Solve the inequality -9x/11 - 7 < -5. x > x < - x < x > -
The disparity -9x/11 - 7 < -5 is x > -22/9
Explain about the inequality?The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. This is a prime instance of inequality. This indicates that the left half, 5x 4, is larger than the right part, 2x + 3, in the equation.
Mathematical expressions with inequalities on both sides are known as inequalities. In an inequality, we compare two values as opposed to equations. In between, the equal sign is changed to a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. This is a prime instance of inequality.
-9x/11 < 2 (add 7 to both sides) (add 7 to both sides)
-9x < 22 (multiply both sides by 11) (multiply both sides by 11)
x > 22/-9 Because you are dividing by a negative integer, change the sign.
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Answer: x > [tex]\frac{-22}{9}[/tex]
Step-by-step explanation:
To solve this inequality, we will isolate the variable, x, with inverse operations.
Given:
[tex]\frac{-9x}{11}[/tex]- 7 < -5
Add 7 to both sides of the inequality:
[tex]\frac{-9x}{11}[/tex] < 2
Multiply both sides of the inequality by 11:
-9x < 22
Divide both sides of the inequality by -9:
* note, we must "flip" the sign since we are dividing by a negative integer
x > [tex]\frac{-22}{9}[/tex]
Magan went to the grocery store and purchased cans of soup and frozen dinners.
Each can of soup has 350 mg of sodium and each frozen dinner has 650 mg of
sodium. Magan purchased a total of 11 cans of soup and frozen dinners which
collectively contain 4750 mg of sodium. Determine the number of cans of soup
purchased and the number of frozen dinners purchased.
The number of cans of soup purchased and the number of frozen dinners purchased are 8 and 3 respectively.
What is a system of equations?A system having more than two equations is known as a system of equations.
Given that, the can of soup contains 350 mg of sodium and the frozen dinner contain 650 mg of sodium.
Let the numbers of cans of soups and frozen dinners purchased be s and f, then,
s + f = 11
s = 11-f (1)
The total sodium in all 11 cans is 4750 mg which can be expressed as:
350s + 650f = 4750
Substitute s = (11-f) into the above equation:
350(11 - f) + 650f = 4750
3850 - 350f + 650f = 4750
300f = 4750 -3850
300f = 900
f = 3
Substitute f = 3 into equation (1):
s = 11-3
s = 8
Hence, the number of cans of soup purchased and the number of frozen dinners purchased are 8 and 3 respectively.
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A postage box should weigh 1.0 punds. If there is a 5% error on the weight, what is the range of acceptable weight
Answer:
0.95-1.05 (please give brainliest)
Step-by-step explanation
1x.95=.95
1x1.05=1.05
"Marsha has 54% left on her phone. Every 1 minute her battery life decreases by 1/2%. Write an equation to represent marshas phone battery life."
The answer to this Question based on Linear Relation is given below
What is Linear Relation?
It is a relation between two variables in which one variable has linear behaviour as other
means if one variable increases or decreases then other variables does same behaviour linearly
Solution:
let us denote the battery by b and time by t
b = 54 - t/2
this relation satisfies all the conditions that are given in Question and gives variation of battery with time and this if plotted on graph will give a linear straight line
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help meeeeeeeeeee pleaseee
For an average intake of 2200 calories per day, the number of acres of land is approximately 2.
How to solve function?A function having the formula f(x) = ax' + b is said to be linear.
It appears to be a standard linear equation, except the linear function symbol is f rather than y. (x).
You would be given the value of f(x) and asked to locate x when solving a linear function.
C(x) is a variable that tells the number of calories consumed daily by a person
x is the number of acres that person own.
C(x) = 270ln(x+1)+1900
In the given question number of acres ask a person have who consumed 2200 calories in a day.
Therefore,
C(x)=2200
2200=270ln(x+1)+1900
2200-1900=270ln(x+1)
300=270ln(x+1)
300/270 = ㏑(x+1)
10/9 = ㏑(x+1)
x+1 = e^(10/9)
x+1 = 3.037
x= 3.037-1
x=2.037
x=2(round off)
Therefore, 2 acres of land a person can consume 2200 calories in a day.
