Scott's gross income in 4 weeks, rounded to the nearest cent, is $1887.20.
Calculate Scott's daily earnings:
Scott earns $16.85 per hour, and he works for 7 hours per day.
Daily earnings = $16.85/hour × 7 hours = $117.95
Calculate Scott's weekly earnings:
Scott works 4 days per week.
Weekly earnings = Daily earnings × Number of days worked per week
= $117.95/day × 4 days/week
= $471.80
Calculate Scott's gross income for 4 weeks:
Scott works for 4 weeks.
Gross income for 4 weeks = Weekly earnings × Number of weeks
= $471.80/week × 4 weeks
= $1887.20
However, we need to ensure the precision of the final answer. As currency involves cents, it's important to round appropriately.
Since we're dealing with money, we'll round to the nearest cent.
After rounding, the gross income for 4 weeks is $1887.20.
Write the complex number in the form a + bi. 6(cos 330° + i sin 330°)
Answer:
The complex number 6(cos 330° + i sin 330°) in the form of a+bi is:
3√3-3 i
Step-by-step explanation:
6(cos 330° + i sin 330°)
= 6(cos(360°-30°)+ i sin(360°-30°))
=6(cos30°- i sin30°) (since, 360°-30° lies in fourth quadrant and cos is positive there and sin is negative)
=[tex]6(\dfrac{\sqrt{3}}{2}-i\dfrac{1}{2})[/tex]
Distributing 6, we get
=3√3-3 i
Hence, the complex number 6(cos 330° + i sin 330°) in the form of a+bi is:
3√3-3 i
What does the standard error of the estimate tell us?
Fran graphs the equations y = 2x2 – 2 and y = –0.5x + 4. Her graph is shown below.
Which value is an approximate solution of 2x2 – 2 = –0.5x + 4?
A. x = -2
B. x = -1
C. x = 1
D. x = 5
The approximate solution for the given system of equations y = 2x2 – 2 and y = –0.5x + 4 is C. x = 1. This is the value of x where the two graphs intersect, thus making both equations true.
Explanation:The question is asking for the solution to the system of equations given by y = 2x2 – 2 and y = –0.5x + 4. Solving a system of equations means finding the value of x that makes both equations true. In other words, we're looking for the point where the two graphs intersect.
To find this value, we can set the two equations equal to each other and solve for x:
2x2 – 2 = -0.5x + 4
This simplifies to 2x2 + 0.5x - 6 = 0. Solving this quadratic equation can give us multiple solutions for x, but since the question is multiple choice, we can check which of the given options is a solution. Plugging the options into the equation reveals that option C. x = 1 is the correct answer, satisfying the equation.
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Which number is the largest? 23.01247 23.01244 23.01274 23.01277?
The number pi goes on forevermore with no repeating pattern therefore is it rational
You are carving a block of ice for a banquet. It measures 1 ½ feet long, 1 ½ feet wide and 1 ½ feet thick. Ice weighs 57 pounds per cubic foot. What is the weight of the ice block?
volume = l x w x h
1.5 x 1.5 x 1.5 = 3.375 cubic feet
3.375 * 57 = 192.375 pounds
1. If m<1 = 43, what is m<4?
A. 53
B. 43
C. 37
D. 27
2. If m<1 = 50, what is m<5?
A. 50
B. 40
C. 35
D. 25
3 use the figure. Assume that lines JL and MP are parallel.
Name a pair of corresponding angles.
A. <1 and <6
B. <2 and <6
C. <3 and <5
D. <4 and <5
By using what we know about intersecting lines, we will see that the correct options are:
1) B2) A3) BHow to get the measures?
In an intersection of two lines, if two angles are adjacent, then their measures must add to 180°. And if the angles are not adjacent, then the angles have the same measure.
a) 1 and 4 are not adjacent, so these angles have the same measure.
so if m<1 = 43, then m<4 = 43
The correct option is B.
b) 1 and 5 are equivalent (where we assume that JL and MP are parallel, so all the angles formed in the two intersections are equal).
Then if m<1 = 50, m<5 = 50.
So the correct option is A.
c) The corresponding angles occupy equivalent positions.
For example:
2 and 6 are corresponding.3 and 7 are corresponding4 and 8 are corresponding.etc.
The correct option is B.
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Dan opened up his piggy bank and found a total of thirty-five coins, made up of nickels, dimes, and quarters. if he has five more nickels than dimes and a total of $6, how many of each coin were in his bank?
