-13x<65 what is the solution to this inequality
Beau has a 30-mile commute for work each day. He drives at least an additional 225 miles every month. He needs an inequality to relate his monthly mileage, y, to the number of days he commutes, x. Which answer choice correctly describes this scenario?
A His monthly mileage is greater than the difference between 30 times the number of days and 200.
B His monthly mileage is less than the difference between 30 times the number of days and 200.
C His monthly mileage is greater than or equal to the sum of 30 times the number of days and 200.
D His monthly mileage is less than or equal to the sum of 30 times the number of days and 200.
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.
Find the slope of the line whose equation is 5y = x - 3.
-3
-3/5
1/5
5
Answer:
1/5
Step-by-step explanation:
5y = x - 3
To find the slope of a line, we need to get the equation in the form y= mx+b where m is the slope and b is the y intercept
5y = x - 3
Divide each side by 5
5y/5 = x/5 - 3/5
y = 1/5 x - 3/5
The slope is 1/5 and the y intercept is -3/5
Answer:
1/5
Step-by-step explanation:
What is 5x-y=35 in slope form
On a 1616 scale drawing of a bike, one part is 3 inches long. How long will the actual bike part be?
If Consider today’s stock listing for Enam Telecom, shown below.
52 wk High52 wk LowSymbolDiv.CloseNet Change122.8664.77ENM3.4599.144.74if the lowest price in the past year occurred 48 days ago, find the approximate average change per day since then. a. $4.74 b. $0.72 c. $0.49 d. $1.34
Answer:
Average change per day since then = $0.72
Step-by-step explanation:
Stock listing for Enam Telecom is given as
52 wk high 52 wk low Symbol Div. Close Net change
122.866 64.77 ENM 3.45 99.14 4.74
The lowest price $64.77 occurred 48 days ago.
Today's close for the stock was $99.14.
Now we have been asked to tell the approximate average change per day since then.
Therefore Average change per day = (closing value for today - closing value 48 days ago) ÷ (number of days)
Since closing value 48 days ago = 52 week low = $64.77
Now average change = [tex]\frac{(99.14-64.77)}{48}=0.72[/tex]
Therefore answer is $0.72 is the average change per day.
The approximate average change per day since the lowest price occurred is approximately $0.72, option B is correct.
To find the approximate average change per day since the lowest price occurred 48 days ago, we need to calculate the total change and divide it by the number of days.
The lowest price in the past year was 64.77, and the current price is 99.14.
The change in price is the difference between these two values:
Change = 99.14 - 64.77
= 34.37
Now, we divide the total change by the number of days:
Average Change per Day = Change / Number of Days
Average Change per Day = 34.37 / 48
Average Change per Day = 0.716
Hence, the approximate average change per day since the lowest price occurred is approximately $0.72.
Therefore, the correct option is b. $0.72.
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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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Which of the following is the correct action to take when simplifying the expression A. add the exponents B. subtract the exponents C. multiply the exponents D. divide the exponents
Final answer:
To simplify an expression involving division of exponential terms with the same base, subtract the exponents of those terms. Numerical coefficients are divided normally while applying the subtraction rule to the exponents.
Explanation:
When simplifying the expression that involves division of exponentials, the correct action is to subtract the exponents. This rule applies when the bases of the exponential terms are the same. For example, when dividing [tex]a^m[/tex] by [tex]a^n[/tex], you would calculate a^(m-n). If we have numerical coefficients in front of the terms, we divide those normally, then apply the rule for exponents. An example is 4.5 × [tex]10^9[/tex] / [tex]10^6[/tex] = 4.5 × [tex]10^(9-6)[/tex] = 4.5 × [tex]10^3[/tex].
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).
How many ways are there of seating six people at a round table so that two specific people sit together?
Answer:
6 People in a round table can be seated in (6 - 1) ! ways = 120. Now we need to subtract the number of cases when one of those is sitting next to 2 of the other 5. We can consider as if 5 people are sitting in a row because it is round table.
PLZ HELP SOLVE: 6b - 1 < -7 or 2b + 1 > 5
The given expressions need to be solved.
[tex]b[/tex] will include all numbers less than but not equal to [tex]0[/tex].
[tex]b[/tex] will include greater than but not equal to [tex]2[/tex].
The given expression is
[tex]6b-1<-7\\\Rightarrow 6b<-7+1\\\Rightarrow 6b<-6\\\Rightarrow b<-1[/tex]
So, [tex]b[/tex] will include all numbers less than but not equal to [tex]-1[/tex].
[tex]2b+1>5\\\Rightarrow 2b>5-1\\\Rightarrow 2b>4\\\Rightarrow b>\dfrac{4}{2}\\\Rightarrow b>2[/tex]
[tex]b[/tex] will include all numbers greater than but not equal to [tex]2[/tex]
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How would you graph this parabola? it's just confusing because of the fractions ...
To graph the parabola [tex]f(x) = -1/3x^2 + 4/3x - 16/3[/tex], plot the vertex at (2, -4), note the axis of symmetry at x = 2, and create a downward-opening parabolic shape on a coordinate plane.
To graph the parabola given by the function [tex]f(x) = -1/3x^2 + 4/3x - 16/3[/tex], follow these steps:
1. Identify the vertex: The vertex of a parabola in the form of [tex]y = ax^2 + bx + c[/tex] is given by (-b/2a, f(-b/2a)). In this case, a = -1/3 and b = 4/3. Calculate the x-coordinate of the vertex using -b/2a:
x-coordinate of the vertex = -b / (2a) = -(4/3) / (2 * (-1/3)) = 2.
Now, find the corresponding y-coordinate by plugging the x-coordinate back into the function:
[tex]f(2) = (-1/3)(2)^2 + (4/3)(2) - 16/3 = (-4/3) + (8/3) - 16/3 = -12/3 = -4.[/tex]
So, the vertex is at (2, -4).