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Consider the piecewise function shown on the graph, which is composed of three different function types.
-10 -8 -6 -4 -2
10-
8
6
4
2
-2
-4
6
-8-
02
-10-
4 6
Match each piece of the function with its domain.
8 10
The quadratic is the left-most piece. This exists on the interval (-infty, -2).
The linear piece is the center piece and exists on the interval (-2,6).
The square root piece is the right-most piece and exists on (6, infty).
These intervals are describing how each piece lines up with the x-axis, as illustrated in the picture.
The required description of the given piecewise function are as follows:
quadratic → (-∞, -2); linear → (-2, 6) and square root → (6, ∞).
What is a piecewise function?A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).
The graph is given in the question, as shown
1. quadratic function:
This the sub-function define between the interval (-∞, -2).
2. linear function:
This the sub-function define between the interval (-2, 6).
3. square root function:
This the sub-function define between the interval (6, ∞).
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Solve the following inequalities 1/2(3x - 2) ≤ (x+4)
Answer:
x ≤ 10
Step-by-step explanation:
3/2 x - 1 ≤ x +4
3/2 x - x ≤ 1 + 4
(3-2)/2 x ≤ 5
1/2 x ≤ 5
2 * 1/2 x ≤ 2 * 5
x ≤ 10
Simplify each expression. Then drag and drop the equivalent matching expression.
3a+b+13a
20b+11a-5b
20b-5b+2b
You will not use all of the expressions.
From the expression, when simplified, (1) 16a+b (2) 17b+11a (3) 17b.
How to simplify algebraic expressions?An algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.
The given algebraic terms are
3a+b+13a
Collect the like terms
3a+13a+b
Add the like terms
16a+b
Therefore, 3a+b+13a matches 16a+b
20b+11a-3b
Collect like terms
20b-3b+11a
=17b+11a
Therefore, 20b+11a-3b matches 17b+11a
20b-5b+2b
All the terms are alike, therefore do the arithmetic operation
15b+2b
=17b
Therefore, 20b-5b+2b matches 17b
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What is the square root of 144?
Answer:12
Step-by-step explanation:
Is the following statement linear or exponential?
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week. HELP PLEASE
Answer:
exponential
Step-by-step explanation:
the 14% of a number will be always greater because the numbers themselves will be greater
Graph the following features:
Y intercept =-2
Slope =-2/3
Which choice is the solution to the inequality below?
6x>72
OA. x< 12
OB. x> 12
OC. x2 72
OD. x>72
The solution to the inequality 6x > 72 is option B x > 12
What is an inequality?
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
A is not equivalent to b in any scenario. Since a is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered.
There are two forms of inequality relations that are not strict, in contrast to strict inequalities:
The notation a ≤ b or a ⩽ b means that a is less than or equal to b (or, equivalently, at most b, or not greater than b).
The notation a ≥ b or a ⩾ b means that a is greater than or equal to b (or, equivalently, at least b, or not less than b).
Given, the inequality is 6x>72
6x > 72
Dividing by 6 on both sides of inequality, we get,
6x/6 > 72/6
⇒ x > 12
Hence, option B is correct.
The solution to the inequality 6x > 72 is option B, x > 12
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Which system of linear inequalities is graphed?
x ≤ -2
y≤ -x-3
x< -3
y< -x-2
x<-2
y≤ -x+2\
x< -2
y≤-x -2
The system of linear inequalities is graphed is x < -2; y ≤ -x+2. Hence option c is the correct.
What is inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
The graph consists of two inequalities.
Since the one graph line is solid, thus the inequality sign either "less than or equal" or "greater than or equal". The other one is dotted, thus it will be less than or greater than
First find the equation of line.
One line passes through the points (-2,0) and (0,-2).
The equation of line that passes through the point (a,0) and (0,b) is
x/a + y/b = 1
The equation of the line is x/(-2) + y/(-2) =1
x + y = -2
y = -x - 2
The equation of the inequality will be either y ≤ -x - 2 or y ≥ -x - 2.
