Mrs. Van and her family went bowling. The total cost of the shoes was $12 and the cost to bowl was $5 per game. Write an equation y, the cost of bowling and x the number of games they played.

p(x)= (x-4)²-(x-6)². ... 4X - 20 = 0 => X = 20/4 => X= 5.

Answer:

(a) 48/60 = 4/5

(b) 150/60 = 15/6 = 5/2 = 2 1/2

(c) 84/98 = 12/14 = 6/7

(d) 12/52 = 3/13

(e) 7/28 = 1/4

The fractions reduced to their simplest form:

(a) 48/60 simplifies to 4/5.

(b) 150/60 simplifies to 5/2.

(c) 84/98 simplifies to 6/7.

(d) 12/52 simplifies to 3/13.

(e) 7/28 simplifies to 1/4.

Let's discuss each question separately:

(a) To reduce the fraction 48/60 to simplest form, we need to find the greatest common divisor (GCD) of both numbers. The GCD of 48 and 60 is 12. Dividing both the numerator and denominator by 12 gives us the simplified fraction 4/5.

(b) For the fraction 150/60, we find that the GCD of 150 and 60 is 30. Dividing both the numerator and denominator by 30 results in the simplified fraction 5/2.

(c) The fraction 84/98 can be simplified by dividing both the numerator and denominator by their GCD, which is 14. This gives us the simplest form of 6/7.

(d) To simplify the fraction 12/52, we calculate the GCD of 12 and 52, which is 4. Dividing both numbers by 4 yields the simplest form of 3/13.

(e) The fraction 7/28 can be simplified by dividing both the numerator and denominator by their GCD, which is 7. This simplifies the fraction to 1/4.

In summary, the fractions in their simplest forms are:

(a) 4/5

(b) 5/2

(c) 6/7

(d) 3/13

(e) 1/4.

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30% of the eligible students voted.

It is given to us that 650 students at the high school are eligible to vote and 195 of them voted in the last election.

Now let us take the percent of students to be 'x'

x% of 650 students voted whose value is given to be 195.

So the equation can be written as

( x / 100 ) * 650 = 195

x = ( 195 * 100 ) / 650

x = 30

Therefore 30% of  the eligible students voted in the last election.

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Answer:

1/16

Step-by-step explanation:

Since no cards are removed between each shuffle, the chance of drawing a spade both times remains the same, meaning it is 1/4 both times. 1/4 * 1/4 =1/16

The probability of drawing two spades in two draws if the first card is returned to the deck between draws will be 1 / 16.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of samples

Given that the chance of drawing a spade from a deck of cards is 1/4. If the deck is shuffled between draws.

The probability will be calculated as,

Probability = 1 / 4 x 1/ 4

Probability = 1 / 16

Hence, the probability will be equal to 1 / 16.

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Answer:

b

Step-by-step explanation:

The graph of the transformations applied to the function g(x) can be seen at the end of the answer.

Here we have some transformations applied to the function g(x).

g(x) = x^3 - x

First, we start with g(x). Then we apply a vertical contraction of scale factor 0.5, so we get:

h(x) = 0.5*g(x).

Now we translate the function 1 unit upwards, so we get:

h(x) = 0.5*g(x) + 1

Finally, we move the graph 2 units to the right, so we get:

h(x) = 0.5*g(x - 2) + 1.

h(x) = 0.5*( (x - 2)^3 - (x - 2)) + 1

The graph of this function can be seen below.

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Answer:

The area of the quadrilateral ABCD is 114 square units

Step-by-step explanation:

Answer:

1. 405

2. 153

3. -35

4. 132

Step-by-step explanation:

The statement is false. A parameter is a descriptive measure of a whole population.

A parameter tells us about a whole population. It means that a parameter should be found to understand all the characteristics of a population. A population itself is the entire group that we want to study.

For example: A population mean. We take a class as the population. We asked them about age and found that the average age is 20. That is a parameter.

A statistic otherwise tells us about some parts of the population. It describes a sample. A sample itself is a small group taken from the population.

For example: A sample mean. We take some people of the class to interview their age. We found the average age is 21. This is a statistic.

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Find out the maximum number of dimes and nickels that can be included in the 7 coins while staying within the half-dollar limit. Each dime is worth 10 cents, so the maximum number of dimes we can use is 4. Each nickel is worth 5 cents, so the maximum number of nickels we can use is 5.