In his piggy bank, Dan has 10 nickels, 20 dimes and 5 quarters.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Assume that he had [x] nickels, [y] dimes and [z] quarters. Then we can write -
x = y + 5
x + y + z = 35
x/20 + y/10 + z/4 = 6
Now, the equation → x/20 + y/10 + z/4 = 6, can be written as → (x + 2y + 5z) = 120
We can write, the equations as -
x = y + 5
x + y + z = 35
x + 2y + 5z = 120
Solving the simultaneous equations, we get -
y + 5 + y + z = 35
2y + z = 30 Eq [1]
y + 5 + 2y + 5z = 120
3y + 5z = 115 Eq [2]
Plot Eq[1] and Eq[2] on graph. The point of intersection of both will give the values of y and z.
z = 20
y = 5
We can then find [x] as -
x = y + 5 = 10
x = 10
Therefore, in his piggy bank, Dan has 10 nickels, 20 dimes and 5 quarters.
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The table gives the numbers of teachers and students in grades 6 to 8 at Earhart Middle School. Grade Teachers Students 6 1 25 7 2 50 8 3 75 Which teacher-to-student ratio maintains the proportional relationship described in the table?
Answer:
Teachers 4 and Students 100, Teachers 5 and Students 125
Step-by-step explanation:
Going by the chart, by each teacher, the students are increasing by 25. The only ones to follow this pattern is 4:100 and 5:25
A pack of cinnamon-scented pencils sells for $9.00. What is the sales tax rate if the total cost of the pencils is $9.45?
The diameter of each wheel of a bicycle is 28 inches28 inches. if you are traveling at a speed of 30 miles per hour30 miles per hour on this bicycle, through how many revolutions per minute are the wheels turning
Hiro painted his room at a rate of 8 square meters per hour. After 3 hours of painting, he had 28 square meters left to paint. Let A(t) denote the area to paint A (measured in square meters) as a function of time t (measured in hours). What is the Functions formula? A(t)=?
8*3 = 24 + 28 = 52 total square feet
he is painting at 8 sq m per hour
so A(t) = -8t +52
Answer:
[tex]A(t)=-8t+52[/tex]
Step-by-step explanation:
Let
A(t)------> the area to paint
t------> the time in hours
Step 1
Find the total area of the room
[tex]A=8*3+28=52\ m^{2}[/tex]
Step 2
Find the linear equation that represent the situation
[tex]A(t)=-8t+52[/tex]
Which product is the factored form of the polynomial?
(–x2 – 5)(3x2 + 2)
(x2 – 2)(3x2 + 5)
(x2 + 5)(3x2 – 2)
(3x2 – 5)(x2 + 2)
From this year to ten years later the number of people employed as physician assistants in the country is expected to increase by 47% the number of people employed as physician assistants today is 55000 find the predicted number of physician assistants after ten years
What is the value of the expression 4x+y2y−x when x = 2 and y = 4?
To date, this year, Company XYZ has sold 450 units. They sell units at an average rate of 15 per week. The company wants to sell more than 750 units this year. Which of the following inequalities could be used to solve for x, the number of weeks necessary to reach the company's year-end goal?
Final answer:
To reach the goal of selling more than 750 units this year, it will take more than 50 weeks.
Explanation:
To determine the number of weeks necessary to reach the company's year-end goal of selling more than 750 units, we can set up an inequality using the average rate of sales per week. Let x represent the number of weeks needed to reach the goal. The total number of units sold in x weeks can be calculated by multiplying the average rate of sales per week (15) by the number of weeks (x). So, the inequality would be: 15x > 750. To solve for x, divide both sides of the inequality by 15: x > 50. Therefore, it would take more than 50 weeks to reach the company's goal.
Final answer:
The inequality to solve for x, the number of necessary weeks, is 450 + 15x > 750.
Explanation:
To determine for x, the number of weeks necessary for Company XYZ to reach their goal of selling more than 750 units this year, we need to set up an inequality.
They have already sold 450 units and sell units at an average rate of 15 per week.
The company's target is more than 750 units.
Therefore, we can represent this scenario with the following inequality:
450 + 15x > 750
Here's how to solve for x:
Subtract 450 from both sides of the inequality to isolate the term with x on one side:15x > 750 - 45015x > 300Divide both sides of the inequality by 15 to solve for x:x > 300 / 15x > 20Therefore, Company XYZ will need to sell for more than 20 additional weeks to exceed their goal of 750 units.
What point in the feasible region maximizes P for the objective function P = 2x + 3y? Constraints
2x+y≤15
x+3y≤20
x≥0,
y≥0 A. (0, 15) B. (5, 5) C. (8, 7) D. (2, 6)
Final answer:
To find the point that maximizes P for the objective function P = 2x + 3y, calculate P at each vertex of the feasible region created by the constraints. Point A (0, 15) yields the highest value of P, which is 45. Therefore, point A (0, 15) is the correct answer.
Explanation:
To determine which point in the feasible region maximizes P for the objective function P = 2x + 3y, consider the given constraints: 2x + y ≤ 15, x + 3y ≤ 20, x ≥0, y ≥0. To find the maximum value of P, we need to check the value of P at all vertices of the feasible region formed by the constraints. In such linear programming problems, the maximum or minimum value of the objective function occurs at one of the vertices of the feasible region.
