Given the equation −4 Square root of x minus 3= 12, solve for x and identify if it is an extraneous solution

Final answer:

The total cost for fixing a drain that takes 7 hours is $226. If the plumber charges a total of $310, he spent 11 hours fixing the drain.

Explanation:

The cost function given by the plumber is C(h) = 79 + 21h, where C represents the total cost and h represents the number of hours spent fixing the drain.

First let us calculate for his salary this year. We know that 3000 is only 8% of his salary, hence:

0.08 * salary = 3000

salary = 3000 / 0.08

salary = 37,500

Therefore his previous salary is:

previous salary = 37,500 + 2,000

previous salary = $39,500

Answer:

First let us calculate for his salary this year. We know that 3000 is only 8% of his salary, hence:

0.08 * salary = 3000

salary = 3000 / 0.08

salary = 37,500

Therefore his previous salary is:

previous salary = 37,500 + 2,000

previous salary = $39,500

Step-by-step explanation:

m∠PTS and m∠RTQ are vertically opposite angles thus both will be the same so the measure of m∠PTS will be 55°.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

Angle is shown by the sign ∠

Given the line segments, PQ and SR is intersecting at T

Thus m∠PTS and m∠RTQ will be vertically opposite angles

m∠PTS = m∠RTQ

Given that,

m∠PTS = 11(y - 10)

m∠RTQ  = 4y - 5

11(y - 10) = 4y - 5

11y - 110 = 4y - 5

11y - 4y = -5 + 110

7y = 105

y = 15

Therefore m∠PTS = 11(15 - 10)

m∠PTS = 55°

Hence "m∠PTS and m∠RTQ are vertically opposite angles thus both will be the same so the measure of m∠PTS will be 55°".

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354,738 rounded to the nearest thousand is 355,000.

In Mathematics and Euclidean Geometry, a place value is a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:

The number in the thousand place in the number 354,738 is 7 and it is greater than or equal to 5. This ultimately implies that, we would round up the number 4 to 5.

354,738 ≈ 355,000.

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For 2 1/2 times the doubled recipe, starting with an initial amount of 3 1/3 cups of heavy cream, the total amount needed would be 16 2/3 cups of heavy cream.

To calculate how much heavy cream is needed, we must first understand the initial amount required and then apply the necessary adjustments to upscale the recipe.

If the original recipe calls for 3 1/3 cups of heavy cream and we want to double the recipe, we would need 2 x 3 1/3 cups which is 2 x (10/3) cups = 20/3 cups or 6 2/3 cups.

Now, if we want to make 2 1/2 times the amount of the doubled recipe, we multiply 6 2/3 cups by 2 1/2 (5/2), resulting in (20/3) x (5/2) cups. Simplifying this, we get:

(20/3) x (5/2) = (100/6) cups = 16 2/3 cups.

Therefore, for 2 1/2 times the doubled recipe, you would need 16 2/3 cups of heavy cream.

multiply 19.7 x 4 for total gallons

19.7 * 4 = 78.8 total gallons

 multiply that by price:

78.8 * $3 = $236.40 total price

Mrs. Blanka spent $236.4 on gas last month by filling up her truck's 19.7-gallon tank 4 times at a price of $3 per gallon.

To calculate how much Mrs. Blanka spent on gas last month, we need to consider the amount of gas her truck holds, the number of times she filled up her tank, and the price per gallon of gas. Mrs. Blanka's truck holds 19.7 gallons of gas, and she used 4 full tanks of gas last month. Given the price of gas was $3 per gallon, the calculation would be as follows:

Therefore, Mrs. Blanka spent $236.4 on gas last month.

Answer:

Which equation represents the scenario?

✔ 6.25x + 12 = 30.75

How many people went to the movies?

✔ 3

Step-by-step explanation:

1. There are 3 peoples go to the movie.

2. The equation to represent the scenario is,

⇒ 6.25x + 12 = 30.75

Where, x is number of people.

What is an expression?

Expression in math is defined as the collection of the number, variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

The price of a ticket = $6.25

As a group, they spend $12 on refreshments.

Total spent money = $30.75

Now,

Let number of people go to the movie = x

Then, Total price spent on ticket = $6.25x

And, As a group, they spend $12 on refreshments.

So, Total spent money is equal to $30.75, as;

$6.25x + $12 = $30.75

This equation represents the scenario.

Now, Solve the equation for number of people as;

$6.25x + $12 = $30.75

Subtract 12 both side,

6.25x + 12 - 12 = 30.75 - 12

6.25x = 18.75

Divide by 6.25,

x = 3

Thus, There are 3 peoples go to the movie.

Therefore,

1. There are 3 peoples go to the movie.

2. The equation to represent the scenario is,

⇒ 6.25x + 12 = 30.75

Where, x is number of people.

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Answer: The area of the cover = 56 square inches.

Step-by-step explanation:

We know that the shape of a tablet is rectangle.

Thus to calculate the area of the protective cover we apply the formula to calculate area of rectangle.

The area of rectangle is given by :-

[tex]\text{Area}=\text{Length*width}\\\\\Rightarrow\text{Area}=8\times7\\\\\Rightarrow\text{Area}=56\text{ inches}^2[/tex]

Therefore, the area of the protective cover is 56 square inches.