Putting x =0 and y = 0 in y ≤ -x - 2
0 ≤ - 0 -2
0≤ -2 (false)
In the graph (0,0) does not include in the shaded region. Therefore the inequality is y ≤ -x - 2.
The second line is parallel to y-axis.
The equation of line will be x = a
The line passes through the point (-2,0)
Putting x = -2 and y =0 in x = a
-2 = a
Therefore the equation of the dotted line will be x = -2
The equation of the inequality will be either x > -2 and x < -2:
Putting x =0 and y = 0 in x < -2
0 < -2
0 < -2 (false)
In the graph (0,0) does not include in the shaded region. Therefore the inequality is x < -2.
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The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.37 and the probability plot support the assumption that the population is normally distributed. Construct a 95% two-sided confidence interval for ?.
A 95% two-sided confidence interval is 0.46 < a <0.31 .
The formula for confidence interval for population standard deviation is,
[tex]s\sqrt{\frac{n-1}{X^{2} _{1-a/2,n-1} } }[/tex] < a < [tex]s\sqrt{\frac{n-1}{X^{2} _{a/2,n-1} } }[/tex]
Given in question,
Significance level, a = 1 - 0.95
= 0.05
Sample size, n = 51
Sample standard deviation, s = 0.37
By using chi-square distribution table, we get
[tex]X^{2} _{1-a/2,n-1}[/tex] = [tex]X^{2} _{0.975,50}[/tex]
= 32.36
[tex]X^{2} _{a/2,n-1}[/tex] = [tex]X^{2} _{0.025,50}[/tex]
= 71.42
Confidence interval for population standard deviation is :
[tex]0.37\sqrt{\frac{50}{32.36} }[/tex] < a < [tex]0.37\sqrt{\frac{50}{71.42} }[/tex]
0.45992018426 < a < 0.30958278534
Hence, a 95% two-sided confidence interval is 0.46 < a <0.31 .
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g(x)=3(2)^x find g(3)
Answer:
g(3) is 24
Step-by-step explanation:
To find the value of g(3), we need to plug 3 into the function g(x) and evaluate the resulting expression. The function g(x) is defined as g(x) = 3(2)^x. When we plug 3 into this function, we get g(3) = 3(2)^3. To evaluate this expression, we need to calculate 2^3, which is 8. Therefore, g(3) = 3 * 8 = 24.
In summary, the value of g(3) is 24.
Answer:
g(3) = 24
Step-by-step explanation:
Given information,
→ g(x) = 3(2)^x
Then the value of g(3) will be,
→ g(x) = 3(2)^x
→ g(3) = 3(2)³
→ g(3) = 3(8)
→ [ g(3) = 24 ]
Hence, the value of g(3) is 24.
find the solution to the following system substitution y=-2 x -3 y= 3 x + 12
The solution to the system substitution is (x , y) = (-3,3).
What is substitution?The substitution operation in algebra is used to systematically replace instances of a symbol with a given value in various settings involving formal objects containing symbols (commonly called variables or indeterminates).A fundamental operation in computer algebra is substitution.In computer algebra systems, it is frequently abbreviated as "subs" or "subst."Here it is given that,
y=-2 x -3 and y= 3 x + 12
Take y=-2 x -3 as equation 1,
y= 3 x + 12 as equation 2'
by equating both equations,
-2x-3=3x+12
-3-12=3x+2x
5x=-15
x=-15/5
=-3
substituting the value of x in the equation1
y=-2x-3
y=-2(-3)-3
=3
Hence, The solution to the system substitution is (x , y) = (-3,3).
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I need help guys I don’t know what to do or how to do it can someone help me out?
Answer:
I'll help
Step-by-step explanation:
the entrance fee to the skating rink=$5
each minute the skater uses the rink costs=$0.25
Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases.
Refer to the attachment for graph.
What are vector equations ?
