Pat’s Painting Company charges a $125 painting fee, plus $17.50 per hour. Write and solve an equation to determine how many hours the company worked if they were paid $221.25 for one job.

The domain of a function is the set of all possible inputs for the function,

Domain: (−∞,∞), {x | x ∈ R}

Range: (1, ∞], {y | y ≥ 1}

What are the domain and range?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

We have,

f(x) = x² + 1

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation: (-∞, ∞)

Set-Builder Notation: {x | x ∈ R}

The range is the set of all valid y values. Use the graph to find the range.

Interval Notation: [1. ∞)

Set-Builder Notation: {y | y ≥ 1}

Hence, the domain of a function is the set of all possible inputs for the function,

Domain: (−∞,∞), {x | x ∈ R}

Range: (1, ∞], {y | y ≥ 1}

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Answer:

x= y/e (or the last answer choice on your screen)

Step-by-step explanation:

The slope of the ideal vector, determined by examining the coefficients of the variables in the regression equation is:

Cleaning Ability: 2.3

Cost: 1.0

Disinfecting Ability: 0.6.

In this case, the regression equation is:

Overall Preference = -2.1 + 2.3 * Cleaning Ability + 1.0 * Cost + 0.6 * Disinfecting Ability

The coefficients of the variables represent the weights or importance assigned to each variable in determining the overall preference. Therefore, the slope of the ideal vector would be the coefficients of the variables in the regression equation.

Based on the given regression equation, the slope of the ideal vector would be:

Cleaning Ability: 2.3

Cost: 1.0

Disinfecting Ability: 0.6

These values indicate the relative importance or impact of each variable on the overall preference for Slippery Soap.

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The simplified expression of the expression given as (62)4 is 248

From the question, we have the following parameters that can be used in our computation:

(62)4

Remove the bracket and rewrite the expression as a product expression

So, we have the following representation

(62)4 = 62 * 4

Evaluate the products

This gives

(62)4 = 248

The above expression cannot be further simplified

Hence, the solution is 248

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Answer:

The answer would be A

Step-by-step explanation:

Step-by-step explanation:

according to the property of the parallelogram m(OPE)=m(OHE), then  2x+25=3x-15, then (after calculation the 'x'):

1. x=40;

2. m(OHE)=2*40+25=105°;

3. m(OPE)=3x-15=3*40-15=105°;

4. m(HOP)=180-m(OPE)=180-105=75°;

5. m(HEP)=m(HOP)=75°.

Answer:

25. Not a function because when you use vertical line test, you came across two points at the same time.

26. This is a function because when you vertical line test, you don't come across two points at the same time.

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

To find the vector projv u, you can use the formula: (v⋅u / |v|²) * v.

To find v⋅u (the dot product of v and u), you can multiply the corresponding components of v and u and then add the results.

To find |v| (the magnitude or length of v), you can use the Pythagorean theorem. Square each component of v, add the results, and take the square root of the sum.

Similarly, to find |u| (the magnitude or length of u), you can use the same process as above.

To find the cosine of the angle between v and u, you can use the dot product formula: cosθ = (v⋅u) / (|v| * |u|).

To find the scalar component of u in the direction of v, you can use the formula: (v⋅u) / |v|.

Lastly, to find the vector projv u, you can use the formula: (v⋅u / |v|²) * v.

Remember to plug in the values for v and u to get the specific results for each exercise.

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Answer:

Carl traveled 281.25 km by bus and 1,618.75 km by plane.

Step-by-step explanation: v1 = 60 km/h average speed by bus to Toronto

v2 = 700 km/h average speed by plane to Winnipeg

d = 1,900 km the total distance traveled

t = 7 h total traveling time

t1 = the time of the travel by bug

t2 = the time of the travel by plane

t = t1 + t2 the total time

d1 = the distance traveled by bus

d2 = the distance traveled by plane

d = d1 + d2 the total distance

Since average speed = distance/time we have time = distance/avg.speed

t1 = d1/v1 that is t1 = d1/60

t2 = d2/v2 that is t2 = d2/700

Plug the above values into t1 + t2 = t.

We have the following system of equations:

d1/60 + d2/700 = 7

d1 + d2 = 1900

.......

Click here to see the step by step solution for 'd1' and 'd2'

.......

d1 = 281.25 km

d2 = 1,618.75 km

Carl traveled 281.25 km by bus and 1,618.75 km by plane.


