In a network of 30 computers, 4 have a copy of a particularly critical file to sustain an organization's regular operations. Suppose that 9 computers at random fail. What is the probability that all 4 computers with the critical file fail in this incident? (Round to four decimal places.)
The probability that all 4 computers with the critical file fail in this incident is given as follows:
0.0046 = 0.46%.
What is the hypergeometric distribution formula?The mass probability formula is presented as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.The values of these parameters for this problem are given as follows:
N = 30, k = 4, n = 9.
The probability that all fail is P(X = 4), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 4) = h(4,30,9,4) = \frac{C_{4,4}C_{26,5}}{C_{30,9}} = 0.0046[/tex]
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f(x) = 3x² +5
g(x) = 4x - 2
h(x) = x²-3x+1
Find f(x) + g(x) — h(x)
Answer:
2x² + 7x + 2
Step-by-step explanation:
f(x) = 3x² + 5
g(x) = 4x - 2
h(x) = x² - 3x + 1
f(x) + g(x) — h(x) =
(3x² + 5) + (4x - 2) - (x² - 3x + 1) = ==> plugin the values of f(x), g(x), and h(x)
3x² + 5 + 4x - 2 - (x² - 3x + 1) =
3x² + 5 + 4x - 2 - x² + 3x - 1 = ==> distribute the negative sign to x², -3x, 1
x² ==> -x², -3x ==> 3x, 1 ==> -1
3x² - x² + 4x + 3x + 5 - 2 - 1 = ==> combine like terms
2x² + 7x + 2 = ==> simplify
Find an equation of a line that is perpendicular to the line x=4 that contains the point (4,−5). Write the equation in slope–intercept form.
The equation of the perpendicular line is y = -5
What is the equation of the line?
We have to recall that the general form of the equation of a line can be given by the expression that is written as y = mx + c. m is the slope of the graph while c is the intercept of the graph.
We would then have;
y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])
We can see that m = 0 from the first line that has been given the we have;
y - (-5) = 0(x - 4)
y + 5 = 0
y = -5
This is the equation that has been required in the problem above.
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evaluate the iterated integral. 1 0 s4 cos(s5) dt ds 0
The final solution is -sin(1).
To evaluate the iterated integral, we need to integrate with respect to the outer variable first, then integrate with respect to the inner variable.
The given iterated integral is:
[tex]∫(1 to 0) ∫(s^4 to 0) cos(s^5) dt ds[/tex]
To evaluate this, we need to integrate with respect to t first, and then integrate with respect to s.
[tex]∫(1 to 0) ∫(s^4 to 0) cos(s^5) dt ds = ∫(1 to 0) [∫(s^4 to 0) cos(s^5) dt] ds= ∫(1 to 0) (-1/s^5 * sin(s^5)) \\ds= [-1/s^5 * sin(s^5)] \\evaluated at s = 1,0= (-1/1^5 * sin(1^5)) - (-1/0^5 * sin(0^5))= (-1/1 * sin(1)) - (0)= -sin(1)[/tex]
So the final solution is -sin(1)
Note that the integral is not defined for s=0, [tex]s^5=0[/tex] , as the function is not defined there.
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Put the following in order from least to greatest:
0.25, 1/3, 30%
Answer: 0.25 30% 1/3
Step-by-step explanation:
1/3 is the largest because when made in a decimal it would be 3.3 reapeting, 30 % is 0.3 and 0.25 . So the order will be 0.25 30% and 1/3.
The left and right page numbers of an open book are two consecutive interfere whos sum is 361. Find these page numbers.
What would the two page numbers be?
The left page number is 180 and the right page number is 181.
What is consecutive integers?
Consecutive integers or consecutive numbers are the terms used to describe the sequence of numbers. In this case, the integers are arranged in ascending order from smallest to highest. The following are a few examples: -4, -3, 2, 1, 0, 1, 2, 3, 4.
Given:
The left and right page numbers of an open book are two consecutive interfere whos sum is 361.
We have to find the page numbers.
Let
The left page number is n.
The right page number is n + 1.
As the sum of numbers is 361.
⇒ n + (n + 1) = 361
2n + 1 = 361
2n = 360
n = 180
Hence, the left page number is 180 and the right page number is 181.
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calculate the iterated integral. 3 0 1 6xy x2 + y2 dy dx 0
The final value of the iterated integral is 945[tex]\sqrt{10}[/tex].
