Which of the following rational functions is graphed below

Answer:

see below

Step-by-step explanation:

a) The unknown is the price of a large pizza

b)  Each pizza cost is positive,

c) The the price of a pizza be p,

so the price of one pizza is p

d) The expression is  

6 pizzas minus 3 dollar off each pizza

6p -3p

e) Set this equal to the total cost

6p -3p= 38.94

f) Combine like terms

3p = 38.94

Divide each side by p

3p/3 = 38.94/3

p = 12.98

The price of each pizza before discount is 12.98

Answer:

$51.2

Step-by-step explanation:

4 x 12.8 = 51.2

In general, the definition of the function composition is given by the expression below

Therefore, in our case,

The random selection of a sample to represent the proportions of a population divided by sex and size of school attended is called stratified random sampling.

Stratified random sampling is a sampling method used when a population is divided into subgroups or strata based on certain characteristics, such as sex and size of school attended. In this method, a random sample is taken from each subgroup proportionate to its size in the population. This ensures that each subgroup is represented in the sample and reduces the chance of sampling bias.

For example, if the population of high school seniors is divided into two strata based on sex and two strata based on size of school attended, there would be four subgroups. A random sample would then be taken from each subgroup to create a representative sample of the entire population.

Stratified random sampling is commonly used in research studies and surveys to ensure that the sample accurately represents the population being studied. It allows for more precise estimates and statistical inferences to be made about the population as a whole.

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Answer:

a. y=x^2

Step-by-step explanation:

desmos graphing calculator

By using normal distribution of probability, it is obtained that

Percentile rank of a turtle whose length is 21 inches is 22%

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probality of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Here, Normal Distribution of probability is used

Mean = 25.9 inches

Standard deviation = 6.3 inches

P(X \(\leq\) 21) = P(z \(\leq\) \(\frac{21 -25.9}{6.3}\))

               = P(z \(\leq\) -0.78)

               = 0.22

               = 22%

Percentile rank of a turtle whose length is 21 inches is 22%.

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Answer:

yes they do

Step-by-step explanation:

they share a ray

It is more unusual to have a day with a high temperature of 55 F. A high temerature of 55 F in July is 2.2 std deviation below the mean and a high temperature of 55 F in January is only 1.889 std deviation above the mean.

Which month is more unusual to have a day with a high temperature?

Here z score =(X-mean)/std deviation

Therefore for temperature 55 F ; zscore for January =(55-38)/9=1.889

And for temperature 55 F ; zscore for July =(55-77)/10=-2.2

As z score reflect that 55 F is farthest from the mean of July in terms of std deviation

It is more unusual to have a day with a high temperature of 55 F. A high temperature of 55 F in July is a 2.2 std deviation below the mean, and a high temperature of 55 F in January is only a 1.889 std deviation above the mean.

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The value of the definite integral is (175/3) - (3730/3√5) - 600√5/3.

We can use the substitution \(u = x^2 + 25\) to simplify the given integral.

Then du/dx = 2x, and solving for x we get \(x = (u - 25)^{(1/2)\).

We also need to find the new limits of integration when x = 0 and x = 5.

When x = 0, \(u = 0^2 + 25 = 25\), and when x = 5, \(u = 5^2 + 25 = 50\).

Using the substitution, the integral becomes:

∫[\(x^2 + 25 - x^3\)] dx from 0 to 5

= ∫(\(u - x^3\)) × (1/2x) dx from 25 to 50 (substituting for x and solving for dx)

=\((1/2) \times \int(u^{(1/2)} - u^{(3/2)} + 25u^{(-1/2)} - 25u^{(1/2)}) du\) from 25 to 50

(substituting for x and simplifying)

= \((1/2) \times [(2/3)u^{(3/2)} - (2/5)u^{(5/2)} + 50u^{(1/2)} - 50u^{(3/2)}]\) from 25 to 50

(integrating and simplifying)

=\([(2/3)(50^{(3/2)} - 25^{(3/2)}) - (2/5)(50^{(5/2)} - 25^{(5/2)}) + 50(50^{(1/2)} - 25^{(1/2)}) - 50(50^{(3/2)} - 25^{(3/2)})] / 2\)

= [(2/3)(1250 - 625) - (2/5)(125000 - 15625) + 50(5 - 5√5) - 50(125√5 -

25√5)] / 2

= (175/3) - (3730/3√5) - 600√5/3

Therefore, the value of the definite integral is (175/3) - (3730/3√5) -

600√5/3.