Answer:

a. 0.6975

b. 0.25

c. The events are independent and inclusive

Step-by-step explanation:

a. The proportion of five-star football recruits in the nation that go to universities in the three most competitive athletic conferences = 75%

Therefore, the probability of a five-star football recruits chooses to go to a university in the three most competitive athletic conferences p(A) = 75% or 0.75

The proportion of the times five-star football recruits get full football scholarships = 93%

Therefore, the probability that a five-star football recruit get full football scholarships p(B) = 93% or 0.93

Therefore, the probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship can be written as -the probability that a randomly selected five-star recruit who chooses one of the best three conferences and will be offered a full football scholarship is therefore;

p(A) ∩ p(B) = p(A) × p(B) = 0.75×0.93 = 0.6975

b. The probability that a randomly selected five star recruit will not select a university from one of the three best conferences = 1 - p(A) = 1 - 0.75 = 0.25

c. The events are independent as the given probability of occurrence of one event does not alter the probability of the other event

The events are inclusive events are exclusive events as P(A)and P(B) can take place simultaneously.

Answer:6 kits with 9 bottles of water and 7 cans of food in each kit

9

Step-by-step explanation:

Find the greatest common factor between 54 and 42 which is 6. so that is how many kits can be made and divide each by 6 to see how many items are in each kit.

a. The probability that this person , reads financial magazines or sports magazines is 81%.

b.  The probability that this person never reads sports magazines and never reads financial magazines is  19%.

a. The probability that this person , reads financial magazines or sports magazines is calculated as follows;

P(A or B) = P(A) + P(B) - P(A ∩ B)

where;

P(A) = 63% = 0.63

P(B) = 48% = 0.48

P(A ∩ B) = 30% = 0.30

P(A or B) = 0.63 + 0.48 - 0.30

P(A or B) = 0.81 = 81%

question b.

The probability that a person never reads sports magazines and never reads financial magazines is calculated as follows;

P(not A and not B) = 1 - P(A or B)

P(not A and not B) = 1 - 0.81 = 0.19

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Answer:

Step-by-step explanation:

true

Step-by-step explanation:

Sin(30 degrees) = 1/2

The value of sin 30° is 1/2 and it lies in 1 st quadrant.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

sin 30° can be calculated using the unit circle or a calculator that has a sin function.

In the unit circle, 30° is in the first quadrant, and the sine of an angle in the unit circle is defined as the y-coordinate of the point on the circle that corresponds to that angle.

For a 30° angle, the point on the unit circle is (cos 30°, sin 30°)

= (√3/2, 1/2).

Therefore, the value of sin 30° is 1/2.

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Answer:

Following are the solution to this question:

Step-by-step explanation:

An alternative black, white, and grey design of the tile is also desired. She needs her color scheme to suit the top boundary of the tile. Therefore, the central tile paint should be grey to ensure a white top boundary. To ensure, that perhaps the outer end is white, the color of the center tile shall be dark.

In mutually exclusive data, you cannot find any overlap or intersection between the categories or events being analyzed.

This means that the occurrence of one event or category precludes the occurrence of the other. On the other hand, in dependent data, the occurrence of one event or category may have an effect on the occurrence of the other, and thus, they are not completely independent or separate. Therefore, in both cases, you cannot find any shared or common outcomes or occurrences between the categories or events being analyzed.

You cannot find a direct correlation or causal relationship between mutually exclusive or dependent data. In mutually exclusive events, the occurrence of one event prevents the occurrence of the other, meaning they cannot happen at the same time. In dependent events, the probability of one event happening is influenced by the outcome of a previous event. Due to these characteristics, it is not possible to establish a direct correlation or causal relationship between such events.

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Using probability,

a) 61/100

b) 61/210

c) 305/536

The probability formula can be used to calculate the likelihood of an event by simply dividing the favourable number of possibilities by the total number of options.

The likelihood of an event occurring can range from 0 to 1, as there can never be more favourable outcomes than there are potential outcomes. Because of this, the percentage of effective outcomes cannot be 0.

Here in the question,

It has asked to find probability that a randomly selected person did not have a child under 18 years old, given that they said no is:

P = 305/500

= 61/100

It is asked to find probability that a randomly selected person said No, given that the person did not have a child under 18 years old is:

P = 305/1050

= 61/210

It is asked to find probability that a randomly selected person from the group did not have a child under 18 years old and said no is:

P = 305/536

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Answer:

y=1/5 x -4

Step-by-step explanation:

Basically, we first start with perpendicular. Note that 2 lines' that are perpendicular have product = -1. Thus, the slope of the line (in question) is 1/5.