To calculate the iterated integral, we need to evaluate the inner integral with respect to y first and then the outer integral with respect to x.
The inner integral is to be integrated with respect to y is:
∫(6xy[tex]\sqrt{(x^2 + y^2)}[/tex])dy from 0 to 1 = [3y([tex]x^2 + y^2[/tex][tex])^{(3/2)}[/tex])] from 0 to 1
= [3y*[tex](x^2 + y^2[/tex][tex])^{(3/2)}[/tex]] from 0 to 1
= 3(1)*([tex]x^2[/tex] + 1[tex])^{(3/2)}[/tex]
= 3([tex]x^2[/tex] + 1[tex])^{(3/2)}[/tex]
Now, we can use this result as the inside function to evaluate the outer integral with respect to x.
The outer integral is to be integrated with respect to x is:
∫(3([tex]x^2[/tex] + 1[tex])^{(3/2)}[/tex])dx from 0 to 3
= [x([tex]x^2[/tex] + 1[tex])^{(5/2)}[/tex]] from 0 to 3
= [3[tex](3^2 + 1[/tex] [tex])^{(5/2)}[/tex] - 0(0^2 + 1[tex])^{(5/2)}[/tex]]
= [3(10 - 0]
= [945[tex]\sqrt{10}[/tex])]
So the final value of the iterated integral is 945[tex]\sqrt{10}[/tex].
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The complete question is -
Calculate the iterated integral. Integral from 0 to 3 integral from 0 to 1 of 6xy[tex]\sqrt{(x^2 + y^2)}[/tex] dy dx
Find the ratio
People 6: :18
Benches 3:12:
The ratio of people in its simplest form is 1 : 3
The ratio of benches in its simplest form is 1 : 4
What is the ratio in simplest form?A ratio is the number representing a comparison between two named things.
It also refers to the relative magnitudes of two quantities usually expressed as a quotient.
For instance, if there are 12 students in a class which includes 8 girls and 4 boys,
The ratio of girls to all students = 8 : 12
= 8/12
= 2/3
= 2 : 3
The ratio of boys to girls = 4 : 8
= 4/8
= 1/2
= 1 : 2
The ratio of all students to boys = 12 : 4
= 12/4
= 3/1
= 3 : 1
Hence,
People = 6 : 18
= 6 / 18
= 3 / 9
= 1/3
= 1 : 3
Benches = 3 : 12
= 3 / 12
= 1 / 4
= 1 : 4
Therefore, the ratio of people and benches in its simplest form is 1 : 3 and 1 : 4 respectively.
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10. Gianna is taking a walking tour in her city. The entire tour is
10 kilometers long. According to an app on her phone, Gianna's
average walking rate is 1.6 meters per second.
10
A. What is Gianna's average walking rate in kilometers per hour?
22,725
B. About how long will it take Gianna to complete the walking tour?
Express your answer in hours and minutes.
C. MP Construct Arguments Explain how you know your answer is
reasonable.
Therefore , solution of ratio problem is 5760 m & 5.76 km, respectively, are the distances covered per hour for the two halves.
What are the application proportion and ratio?As a/b, a ratio shows the variable relationship between two numbers. When two ratios are equal, as when a/b = c/d, we get a proportion. Mathematical issues involving the unit numbers of the quantities can be resolved using ratio and proportion.
Here,
The ratio approach can be used to solve the above problem as follows:
(A) A 1.6 m/s walking speed is typical.
The calculation for the speed in meters per hour is
1/3600 of an hour is equal to one second.
Take the following 1.6:3600 ratio as an example:
1.6 ÷ 1/3600
= 3600 × 1.6
= 5760
The typical walking speed is 1.6 m/s.
It implies a speed of 1.6 meters per second.
Now, 1 m equals 1/1000 km.
=> 1.6 m = 1.6/1000 km
Moreover, one second is equal to three thousand six hundredths of an hour.
As a result, the distance traveled in kilometers per hour can be calculated by using the following ratio:
1.6/1000 ÷ 1/3600
= (3600 × 1.6)/1000
= 5.76
Therefore, 5760 m and 5.76 km, respectively, are the distances covered per hour in meters and kilometers.
