A counterexample showing the conclusion 'All the marbles in the bag are black' as false.
A counterexample is a scenario where the premises are true but the conclusion is false, demonstrating the invalidity of an argument. In this case, to prove invalidity, a counterexample could be a situation where there is at least one marble in the bag that is not black. For instance, if there are three black marbles and one red marble inside the bag, the selection of three black marbles is still possible, but the conclusion that all marbles are black is false.
The value of 110 coins, consisting of dimes and quarters, is $20.30. how many of each kind of coin are there?
Sheila is building a model for class. It's a tower that's designed to withstand high winds. She can use a maximum of 700 support beams and knows that each floor will require 22 beams. Sheila will track the number of beams that remain as she adds floors.
She can predict the number of beams that remain by using this function: remaining beams (y) is function of floor number (x).
How many beams will remain after she built 6 floors? Y=700-22(x)
which equation best represents the line graphed above
a x=4
b x= _ 4
y= x -4
y= - 4
The correct answer is option B. The equation best represents the line graphed is x = -4.
What is an equation of a line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
Since x = -4 is a vertical line(perpendicular to horizontal), there is no y-intercept and the slope is undefined.
A vertical line has an undefined slope because all points on the line have the same x-coordinate.
So, the slope is undefined and we also don't have the y-intercept.
To know more about an equation of the line follow
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Solve for x: |2x + 12| = 18
What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit?
24.8 units
27.8 units
28.5 units
30.9 units
Answer:
The answer would be 27.8
Children younger than ______ years of age must be restrained in an approved child passenger safety seats unless they are at least 4 ft, 9 inches in height.
FOR 30 POINTS WILL MARK BRAINLIEST you have 500 sheets of notebook paper after one week you have 72% of the sheets left. you use the same number of sheets each week write an equation that represents the number y of pages remaining after 8 weeks
By graphing the system of constraints find the values of x and y that maximize the objective function, find the maximum value.
3x+y<=7
x+2y<=9
x>=0
y>=0
Maximum for P=2x+y
A. P=3
B. P=4
C. P=6
D. P=10
Answer:
x=1, y=4
P=6
Step-by-step explanation:
We are given that
[tex]3x+y\leq 7[/tex]
[tex]x+2y\leq 9[/tex]
[tex]x\geq 0[/tex]
[tex]y\geq 0[/tex]
Objective function
[tex]P=2x+y[/tex]
We have to values of x and y that maximize the P and maximum value of P .
First we change inequality equation into equality equation
[tex]3x+y=7[/tex] (I equation )
[tex]x+2y=9[/tex] (II equation)
Equation I multiply by 2 and then subtract from II equation
[tex]-5x=-5[/tex]
[tex]x=1[/tex]
Substitute x=1 in equation I
Then, we get
[tex]3(1)+y=7[/tex]
[tex]3+y=7[/tex]
[tex]y=7-3=4[/tex]
The two equation intersect at point (1,4).
Substitute x=0 in equation I
Then , we get y=7
Substitute y=0 then
[tex]3x=7[/tex]
[tex]x=\frac{7}{3}=2.3[/tex]
The equation I cut the x- axis at point (2.3,0)and y-axis at (0,7).
Substitute x=0 in equtaion II
[tex]2y=9[/tex]
[tex]y=\frac{9}{2}=4.5[/tex]
Substitute y=0
Then, we get
[tex]x=9[/tex]
Therefore, the equation II cut the x- axis at point (9,0) and y axis at point (0,4.5).
Substitute x=0 and y=0 in inequality Equation I
[tex]3(0)+0=0< 7[/tex]
It is true . Therefore, shaded region below the line.
Substitute x=0 and y=0 in inequality equation II
Then, [tex]0+2(0)=0 < 9[/tex]
It is true. Therefore, the shaded region below the line.
The feasible region is bounded.The feasible region bounded by (0,0),(0,4.5),(2.3,0) and (1,4).
