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3 years ago

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The daily cost of hiring a plumber , y , to work x hours on a repair project can be modeled using a linear function. The plumber

charges a fixed cost of $80 plus an additional cost of $45 per hour. The plumber works a maximum of 8 hours per day. For one day of work, what is the range of the function for this situation?

1 answer:

Paladinen [302]3 years ago

3 0

Answer:

The range of the function is $80\leq y\leq 440$

Step-by-step explanation:

Consider the provided information.

The plumber charges a fixed cost of $80 plus an additional cost of $45 per hour.

Let plumber works for x hours, then the required linear function will be:

$y=45x+80$

The plumber works a maximum of 8 hours per day.

That means the minimum value of x is 0 and maximum value of x is 8.

We need to find the range of the function.

Range of the function is the set of y values.

Substitute x=0 in above function,

$y=45(0)+80$

$y=80$

Now substitute x=8 in above function.

$y=45(8)+80$

$y=360+80$

$y=440$

Hence, the range of the function is $80\leq y\leq 440$

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I need some one to help me!! <br><br> Is (7, 0) a solution to the equation y = x − 7?

Marianna [84]

Answer:

Yes

General Formulas and Concepts:

<u>Pre-Algebra</u>

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Left to Right<u> </u>

Coordinates (x, y)

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

Point (7, 0)

Equation y = x - 7

<u>Step 2: Find</u>

Substitute in point [Equation]: 0 = 7 - 7
Subtract: 0 = 0

Since 0 = 0 is true, then it would be a solution to the equation.

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3 years ago

Brent claims that more students at his school prefer hot dogs over hamburgers. His friend Shaun doesn’t agree. To settle their a

photoshop1234 [79]

Answer:

Using conditional probabilities it can be shown that the results are influenced by the gender.

Explanation:

To prove that the results are influenced by <em>gender</em> you can calculate both the probability of preferring hot dogs and the conditional probability of preferring a hot dog given that is a female.

If the two results are different the probability of preferring hot dog is dependent on whether the person is a female or a male.

The probability of preferring hot dogs given that is a female is stated by the problem: 34.2%.

The probability of preferring hot dogs by the whole sample is:

Number of males that prefer hot dogs: 184 (stated by the problem)
Number of females that prefer hot dogs:

100% - 34.2% = 65.8%

65.8% of 635 = 0.658 × 635 = 417.83 ≈ 418

Samples size: 542 males + 635 females = 1177

Probability of preferring hot dogs =

number of students that preffer hot dogs / number of students =

(184 + 418) / 1177 = 602 / 1177 = 0.5115 ≈ 51.2%

Thus, the probability of preferring hot dogs given that the student is a female (34.2%) is different from the probability of preferring hot dog for the whole sample, making the results dependent of the gender.

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4 years ago

Algebraic Proof<br> Given: 3w + 4w - 2 = 12<br> Prove: w = 2

choli [55]

Answer:

Step-by-step explanation:

Replace W with 2

(3 x 2) + (4 x 2) -2 = 12

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add 6 + 8 = 14

14 - 2 = 12

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which your answer in the end would be 12 = 12

which proves W is 2

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4 years ago

Ice cream usually comes in 1.5-quart boxes (48 fluid ounces), and ice cream scoops hold about 2 ounces. However, there is some v

Troyanec [42]

Answer:

(a) The expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.

(b) The expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.

(c) Because the variance of each variable is dependent on the other.

Step-by-step explanation:

The random variable <em>X</em> and <em>Y</em> are defined as follows:

<em>X</em> = amount of ice cream in the box

<em>Y</em> = amount of ice cream scooped out

The information provided is:

E (X) = 48

SD (X) = 1

V (X) = 1

E (Y) = 2

SD (Y) = 0.25

V (Y) = 0.0625

(a)

The total amount of ice-cream served at the party can be expressed as:

<em>X</em> + 3<em>Y</em>.

Compute the expected value of (<em>X</em> + 3<em>Y</em>) as follows:

$E(X+3Y)=E(X)+3E(Y)\\= 48+(3\times2)\\=48+6\\=54$

Compute the variance of (<em>X</em> + 3<em>Y</em>) as follows:

$V(X+3Y) = V (X)+3^{2}V(Y)+2\times 3Cov (X,Y)\\=1+(9\times0.0625)+0\\=1.5625$

Then the standard deviation of (<em>X</em> + 3<em>Y</em>) is:

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Thus, the expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.

(b)

The amount of ice-cream left in the box after scooping out one scoop is represented as follows:

<em>X</em> - <em>Y</em>.

Compute the expected value of (<em>X</em> - <em>Y</em>) as follows:

$E(X-Y)=E(X)-E(Y)\\=48-2\\=46$

Compute the variance of (<em>X</em> - <em>Y</em>) as follows:

$V(X - Y) =V(X)+V(Y)-2Cov(X,Y)\\=1+0.0625-0\\=1.0625$

Then the standard deviation of (<em>X</em> - <em>Y</em>) is:

$SD(X-Y) =\sqrt{V(X -Y)}\\\sqrt{1.0625}\\=1.031$

Thus, the expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.

(c)

The variance of the sum or difference of two variables is computed by adding the individual variances. This is because the variance of each variable is dependent on the others.

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3 years ago

Assume that a procedure yeilds a binomial with n trial and the probability of success for one trial is p. Use the given values o

Alexeev081 [22]

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Given the values of the parameters of Binomial Distribution are,

Total number of trials (n) = 1490

probability of success in one trial is (p) = 2/5

The probability of failure in on trial is given by,

$q=1-p=1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}$

For Binomial distribution we know that,

Mean $(\mu)=np=1490\times\frac{2}{5}=596$

and Standard Deviation $(\sigma)=\sqrt{npq}=\sqrt{1490\times\frac{2}{5}\times\frac{3}{5}}=357.6$

Now, calculating the required measurement we get,

The minimum usual value is given by,

Mean -2 Standard Deviation $=\mu-2\sigma=596-2\times357.6=-119.2$

The maximum usual value is given by,

Mean + 2 Standard Deviation $=\mu+2\sigma=596+2\times357.6=1311.2$

Hence the minimum and maximum usual values are -119.2 and 1311.2 respectively.

Learn more about Binomial Distribution here -

brainly.com/question/15246027

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4 0

3 years ago