Vector equations allow for the creation of parametric curves. That is, points in space are formed for each value of the parameter by the equation of a vector, where each of its elements has a function with an independent variable that we refer to as a parameter.
Given vector equation:
r(t) = < t², t, 2 >
When t= -2,
r(-2) = < (-2)², -2, 2 >
= < 4, -2, 2 >
This means. when t= -2, the curve touches the point ( 4, -2, 2 )
Similarly, when t= -1, the curve touches the point ( 1, -1, 2 )
Table is attached.
graph is attached.
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URGENT HELP PLeASE please just answer b and c
Answer:
b) 2/9
c) 1/3
Step-by-step explanation:
The probability of a desired event happening is the number of ways the desired event can happen divided by the total number of possible outcomes.
a) Correct
b)
There are 9 possible outcomes.
2 outcomes are negative.
p(negative) = 2/9
c)
There are 3 outcomes that are more then 3.
p(more than 3) = 3/9 = 1/3
HOME VALUE The average value of a house changes over time. The average
values of a house in January in Denver, Colorado, for different years are as
follows: 2014, $254,000; 2015, $293,000; 2016, $338,000; 2017, $372,000.
a. Make a table.
b. Determine the domain and range of the relation.
c. Determine whether the relation is a function.
a. The table for the given data is as follows :
Year 2014 2015 2016 2017
Value (in $) 254000 293000 338000 372000
b. Domain and Range for the given relation is:
Domain : {2014, 2015, 2016, 2017}
Range : {254000, 293000, 338000, 372000}
c. From the table we observe that for each year it is having a unique value so it is related to the function.
What is Domain?
The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).
What is Range?
The range of a function is the set of values that the function assumes.
What is Relation?
A collection of ordered pairs having one item from each set makes up a relation between two sets. If the ordered pair (x,y) is present in the relation and the items x and y come from different sets, then the objects are said to be connected
a. The table for the given data is as follows :
Year 2014 2015 2016 2017
Value (in $) 254000 293000 338000 372000
b. Domain and Range for the given relation is:
Domain : {2014, 2015, 2016, 2017}
Range : {254000, 293000, 338000, 372000}
c. From the table we observe that for each year it is having a unique value so it is related to the function.
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Which of the following makes NO distinction between an explanatory variable X and a response variable Y (i.e., you can interchange the roles of X and Y and get the same result)?CorrelationOnly correlation makes no distinction between the X and Y variables. With regression the line would be flipped.
The term that makes NO distinction between an explanatory variable X and a response variable Y is Correlation , the correct option is (a) .
In the question ,
four options are given ,
we have to select the option that makes no distinction between explanatory variable X and a response variable Y .
Response Variable is the (dependent variable) measures the outcome of the study.
Explanatory Variable is the (independent variable) helps to explain or influence changes in a response variable.
So , Correlation makes no distinction between explanatory and response variables.
So , it makes no difference in calculating the correlation , which variable you call x and which you call y .
Therefore , the correct option is (a) .
The given question is incomplete , the complete question is
Which of the following makes NO distinction between an explanatory variable X and a response variable Y (i.e., you can interchange the roles of X and Y and get the same result) ?
(a) Correlation
(b) Regression
(c) Both correlation and regression make no distinction between X and Y.
(d) Both correlation and regression make distinction between X and Y.
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PLEASE ANSWER NEED THIS REALLY SOON!!!! OFFERING 100 PTS
A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive states that the revenues for online ads have more than doubled that of the revenues for printed ads since starting the online version of the paper. Use the graph below to justify the lead executive’s statement and to determine the approximate year that the two ad revenues were equal.
Graph with x axis labeled years. Y axis labeled revenue in dollars. The line for printed ad revenue starts at 0, 3 and goes through the10, 2. The line for online ad revenue starts at 0, 0 zero and goes through the 10, 3.
A) The lead executives statement has been justified below considering the fall and rise of the graph line.
B) Between the years 7 and 8.