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Answer:jusk click that the answer is there i hope its correct correct me if im wrong

Step-by-step explanation:

Answer:

The answer is x³ + 4x² + x - 6.

Step-by-step explanation:

You have to expand it :

\((x - 1)(x + 2)(x + 3)\)

\( = ( {x}^{2} + 2x - x - 2)(x + 3)\)

\( = ( {x}^{2} + x - 2)(x + 3)\)

\( = {x}^{3} + 3 {x}^{2} + {x}^{2} + 3x - 2x - 6\)

\( = {x}^{3} + 4 {x}^{2} + x - 6\)

The expression (x - 1) (x + 2) (x + 3) is written in form of ax³ + bx² + cx + d as;

⇒  (x - 1) (x + 2) (x + 3) = x³ + 4x² + x - 6

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is;

⇒  (x - 1) (x + 2) (x + 3)

Now, It can be solve by multiplying as;

The expression is;

⇒  (x - 1) (x + 2) (x + 3)

⇒ (x - 1) (x² + 3x + 2x + 6)

⇒ (x - 1) (x² + 5x + 6)

⇒ x³ + 5x² + 6x - x² - 5x - 6

⇒ x³ + 4x² + x - 6

Thus, By comparing with the equation of the form ax³ + bx² + cx + d , we get;

⇒ a = 1 , b = 4 , c = 1 and d = -1

Clearly, a, b and c are positive integers, and d is negative integer.

Hence, The expression (x - 1) (x + 2) (x + 3) is written in form of

ax³ + bx² + cx + d.

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9514 1404 393

Answer:

  yes, about 2.05 inches

Step-by-step explanation:

The Pythagorean theorem can be used to find the width of the TV.

  w^2 +h^2 = d^2

  w = √(d^2 -h^2)

  w = √(42^2 -18^2) = √1440 = 12√10

  w ≈ 37.95 . . . inches

This dimension is less than 40 inches by a margin of ...

  40 -37.95 = 2.05 . . . inches

The TV will fit, with 2.05 inches of space remaining.

Answer:

Option B is correct.

Step-by-step explanation:

6 3/7 = 45/7

1 3/6 = 9/6 = 3/2

=> 45/7 - 3/2

=> 90/14 - 21/14

=> 69/14

=> 4 13/14

Therefore, Option B is correct.

Answer:

Step-by-step explanation:

4000 x 8% = 320 annually

since you are asking for only 60 days

320 x 60/365 = &52.6

Answer:

The rate of change per week is $6.

Step-by-step explanation:

56 - 14 = 42

42/7 = $6

6 dollars were added each week.

(a) Prοbability οf at least 3 peοple believe that they have seen a UFO 0.857.

(b) Prοbability οf 3 οr 4 peοple believe that they have seen a UFO 0.181.

(c) Prοbability οf Exactly 4 peοple believe that they have seen a UFO 0.00049 (rοunded tο 3 decimal places).

Prοbability is a branch οf mathematics that deals with the study οf randοmness and uncertainty in events. It is the measure οf the likelihοοd οr chance that an event will οccur. Prοbability is expressed as a number between 0 and 1, where 0 indicates that the event will nοt οccur and 1 indicates that the event will οccur with certainty.

This is a binοmial prοbability prοblem, where the prοbability οf success (p) is 0.1 and the sample size (n) is 15.

(a) At least 3 peοple believe that they have seen a UFO:

Using the cοmplement rule, the prοbability οf having less than 3 peοple whο believe they have seen a UFO is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = (0.9)¹⁵ + 15(0.1)(0.9)¹⁴ + (105)(0.1)²(0.9)¹³

where X is the number οf peοple whο believe they have seen a UFO in the sample. Therefοre, the prοbability οf having at least 3 peοple whο believe they have seen a UFO is:

P(X ≥ 3) = 1 - P(X < 3) = 1 - [(0.9)¹⁵ + 15(0.1)(0.9)¹⁴ + (105)(0.1)²(0.9)¹³] = 0.170

Sο the prοbability οf at least 3 peοple believing they have seen a UFO is 0.170.

(b) 3 οr 4 peοple believe that they have seen a UFO:

Using the binοmial prοbability fοrmula, we can calculate the prοbabilities fοr 3 and 4 peοple believing they have seen a UFO and then add them tοgether:

P(X = 3) = (15 chοοse 3)(0.1)³(0.9)¹² = 0.185

P(X = 4) = (15 chοοse 4)(0.1)⁴f(0.9)¹¹ = 0.099

Therefοre, the prοbability οf having 3 οr 4 peοple whο believe they have seen a UFO is:

P(3 οr 4) = P(X = 3) + P(X = 4) = 0.185 + 0.099 = 0.284

Sο the prοbability οf 3 οr 4 peοple believing they have seen a UFO is 0.284.

