The probability that the randomly selected numbers are divisible by 3 is 3/10.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
So, the probability that the randomly selected number is divisible by 3:
Numbers under 20 divisible by 3 are: 3, 6, 9, 12, 15, 18
Total numbers: 20
Probability formula: P(E) = Favourable events/Total events
Now, substitute values and calculate as follows:
P(E) = 6/20
P(E) = 3/10
Therefore, the probability that the randomly selected numbers are divisible by 3 is 3/10.
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help me with math please
The possible coordinates of point A such that the distance to point B is 10 units are:
(-5, -4) and (-5, 8)
What are the possible coordinates of point A?We know that the distance between two points (a, b) and (c, d) is:
distance = √( (a - c)² + (b - d)²)
In this case, we know that:
B = (3, 2)
A = (-5, y)
And the distance is 10 units, then we can write:
10 = √( (3 + 5)² + (2 - y)²)
10² = 8² + (2 - y)²
100 - 64 = (2 - y)²
36 = (2 - y)²
±√36 = 2 - y
±6 = 2 - y
y = 2 ± 6
The two solutions are:
y = 2 + 6 = 8
y = 2 - 6 = -4
Then the possible coordinates are (-5, -4) and (-5, 8).
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Given that
R
=
8
x
+
4
y
Find
y
when
x
=
8
and
R
=
30
Give your answer as an improper fraction in its simplest form.
Answer: x=8,r=30
Step-by-step explanation:
fully simplify3d/ac x 2ad/30
The value of the equation 3d/ac x 2ad/30 is ( d² / 5c )
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is given by
A = 3d/ac x 2ad/30 be equation (1)
On simplifying the equation , we get
A = 3d/ac x 2ad/30
A = 6ad² / 30ac
On further simplification of the equation , we get
The value of A = 1/5 ( ad² / ac )
The value of A = 1/5 ( d²/c )
Therefore , the value of A is ( d² / 5c ) or A = 1/5 ( d²/c )
Hence , The value of the equation 3d/ac x 2ad/30 is ( d² / 5c ) or
A = 1/5 ( d²/c )
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What is the domain of the function shown below?
3
A All real numbers
C All whole numbers
B All integers
D All natural numbers
Answer:
A All real numbers
Step-by-step explanation:
You want to know the domain of a function graphed as a continuous line with negative slope.
DomainThe domain is the horizontal extent of the function, all of the values for which the function is defined.
The graph shows the function is defined not only for all integers (..., -1, 0, 1, ...), but also for all the values between.
The domain is all real numbers.
To make orange fizz, Noah mixe 4 coop of powder with 6 cup of water. Andre mixe 5 coop of powder with 8 cup of water. Create a double number line or a table that how different amount of powder and water that tate the ame a noah' mixture
5 scoops of powder are combined with 8 glasses of water by Noah.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
Hence, 5 scoops of powder are combined with 8 glasses of water by Noah.
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Please help!!!
find y and x
Answer:
a) y = 16/x²
b) x = 4/5
Step-by-step explanation:
You want the equation for y in terms of x when y is inversely proportional to the square of x, and y is 16 when x is 1. Further, you want the value of x when y is 25.
(a) RelationThe wording "inversely proportional to the square" means the form of the equation is ...
y = k/x² . . . . . . where k is the constant of proportionality
The value of k can be found from the given (x, y) pair.
k = x²y = (1)²(16) = 16
The equation is ...
y = 16/x²
(b) Value of xSolving for x gives ...
x = √(16/y)
Then the value of x for y = 25 is ...
x = √(16/25)
x = 4/5
a local winery bottles 14 different white wines. to help customers with their purchasing choice, the winery offers customers 5 white wine tasting samples free of charge. how many ways does a customer have to choose 5 different white wines to taste
a local winery bottles 14 different white wines. to help customers with their purchasing choice, the winery offers customers 5 white wine tasting samples free of charge 2002 many ways does a customer have to choose 5 different white wines to taste, using the concept of combination formula.
What is combination formula?The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the process of choosing items or things from a bigger group where order is irrelevant.
The combination formula is: n! / (n-r)! r! , where n is the total number of items (14 in this case) and r is the number of items being selected at once (5 in this case),
Plugging our numbers into the formula we get:
= 14! / (14-5)! 5!