How to Interpret Linear Graphs?A) Looking at the attached graph, we can trace that the printed ad's revenue peaked at $3 million and then began to fall steadily. The online ad revenue started with nothing and thereafter gradually increased in value to millions of dollars. Now, since the printed ad revenue has been declining and online ad revenue is seen to be increasing, it means that the lead executive's assertion is accurate.
B) Both curves are seen to intersect between the seventh and eighth year, I would say around the middle of year 7, and both online ads and printed ads generated an approximate revenue of $2.2 million each
Between the years 7 and 8.
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PLEASE HELP
A parking garage bases its
prices on the number of hours
that a vehicle parks in the
garage.
The first two hours cost $2 per
hour, between two hours and
six hours cost $2 per hour, and
all hours after that cost $1.
b
The first two hours cost $2 per
hour, between two and four
hours cost $1 per hour, and all
hours after that cost $0.50.
C
The first two hours cost $4.
between two hours and six
hours cost $2 per hour, and all
hours after that cost $1.
à
The first two hours cost $4.
between two hours and six
hours cost $1 per hour, and all
hours after that cost $0.50.
Answer:
Option C
The first two hours cost $4. Between two hours and six hours cost $2 per hour, and all hours after that cost $1.
Step-by-step explanation:
From the first part of the graph we can see that there is a flat rate of $4 for the first two hours. So the first two hours cost $4.
We can eliminate options A and B leaving C and D as only possible options.
Look at the second part of the graph
Between 2 hours and 6 hours(difference of 4 hours), the cost increases from $4 to $8 or an increase of $8
So rate per hour is $8/4 = $ 2 per hour between 2 hours and 6 hours
This information alone is enough to eliminate D but let's go to the rate beyond 6 hours just to make sure. This is the third part of the graph
Between 6 and 7 hours (1 hour) we can see the cost goes from $12 to $13 or a difference of $1. This means for every hour after 6 hours, the rate is $1 per hour.
So option C is the correct choice
Pls answer as fast as you can, no pressure.
Pavel is designing a restaurant and wants a unique dining area to add to the interest of the design. He thinks that an obtuse isosceles triangle would fulfill this requirement. He has two lengths of railing already in his possession—one that is 12 meters in length and one that is 22.8 meters in length. If he wants to keep his obtuse isosceles triangle design, which railing should he order a duplicate of to create his dining area. Explain.
To keep the obtuse isosceles triangle design, the railing that he should order a duplicate of to create his dining area is of:
12 meters.
When does a set of three measurements can represent a triangle?A set of measurements can represent a triangle if the sum of the two smaller measurements is greater than the greater measures.
The measurements in this triangle are given as follows:
Smallest: 12 meters.Largest: 22.8 meters.If he orders a duplicate of the largest measurement, the smallest measurement would be the base of the isosceles triangle, meaning that it would be an acute isosceles triangle.
Then he should order a duplicate of the smallest measurement, of 12 meters, as then they would be the sides between the obtuse angle of the isosceles triangle.
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Answer:
Step-by-step explanation:
To keep the obtuse isosceles triangle design, the railing that he should order a duplicate of to create his dining area is of:
12 meters.
When does a set of three measurements can represent a triangle?
A set of measurements can represent a triangle if the sum of the two smaller measurements is greater than the greater measures.
The measurements in this triangle are given as follows:
Smallest: 12 meters.
Largest: 22.8 meters.
If he orders a duplicate of the largest measurement, the smallest measurement would be the base of the isosceles triangle, meaning that it would be an acute isosceles triangle.
Then he should order a duplicate of the smallest measurement, of 12 meters, as then they would be the sides between the obtuse angle of the isosceles triangle.
(8.08) Graph the first six terms of a sequence where a1 = 3 and d = −10. (2 points) Group of answer choices graphed sequence showing point 1, negative 10, point 2, negative 7, point 3, negative 4, point 4, negative 1, point 5, 2, and point 6, 5 graphed sequence showing point 1, negative 7, point 2, negative 4, point 3, negative 1, point 4, 2, point 5, 5, and point 6, 8 graphed sequence showing point 1, 3, point 2, negative 7, point 3, negative 17, point 4, negative 27, point 5, negative 37, and point 6, negative 47 graphed sequence showing point 1, negative 7, point 2, negative 17, point 3, negative 27, point 4, negative 37, point 5, negative 47, and point 6, negative 57
The first six terms of the given sequence are given as 3, -7, -17, -27, -37 and -47.
