Nadia bought five tickets to attend a spaghetti supper fund raiser at her school. The equation 5x = 32. 50 can be used to find X, the cost of each ticket in dollars. Which equation represents the cost of each ticket. A. X=32. 50/5

B. X=32. 50(5)

C. X= 32. 50-5

D. X= 32. 50+5

1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:

Volume = 3 cm x 3 cm x 3 cm = 27 cm³.

Therefore, the volume of the cube is 27 cubic centimeters.

1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:

Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.

Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:

Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.

Therefore, the mass of the water cube is 27 grams.

1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.

Therefore, the weight of the water and the ice would be the same under the same conditions.

1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.

When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.

In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

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The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

We have,

To prove the equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 using mathematical induction,

We will follow the three steps of mathematical induction:

The base case, the induction hypothesis, and the inductive step.

Step 1: Base case

Let's start by checking if the equation holds true for the base case, which is n = 1.

When n = 1, the left-hand side (LHS) is 1² = 1, and the right-hand side (RHS) is 1(1 + 1)(2(1) + 1) / 6 = 1.

Since LHS = RHS for the base case, the equation holds true.

Step 2: Induction hypothesis

Assume the equation holds true for some positive integer k, where k ≥ 1. This is our induction hypothesis:

1 + 4 + 9 + ... + k² = k(k + 1)(2k + 1) / 6

Step 3: Inductive step

We need to prove that if the equation holds true for k, it also holds true for k + 1.

Starting with the left-hand side of the equation, we add (k + 1)² to both sides:

1 + 4 + 9 + ... + k² + (k + 1)² = k(k + 1)(2k + 1) / 6 + (k + 1)²

Simplifying the right-hand side:

= [k(k + 1)(2k + 1) + 6(k + 1)²] / 6

= [(2k³ + 3k² + k) + (6k² + 12k + 6)] / 6

= (2k³ + 9k² + 13k + 6) / 6

= [(k + 1)(k + 2)(2k + 3)] / 6

We can see that the right-hand side is now in the form

(k + 1)((k + 1) + 1)(2(k + 1) + 1) / 6, which matches the equation for k + 1.

Since the equation holds true for k implies it holds true for k + 1, and the base case is true, we have proven the equation using mathematical induction.

Therefore,

The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

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Answer: The greatest common factor is 5.

The number of questionnaires returned or completed divided by the number of eligible people who were asked to participate in the survey is called the response rate.

The response rate represents the quotient of the division operation between the number of respondents and the total number of survey participants.

The response rate can also be referred to as the completion rate or the return rate.

Thus, the response rate can be expressed as a percentage, fraction, or decimal.

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There is a need to randomly sample at least 105 players from the team to estimate the mean weight with a 95% confidence interval half-width of at most 4.73 pounds.

To determine the sample size needed for a given half-width of a confidence interval, we need to use the formula:

n = \((Z*σ / E)^2\)

where:

n = sample size

Z = the Z-score associated with the desired level of confidence (e.g., for 95% confidence, Z = 1.96)

σ = the population standard deviation (if unknown, we can use the sample standard deviation as an estimate)

E = the maximum desired half-width of the confidence interval

Without additional information, we cannot determine the population standard deviation. However, we can use a conservative estimate based on the maximum range of the data. Suppose the maximum range of the player's weight is 100 pounds, then we can use a standard deviation of σ = 100/4 = 25 pounds (assuming a normal distribution).

Using the given half-width of E = 4.73 pounds and a desired confidence level of 95%, the Z-score is 1.96.

Substituting these values into the formula, we get:

n = \((Zσ / E)^2\) = \((1.9625 / 4.73)^2\) ≈ 105

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Answer:

The vertex is at (2, 8) and the axis of symmetry is x = 2

Step-by-step explanation:

First, let's find the zeros of the equation

Factor the equation

-2x² + 8x = -2x(x - 4) = 0

-2x = 0

x - 4 = 0

h(x) is 0 when x = 0 or 4

Now we add those zero's together and divide by 2 to find the middle (the axis of symmetry)

4 + 0 = 4

4 ÷ 2 = 2

Now plug 2 into the original equation to find the vertex

h(x) = -2(2)² + 8(2) = 8

Since h(x) equals 8 at the axis of symmetry, which is 2, our vertex is (2,8)

The correct statement concerning the vertex and axis of symmetry of

h(x) = −2x^2 + 8x is:

The vertex is at (2, 8) and the axis of symmetry is x = 2.