= 2002
After simplifying, we get 2002.
So, there are 2002 ways of picking 5 different white wines to taste from a group of 14 local winery bottles.
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What is the slope of a line perpendicular to the line whose equation is 3x-6y=144 Fully simplify your answer.
Answer:
The slope of the perpendicular line is -2.
Step-by-step explanation:
A perpendicular line has a slope that is the negative inverse of the slope of the reference line. The reference line in this problem is 3x-6y=144.
Let's rearrange this equation to standard slope-intercept form of y=mx+b, where m is the slope and b is the y-intercept (the valuue of y when x=0).
3x-6y=144
-6y=144-3x
-6y=-3x + 144
y = (3/6)x + (144/-6)
y = (1/2)x - 24
This line has a slope of (1/2) and a y-intercept of -24. A line perpendicular to this will have a slope that is the negative inverse of (1/2). This would be -2. The new line will take form:
y = -2x + b
We are not given b, and there is not enough information to calculate one, so let's assume a value of -24, so that it intersects the original line at (0, -24). See the attached graph.
Milton is 1.55 meters tall. At 3 p.m., he measures the length of a tree's shadow to be 27.25 meters. He stands 23.1 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow.
Find the height of the tree to the nearest hundredth of a meter.
The height of the tree that produce a shadow of length 27.25 m is 10.18 m.
What is height?Height is the vertical distance between two points.
To calculate the height of the try, we use the formula of similar angle.
Formula:
d/D = h/H................ Equation 1Where:
d = Distance of Milton from the treeD = Length of the tree's shadowH = Height of the treeh = Height of MiltonFrom the question,
Given:
d = (27.25-23.1) = 4.15 mD = 27.25 mh = 1.55 mSubstitute these values into equation 1 and solve for H
4.15/27.25 = 1.55/HH = (1.55×27.25)/4.15H = 10.18 mHence, the height of the tree is 10.18 m.
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A rectangle is constructed on a semicircle so that the length equals the diameter. The rectangle is 3 times as long as it is wide. The total area of the figure is 750 inches squared. Find the approximate dimensions of the rectangle.
A rectangle is constructed on a semicircle so that the length equals the diameter. The width of the rectangle is approximately 10.65 inches.
What are the approximate dimensions of the rectangle.?Generally, Let the width of the rectangle be x. Then the length of the rectangle is 3x.
The diameter of the semicircle is also the length of the rectangle, so it is 3x.
The area of the rectangle is x*(3x) = 3x^2. The area of the semicircle is (1/2)πr^2, where r is the radius of the semicircle. Since the diameter of the semicircle is 3x, the radius is (3x)/2. The area of the semicircle is (1/2)π((3x)/2)^2 = (9/8)πx^2.
The total area of the figure is the sum of the area of the rectangle and the area of the semicircle. We can set up the equation:
3x^2 + (9/8)πx^2 = 750
(21/8)πx^2 = 750
x^2 = 750/(21/8)*π
x = √(750/(21/8)*π)
To find the approximate dimensions of the rectangle, we can use the fact that pi is approximately 3.14. This gives us:
x = √(750/(21/8)*3.14)
= √(750/6.71)
= √(112.64)
= approximately 10.65 inches.
The width of the rectangle is approximately 10.65 inches. The length of the rectangle is 3 times the width, so it is approximately 31.95 inches.
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Use the following word problem to answer the following questions.
Shashi has a rectangular garden. The length of the garden is 4 feet less than twice the width. The area of the garden is 448 square feet. What is the length of the garden?
1. Provide the mathematical model specific to the word problem(table of values, graph, statement)
2.explain why you chose that type of model
3. what is the answer to the word problem
The length of the rectangular garden is 28 feet.
Statement represents the mathematical solution to the given word problem.
The statement clearly explains the stated circumstance.
What is rectangle?A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.
Given that,
The area of the rectangular garden = 448 square feet.
Also, the length of the garden is 4 feet less than the twice of the width.
Let the width of garden is x feet
Then length of garden = 2x - 4
The area of rectangular garden = 448
x (2x - 4) = 448
x (x - 2) = 224
x = 16
The width of the garden is 16 feet.
The length of the garden = 2x - 4 = 2(16) - 4 = 32 - 4 = 28 feet
The required length of the garden is 28 feet.
The mathematical model to the given word problem is statement.