At (0,4.5)
[tex]P=2(0)+4.5=4.5[/tex]
At (2.3,0)
[tex]P=2(2.3)+0=4.6[/tex]
At (1,4)
[tex]P=2(1)+4=6[/tex]
At (0,0)
[tex]P=2(0)+0=0[/tex]
Hence, maximum value of P is 6 at (1,4).
x=1 and y=4
Mrs. Noyes fills up a 5 gallon can of gas from the McIntosh’s local convenience store. They are selling gas at $2.099 a gallon. How much is she going to pay at the pump
Points d, e, and f are plotted on a number line. the coordinate of point f is 5. points d and e are the same distance from point f. what could be the coordinates of d and e?
a. d = –7, e = –1
b. d = –2, e = 12
c. d = 0, e = 5
d. d = 8, e = 11
The coordinates of d and e b. d = –2, e = 12.
To find the coordinates of points D and E, we need to remember that they are the same distance from point F, which has a coordinate of 5. This means D and E are equidistant from F on the number line. Let's check each option to see which one satisfies this condition:
Option a: d = -7, e = -1
The distance from -7 to 5 is 12.
The distance from -1 to 5 is 6.
Since the distances are not equal, this option is incorrect.
Option b: d = -2, e = 12
The distance from -2 to 5 is 7.
The distance from 12 to 5 is also 7.
Since the distances are equal, this option is correct.
Option c: d = 0, e = 5
The distance from 0 to 5 is 5.
The distance from 5 to 5 is 0.
Since the distances are not equal, this option is incorrect.
Option d: d = 8, e = 11
The distance from 8 to 5 is 3.
The distance from 11 to 5 is 6.
Since the distances are not equal, this option is incorrect.
Therefore, the correct answer is option b: d = -2, e = 12.
what is the vertex of the graph of the function below y=x^2-10x+21
Which ordered pair (a,b) is a solution to the given system of linear equations.
Answer:
A. (-13,-3)
Step-by-step explanation:
Solve the system of two equations:
[tex]\left\{\begin{array}{l}-2a+3b=14\\a-4b=3\end{array}\right.[/tex]
From the second equation:
[tex]a=3+4b[/tex]
Substitute it into the first equation:
[tex]-2(3+4b)+3b=14\\ \\-6-8b+3b=14\\ \\-8b+3b=14+6\\ \\-5b=20\\ \\5b=-20\\ \\b=-4[/tex]
So,
[tex]a=3+4b=3+4\cdot (-4)=3-16=-13[/tex]
The solution is (-13,-4)
Answer:
A
Step-by-step explanation:
Carla bought a shirt for $14 and a jacket for $69. She gave the cashier $100.
How much change should Carla get back?
Suppose the weights of farmer carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.1 ounces. suppose carl bags his potatoes in randomly selected groups of 6. what percentage of these bags should have a mean potato weight between 7.5 and 8.5 ounces?
6.
The sum of two consecutive odd integers is 236. What is the smaller integer? (4 points)
a) 115
b) 117
c) 119
d) 113
Jana is on a two-day hike. The function graphed shows the total distance she hiked, in miles, after x hours on the second day.
Select from the drop-down menus to correctly identify the information about Jana's hike provided by the graph.
Answer:
The slope is 2.
Step-by-step explanation:
The function graphed shows the total distance she hiked, in miles, after x hours on the second day.
Seeing at the graph, we have the following points.
(2,8) , (3,10) , (4,12)
For slope we will do the following.
[tex]\frac{10-8}{3-2} =\frac{2}{1}[/tex] = 2
[tex]\frac{12-10}{4-3} =\frac{2}{1}[/tex] = 2
So, the slope is 2.
The slope represents that 2 miles is hiked in each hour.
What is the measure of an exterior angle in a regular dodecagon?
2. Pat is six years older than twice his Cousin Zach’s age. The sum of their ages is less than 36.
What is the greatest age that Zach could be?
BRAINLIEST!
Henry's rocket is designed to launch to a height of 100 feet in the air. The measurements so far have the launch height (h) varying no more than 4 feet. Which inequality below represents this scenario?
|h − 4| less than or equal to 100
|h + 4| greater than or equal to 100
|h − 100| less than or equal to 4
|h + 100| greater than or equal to 4
Answer:
|h − 100| less than or equal to 4
Step-by-step explanation:
We know the difference between h, the actual height, and the designed height, 100, is no more than 4.
This means that the actual height h could be up to 4 more than the designed height or up to 4 less than the designed height. This is why we use an absolute value inequality; this considers just the distance of 4 regardless of direction.
