Squaring a number (a+b) for example is a^2+2ab+b^2. So you square root x^2 and 49, you get x and seven respectively. you multiply them together and on top of that multiply the product by 2. so 7x*2 is 14x and ye

Answer:

4.5

Step-by-step explanation:

To find the instantaneous rate of chance, take the derivative:

[tex]f(x) = {x}^{2} - \frac{2}{x} - 1 \\ \frac{d}{dx} f(x) = 2x + \frac{2}{ {x}^{2} } [/tex]

Remember to use power rule:

[tex] \frac{d}{dx} {x}^{a} = a {x}^{a - 1} [/tex]

To differentiate -2/x, think of it as:

[tex] - 2 {x}^{ - 1} [/tex]

Then, substitute 2 for x:

[tex]2(2) + \frac{2}{ {2}^{2} } \\ 4 + \frac{2}{4} = 4.5[/tex]

Answer:

2

Step-by-step explanation:

Assuming the function is:

f(x) = (x² − 2) / (x − 1)

Use quotient rule to find the derivative.

f'(x) = [ (x − 1) (2x) − (x² − 2) (1) ] / (x − 1)²

f'(x) = (2x² − 2x − x² + 2) / (x − 1)²

f'(x) = (x² − 2x + 2) / (x − 1)²

Evaluate at x=2.

f'(2) = (2² − 2(2) + 2) / (2 − 1)²

f'(2) = (4 − 4 + 2) / 1

f'(2) = 2