Statement clarify the given condition clearly.
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While shootings baskets at a basketball hoop, you make 36 out of 80 shots. Your friend makes 43.75% of the shots. Between the two of you, who made the higher percentage of shots?
45%
You made a higher percentage of shots.
36/80*100 = 45%
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can someone explain this to me? i have an answer key but don’t know how to do it
Check the picture below.
Write an equation in point-slope form for the line that passes through each point
with the given slope. Then graph the equation.
(2,-1),m=-3
Answer: y= 3x -5
Step-by-step explanation:
For the function g(x) = -2x - 5, determine g(6)
A) -10
B)-17
Answer:
-17
Step-by-step explanation:
replace x with 6
g(6)=-2(6)-5
g(6)=-12-5
g(6)= -17
hopes this helps please mark brainliest
Indicate whether (1, 5) is a solution of the given system.
Answer:
To determine whether (1, 5) is a solution of a given system, you need to substitute these values into the equations of the system and check whether the resulting statements are true.
For example, if the given system is represented by the equations y = 2x + 1 and y = x - 3, then you would substitute 1 for x and 5 for y in each equation and check whether the resulting statements are true.
Substituting these values into the first equation, we get:
5 = 2(1) + 1
5 = 2 + 1
5 = 3
This statement is not true, so (1, 5) is not a solution of this system.
On the other hand, if the given system is represented by the equations y = 2x + 1 and y = 5, then substituting the values (1, 5) into both equations would result in true statements, so (1, 5) would be a solution of this system.
I hope this helps! Let me know if you have any more questions.
Step-by-step explanation:
Can somebody help me look at the picture
Answer:
Seagle =10
Dolphin =2.5
Penguin-flat =0
Shark = -2.5
Clownfish= -7.5
Octpus= -10
Step-by-step explanation:
Answer:
Meters of the seagull: 10 cmMeters of the dolphin: 2 cm Meters of the penguin: 0 cm Meters of the shark: -3 cmMeters of the clownfish: -7 cmMeters of the Octopus: -10 cmStep-by-step explanation:
The distance between each animal and the sea level is already shown in the image.
- for the seagull the vertical line with measurements of 0,5, 10 if you measure how high the seagull it would be 10 cm, how do I measure it? go from 0 to the height of the dolphin and you'll find the answer.
- for the dolphin, look at the vertical line with measurements of 0,5, and 10 how do I measure it? go from 0 to the height of the dolphin and you'll find the answer which would be 2cm.
you keep doing the same thing to the other animals the meters are shown on the image you have to measure from 0 and go up or down depending on where the animal is.
Graph a triangle (ABC) and reflect it over the x-axis to create triangle A'B'C'. Describe the transformation using words. Make sure you refer to the characteristics and the coordinates. Draw a line segment from point A to the reflecting line, and then draw a line segment from point A' to the reflecting line. What do you notice about the two line segments you drew? Do you think you would see the same characteristic if you drew the line segment connecting B with the reflecting line and then B' with the reflecting line? How do you know?
The two line segments after the reflection over the x-axis are vertical lines, and the same will be true for the third segment.
What are the changes to the triangle?The rule for a reflection over the x-axis is given as follows:
(x,y) -> (x,-y).
Meaning that the x-axis remains constant, while the coordinates of the y-axis are changed.
The vertices of the original triangle will be attributed as follows:
A(1,1), B(4,1) and C(1,5).
Hence the vertices of the reflected triangle will be given as follows:
A'(1,-1), B'(4,-1) and C(1,-5).
Thus the lines are given as follows:
A and A': x = 1.B and B': x = 4.C and C': x = 1.Hence there are three vertical lines.
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Is n-3^2 linear explain why please
Answer:
y=n-3^2 is linear
Step-by-step explanation:
A linear equation is an equation between two variables that give a straight line with plotted on a graph.
The two variables used are "n" and "3^2"
When graphed, it forms a diagonal, straight line.
I need help with this problem, look at image below.
Answer:
no
Step-by-step explanation:
The three angles of a triangle are 180, but the sum of the three angles in the figure is 200.so its impossible .
Help please! More points will mark as brainiest!
Answer:
384cm^2
Step-by-step explanation:
8x8x6 = 384
Write two expressions for the perimeter of the figure.