In order to find out the number of ways we can choose 7 coins consisting of dimes and nickels so that their total value does not exceed half a dollar, we will use the following steps:

Step 1: Find out the maximum number of dimes and nickels that can be included in the 7 coins while staying within the half-dollar limit. Each dime is worth 10 cents, so the maximum number of dimes we can use is 4. Each nickel is worth 5 cents, so the maximum number of nickels we can use is 5. Therefore, we have two possible scenarios: Use 4 dimes and 3 nickels. This gives us a total value of 4 x 10 + 3 x 5 = 50 cents, which is exactly half a dollar. Use 3 dimes and 4 nickels. This gives us a total value of 3 x 10 + 4 x 5 = 45 cents, which is less than half a dollar.

Step 2: Find out the number of ways we can choose 7 coins consisting of dimes and nickels with the above constraints. For scenario 1, we have to choose 4 dimes from 4 available dimes, which can be done in 1 way. We also have to choose 3 nickels from 5 available nickels, which can be done in 5C3 = 10 ways. Therefore, there are 1 x 10 = 10 ways to choose 7 coins consisting of 4 dimes and 3 nickels. For scenario 2, we have to choose 3 dimes from 4 available dimes, which can be done in 4 ways. We also have to choose 4 nickels from 5 available nickels, which can be done in 5C4 = 5 ways. Therefore, there are 4 x 5 = 20 ways to choose 7 coins consisting of 3 dimes and 4 nickels. In total, there are 10 + 20 = 30 ways to choose 7 coins consisting of dimes and nickels so that their total value does not exceed half a dollar.

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Answer:

  5

Step-by-step explanation:

Simplify the equation:

  2m -10 = -3m +15

Add 3m

  5m -10 = 15

Add 10

  5m = 25

Divide by 5

  m = 5

Answer:

5/2

Step-by-step explanation:

5/2= 2 1/2

while 16/9=1 7/9

ANSWER

4/5

EXPLANATION

The slope of a line is given by,

In this roof, the rise is the height of the roof, 12ft, and the run is half the width of the roof, 15ft,

Hence, the pitch is 4/5.

When we roll three fair coins, there are two possible outcomes for each coin - either it lands heads up or tails up. There are 8 elementary events in the sample space of the experiment of rolling three fair coins.

The sample space of this experiment consists of all possible combinations of three outcomes, which can be calculated by multiplying the number of outcomes for each coin: 2 x 2 x 2 = 8.
Each of these combinations is called an elementary event, which means that there are 8 elementary events in the sample space of the experiment of rolling three fair coins. We can list them as follows:
1. HHH (all three coins land heads up)
2. HHT (two coins land heads up, one lands tails up)
3. HTH (two coins land heads up, one lands tails up)
4. THH (two coins land heads up, one lands tails up)
5. HTT (one coin lands heads up, two land tails up)
6. THT (one coin lands heads up, two land tails up)
7. TTH (one coin lands heads up, two land tails up)
8. TTT (all three coins land tails up)

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828uwbb8w7wvhwwjw8u1h1

Answer:

hope this helps you to solve it

We must solve for n the following equation:

1) First, we assume n ≠ 0 and multiply both sides by √n, we get:

2) Now, we divide both sides by E:

3) Finally, taking the square on both sides, we get:

We have proved the sequent Bb, ꓱ xBx↔ꓯ yDy ├ D, using Universal Elimination, Material Implication, and Modus Ponens. Bb, ꓱ xBx↔ꓯ yDy ├ D is valid.

b (Premise)

ꓱ xBx↔ꓯ yDy (Premise)

Bb ↔ ꓯ yDy (3, 2 ↔E)

Bb → ꓯ yDy (3 ↔E)

Dd (Assumption)

Bb (1)

Bb → Dd (4, 6 ꓯE)

Dd (5)

Dd V Ed (8 ꓯI)

ꓯ y(Dy V Ey) (9 ꓯI)

Bb → (Dd V Ed) (4, 7-10 ꓯI)

D (Assumption)

Bb (1)

Bb ↔ D (13, 2 ↔E)

Bb → D (14 ↔E)

D (12)

D V E (16 ꓯI)

ꓯ y(Dy V Ey) (17 ꓯI)

Bb → (Dd V Ed) (4, 7-18 ꓯI)

D (1-19 MP)

D (5-10, 12-18 CD)

D ├ D (5-10, 12-21 ꓯI)

Therefore, Bb, ꓱ xBx↔ꓯ yDy ├ D is valid.

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Answer: If you’re talking on a percentage basis, it would be extremely unlikely to get a majority of the questions correct.

Step-by-step explanation:

A scatter plot chart of stock returns versus past stock returns will typically appear as a random pattern mostly concentrated in the top-right and lower-left quadrants.

This pattern indicates that there is a positive correlation between past and current stock returns, but there are also instances where current returns are negative despite past positive returns.

The top-right quadrant represents instances where both past and current returns are positive, while the lower-left quadrant represents instances where both past and current returns are negative.