Option C is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The correct statement concerning the vertex and axis of symmetry of

h(x) = −2x^2 + 8x is:

To find the vertex and axis of symmetry of a quadratic function in standard form (y = ax² + bx + c), we can use the formulas:

x = -b / 2a (for the x-coordinate of the vertex)

y = (c - b²) / 4a (for the y-coordinate of the vertex)

and

x = -b / 2a (for the equation of the axis of symmetry)

In this case,

a = -2, b = 8, and c = 0.

Substituting these values into the formulas above, we get:

x = -8 / 2(-2) = 2 (x-coordinate of vertex)

y = 0 - 8² / 4(-2) = 8 (y-coordinate of vertex)

x = 2 (equation of the axis of symmetry)

Therefore,

The vertex is at (2, 8) and the axis of symmetry is x = 2.

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Answer:

The average cost per vet visit was $19.25.

Step-by-step explanation:

From the information given, you can find the average cost per visit by dividing the total amount paid for a year's worth of vet visits by the number of visits:

269.50/14= $19.25

According to this, the answer is that the average cost per vet visit was $19.25.

-83843/21 is the partial fraction of Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.

Two or more expressions with an Equal sign is called as Equation.

Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.

4357/21 - 4200

Take LCM as 21.

4357-88200/21

-83843/21

=-3992.5

Hence -83843/21 is the partial fraction of Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.

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Answer:

7-B (congruent)

8-D (supplement)

9-B (congruent)

10-B (congruent)

11-D (supplement)

Step-by-step explanation:

7- 1 and 3 are congruent using the corresponding angles theorem

8- they are supplements using the same side interior angle theorem

9- they are congruent using alternate interior angle theorem

10- they are congruent using the alternate exterior angle theorem

11- they are supplements using the same side exterior angle theorem

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The function of x giving the length of each of the original sides would be  \((x + 100) * (x + 60) = x^2 + 160x + 6000\).

What is Function of x?

A function is a formula that expresses one variable in terms of another. The statement "y is a function of x" (denoted y = y(x)) states that y changes depending on the value of x.

The original length of each side of the lawn can be represented by the function x + 100, and the original width can be represented by the function x + 60.

To find the area of the original lawn, we can multiply the length and width functions.

So, the function for the area of the original lawn is:

         \((x + 100) * (x + 60) = x^2 + 160x + 6000\)

This is a quadratic function in x, whose leading coefficient is 1, and the value of x is the same amount of length added to each side of the lawn.

Hence, The function of x giving the length of each of the original sides would be  \((x + 100) * (x + 60) = x^2 + 160x + 6000\).

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Answer:72

Step-by-step explanation:

115+115=230

230-158=72

If you add the 115 a month that she earns from babysitting, then add both the months pay together, than subtract 158(cost of the bicycle) by the total pay, you should get 72$

Answer:  D. $72

Step-by-step explanation:

If she earns $115 a month and June and July is a combination of two months then we will have to find the amount she earn toegther in June and July by multiplying 2 by $115.

2(115) = 230

She earned $230 in those months, and if the bicycle cost $158 , then we will have to subtract $158 from $230 to find her remaining amount.

$230 - $158 = $72  

Answer:

Options b) d) e)

Step-by-step explanation:

Let the numbers be x and y

2 consecutive even nos.

therefore y = x+2

twice of the first (2x) is 46 more than y

2x = y+46

Solving both the equations

x - y + 2 = 0

(-)2x - y - 46 = 0

____________

-x + 0 + 48 = 0

____________

x = 48

y = x+2

= 48 +2

= 50

Therefore the 2 nos. are 48 and 50

Hope this answers helps you

Answer: a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (4 in 4xy)

Step-by-step explanation: the coefficient is the number or digit that is being multiplied and it is placed before a constant quantity

Answer:

RS and ST must be equal so 5x + 17 = 8x -31. Thus, x = 16 and therefore RS = ST = 97

Step-by-step explanation:

hope this helps

Answer:

\(given \: that \: s \: is \: mid \: point \: then \\ rs = st \\ 5x + 17 = 8x - 31 \\ x \: terms \: togather \\ 5x - 8x = - 31 - 17 \\ - 3x = - 48 \\ 3x = 48 \\ x = 48 \div 3 = 16x = 16 \\ thank \: you\)

The probability that exactly one of the coins is a 10p piece is 1/2.