Let's test the given points against the objective function:
A. (0, 15) yields P = 2(0) + 3(15) = 45
B. (5, 5) yields P = 2(5) + 3(5) = 25
C. (8, 7) yields P = 2(8) + 3(7) = 37
D. (2, 6) yields P = 2(2) + 3(6) = 22
Comparing these values, we see that point A (0, 15) gives us the highest value of P, which is 45. Hence, the correct answer to the question is point A (0, 15).
Which of the following is the inverse of the statement if you lift weights then you will be strong
Answer:
Inverse statement : "If you don't lift weights, then you will not be strong".
Step-by-step explanation:
If a statement is defined as
p → q : If p is true, then q is true.
then the inverse of the given statement is
¬ p → ¬ q : If p is not true, then q is not true.
The given statement is "If you lift weights then you will be strong".
We need to find the inverse of the given statement.
Here,
p = you lift weights
q = you will be strong
The inverse of the given statement is "If you not lift weights, then you will not be strong".
Negative four times a number plus nine is no more than the number minus twenty one
If 15 percent of the sixth graders have blonde hair, and there are 120 sixth graders, how many of them have blonde hair?
Jeff's average math grade is 92.8. Sarah's average math grade is 67.9.
How much higher is Jay's average math grade than Sarah's?
A) 24.9
B) 25.1
C) 25.9
D) 34.9
Absolute Value equations and equalities, please help
|x| + 5 = 18
a. 5 or -5
B. 13 or -13
C. 18 or -18
D. 23 or -23
|y +4| < 1
a. -5 < y< -3
b. -3
c. -4
d.1
In a random sample of 200 cars of a particular model, 3 have a manufacturing defect. At this rate, how many of 10,000 cars of the same model will have a manufacturing defect?
*SHOW WORK*
Answer:
There will be 150 defective cars among the set of 10,000 cars
Step-by-step explanation:
For every 200 cars 3 are defective
Let X numbers of car be defective out of 10000 cars
There is a proportional relationship between the two
Thus,
[tex]\frac{3}{200} = \frac{X}{10,000} \\X = \frac{(10,000)(3)}{(200)} = 50 * 3\\= 150[/tex]
The snow fox can run at a rate of 8.5 feet per second. Write and solve an equation to find the time it takes the snow fox to travel 120ft. Please show your work.
divide distance by speed
equation: time = distance / speed
120/8.5 = 14.117 seconds
The dimensions of a rectangular prism are 1 mm, 6 mm, and 11 mm. Find the volume and the surface area.
THX :)
The volume and the surface area of the rectangular prism will be 66mm and 166mm² respectively.
Length = 11m
Width = 1mm
Height = 6mm
The volume of the rectangular prism will be:
= Length × Width × Height
= 11mm × 1mm × 6mm
= 66mm
The surface area of the rectangular prism will be:
= 2(wl + hl + hw)
= 2(11 + 66 + 6)
= 2(83)
= 166
Therefore, the surface area of the rectangular prism will be 166mm²
In conclusion, the volume and the surface area of the rectangular prism will be 66mm and 166mm² respectively.
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Classify each of the triangles as acute, obtuse, or rights?
Triangle JKL is obtuse triangle.
Triangle XYZ is acute triangle.
What is an obtuse trianglesAn obtuse triangle is a type of geometric figure with three sides and three angles. In an obtuse triangle, one of the angles measures more than 90 degrees (∠A, ∠B, or ∠C > 90°). The other two angles are acute angles, measuring less than 90 degrees each. Consequently, the sum of the angles in an obtuse triangle is greater than 180 degrees.
what is the acute triangle
An acute triangle is a type of geometric shape defined by its angles. It consists of three sides and three angles, all of which are acute angles, meaning each angle measures less than 90 degrees (∠A, ∠B, and ∠C < 90°)
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Candy bags is sold in 4 pound bags.How many full bags will Gina need to purchase?
Are the below pairs of lines parallel, perpendicular, or neither?
9x+12y = 8 and 6x+8y = −1
Parallel
Perpendicular
Neither
Insert commas in the following numbers. a. 13886 b. 365 c. 719463 d. 40047209 e. 2145739180 f. 1783457
Write an inequality for the word sentence: k is less than zero
The sentence 'k is less than zero' can be translated into the inequality 'k < 0', where 'k' can be any value that is less than zero. The inequality for the word sentence 'k is less than zero' is k < 0.
Explanation:The sentence 'k is less than zero' can be translated into an inequality as 'k < 0'. This is an inequality to represent a situation where 'k', a variable, takes values that are less than zero. It's a way of understanding the relationship of 'k' to zero in mathematical terms. For example, -1, -2, -3, etc. are all numbers that meet this less than zero inequality because they are less than zero.
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