1/13 = 0.0769 = 7.7%

9/26 = 0.346 = 34.6%

5/26 = 0.192 = 19.2%

The quotient of any two rational numbers is always a rational number. This can be proved by expressing the division as multiplication by the reciprocal and demonstrating that the result is a rational number. Therefore, the property of being rational is preserved under division.

Let's define rational numbers first. A rational number is any number that can be expressed as the quotient of two integers, where the denominator is not zero. Mathematically, if a and b are integers and b ≠ 0, then r = a/b is a rational number.

Thus, we have proved that the quotient of any two rational numbers is a rational number.

Answer:

On Zira's birthday Lizzy, Amy Wilson Amara, and Ria want only 3/4 inches of the cake how much cake do you need for all of them?

Solutions 5 x3/4 = 3.75 inches of cake

Step-by-step explanation:

An equation is formed when two equal expressions. Max's total earnings for the given month are $4,325. The correct option is C.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that Max has a monthly salary of $1,100 and also earns a 7.5% commission on his sales. Therefore, the equation that can represent Max's monthly salary for any month is,

y = $1,100 + $(0.075x)

where y is the month's salary and x is the number of sales he made.

Given in the last month Max had $43,000 in sales last month. Therefore, Max's total salary for the given month is,

Max Salary = $1,100 + $(0.075x)

= $1,100 + $(0.075 × 43,000)

= $1,100 + $3,225

= $4,325

Hence, Max's total earnings for the given month are $4,325.

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We know that Richard can apply fertilizer to 4485 square feet = 3/4 hour

To solve this problem, one approach is to find 1/4 then multiply by 4 to get the whole 4/4 or 1 hour.

So the solution would be:

4485/3=1495
Then multiply this by 4.

1495 multiplied by 4 is equal to 5980 square feet.

So Richard can apply fertilizer to 5980 square feet in 1 hour.

The question is about calculus and requires finding the limit of a multivariable function as it approaches a particular point. Evaluating such limits can be very complex and typically requires application of theorems and techniques from multivariable calculus. In this specific case evaluation of limit goes beyond the scope of this platform.

The subject of this question is mathematics, specifically it is about

Calculus

and more specifically about finding limits of functions of multiple variables. In this case, the function given is f(x, y, z) =  (xy + 3yz2 + 4xz2) / (x2 + y2 + z4). To determine the limit of the function (if it exists) as (x, y, z) approaches (0, 0, 0), we would use substitution method. When we substitute x=0, y=0, and z=0 to the function, we get undefined format (0/0) which means we need to apply the L'Hopital's rule. But application of this rule to multivariable function involves evaluating multiple partial derivatives of function which is beyond the scope of this platform. Hence, a full evaluation of the limit of this particular function requires use of theorems and techniques from

multivariable calculus

.

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Answer:

[tex]344=12x+80[/tex]

[tex]a=344[/tex]

[tex]b=12[/tex]

[tex]c=80[/tex]

Step-by-step explanation:

Let x be number of balls shot through the hoop by Central City High School's robot.

We have been given an equation [tex]a=bx+c[/tex] and we are asked to find the values of a, b and c.

We are told that Central City High School's team earned an additional 12 points for each ball the robot shot through a hoop. So the points earned by shooting x balls through the hoop will be 12x.

The team also earned 80 points for their robot climbing over an obstacle. So total number of points earned by team will be equal to [tex]12x+80[/tex].

We are also told that the team won the round with 344 total points. We can represent this information in an equation as: [tex]344=12x+80[/tex]

Upon comparing this equation with our given equation we will get,

[tex]a=344[/tex]

[tex]b=12[/tex]

[tex]c=80[/tex]

Therefore, the equation [tex]344=12x+80[/tex] can be used to find the number of balls, x, team's robot shot through the hoop.

To find (f+g)(x), add the functions f(x) and g(x), substituting x into both functions and then adding the results together. The result is (f+g)(x) = 4x + 16.

To find (f+g)(x), we need to add the two functions f(x) and g(x). f(x) = 3x + 7 and g(x) = x + 9. To determine (f+g)(x), we substitute x into both f(x) and g(x) and then add the results together.

So, (f+g)(x) = f(x) + g(x) = (3x + 7) + (x + 9) = 4x + 16.

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a) P(X >= 6) = 0.0160

b) P(X > 10) ≈ 6.88 x 10^-6

c) P(X = 0) ≈ 0.1339

d) P(X < 5) ≈ 0.9482

a. Probability of six or more pages with errors:

This is the sum of probabilities for 6, 7, 8, ..., 200 errors:

P(X >= 6) = 1 - [P(X < 6)] = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]

Using a calculator or statistical software, we can find these individual probabilities and sum them up. Alternatively, we can use binomial distribution tables or functions available in programming languages.

P(X >= 6) ≈ 0.0160

b. Probability of more than 10 pages with errors:

Similar to part (a), but calculating from 11 errors onwards:

P(X > 10) = 1 - [P(X=0) + P(X=1) + ... + P(X=10)]

P(X > 10) ≈ 6.88 x 10^-6 (very small probability)

c. Probability of none of the pages containing errors:

P(X = 0) = (0.99)^200 ≈ 0.1339

d. Probability of fewer than five pages containing errors:

P(X < 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)

P(X < 5) ≈ 0.9482