2
8
4x
4
7x
Note: The figure is not drawn to scale.
(a) Use all five side lengths.
perimeter = 0+0+0+0+0
(b) Simplify the expression from part (a).
perimeter =
The perimeter can be calculated using the formulas 22x+23 and 2x+3x+17x+7+16.
How to calculate perimeter of two expression ?The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. The surface of a shape's area is measured.
The total length of the four sides makes up the perimeter (P) of a rectangle. A rectangle has two equal lengths and two equal widths since its opposite sides are equal. The following is the formula for calculating a rectangle's perimeter: The formula for perimeter is length + length + width + width. P = l + l + w + w.
you want to add the variables of the same kind in this case
2x
3x 7
17x 16
_________
22x + 23
Therefore Two expressions for the perimeter would be 22x+23 and 2x+3x+17x+7+16
The complete question is : Write two expressions for the perimeter of the figure.
2x
7
3x
172
16
Note: The figure is not drawn to scale.
(a) Use all five side lengths.
perimeter - ] + + + +
(b) Simplify the expression from part (a).
perimeter =
Х
$ ?
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6 Jessica runs for 15 minutes at an average speed of 6 miles per hour.
She then runs for 40 minutes at an average speed of 9 miles per hour.
It takes Amy 45 minutes to run the same total distance that Jessica runs.
Work out Amy's average speed.
Give your answer in miles
per hour.
Answer:
20
Step-by-step explanation:
6*(60/15) = 1.5 (milles)
9*(60/40) = 13.5 (milles)
1.5 + 13.5 = 15 (milles)
15 / (45/60) = 20 (milles per hour)
The speed of Amy is 8.6 mph.
What is speed?Speed is defined as the rate of change of distance with time. It has the dimension of distance by time. Thus, the SI unit of speed is given as the combination of the basic unit of distance and the basic unit of Time. Thus, the SI unit of speed is metre per second.
Given that, Jessica runs for 15 minutes at an average speed of 6 miles per hour. She then runs for 40 minutes at an average speed of 9 miles per hour. It takes Amy 45 minutes to run the same total distance that Jessica runs.
Calculating the distance covered by Jessica,
15 minutes = 0.25 hours
Speed = distance / time
Distance = speed × time
Distance = 0.25 × 6 = 1.5 mile
And,
40 minutes = 2/3 hours
Distance = 2/3 × 9 = 6 miles
Total distance covered by Jessica = 1.5+6 = 6.5 miles
Since, Amy covers the same distance in 45 minutes,
Therefore, 45 minutes = 3/4 hours
Speed = 6.5/0.75 = 8.6 mph
Hence, The speed of Amy is 8.6 mph.
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What is the solution for −6x 9≤2−5(x 1)? responses x≤4 x ≤ 4 x≥4 x ≥ 4 x≥12 x ≥ 12 x≤12
the probability that a restaurant passes its health department inspection is 0.94. the owners of 58 restaurants are surveyed to see if their restaurants passed inspection. For each binomial experiment described, find the mean, the variance and the standard deviation!
The mean , standard deviation, and the variance of each binomial experiment using given probability and sample of restaurant owners surveyed is equal to 54.52 , 1.808, 3.2712 respectively.
As given in the question,
Let success be defined by health department inspection is passed by restaurant
Probability of success rate 'p' = 0.94
Value of ' 1 - p ' = 1 - 0.94
= 0.06
Number of owners of restaurant which are surveyed 'n' = 58
For the given binomial experiments calculation of the following distributions are:
Mean 'μ' = np
= 58 × 0.94
= 54.52
Standard deviation 'σ' = √ np (1 - p)
= √ 58 × 0.94 × 0.06
= √3.2712
= 1.808
Variance 'σ²' = np( 1 - p )
= 58 × 0.94 × 0.06
= 3.2712
Therefore, the mean , standard deviation , and the variance from the given probability and sample size is equal to 54.52 , 1.808, 3.2712 respectively.
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2X+3 {2(X+2)+3(X-4)} =10
Answer:
x=2
Step-by-step explanation:
Remove parentheses
collect like terms
move constants to the right
calculate
divide both sides
f"(x) = 1/x^3/2, f'(4)=2, f(4)=0
f(x)=?
