Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than or equal to y. Also, the sum of y and two-third of x is less than 4. Which graph represents the possible solutions?
Answers
[tex] \frac{2}{3}x-3 \geq y[/tex]
to plot the pairs (x, y) for which the inequation holds, draw the line [tex]y=\frac{2}{3}x-3[/tex]
then pick a point in either side of the line. If that point is a solution of the inequation, than color that region of the line, if that point is not a solution, then color the other part of the line.
we do the same for the second inequation. Then the solution, is the region of the x-y axes colored in both cases.
inequation 2:
[tex]y+ \frac{2}{3}x\ \textless \ 4 [/tex]
[tex]y\ \textless \ - \frac{2}{3} x+ 4 [/tex]
draw the lines
i) [tex]y=\frac{2}{3}x-3[/tex] use points (0, -3), (3, -1)
ii)[tex]y=- \frac{2}{3} x+ 4 [/tex] use points ( 0, 4), (3, 2)
let's use the point P(3, 3) to see what region of the lines need to be coloured:
[tex]\frac{2}{3}x-3 \geq y[/tex] ;
[tex]\frac{2}{3}(3)-3 \geq 3[/tex]
[tex]2-3 \geq 3[/tex], not true so we color the region not containing this point
[tex]y+ \frac{2}{3}x\ \textless \ 4 [/tex]
[tex](3)+ \frac{2}{3}(3)\ \textless \ 4 [/tex]
[tex]3+ 5\ \textless \ 4 [/tex] not true, so we color the region not containing the point (3, 3)
The graph representing the system of inequalities is the region colored both red and blue, with the blue line not dashed, and the red line dashed.
Answer:
in other words b
Step-by-step explanation:
Related Questions
Suppose a and b are independent events. if p(a)=0.4 and p(b)=0.1, what is p(a u
b.?
Answers
To find the probability of the union of two independent events, use the formula P(A U B) = P(A) + P(B). In this case, P(A U B) = 0.4 + 0.1 = 0.5.
Explanation:To find the probability of the union of two independent events, we can use the formula:
P(A U B) = P(A) + P(B) - P(A ∩ B)
Since the two events, A and B, are independent, the probability of their intersection, P(A ∩ B), is 0. This is because the occurrence of one event does not affect the occurrence of the other event. Therefore, we have:
P(A U B) = P(A) + P(B)
Substituting the given values, we get:
P(A U B) = 0.4 + 0.1
= 0.5
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A total of
644
tickets were sold for the school play. They were either adult tickets or student tickets. There were
56
fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answers
s = a - 56
a + (a - 56) = 644
2a - 56 = 644
2a = 644 + 56
2a = 700
a = 700/2
a = 350 <=== adult tickets
s = a - 56
s = 350 - 56
s = 294 ...student tickets
A recipe calls for 1/2 cup of ingredient A for every 1 2/5 cups of ingredient B. You use 4 cups of ingredient A. How many cups of ingredient B do you need?
Answers
(1/2)x = 14/5, so x = 28/5 = 5 3/5 cups.
Tim count his friends fingers by fives. he counts the fingers on six hands. what number does he say?
Answers
The perimeter of a triangle is 240. Its sides are proportional to 3:4:5. The largest side of the triangle is ?
Answers
3x + 4x + 5x = 240 and solve for x.
which is: 12x = 240
x = 20
The longest side is 5x, so the longest side is 100.
What is the greatest angle measure in the diagram?
95˚
105˚
119˚
180˚
Answers
The solution is, The greatest angle measure is angle F which is 119°
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
The sum of all the angles of a quadrilateral is 360°
(15x-10)°+(15x+14)°+(9x-4)°+(11x+10)° = 360°
Open up the brackets and rearrange the expression
15x-10°+15x+14°+9x-4°+11x+10°=360°
15x+15x+9x+11x-10°+14°-4°+10° = 360°
50x+10°=360°
Collect like terms
50x=360°-10°
50x=350°
Divide by the coefficient of x
x= 350/50
X=7°
Substitute the value of x into the various angles
15x-10°=(15×7)-10= 105-10=95°
15x+14°=(15×7)+14=105+14=119°
9x-4°=(9×7)-4=63-4=59°
11x+10°=(11×7)+10=77+10=87°
The greatest angle measure is angle F which is 119°
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11. Edgar Anderson earns $200 a week plus a 15% commission on all sales over $1,000. If Mr. Anderson's sales for one week are $2,500, what is his gross pay for that week?