Now, we know y = mx + b by slope intercept. Note that y intercept means (0,-4). Thus, plugging in give the answer.

Hope this helps! (Please mark brainliest :))

The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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The x - intercepts of the equation is x = 0

X - intercept refers to the value of x when y = 0

On a graph this refers to the value where the graph cuts the x axis

The given function is

y = ( 4x² - 36x ) / ( x - 9 )

equating y to zero and factorizing the function gives

0 = ( 4x² - 36x ) / ( x - 9 )

0 = 4x ( x - 9 ) / ( x - 9 )

0 = 4x

x = 0

hence at y = 0, x is 0

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Answer: I believe that the answer would be "In an isosceles triangle, two of the angles are congruent."

Step-by-step explanation:

Answer:

In an isosceles triangle, two of the angles are congruent.

hope this helps :)

Answer:

5- and 4-

Step-by-step explanation:

If the number line is incorrect keep checking

Answer: 6/8 , 9/12 , 12/16 , 15/20, ect...

Step-by-step explanation:

Example:3*2   = 6

               4*2      8

You can check if it is equivalent by dividing the numerator and denominator by 2

Example:6 divided by 2= 3

               4  divided by 2   4

You can replace 2 with 3,4,5,6 ect...

3/4 multiplied by 3 =9/12, 3/4 multiplied by 4 is 12/16, 3/4 multiplied by 5 is 15/20.

Hope this helps, let me know if you want more examples.

        - - - - - - - - - - - -- - - - - - - - -  - - - - --  -- - - - - -- - - - - - - - - -- - - - - - - - -

\(\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\)

Find an equivalent fraction for the fraction below. 3/4

\(\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\)

If fractions are equivalent, they are equal to each other.

An example of a fraction equal to 3/4 is:-

\(\bold{\displaystyle\frac{6}{8}} \dashleftarrow\sf{The\:numerator\:and\:denominator\:are\:multiplied\:by\:2}\)

This is just one example; in fact, there are infinitely many fractions equivalent to 3/4; you can multiply the numerator & denominator by 2:

6/8 = 12/16 =24/32...

You can also multiply by 3:-

9/12 =12/36...

You can multiply by 4, 5, 6, 7, 8....

Overall, you can multiply by any number you wish. As long as you multiply the numerator and denominator by the same number, you will get a fraction that's equivalent to the original fraction.

      -- - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - -- - - - -  - -- - - - - - - - -- -

The rate of return (RoR) needed for an population to increase from its starting balance to its ending balance, providing growth were repopulated at the conclusion of each period of the population life span

To determine an population CAGR:

Divide the population worth at the end of the time by the value it had at the start of the period.

The result should be multiplied by one and divided by the number of years.

The outcome is then reduced by one.

To convert the response into a percentage, multiply by 100.

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The correlation here in the provided graph is a positive trend and the equation for line of best fit will be as follows:

y = 1/4x

Correlation is a statistical method for determining the association or relationship between two variables. To put it another way, the correlation coefficient formula facilitates the calculation of the correlation coefficient, which assesses the degree to which one variable depends on another.

The correlation coefficient is a numerical indicator of correlation. Between -1 and 1, the correlation coefficient is found. An inverse association between two variables is shown by a negative correlation coefficient. A high correlation coefficient means that the two variables directly affect one other's values. There is no association between the two variables, according to a zero-correlation coefficient.

Here in the question,

The graph shows a positive trend as its increasing upwards. The equation for the line of best fit will be y =1/4x.

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The simplified form of the expression 4(3 - 4x) - 4x + 7 - 8x + 12 - 16x is \(16x^2\) - 52x + 31.

Simplify the given expression, we apply the distributive property first. We multiply 4 with each term inside the parentheses:

4(3 - 4x) - 4x + 7 - 8x + 12 - 16x

This simplifies to:

12 - 16x - 16x + 16x^2 - 4x + 7 - 8x + 12 - 16x

We combine like terms by grouping the variables and constants together:

(-16x - 16x - 4x - 8x - 16x) + (12 + 7 + 12)

This simplifies to:

-52x + 31

Hence, the simplified form of the expression is 16x^2 - 52x + 31. It is a quadratic expression with a coefficient of 16 for the x^2 term.

The -52x term represents the combined coefficient of all the x terms, and the constant term is 31.

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