What is an arithmetic sequence?An arithmetic sequence is a kind of sequence of numbers where the difference of any two consecutive terms are the same.
This difference is known as the common difference of the sequence.
The given problem can be solved as follows,
The first term of the sequence is a₁ = 3
And, the common difference is d = -10.
Now, the first six terms can be written as,
a₁ = 3
a₂ = 3 - 10
= -7
a₃ = -7 - 10
= -17
a₄ = -17 - 10
= -27
a₅ = -27 - 10
= -37
a₆ = -37 - 10
= -47
They can be graphed on the number line as follows,
Hence, the first six terms are given as 3, -7, -17, -27, -37 and -47.
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Find the value of x.
It’s using the intersecting secant formula for exteriors but I keep getting decimals and it’s wrong.
Answer:
x = 7
Step-by-step explanation:
x(XY) = 6(WX)
x(x + 11) = 6(6 + 15)
x² + 11x = 126
x² + 11x - 126 = 0
126 = 7 × 18
(x + 18)(x - 7) = 0
x + 18 = 0 or x - 7 = 0
x = -18 or x = 7
We discard the negative answer.
x = 7
Warm Up:
When designing a survey, what is one of the first things you need to know? What would you ask yourself?
Answer: Come up with questions that make sence. That are good solvablequestions. Make sure that you are able to take data off of it to see how people result in it.
Step-by-step explanation:
If xy(-z) = 150, find the values of (-2x)(2y)(-4z)
WILL GIVE BRAINLIEST IF THE ANSWER IS CORRECT!
Answer:
a=-2400
Step-by-step explanation:
We have -x*y*z = 150. We want to find the value of -2x*2y*-4z. Let's set this to a variable, a. We have now that [tex]2x*2y*4z = a[/tex] (because the negatives combine to a positive), where we want to solve for a. This is equal to [tex]16xyz = a[/tex], and dividing by 16 on both sides results in [tex]xyz = a/16[/tex]. Recall that we know [tex]-xyz = 150.[/tex] Negating each side gives us [tex]xyz = -150.[/tex]
Now we have two equations that are equal to the same thing(xyz), so we can set them equal to each other. This gives us [tex]-150 = a/16[/tex]. To solve for a, we multiply both sides by 16, giving us a = -2400. This is our answer!
Hope this helps!
the artist r. locklen jones selects 5 paintings from a collection of 7 to display in a row. how many different arrangements of the display are possible?
Different arrangements of the display are possible is 2520.
Given:
the artist r. locklen jones selects 5 paintings from a collection of 7 to display in a row.
Permutation :
A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order.
= [tex]7_P_5[/tex]
we know that,
[tex]n_P_r[/tex] = n! / ( n - r ) !
[tex]7_P_5[/tex] = 7! / ( 7 - 5 ) !
= 7! / ( 2 ) !
= 7! / 2!
= 7 * 6 * 5 * 4 * 3 * 2! / 2!
= 42 * 20 * 3
= 840 * 3
= 2520
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A bag contains 1 orange, 1 yellow, and 2 blue balls. The balls are replaced after each selection.
Draw a sample space to find the probability that the two selected balls are an orange ball and a blue ball.
The probablity that the two balls are orange and blue is 1/8
Describe Probability:
This is the chance or likelihood that an event will take place.
One orange ball, one yellow ball, and two blue balls are there in a bag.
The total number of sample space or outcome can be given as
Total outcome = 1 + 1 + 2=4
Probablity of occouring an orange ball can be given as, 1/4
Probablity of occouring a blue ball can be given as, 2/4
Probablity of an orange ball and a blue ball = 1/4 * 2/4
Probablity of an orange ball and a blue ball = 1/8
Consequently, there is a 1/8 chance that the two chosen balls are orange and blue
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