Answers
so, what's 15% of 2500? well, is just (15/100) * 2500.
so, add that to his $200 salary, and that's his gross pay.
An object is thrown from an initial height of 0 feet with an initial velocity of 160 feet per second. Solve for when it will return to the ground. Show your work and explain the steps used to solve.
Answers
Hence, we can solve this using rectilinear motion equations.
y = vt + 1/2*a*t^2, where
y is the vertical distance
v is the initial velocity
a is the acceleration due to gravity equal to -32.2 ft/s^2
t is the time of flight
However, it would be impossible to have 0 height. I think there is some typographical error right there. Let's just assume a height of 1000 ft. Substituting the values,
100 = 160*t + 1/2*-32.2*t^2
t = 9.3 seconds
PLEASE HELP
If AD is median in triangle ABC and BD=24, then CD is:
24.
12.
6.
None of the choices are correct.
Answers
To solve this problem, let us first define what a median is. A median is a line segment that connects a vertex and the midpoint of the side opposite to that vertex.
In this case, the vertex is point A while the opposing side is side CB. Since it connects to the midpoint of CB, therefore this means that the median AD equally divides side CB into 2 parts. Since the length side CB is the sum of the lengths side CD and side BD. Therefore this means that:
length of CD = length of BD
length of CD = 24
Answer:
24
Find the point on the line y = 3x + 2 that is closest to the origin.
Answers
the slope of the line y=3x+2 is the coefficient of x, that is 3.
2.
the slope of any line perpendicular to the line y=3x+2, is m, such that:
[tex]3*m=-1[/tex]
so [tex]m= \frac{-1}{3} [/tex]
3.
so any line with equation y=-1/3x+k is perpendicular to y=3x+2.
moreover, the line y=-1/3x (so k=0) is the line passing through the origin
(0, 0) and perpendicular to y=3x+2
4. This means that the closest point of y=3x+2 to the origin is the intersection point of lines y=3x+2 and y=-1/3x
5.
to find this point:
3x+2=(-1/3)x
x(3+1/3)=-2
x(9/3+1/3)=-2
x*10/3=-2
[tex]x= \frac{-2*3}{10} = \frac{-6}{10}=-0.6 [/tex]
thus y is : (-1/3)(-6/10)=0.2
Answer: (-0.6, 0.2)
The point on the line [tex]y=3x+2[/tex] that is closest to the origin is [tex](-0.6, 0.2)[/tex].
Given, [tex]y=3x+2[/tex], whose slope is [tex]3[/tex].
Let [tex]m[/tex] is the slope of the line perpendicular to the above line.
So,
[tex]3\times m=-1\\m=-1/3[/tex]
Then, the general equation of a line perpendicular line will be [tex]y=-1/3x+k[/tex].
So the equation line passing through the origin [tex](0,0)[/tex] and perpendicular to the line [tex]y=3x+2[/tex] is [tex]y=-1/3x[/tex] , [tex](k=0)[/tex].
Then the closest point will be the intersection point of these two lines, i.e.
[tex]3x+2=-1/3x\\9x+6=-x\\10x+6=0\\x=-0.6[/tex]
and
[tex]y=\dfrac{-0.6}{3} \\y=0.2[/tex]
Therefore, the point on the line [tex]y=3x+2[/tex] that is closest to the origin is [tex](-0.6, 0.2)[/tex].
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Outside diameter of a pipe is five and 7/32 inches the wall of the pipe or 5/32 inches thick find the inside diameter
Answers
5 7/32 = 167/32
5/32 + 5/32 (2 wall thicknesses of the pipe) =10/32
167/32 - 10/32 = 157/32
= 4 29/32
The ordered pair (a, b) gives the location of point P on the coordinate plane. The value of a is zero and the value of b is not zero. Where could point P be located on the coordinate plane?
Select one or more:
x-axis
Quadrant IV
y-axis
Quadrant I
Quadrant II
Quadrant III
Answers
Answer:
y axis and
Step-by-step explanation:
The point P(a, b) where the value of a is 0, hence point P is located on the y axis.
Coordinate planeThe coordinate plane is a two-dimensional surface formed by two lines known as the horizontal axis (x axis) and the vertical axis (y axis). The origin is the point of intersection of both axis and it serves as a reference point.