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What are the coordinates of the point on the directed line segment from ( − 5 , 4 ) (−5,4) to ( 1 , 8 ) (1,8) that partitions the segment into a ratio of 3 to 1? pls help
To find the coordinates of the point that partitions the directed line segment from ( − 5 , 4 ) to ( 1 , 8 ) into a ratio of 3 to 1, we can use the following formula:
(x,y) = (1- t) * (x1, y1) + t * (x2, y2)
Where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the directed line segment, t is a value between 0 and 1 that represents the ratio of the partition, and (x, y) are the coordinates of the point that partitions the segment.
In this case, we want the ratio of the partition to be 3 to 1, so t = 3 / (3 + 1) = 3/4
So we can substitute the values into the formula:
(x,y) = (1- 3/4) * (-5, 4) + (3/4) * (1, 8)
(x,y) = (-5/4, 4/4) + (3/4, 6/4)
(x,y) = (-5/4+3/4, 4/4+6/4)
(x,y) = (-2/4, 10/4)
(x,y) = (-0.5, 2.5)
So the point that partitions the directed line segment from ( − 5 , 4 ) to ( 1 , 8 ) into a ratio of 3 to 1 has coordinates (-0.5, 2.5)
Practice PROBLEMS
below
2+
721
2. What is the value of the expression below
when f = 2.5?
A 132
B 18
C 42
D 28
8 + 4f
Answer:
B. 18
Step-by-step explanation:
Given that f = 2.5,
8 + 4f
=8 + 4(2.5)
8 + 10 = 18
Which students ran faster than Amy?
There are a total of 160 passenger seats on a commercial aircraft. Passengers can
book a seat in economy class or in first class. There are 9 times as many economy
seats as there are first class seats. Determine the number of first-class seats and the
number of economy seats on this aircraft.
Answer: 144 economy seats and 16 first class seats
Step-by-step explanation:
1 : 9 first class seats to economy seats
1 : 9 x 16 = 16 : 144
160x9=1440
Step-by-step explanation:
your welcome no explanation just get the answer
Every day your heart creates enough energy to drive a truck for 32 kilometers. If you combined the energy created all the students in your math class for a week, how many meters could the truck drive?
(PLEASE HELP DUE TODAY)
(TYSM FOR THE TIME):)
The number of meters that the truck could go given the energy provided by the students combined, would be 800, 000 meters
How to find the distance the truck would go ?To find the distance the truck would go, first find the number of meters the truck would go with the energy your heart provides :
= 32 x 1, 000 meters per kilometer
= 32, 000 meters
There are 25 people in the math class so the distance the truck would go is:
= Number of students x Distance per person
= 25 x 32, 000
= 800, 000 meters
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the graph represents y as a function of x. which additional point can be plotted so that this graph continues to represent a function? please answer and explain why you chose the answer. i will mark you brainliest.
A point-to-point graph, also called a line graph
Which graphs are used to depict a function?To establish if a graph reflects a function, use the vertical line test. If a vertical line is dragged across the graph and only touches the graph at one location at any time, the graph is a function. If the vertical line intersects the graph more than once, the graph is not a function.
A line graph, also known as a point-to-point graph, is a visual representation of data in which precise values of a function are represented as dots on a coordinate plane. Straight lines link adjacent pairs of dots.
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big lake bob spends his time carving fishing lures and duck decoys. if big lake bob spends all of his time carving fishing lures he can carve 100 lures in a week. if he spends all of his time carving duck decoys he can carve 30 decoys in a week. for every 6 duck decoys big lake bob carves he must give up 20 fishing lures.
Yes, for every 6 duck decoys big lake bob carves he must give up 20 fishing lures.
Production possibility schedule:-
Fish lures:
Fish lures in one week = 100
lures in a day = 20
So, 100-20 = 80
80 - 20 = 60
60 - 20 = 40
40 - 20 = 20
20 - 20 = 0
Duck decoys:
Duck in one day = 0
So, 0 + 6 = 6
6 + 6 = 12
12 + 6 = 18
18 + 6 = 24
24 + 6 = 30
number of duck decoy in a week = 30
Hence, For every 6 duck decoys Bob carves 20 lures.
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To pay for a home improvement project that totals $16,000, Genesis is choosing between taking out a simple interest bank loan at 8% for 3 years or paying with a credit card that compounds monthly at an annual rate of 15% for 7 years. Which plan would give Genesis the lowest monthly payment?
The monthly credit card payment would be $511.11, which is lower than the monthly payment on the bank loan.
The monthly payment on a bank loan would be $480, which is lower than the monthly credit card payment.
The monthly payment on a bank loan would be $551.11, which is lower than the monthly credit card payment.
The monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.
This is $20,330.08 more than the total cost of the bank loan.
What is payment?Payment is the transfer of money from one party to another in exchange for goods, services, or to fulfill a legal obligation. Payment is an important part of any transaction, as it is the final step that completes the exchange of goods or services.
Therefore, the lowest monthly payment would be the credit card payment of $511.11. Paying with a credit card at 15% compounded monthly would be the least expensive option for Genesis. With this option, would pay a total of $36,330.08 over the 7 years, including the interest. This is $20,330.08 more than the total cost of the bank loan.
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Use point-slope form to write the equation of a line that passes through the point (-8,8) with slope 3
Answer:
Step-by-step explanation:
j7yu8iol9ololololol
I NEED #2 DONE PLSS HELPPPP ASAP
As a set of inputs with one output for each, a function is defined as a relationship between them.
What is a definition for function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).
A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.
When examining a graph, one method is to perform a "vertical line test" to see if a relationship is indeed a function. Anywhere on the graph where a vertical line can be created to cross the relation twice indicates that the relationship is not a function.
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A pole 10 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Suav measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.
The length of the guy wire is equal to 48 ft.
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given here: Distance of stake to the pole=14 feet and Distance from the pole to the tower as =25 ft. And height of the pole=10 feet.
Now let the angle that the guy wire makes with the stake is θ
Then we have Tanθ= 10/14
=5/7
Again we also have Tan θ= height of the tower /base of the tower
Thus h/39=5/7 ( where h is the height of the tower).
or, h=27.85
Therefore using pythagoraes theorem we get the length of the wire as
=[tex]\sqrt{27.85^2+39^2}[/tex]
=47.92 feet or 48 ft. (Approx)
Hence, The length of the guy wire is equal to 48 ft.
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The scale of a drawing is 1/4 in = 12ft. Find the actual measurement of 8in
While calculating the measurements given.The correct answer is 384 ft.
ExplanationGiven,
Inches when drawing =1/4
Actual feet according to the drawing =12 ft
To calculate the The mesurement of 8 inch
8 ÷ 1/4 = 8/1 x 4/1 = 32
32 x 12 = 384
How to Calculate Inches to Feet and InchesSometimes we find the value in feet and inches rather than converting the amount to decimals. For instance, 71 inches is equivalent to 5 feet, 11 inches. It's because we get 5 as the quotient and 11 as the remainder when we divide 71 by 12. The residual value will be expressed as the number of inches it is. This is known as converting inches to feet and feet to inches. Let's examine a few of the instances below.
67 inches to feet = (67 ÷ 12) ft = 5 feet and 7 inches80 inches in feet = (80 ÷ 12) ft = 6 feet and 8 inches54 inches in feet = (54 ÷ 12) ft = 4 feet and 6 inchesTo know more about How to Calculate Inches to Feet refer to:
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Sally bought six pencils and three folders for $3.90. Henry bought two pencils and five folders for $3.30.
Which system of equations can be used to find the price in dollars of each pencil, x, and each folder, y.
A
6x + 2y = 3.90
3x + 5y = 3.30
B
2x + 3y = 3.30
6x + 5y = 3.90
C
6x + 3y = 3.30
2x + 5y = 3.90
D
6x + 3y = 3.90
2x + 5y = 3.30
The system of equations that can be used to find the price in dollars of each pencil, x, and each folder, y that Sally and Henry bought is D.
6x + 3y = 3.90
2x + 5y = 3.30.
What is a system of equations?A system of equations is also known as a simultaneous equation.
Simultaneous equations are equations solved concurrently.
Sally Henry
Units of pencils 6 3
Units of folders 3 2
Total costs $3.90 $3.30
Let pencils = x and folders = y
Equations:Sally's total cost = 6x + 3y = $3.90
Henry's total cost = 3 x + 2y = $3.30
In this situation, to find the price of each pencil and each folder, the system of equations that can be used is from Option D.
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Seven less than the product of 9 and a number equals 8. Use the variable b for the unknown number
The equation formed by the sentence is 9b - 7 = 8.
What is equation ?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
Let the variable be b
By the given sentence we get the equation
9b - 7 = 8
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If the speed of light is 300,000 km/s, how many kilometers (km) are in a light-year (ly)? Show all your work.
300,000 km/s × Distance traval by light in one year
300,000 × 365days
300,000 × 365 × 24
300,000 × 365× 24 × 60
300,000 × 365× 24 × 60 × 60
9.46 × 10¹²
can someone help? This is due today!