The random pattern indicates that stock returns cannot be predicted with certainty based on past returns alone.

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Answer:

0.32

Step-by-step explanation:

plato

Answer:-1/2

Step-by-step explanation:

-3/7 x 1-1/14

Multiply first

-3/7-1/14

-7/14=-1/2

Answer:

-1/2

Step-by-step explanation:

A linear system with 3 equations and 4 variables by representing it with an augmented matrix and bringing the matrix to reduced row-echelon form can be solved.

A mathematical representation of a system based on the application of a linear operator is known as a "linear system" in systems theory. Ordinarily, compared to nonlinear systems, linear systems display much simpler features and properties. The automatic control theory, signal processing, and telecommunications all heavily rely on linear systems as a mathematical abstraction or idealisation.

Linear systems, for instance, are frequently used to model the propagation medium for wireless communication systems. An operator, H, that converts an input, x(t), into an output, y(t), a kind of black box description, can be used to describe a general deterministic system.

The superposition principle, or alternatively both the additivity and homogeneity properties, must be satisfied by a system to be considered linear, and only then.

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The probability that the marble is large or white is 0.5714.

Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.

Probability of an event is

P(A) = Number of favorable outcomes/ Total Number of outcomes      

       = n(A)/n(S)

where

P(A) is the probability of an event “A”

n(A) is the number of favorable outcomes

n(S) is the total number of events in the sample space.

We have,

Number of large marbles = 14

Number of small marbles = 10

Number of large green marbles = 8 which implies

Number of large white marbles = 14 - 8 = 6

Number of small white marbles = 4 which implies

Number of small green marbles = 10 - 4 = 6.

Now, let

Let X be the event of drawing large marble.

Let Y be the event of drawing small marble.

Let M be the event of drawing white marbles.

Let N be the event of drawing green marbles.

Since only one marble is drawn at a time ,

so P(X) =  14/24

    P(Y) = 10/24

    P(M) = 10/24

    P(N) = 14/24

We have to find the probability that a marble is large or white i.e. P(X∪M).

P(X∪M) = P(X) + P(Y) - P(X∩M)

P(X∩M) = In 14 large marbles 6 are white marbles = 6/14.

P(X∪M) = P(X) + P(Y) - P(X∩M) = 14/24 + 10/24 - 6/14 = 0.5833+0.4167-0.4286 = 0.5714.

Therefore, the probability of drawing large or white marble is 0.5714.

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The equation for money collected m for h boxes of chocolate bars sold is m = 30h.

We are given that the band is selling every bar of chocolate for $1.50

Now, they have boxes of chocolate, with every box containing 20 bars of chocolate in them.

Hence if we are going to calculate the amount of money collected on selling one box it will be

20 X $1.5

= $30

We need to find the equation for the amount of money collected based on the number of boxes of chocolate bars sold.

We have been given that money collected should be represented b m while the number of chocolate boxes sold should be represented by h

Now we know that

Money collected = price per box X no.of boxes sold

we have already calculated the price per box hence we get

m = 30h

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Answer:

if you are doing times then it would be 216 feet

Step-by-step explanation:

18 x 12 equals 216 I hope it helped

Answer:

width = 2.93 cm

Step-by-step explanation:

Area of picture = 12 x 17 = 204

let x = width of border

2(17 + 2x)(x) + 2(12x) = 204

34x + 4x² + 24x - 204 = 0

4x² + 58x - 204 = 0

Use quadratic formula to find x:  a = 4, b = 58, c = -204

x = 2.93, -17.43       disregard the negative root

x = 2.93 cm

Answer:

11

Step-by-step explanation:

she divides the number of pencils equally

so the number of pencils per student is 152/13

which is 11.692...

but she can't give 0.69 of a pencil so she gives only the whole part 11

and she keeps 9 pencils

i. weekly receipts at a clothing boutique

ii. monthly demand for an automotive part

Time series data refers to information collected and recorded at regular intervals over a specific period. In the case of i. weekly receipts at a clothing boutique and ii. monthly demand for an automotive part, both data sets are examples of time series data.

Time series data consists of observations recorded over regular intervals, allowing for the analysis of patterns and trends over time. In i. weekly receipts at a clothing boutique, the data is collected on a weekly basis, providing insights into the boutique's revenue fluctuations over different weeks. Similarly, ii. monthly demand for an automotive part captures the demand for the part on a monthly basis, enabling analysis of monthly variations and seasonal patterns.

On the other hand, iii. quarterly sales of automobiles do not fall under time series data. While it represents sales data, the intervals between measurements are not consistent enough to qualify as time series. Quarterly intervals are less frequent and may not capture shorter-term trends or variations as effectively as weekly or monthly intervals.

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