A point on the coordinate plane is located using the x and y coordinates.
Given the point P(a, b) where the value of a is 0, hence point P is located on the y axis.
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A continuous random variable is a random variable that can: ?assume any value in one or more intervals ?assume no continuous random frequency ?have no random sample ?assume only a countable set of values
Answers
Evaluate the given answers.
1. Assume any value in one or more intervals.
CORRECT
2. Assume no continuous random frequency.
INCORRECT
3. Have no random sample.
INCORRECT
4. Assume only a countable set of values.
INCORRECT
A continuous random variable can assume any value within one or more intervals and result from measurements, providing an uncountable range of possibilities. Continuous random variables are commonly used in many fields, including reliability engineering and standardized testing, to assess continuous data.
A continuous random variable is a type of random variable that can assume any value within one or more intervals. Unlike discrete random variables, which take on countable values, continuous random variables result from measurements rather than counts. For instance, the temperature of a day measured by a thermometer or the height of students measured by a ruler are examples of continuous random variables. The values are uncountable as they lie on a continuum, like the speed of an automobile or the duration of a telephone call.
Two main characteristics of a discrete probability distribution function include the fact that each probability must be between zero and one, inclusive, and the sum of the probabilities should equal one. These rules do not apply to continuous random variables, which instead use probability density functions to describe their distributions.
Continuous random variables play significant roles in numerous applications such as assessing baseball batting averages, calculating IQ scores, and evaluating SAT scores. In the field of reliability engineering, a variety of continuous random variables are essential for analyzing the life expectancy of components.
x+3menor que 8 qual o resultado
Answers
x+3<8
8-3 =5
X<5
any number less than 5 will work
Find a formula for the general term of the sequence, assuming that the pattern of the first few terms continues. 2, 9, 16, 23
Answers
Where d = 7
a = 2
and the formula will be
[tex] a_{n} [/tex] = a + d (n-1) = 2 + 7*(n-1)
Where n starts from 1 and continues to the infinity
an=a1+d(n-1)
an=2+7(n-1)
an=2+7n-7
Answer: an=7n-5
If a person is randomly selected, find the probability that his or her birthday is in May. ignore leap years
Answers
May has 31 days
there are 365 days in a year
31/365 probability someone has a birthday in May
The probability of the event A that represents that the man's birthday is in May is 0.084.
What is probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. Mathematically -
P(A) = n(A)/n(S)
Given is a person who is randomely selected.
Assume that the Event A represents that the man's birthday is in may.
Total number of days in the month of may = n(A) = 31
Total number of days in a year = n(S) = 365
Therefore, the probability that the man's birthday is in may will be -
P(A) = n(A)/n(S)
P(A) = 31/365
P(A) = 0.084
Therefore, the probability of the event A that represents that the man's birthday is in May is 0.084.
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Megumi earned a salary of $39,312 last year. How much did she earn per month
Answers
2 months in a year
39312/12 = 3276 per month
Answer:
She earned $ 3,276 per month.
Step-by-step explanation:
We know that,
1 year = 12 months,
Given,
Megumi earned a salary of $39,312 last year
⇒ His salary of one year = $ 39,312
⇒ Salary of 12 months = $ 39,312
[tex]\implies \text{salary of 1 month} = \frac{39312}{12}=\$ 3276[/tex]
Hence, she earned $ 3,276 per month.
determine the heat energy received per kilogram of steam produced
Answers
Note : this value varies greatly with pressure and temperature.
To avoid distortion of extreme values, a good indicator would be the A. mean. B. weighted-mean. C. mode. D. median
Answers
To avoid distortion of extreme values, a good indicator would be the
B. median.
median
Match each word from Column A with the correct definition from Column B. Column A Column B 1. impulse 2. muster 3. naught 4. renown 5. vacancy 6. thrifty A. the state of being empty or not filled B. nothing, nonexistence C. to stir up or bring to action D. a sudden stirring to do something E. fame F. careful with money
Answers
2. C
3. B
4. E
5. A
6. F
Answer:
The correct matches are:
1. impulse - a sudden stirring to do something
2. muster - to stir up or bring to action. Like to muster up the courage to speak against the wrong doer.
3. naught - nothing, nonexistence
4. renown - fame ; the condition when you are known or talked about by many people.