Answer:
Question 2: No Solution
Question 4: (2,-3)
Step-by-step explanation:
Question 2: {x-y=7} {x-y=-4}
Question 4: {5x+2y=4} {9x+2y=12}
There is two ways of solving this;
Elimination method and Substitution method.
I will be using the Substitution method for Question 2 and Elimination method for Question 4.
Substitution method is basically substituting in the equation like this;
Question 2:
x - y = 7 and x - y = -4
x - y = 7 into x = 7 + y
Substitute:
7 + y - y = - 4
7 = - 4
7 ≠ - 4
Therefore, there no solution to this equations.
Question 2: No Solution
Question 4:
Elimination Method is basically eliminates one of the variables, so we can solve a more simplified equation.
5x + 2y = 4 and 9x + 2y =12
5x + 2y = 4
-(9x + 2y = 12) - Multiply this equation by -1.
Now we have;
5x + 2y = 4
-9x -2y = -12
-4x = -8
x = 2
We can substitute x to find y.
5(2) + 2y = 4
10 + 2y = 4
2y = -6
y = -3
(2,-3)
Question 4 Solution: (2,-3)
RevyBreeze
complete the statement. Round to the nearest hundredth. 12ft/sec=yd/min
The completed statement would be
12ft/sec = 7.2 yd/min.
What is the unit conversion?
Unit conversion is the process of changing a measurement from one unit to another, while maintaining the same numerical value. It is used to convert measurements from one system of units to another, such as from metric units to imperial units, or from feet to meters.
To convert feet per second to yards per minute, we need to multiply the value in feet per second by the conversion factor of 1 yard/3 feet and then divide the result by the conversion factor of 1 minute/60 seconds.
12 ft/sec = (12 ft/sec) * (1 yard/3 feet) * (1 min/60 sec) = (12*1/3) * (1/60) = 4/5 = 0.8.
So, 12 ft/sec is equal to 0.8 yards per minute. Rounded to the nearest hundredth, this is 7.2 yards per minute
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emmy and roscoe both run every day. Yesterday emmy ran 8 mile in 2 hours. Roscoe ran 6 ½ miles in 1 ½ hours. Who ran faster and why
Roscoe is faster.
What is speed?Speed is a scalar quantity that refers to "how fast an object is moving."
Given that, Emmy and Roscoe both run every day. Yesterday Emmy ran 8 mile in 2 hours. Roscoe ran 6 ½ miles in 1 ½ hours.
Speed = distance / time
Emily's Speed = 8 / 2 = 4 mph
Roscoe's speed = 6 ½ / 1 ½ = 6.5 / 1.5 = 4.33 mph
Since, Roscoe's speed is greater than Emily's speed.
Hence, Roscoe is faster.
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What’s the domain of x-3+5
The domain of the function x - 3 + 5 is x ∈ R(real number)
What is a function ?A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.
The collection of all potential inputs for a function is its domain. Think of this box as the f(x) = 2x function. The domain is only the collection of natural numbers when the input values are x = 1,2,3,4,..., and the values that are returned are referred to as the range.
The collection of all a function's outputs is its range. Example: Let's have a look at the function f: A->B, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output.
The function is
f(x) = x - 3 + 5 = x + 2
for all value of x ∈ real number the function is define
So , the domain of the function x - 3 + 5 is x ∈ R(real number)
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Let f(x)=x2+10x+29. What is the minimum value of the function?
Answer:
54
Step-by-step explanation:
[tex]f(x)=x^2+10x+29 \\ \\ f(x)=(x^2+10x+25)+29+25 \\ \\ f(x)=(x+5)^2+54 \\ \\ \therefore (x+5)^2 \geq 0 \implies (x+5)^2+54=f(x) \geq 54[/tex]
A dance squad needs at least $800 to buy new dance outfits.
They have saved $350 already.
They are selling tickets to a dance performance for $8 each.
They need to sell x tickets to have enough money to buy the new dance outfits. Which inequality represents this situation?
A
8x+350≤800
B
8x+350≥800
C
8(x+350)≤800
D
8(x+350)≥800
Answer:
B) 8x + 350 ≥ 800
Step-by-step explanation:
A dance squad needs at least $800, this means the inequality sign will be greater than or equal to.
They already have $350, and each ticket is $8.
So,
8x + 350 ≥ 800