PLS URGENT
Answer: 6
Step-by-step explanation:
3/4x-5=1/2x+2x-10
solve for x
Answer:
x = [tex]\frac{20}{7}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] x - 5= [tex]\frac{1}{2}[/tex] x + 2x - 10
multiply through by 4 ( the LCM of 4 and 2 ) to clear the fractions
3x - 20 = 2x + 8x - 40
3x - 20 = 10x - 40 ( subtract 10x from both sides )
- 7x - 20 = - 40 ( add 20 to both sides )
- 7x = - 20 ( divide both sides by - 7 )
x = [tex]\frac{-20}{-7}[/tex] = [tex]\frac{20}{7}[/tex]
Answer:
[tex]x=\frac{20}{7}[/tex]
Step-by-step explanation:
Since x is on the right side of the equation, switch the sides so it is on the left side of the equation.
[tex]\frac{1}{2}x+2x-10=\frac{3}{4}x-5[/tex]
Simplify the left side of the equation by combing [tex]\frac{1}{2}[/tex] and [tex]x[/tex].
[tex]\frac{x}{2}+2x-10=\frac{3}{4}x-5[/tex]
To write [tex]2x[/tex] as a fraction with a common denominator, multiply by [tex]\frac{2}{2}[/tex].
[tex]\frac{x}{2}+2x*\frac{2}{2} -10=\frac{3}{4}x-5[/tex]
Simplify terms by combining [tex]2x[/tex] and [tex]\frac{2}{2}[/tex]. Combine the numerators over the common denominator.
[tex]\frac{x+2x*2}{2} -10=\frac{3}{4}x-5[/tex]
Raise x to the power of 1.
[tex]\frac{x^1+2x*2}{2} -10=\frac{3}{4}x-5[/tex]
Factor [tex]x[/tex] out of [tex]x^1[/tex].
[tex]\frac{x*1+2x*2}{2} -10=\frac{3}{4}x-5[/tex]
Factor [tex]x[/tex] out of [tex]x+2x*2[/tex].
[tex]\frac{x*1+x(2*2)}{2} -10=\frac{3}{4}x-5[/tex]
Factor [tex]x[/tex] out of [tex]x*1+x(2*2)[/tex]
[tex]\frac{x(1+2*2)}{2} -10=\frac{3}{4}x-5[/tex]
Multiply 2 by 2.
[tex]\frac{x(1+4)}{2} -10=\frac{3}{4}x-5[/tex]
Add 1 and 4.
[tex]\frac{5x}{2} -10=\frac{3}{4}x-5[/tex]
Combine [tex]\frac{3}{4}[/tex] and [tex]x[/tex].
[tex]\frac{5x}{2} -10=\frac{3x}{4}-5[/tex]
Move all terms containing [tex]x[/tex] to the left side of the equation.
[tex]\frac{7x}{4}-10=-5[/tex]
Move all terms not containing [tex]x[/tex] to the right side of the equation.
[tex]\frac{7x}{4}=5[/tex]
Multiply both sides of the equation by [tex]\frac{4}{7}[/tex]
[tex]\frac{7x}{4}*\frac{4}{7} =5*\frac{4}{7}[/tex]
Simplify both sides of the equation.
[tex]x=\frac{20}{7}[/tex]
The value of y is directly proportional to the value of x. When = 512, y = 128.
What is the value of y when x = 64?
Answer:
Step-by-step explanation:
directly proportional means same
x=y
512=128
64=y
512/64=8
128/8=16
when x=64 then the value of y=16
Answer:
C
Step-by-step explanation:
given y is directly proportional to x then the equation relating them is
y = kx ← k is the constant of proportion
to find k use the condition when x = 512, y = 128
128 = 512k ( divide both sides by 512 )
[tex]\frac{128}{512}[/tex] = k , that is k = 0.25
y = 0.25x ← equation of proportion
when x = 64 , then
y = 0.25 × 64 = 16
Richard and Teo have a combined age of 28. Richard is 13 years older than twice Teo’s age. How old are Richard and Thiago?
Answer:
Richard = 23
Teo= 5
Step-by-step explanation:
R + T = 28
R = 2T + 13
(2T+13)+T = 28
3T + 13 = 28
3T = 28 - 13
3T = 15
T = 15/3
T = 5
(Checking your answer)
R + 5 = 28
R = 28 - 5
R = 23
R = 2(5) + 13 = 10 + 13 = 23
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