To find the probability that exactly one of the coins is a 10p piece, we can consider the possible outcomes.

There are two coins, and each coin can be either a 10p piece or a non-10p piece. Let's consider the four possible outcomes:

1. Erin's coin is a 10p piece, and Jack's coin is a non-10p piece.

2. Erin's coin is a non-10p piece, and Jack's coin is a 10p piece.

3. Both Erin's and Jack's coins are 10p pieces.

4. Both Erin's and Jack's coins are non-10p pieces.

Since the total amount of the two coins is less than 50p, we can eliminate the third possibility (both coins being 10p pieces).

Now, let's calculate the probability for each of the remaining possibilities:

1. Erin's coin is a 10p piece, and Jack's coin is a non-10p piece:

The probability of Erin having a 10p piece is 1/2, and the probability of Jack having a non-10p piece is also 1/2. Therefore, the probability of this outcome is (1/2) * (1/2) = 1/4.

2. Erin's coin is a non-10p piece, and Jack's coin is a 10p piece:

This is the same as the previous case, so the probability is also 1/4.

3. Both Erin's and Jack's coins are non-10p pieces:

The probability of Erin having a non-10p piece is 1/2, and the probability of Jack having a non-10p piece is also 1/2. Therefore, the probability of this outcome is (1/2) * (1/2) = 1/4.

Now, we sum up the probabilities of the two cases where exactly one of the coins is a 10p piece:

1/4 + 1/4 = 2/4 = 1/2.

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The given statement " When the film is placed into the XCP (extension cone paralleling) holder with the smooth side of the film towards the throat, after processing, it will appear darker" is false because it will  lighter, not darker.

The smooth side of the film is the side that interacts with the X-ray radiation and receives the image, while the emulsion side contains the light-sensitive crystals that react to the radiation.

Placing the smooth side towards the throat ensures that the image is sharp and clear, as the X-ray beam travels through the teeth and soft tissues before reaching the film.

After processing, the exposed areas of the film turn dark, representing the captured X-ray image, while the unexposed areas remain light or clear.

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There are 144 ways to list the digits {1, 1, 2, 2, 3, 4, 5} such that two identical digits are not in consecutive positions.

We have to list the digits {1, 1, 2, 2, 3, 4, 5} so that two identical digits are not in consecutive positions. We can use the knowledge of permutations and combinations to solve this problem. We can start by selecting the positions for the distinct digits, i.e., (3, 4, 5). There are 3 distinct digits, so there are 3! = 6 ways to arrange them.

Once we have placed the distinct digits, we can place the two 1's and two 2's in the remaining positions such that no two identical digits are in consecutive positions. To do this, we can use the following approach:

We can start by placing one of the 1's. There are 4 positions available for the first 1.

We can then place one of the 2's. There are 3 positions available for the first 2.

We can then place the second 1. There are 2 positions available for the second 1.

We can then place the second 2. There are 1 positions available for the second 2.

Therefore, the total number of ways to list the digits {1, 1, 2, 2, 3, 4, 5} such that two identical digits are not in consecutive positions is:

6 (arrangements of distinct digits) x 4 x 3 x 2 x 1 = 144.

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5 turning points are in the graph of the polynomial function given in the picture.

Given that,

We have to find how many turning points are in the graph of the polynomial function given in the picture.

We know that,

Turning points are places on a graph where the direction of the line switches from upward to downward and downward to upward

The graph's direction is changing at five separate points, and those points are:

(-5,6) ,(-3,-3) ,(0.5,0.5) ,(3,2.5) ,(5,5)

Therefore, 5 turning points are in the graph of the polynomial function given in the picture.

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Answer:

9 and 45

Step-by-step explanation:

x + 5x = 54

6x = 54

x = 9

5x = 45

Answer:

let the number be x

hence the other number is 5x

we know that

5x + x = 54

6x = 54

x = 54/6

x = 9

so as x equals to 9,

5x = 9×5

5x = 45

An average of 3 people are stepping onto the roller coaster per minute at peak time. The answer is option B) 6.

To determine the number of people who are stepping onto the roller coaster per minute at peak time, you need to divide the number of people on the roller coaster by the duration of the ride. Hence, the correct option is B) 6.