2. Find the axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex. In this case, it's the vertical line x = 2.
3. Calculate additional points: To create a more accurate graph, you can choose additional x-values and calculate their corresponding y-values. For instance, you can select x-values to the left and right of the vertex.
- For x = 0:
[tex]f(0) = (-1/3)(0)^2 + (4/3)(0) - 16/3 = -16/3.[/tex]
- For x = 4:
[tex]f(4) = (-1/3)(4)^2 + (4/3)(4) - 16/3 = -64/3 + 16/3 - 16/3 = -64/3.[/tex]
4. Plot the points: Plot the vertex (2, -4) and the additional points you calculated on a coordinate plane.
5. Draw the parabola: Connect the points smoothly to form the parabolic shape. Since the leading coefficient (-1/3) is negative, the parabola opens downward.
6. Label the axis of symmetry: Label the vertical line x = 2 as the axis of symmetry.
Your graph of the parabola f(x) = -1/3x^2 + 4/3x - 16/3 should resemble a downward-opening parabola with the vertex at (2, -4) and the axis of symmetry at x = 2.
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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
can someone help me with a few easy math questions?
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]
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
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
A picture framer has a board 10 1/12 feet long. The framer notices that 2 3/8 feet of the board is scratched and cannot be used. The rest of the board will be used to make small picture frames. Each picture frame needs 1 2/3 feet of the board. At most, how many complete picture frames can be made?
Final answer:
The framer can make at most 4 complete picture frames from the usable length of the board, after deducting the scratched section, and each frame using 1 2/3 feet of the board.
Explanation:
The picture framer has a board that is 10 1/12 feet long. However, part of this board is unusable due to scratches, and that section is 2 3/8 feet. Therefore, the usable length of the board is 10 1/12 feet - 2 3/8 feet. Each picture frame requires 1 2/3 feet of this board. To find out how many complete picture frames can be made, we need to divide the usable length of the board by the length required for each frame.
First, convert the mixed numbers to improper fractions:
Total length of the board: 121/12 feet
Scratched section: 19/8 feet
Frame length: 5/3 feet
After subtracting the scratched section from the total length, we have:
(121/12) - (19/8) = (968/96) - (228/96) = 740/96 feet
Now we divide the usable length by the frame length:
(740/96 feet) / (5/3 feet) = (740/96) * (3/5) = 740/160 = 4.625
Since we cannot have a partial frame, the framer can make at most 4 complete picture frames.
Dylan scored a total of 48 points in first 4 games of the basketball season. Which equation can be used to find g, the average number of points he scores per game?
Answer:
[tex]g = \frac{48}{4}[/tex]
Step-by-step explanation:
[tex]Average = \frac{\text{Sum of all observations}}{\text{No. of observations}}[/tex]
[tex]Average = \frac{\text{Total score}}{\text{Total no. of games}}[/tex]
Since we are given that Dylan scored a total of 48 points in first 4 games of the basketball season.
So,[tex]Average = \frac{48}{4}[/tex]
Let the average be g
So, [tex]g = \frac{48}{4}[/tex]
Hence The equation can be used to find g, the average number of points he scores per game is [tex]g = \frac{48}{4}[/tex]
The set of complex numbers is closed under subtraction. true or false
The set of complex numbers is indeed closed under subtraction because the subtraction of any two complex numbers always results in another complex number.
Explanation:The set of complex numbers being closed under subtraction is indeed true. In mathematics, a set is said to be closed under a particular operation if performing that operation on members within the set always results in a member that is also within that set.
In the case of complex numbers, if we subtract one complex number from another, the result is a complex number. For example, if we have two complex numbers, (a + bi) and (c + di), and we subtract the latter from the former, the result will be a complex number (a - c) + (b - d)i.
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A school choir has 36 members. There are three times as many underclassmen as seniors. How many seniors are in the choir?
I NEED HELP QUICK, PLEASE!
Find f(-10). f(x) = 7x - 5
f(x) = 7x-5
find f(-10)
replace x with -10
so you have 7(-10)-5
7*-10=-70 - 5 = -75
so f(-10) = -75
f(x) = 7x-5
find f(-10)
replace x with -10
so you have 7(-10)-5
7*-10=-70 - 5 = -75
so f(-10) = -75
solve -5x-42>-2-(x+4)
Ther are 120 crayons and 30 pieces of paper to give to students. what is the largest number of students to have in class so each student gets equal number of crayons and equal number of paper?
Daniel, ryan, and sam are friends. daniel is ryan's brother. ryan is sam's brother. sam is not daniel's brother. how is this possible?
So we know that the three boys are friends – Sam, Ryan and Daniel.
We also know that Daniel is Ryan’s brother and Ryan is Sam’s brother.
But the question here is why does Sam is not Daniel’s brother.
Because the answer here is Sam is a girl which makes her a sister of Daniel, not a brother.
if the given square is one side of a cube the volume of the cube will be the cube of the side length of the square write and evaluate an exponential expression for the volume of the cube.
P.S. the side length of said square is 8cm
A washer and a dryer cost $600 combined. the cost of the washer is three times the cost of the dryer. what is the cost of the dryer? answer
Is a flame test qualitative or quantitative test for the identity of an unknown explain?
the rule for the tile pattern is y=10x-18, figure 12 will be...?
By substituting '12' into the given linear equation 'y = 10x - 18', we find that figure 12 in this tile pattern would be 102.
Explanation:The given pattern follows the linear equation y = 10x - 18. To find the value of figure 12, smaller 'x' with '12' in the equation: y = 10 * 12 - 18 = 102. Therefore, figure 12 in this tile pattern would be 102.
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