Since it can be "no more than" 4, we use less than or equal to; this gives us
|h − 100| less than or equal to 4
what is 230000 in standard form
Final answer:
To write 230,000 in standard form, place the decimal point after the first non-zero digit. For 230,000, the standard form is 2.3 x 10⁵.
Explanation:
To express the number 230,000 in standard form, you simply write it as it is, moving the decimal point to the right until only one non-zero digit appears before the decimal. In this case, 230,000 in standard form is 2.3 x 10⁵.
Marc earned $1,650 per month as an assistant technician at a recording studio. His new job pays $9.80 per hour with time and a half for all hours over 36 hours per week. How many hours of overtime per week will he need to work to earn the same amount per week as his current job?
Marc will need to work just over 4 hours of overtime each week at his new job, which pays $9.80 per hour and $14.70 per hour for overtime, to earn the equivalent of his previous monthly income of $1,650.
To determine the number of overtime hours Marc needs to work at his new job to earn the same monthly income he did at his previous job, we'll first calculate his weekly income at his old job, then use the overtime pay rates at the new job to find the equivalent number of hours needed.
Marc previously earned $1,650 per month. Assuming a standard 4-week month, his weekly income was:
$1,650 per month / 4 weeks per month = $412.50 per week.
At his new job, Marc earns $9.80 per hour with time and a half for all hours over 36 hours a week. This means his overtime pay is 1.5 times his hourly rate, which is:
$9.80 per hour x 1.5 = $14.70 per hour for overtime.
Marc's income for the first 36 hours at his new job would be:
36 hours x $9.80 per hour = $352.80
To earn the equivalent of his old weekly salary, we must make up the difference with overtime pay:
$412.50 (old weekly income) - $352.80 (new regular pay) = $59.70 needed from overtime.
To determine the overtime hours needed to make $59.70: $59.70 / $14.70 per hour = approximately 4.06 hours.
Therefore, Marc will need to work just over 4 hours of overtime each week to earn the same amount he did at his previous job.
what is the constant rate of change of y=7-13x
The constant rate of change in the linear equation y=7-13x is -13, representing the slope of the line which remains constant for any value of x. This is different from nonlinear functions, where the rate can vary with x.
Explanation:The constant rate of change in the equation y=7-13x refers to the slope of the line represented by this linear equation. In this case, the constant rate of change, or the slope, is -13. This means for every one unit increase in x, y decreases by 13 units. Since the equation is linear, this rate does not change regardless of the value of x, unlike in nonlinear functions where the rate of change can vary with x.
To elaborate, if we have a nonlinear function, the rate of change depends on the interval of x we are looking at. For a linear function like this one, the slope is the same over any interval, so there's no need to compute it over smaller ranges of x to understand the rate of change.
Moreover, in calculus, the derivative represents the rate of change, and for a linear function, the derivative is simply the coefficient of x. Hence, the derivative of y with respect to x is -13. The derivative is zero for any constant term in a function, such as the 7 in the given equation.
Anyone wanna help me please?!
Allen has a photo that is 6 in by 8 in. What will the dimensions of the photo be if he scales it down by a factor of one-half ?
3 in by 4 in
6 in by 8 in
12 in by 16 in
1.5 in by 2 in
Help me please its math under 10 minutes!!!
Which amount is the best estimate for the cost of the vehicle to drive through the safari in 2009?
Evaluate the determination for the following matrix [144] [522] [155]
Deon is saving money to buy a game. so far he has saved $20 , which is four-fifths of the total cost of the game. how much does the game cost?
The solution to the equation 4(x – 7) = 64 is shown. Which step is a result of combining like terms?
A) Step 2
B) Step 3
C) Step 4
D) Step 5
Francis has five more dollars than Julia. Together they have at most $45. Let x represent the amount of money Francis has. Which inequality can be used to find the possible amounts of money that Francis has?
Answer:
B) 2x - 5 ≤ 45
Step-by-step explanation:
What is an equation of the line that passes through the points (1 3) and (8 5)? y+1+2/7(x+3), y-5=2/7(x-8), y-1=2/7(x+3), y+5=2/7(x-8)?