To be more specific, this means that at peak time, an average of 3 people is getting on the ride per minute. This is how you calculate it:

Number of people per minute = Number of people on the roller coaster / Duration of the ride

Number of people on the roller coaster = 24

Duration of the ride = 8 minutes

Number of people per minute = 24 / 8 = 3

Therefore, an average of 3 people are stepping onto the roller coaster per minute at peak time. The answer is option B) 6.

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Answer:

10/20 for green, then 4/19 for blue. 10/20 * 4/19 = 2/19

Step-by-step explanation:

Explanation is above. If you need any more help let me know.

Answer: Non proportional

Step-by-step explanation:

To know if the values given are proportional or not, we will use the formula:

y = kx

where

y = number of organisms

x = number of minutes

k = constant of proportionality

After 5 minutes, a bacteria colony has 1.3 million organisms. Using the formula, y = kx

1,300,000 = 5k

k = 1,300,000 / 5

k = 260,000

After 12 minutes, the same colony has 41.5 million organisms. Using y= kx

41,500,000 = 12x

x = 41500000 / 12

x = 3458333.8

After 15 minutes, the colony has grown to 101.3 million organisms.

y = kx

101,300,000 = 15k

k = 101,300,000 / 15

k = 6753333.8

It is a non-proportional relationship as the constant of proportionality is different for each.

According to the given statement The two real solutions of the equation x² = 100 are x = 10 and x = -10.

To find the two real solutions of the equation x² = 100, we need to take the square root of both sides of the equation.
Taking the square root of both sides, we get:

√(x²) = √100

Simplifying, we have:

|x| = 10

This equation tells us that the absolute value of x is equal to 10.

To find the two real solutions, we consider both the positive and negative values of x.

First, we consider the positive value:

|x| = 10

x = 10

Next, we consider the negative value:

|x| = 10

x = -10

Therefore, the two real solutions of the equation x² = 100 are x = 10 and x = -10.

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When solving the equation x² = 100, we find that there are two real solutions: x = 10 and x = -10.

The equation x² = 100 represents a quadratic equation in which the variable x is squared. To find the real solutions of this equation, we need to determine the values of x that satisfy the equation.

Step 1: Take the square root of both sides of the equation. √(x²) = √100

Simplifying, we get: x = ±10

Step 2: The two real solutions of the equation x² = 100 are x = 10 and x = -10.

In this case, the square root of 100 is 10, and since the equation involves the square of x, we have two possible values for x: 10 and -10. Both of these values satisfy the equation x² = 100.

Therefore, the two real solutions of the equation x² = 100 are x = 10 and x = -10.

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Answer:

1.  $76,000

2. $58,000 + $2,000 * t

Step-by-step explanation:

2. Now, you might be questioning why we are going with the second question first, but this will be useful as it sets up our equation to make the first question easier. So, we will start with Luke's base salary of $58,000. Then, we will add $2,000 for every year he works at the company. If he works for t years and gains $2,000 on his salary per year, our equation will look like this:

$58,000 + $2,000 * t

That is the equation.

1. Now, using our previous equation, $58,000 + $2,000 * t, we will substitute 9 in for t. We get:

$58,000 + $2,000 * 9

Then, we simplify, giving us:

$58,000 + $18,000 = $76,000

Answer:

POINTFARMER.EXE=EZ

Step-by-step explanation:

Answer:

120 feet^2

Step-by-step explanation:

Answer:

A parallelepiped has three sets of four parallel edges; the edges within each set are of equal length. Parallelepipeds result from linear transformations of a cube (for the non-degenerate cases: the bijective linear transformations).

Step-by-step explanation:

A parallelepiped focuses on three-dimensional figures formed by six parallelograms.

A parallelepiped shape has the following features

Think of a cube or a cuboid.

Notice that they contain squares and rectangles

A parallelepiped is to a parallelogram as a square is to a cube and a rectangle to a cuboid

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The quadratic inequality that models the situation is given by:

y < -7.4(x - 25)² + 200.

The equation of a quadratic function, of vertex (h,k), is given by the rule presented as follows:

y = a(x - h)² + k

In which:

The vertex is of (25, 200), hence the parameters are as follows:

h = 25, k = 200.

Hence the equation is:

y = a(x - 25)² + 200.

When x = 30, y = 15, hence the leading coefficient is calculated as follows:

15 = a(30 - 25)² + 200

25a = -185

a = -185/25

a = -7.4.

Hence, considering that the company did not meet it's goals, the inequality is:

y < -7.4(x - 25)² + 200.

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