5. vacancy - the state of being empty or not filled. Like vacancy for new candidates for a job.
6. thrifty - careful with money . Like a person is thrifty about his own time.
A carpenter is assigned a job of installing a spa into a pre-existing deck. The dimensions of the deck are (6x + 1) wide by (4x - 3) long. The dimensions of the spa are (4x + 5) wide by (x + 6) long.
Write the polynomial that represents the remaining area of the deck after the carpenter cut the hole out for the spa.
Answers
A=(6x+1)(4x-3)-(4x+5)(x+6)
A=24x^2-18x+4x-3-4x^2-24x-5x-30
A=24x^2-14x-3-4x^2-29x-30
A=20x^2-43x-33 or if you factor...
A=20x^2+12x-55x-33
A=4x(5x+3)-11(5x+3)
A=(4x-11)(5x+3)
There are 65 people who want to go on a tea cups ride at an amusement park. There are 10 tea cups that each seat 4 people. How many people need to wait before they get to go on the ride?
Answers
Kholdy enterprises' outstanding bonds mature in 6 years, have a par value of $1,000, and make an annual coupon payment of $60. the market yield on the bond is currently 10%. what is the bond's price?
Answers
An experiment consist of drawing 1 card from a standard 52 -card deck. Let E be the event that card drawn is a 2. Find P(E').
Answers
that is P(E)+P(E')=1, where E' is "not E".
The event E can happen in 4 ways, because there are four 2's that can be drawn.
P(E)=n(E)/52=4/52=0.08
P(E')=1-P(E)=1-0.08=0.92
Answer: 0.92
Which of the following methods would be easiest to use to solve 2x^2 + 5x - 11 = 0
A) factoring
B) isolating the x^2 term and finding the square root of both sides
C) using quadratic formula
D) all three methods would be easy and effective
Answers
x' = [-b+√(b² - 4ac)]/2a and x" = [-b -√(b² - 4ac)]/2a
Solving : 2x² + 5x - 11 = 0, gives:
x' = [-5+√(25 - 4(2)(-11)]/4 and x" = [-5-√(25 - 4(2)(-11)]/4
x' = (-5+√113)/4 & x" = (-5-√113)/4
Which polygon has an interior angle sum of 1080°?
Answers
The polygon which has an interior angle sum of 1080° is an Octagon
Interior angles of a PolygonFrom the question, we are to determine which polygon has an interior angle sum of 1080°
To find that, we will determine the number of sides the polygon has.
From the formula for sum of the interior angles in a polygon
Sum of interior angles = (n-2)180°
Where n is the number of sides
Then,
1080° = (n-2) 180°
1080° ÷ 180° = n-2
6 = n-2
n = 6 + 2
n = 8
A polygon with 8 sides is called an Octagon
Hence, the polygon which has an interior angle sum of 1080° is an Octagon
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what is 795840000 in a scientific notation
Answers
=
7.9584 x 10^8
hope it helps
a squared + b - c ÷ m , if a=6 , b= 8 ,c = 5 and m = 3. Is it 12 , 13, 14, or 15?
Answers
A^2 + B - C / M; A = 6, B = 8, C = 5, M = 3.
Plug in our numbers.
6^2 + 8 - 5 / 3
36 + 8 - 5 / 3
44 - 5 / 3
39 / 3
13.
Your answer is 13.
I hope this helps!
What percentage of muscle weight would you have if 60 pounds out of 140 pounds is muscle weight?
Answers
all you have to do is divide the muscle weight by the total weight which is...60/140=
ANSWER: about 42.86%
p/100=60/140 multiply both sides by 100
p=6000/140
p=300/7 %
p≈42.86% (to nearest hundredth of a percent)
How do i simplify this?
Answers
[tex]\bf \cfrac{(xy^{-3})^{-5}}{(x^{-3}y)^{-6}}\impliedby \textit{first off, distribute the exponent} \\\\\\ \cfrac{x^{1\cdot -5}y^{-3\cdot -5}}{x^{-3\cdot -6}y^{1\cdot -6}}\implies \cfrac{x^{-5}y^{15}}{x^{18}y^{-6}}\implies \cfrac{y^{15}\cdot y^6}{x^{18}\cdot x^5}\implies \cfrac{y^{15+6}}{x^{18+5}}\implies \cfrac{y^{21}}{x^{23}}[/tex]