(c) Exactly 4 peοple believe that they have seen a UFO:

Using the binοmial prοbability fοrmula, we can calculate the prοbability fοr 4 peοple believing they have seen a UFO:

P(X = 4) = (15 chοοse 4)(0.1)⁴ (0.9)¹¹ = 0.099

Sο the prοbability οf exactly 4 peοple believing they have seen a UFO is 0.099.

Hence,

(a) P(X ≥ 3) = 0.857

(b) P(3 ≤ X ≤ 4) = 0.181

(c) P(X = 4) = 0.00049 (rοunded tο 3 decimal places)

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The mean, variance, and standard deviation of the distribution is 20.74, 1.3210, and 1.1493, respectively.

First, the mean can be found using the following formula:

Mean = ∑x(p(x))

Mean = (19)(0.22) + (20)(0.20) + (21)(0.32) + (22)(0.14) + (23)(0.12)

Mean = 4.18 + 4 + 6.72 + 3.08 + 2.76

Mean = 20.74


Next, the variance can be found using the following formula:

Variance = ∑(x-mean)²(p(x))

Variance = (19-20.74)²(0.22) + (20-20.74)²(0.20) + (21-20.74)²(0.32) + (22-20.74)²(0.14) + (23-20.74)²(0.12)

Variance = 0.5362 + 0.0552 + 0.0173 + 0.1754 + 0.5369

Variance = 1.3210


Finally, the standard deviation can be found using the following formulas:

Standard deviation = √variance

Standard deviation = √1.3210

Standard deviation = 1.1493


So, the mean is 20.74, the variance is 1.3210, and the standard deviation is 1.1493, all rounded to 4 decimal places.

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Answer: To subtract mixed fractions with different denominators, you need to convert the mixed fractions to equivalent fractions with a common denominator. Once the fractions have a common denominator, you can simply subtract the numerators and keep the denominator the same.

Example:

the difference of 2 1/3 and 1 3/4 is 5/12.

Step-by-step explanation:

First, convert 2 1/3 to an improper fraction: 2 1/3 = 7/3

Next, convert 1 3/4 to an improper fraction: 1 3/4 = 7/4

Now, both fractions have the same denominator, 3. So, you can subtract the numerators:

7/3 - 7/4 = (7 * 4 - 7 * 3) / (3 * 4) = 28/12 - 21/12 = 7/12

Finally, convert the answer back to a mixed fraction: 7/12 = 7 ÷ 12 =  5/12.

Answer:

$33.60

Step-by-step explanation:

Original price of shirt: $40

Percent discount: 20%

Amount of discount: 20% of $40 = 0.2 × $40 = $8

Price after discount: $40 - $8 = $32

Percent of tax: 5%

Amount of tax: 5% of $32 = 0.05 × $32 = $1.60

Total paid after discount and tax: $32 + $1.60 = $33.60

Answer: Lydia paid the amount of 33.60 dollar

Step-by-step explanation:

Retail price of shirt = 40 dollar

Discount = 20%

Discount value:

=20% of 40 dollar                   [ 20/100 * 40 ⇒ 1/5 * 40 ⇒ 40/5 = 8 ]

= 8 dollar  [ discount value]

Price of shirt after discount :

= 40 - 8

= 32 dollar

As she paid 5% discount on the discounted price ( 32 dollar )

So,  5% of 32 = 1.6 dollar        [ 5/ 100 * 32 ⇒  1/20 * 32 ⇒ 32/20 = 1.6]

Amount to pay = 32( price after discount)  + 1.6 ( Tax)

= 33.60 dollar

(a) The probability that both John and Jane watch the show is 0.07.

(b) The probability that Jane watches the show, given that John does, is 0.11

(c) No. John and Jane do not watch the show independently of each other.

(a) The probability that both John and Jane watch the show is given by the product of their individual probabilities:

P(John and Jane watch) = P(John watches) x P(Jane watches)

     = 0.7 x 0.1

     = 0.07.

(b) The probability that Jane watches the show, given that John does, is given by Bayes' theorem:

P(Jane watches | John watches) = P(John watches | Jane watches) x P(Jane watches) / P(John watches)

From the information given, we know that:

To find P(John watches), we can use the law of total probability:

P(John watches) = P(John watches | Jane watches) * P(Jane watches) + P(John watches | not Jane watches) * P(not Jane watches)

           = (0.8 x 0.1) + (0.7 x 0.9)

           = 0.71

Therefore,

P(Jane watches | John watches) = 0.8 x 0.1 / 0.71 = 0.1127

(c) John and Jane do not watch the show independently of each other, since the probability that John watches the show changes depending on whether or not Jane watches it. In other words, the events "John watches the show" and "Jane watches the show" are dependent events.

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The solutions of the given equation are x=4 and x=-4. Therefore, options B and E are the correct answers.

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The given quadratic equation is x²-16=0.

Here, x²=16

x=±√16

x=±4

So, the solutions are x=4 and x=-4.

Therefore, options B and E are the correct answers.

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Using the normal distribution, it is found that this type of fishing line have a breaking strength less than the advertised 6 pounds 27.76% of the time.

The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is given by the following rule:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation for the breaking strengths are given as follows:

\(\mu = 6.44, \sigma = 0.75\)

The proportion of times with breaking strength less than 6 inches is given by the p-value of Z when X = 6, hence:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (6 - 6.44)/0.75

Z = -0.59

Z = -0.59 has a p-value of 0.2776.

Hence the percentage is of 27.76%.

The question is:

How often will this type of fishing line have a breaking strength less than the advertised 6 pounds.

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y = 1/2 x + 1

y = 3/2x + 4        Use first equation to sub in for y

1/2 x + 1  = 3/2 x + 4

-3 = x      then use this value in one of the equations to calc  y

y = 1/2 x + 1

y = 1/2 (-3) + 1 =  - 1/2

Let's break this problem down step by step.

First, we can work out the weight of one white ball by subtracting the weight of 6 white and 3 orange balls (20 pounds) from the weight of 2 white and 5 orange balls (8 pounds):

Weight of 1 white ball = 8 - 20 = -12

Next, we can work out the weight of one orange ball by subtracting the weight of 2 white and 5 orange balls (8 pounds) from the weight of 6 white and 3 orange balls (20 pounds):

Weight of 1 orange ball = 20 - 8 = 12

Now that we know how much one white and one orange ball weigh, we can work out the weight of 4 white and 4 orange balls together:

Weight of 4 white and 4 orange balls = (4 x -12) + (4 x 12) = 0

Therefore, the weight of 4 white and 4 orange balls together is 0 pounds.

By solving two given simultaneous equations using algebra, we find that the combined weight of 4 white balls and 4 orange balls is 16 pounds.

The subject matter of this question pertains to simultaneous equations. The equations in question are, 2w + 5o = 8 and 6w + 3o = 20, where w stands for the weight of a white ball and o stands for the weight of an orange ball. We can solve these equations to find the individual weights of these balls. After finding these values, we substitute these into a new equation, 4w + 4o, to find the total weight of 4 white and 4 orange balls together. By solving these equations, we find that the weight of 4 white balls and 4 orange balls together is 16 pounds.

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Answer:

A) $5.5= 0.25(17)+0.05(n) where n = nickels

B) 25 nickels

Step-by-step explanation:

The relative price is a useful measure for comparing the prices of different products or services, especially in the context of consumer preferences and demand.

Relative price refers to the price of a particular product or service in relation to other goods or services in the market.

It is calculated as the ratio of the price of a given product or service to the price of a reference product or service, commonly referred to as a base good or service.

Let the price of a pair of shoes be $5 and the price of a box of tea be $3.

Then the relative price of a pair of shoes is given by:

Relative price of shoes = Price of shoes / Price of tea

= $5 / $3

= 1.67

Thus, the relative price of a pair of shoes is 1.67.

Similarly,

The relative price of a box of tea can be calculated as follows:

Relative price of tea = Price of tea / Price of shoes

= $3 / $5

= 0.6

Therefore, the relative price of a box of tea is 0.6.

This means that the price of tea is relatively cheaper than that of shoes, as its relative price is less than one.

The relative price of shoes is greater than one, which indicates that shoes are relatively more expensive than tea.

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Answer:

3/4 x 2/5 => NO

2/5 x 5/6 => NO

1/10 x 1/5 => NO

1/2 x 3/5 => YES

Step-by-step explanation:

3/4 x 2/5 = 6/20 => NO

2/5 x 5/6 = 10/30 => NO

1/10 x 1/5 = 1/50 => NO

1/2 x 3/5 = 3/10 -> YES

Answer:

10.7

Step-by-step explanation: