Answer:
I'm doing this to complete one of the steps. good luck my friend
Step-by-step explanation:
need the answer asap ! thank you to whoever helps ! <3
The system that has the solution (-2, -2, -2) is the one in option C.
x + 2y = -6
y + 2z = -6
x - y - z = 2
Which system of equations has the given solution?We want to see which of the given systems has the solution (-2, -2, -2).
To check that, we only need to evaluate all the equations of the system on these values and see if all the equations are true.
If we look at the third system we will get:
x + 2y = -6
y + 2z = -6
x - y - z = 2
Replacing all the values of the point we get:
-2 + 2*(-2) = -6
-2 + 2*(-2) = -6
-2 + 2 + 2 = 2
All these equations are true, thus, the correct option is C.
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On a Cartesian plane sketch the region which represents the set of points for which x<2 and y>or= to 2
The inequality for this problem is defined as follows:
x < 2.y >= 2.The Cartesian plan representation of the inequality is given by the image presented at the end of the answer.
How to graph the inequality?The two conditions for the inequality are given as follows:
x < 2.y >= 2.These conditions are plotted as follows:
x < 2 -> values to the left of the dashed vertical line at x = 2.y >= 2 -> values above the solid horizontal line at y = 2.More can be learned about inequalities at https://brainly.com/question/25275758
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Please Help! View the picture below
The order of the angles from least to greatest are given as follows:
<N , <R, <Q.
How to order the angles?The law of sines states that the ratio between the sine of the angle and the length of the opposite side of the triangle is equals.
This means that the higher the side length, the greater the opposite angle will be.
Hence:
The smallest angle is the angle N, which is opposite to the smaller side.The greatest angle is the angle Q, which is opposite to the greatest side.More can be learned about the law of sines at https://brainly.com/question/4372174
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Three siblings have a gift of $169 to split in the ratio of 1/2 : 1/3 : 1/4. What is the greatest number of dollars that any of the siblings will receive?
The greatest amount of dollar shared is $78
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls
The ratio of the three sibling is 1/2 : 1/3 : 1/4. Firstly, we multiply all the terms with the l.c.m which is 12
therefore the ratio = 6: 4: 3
The total money to be share is 169
The total ratio is 13
The share of the first sibling = 6/13 × 169
= $ 78
The share of the second sibling = 4/13 × 169 = $52
The share of the third sibling = 3/13 × 169 = $ 39
Therefore the highest number of dollars shared is $78
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The graphs shows the speed of a car for 30 seconds. A) using a single appropriate trapezium , estimate the distance travelled by the car during this time . B) is your answer an overestimate or underestimate ?
The distance travelled by the car during this time by using single appropriate trapezium is 26.25 and the answer provided is an underestimate
Estimate the distance travelled by the car during this time?A) Using a single appropriate trapezium, the estimated distance travelled by the car during the 30 seconds is approximately 55 metres.
This is calculated by taking the area of the trapezium formed by the two points of the speed graph: 8m/s and 6m/s.
The area is calculated by taking the average of the two points, multiplied by the time duration:
Area = (8+6/2) * 30
Area = 7*30
Area = 210
The area of the trapezium is then divided by the speed of the car at the start of the journey (8m/s) to get the estimated distance travelled:
Distance = 210/8
Distance = 26.25
This is rounded up to give an estimated distance travelled of 55 metres.
B) The answer of 55 metres is an underestimate of the actual distance travelled by the car. This is because the trapezium method only takes into account the start and end points of the graph, and not any of the other points in between. The actual distance travelled by the car is likely to be higher as the speed of the car is likely to have been greater at points in between the start and end points.
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Find two positive numbers satisfying the given requirements.
The product is 154 and the sum is a minimum.
The required two positive numbers are 11 and 14 which product is 154 and the sum is a minimum.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
The product is 154 and the sum is a minimum.
As per the question, the required solution would be as:
product sum
1 x 154 1 + 154 = 155
2 x 77 2 + 77 = 79
11 x 14 11 + 14 = 25
7 x 22 7 + 22 = 29
Here, we can arrange these numbers as:
25 < 29 < 79 < 155
This means the sum (11 + 14 = 25) is a minimum.
So the minimum value = 11
And the maximum value = 14
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a tank with a capacity of 400l is full of a mixture of water and chlorine with a concentration of 0.05g of chlorine per liter. in order to reduce the concentration of chlorine, fresh water is pumped into the tank at a rate of 4 l/s. the mixture is kept stirred and is pumped out at a rate of 10 l/s. find the amount of chlorine in the tank as a function of time.
The amount of chlorine in the tank as a function of time is:
C(t) = 0.05 * e^(-6/400*t)
Let C(t) be the concentration of chlorine in the tank at time t and V(t) be the volume of the tank at time t.
At t=0, we know that:
C(0) = 0.05 g/l
V(0) = 400 l
As fresh water is pumped in at a rate of 4 l/s and the mixture is pumped out at a rate of 10 l/s, the rate of change of the volume of the tank is:
dV/dt = 4 - 10 = -6 l/s
As the concentration of chlorine is being diluted by the addition of fresh water, the rate of change of the concentration is proportional to the rate of change of the volume. So we can write:
dC/dt = - k * C(t) * (dV/dt)
where k is a proportionality constant.
We can integrate the above equation with respect to time to find the concentration of chlorine in the tank as a function of time:
C(t) = C(0) * e^(-kt)
In order to find the value of k we can use the initial condition C(0) = 0.05 g/l and V(0) = 400l
0.05 = C(0) * e^(-k*0)
0.05 = C(0)
so we can substitute this value into the above equation and solving for k:
C(0) = 0.05 = 0.05 * e^(-k*0)
0.05 = 0.05
so k = -6/400
Finally, the amount of chlorine in the tank as a function of time is:
C(t) = 0.05 * e^(-6/400*t)
This equation expresses the amount of chlorine in the tank as a function of time t. As time goes on, the concentration of chlorine will decrease exponentially.
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96x2let be the inverse function of . take to be an output of the function . that is, and . (a) which statement best describes ?
The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) is g(f(x)) is x.
How can you determine a function's inverse?Write the function y as a function of x, i.e., y = f(x), and then solve for x as a function of y, to determine the inverse of a function.
steps for determining a function's inverse.
In the equation expressing the function, swap out f(x) with y.
Swap out x and y. To put it another way, swap out every x for a y and vice versa.
Solve for y.
Change y to f-1 (x).
The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x.
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How do I solve for the missing value
The missing value in the triangle is given as follows:
28.
How to obtain the missing value?The theorem used to solve this problem is given as follows:
A line parallel to one side of a triangle divides the other two proportionately.
As 28 - 16 = 12, the proportional relationship between the side lengths is given as follows:
12/21 = 16/x.
Applying cross multiplication, the value of x is obtained as follows:
12x = 21(16)
Simplifying by 4, we have that:
3x = 21(4)
Simplifying by 3, we have that:
x = 7 x 4
x = 28.
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What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer?
The amount of money Rashon would need to invest is equal to $8,300.46.
How to determine the value of equivalent quarterly interest rate?Mathematically, the compound interest on an investment can be calculated by using this mathematical expression:
A(t) = P(1 + r/n)^{nt}
Where:
A represents the future value.r represents the interest rate.n represents the number of times compounded.P represents the principal.T represents the time measured in years.In this scenario, Rashon's investment is compounded quarterly at an interest rate of 6.9% as follows:
Quarterly interest rate = 0.069/4
Quarterly interest rate = 0.01725%
20,200 = P(1 + 0.01725)^{4 × 13}
20,200 = P(1.01725)^52
20,200 = 2.4336P
Principal, P = 20,200/2.4336
Principal, P = $8,300.46.
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Answer:
In this scenario, Rashon's investment is compounded quarterly at an interest rate of 6.9% as follows:
Quarterly interest rate = 0.069/4
Quarterly interest rate = 0.01725%
20,200 = P(1 + 0.01725)^{4 × 13}
20,200 = P(1.01725)^52
20,200 = 2.4336P
Principal, P = 20,200/2.4336
Principal, P = $8,300.46.
Rewrite the following without an exponent.
(5/3)^-3
Figure ABCDE has vertices A(−2, 3), B(2, 3), C(5, −2), D(0, −4), and E(−2, −2). Plot the points on your own coordinate grid and connect the points in alphabetical order. Decompose Figure ABCDE into rectangles and triangles. Part A: How many triangles and rectangles did you make? (1 point) Part B: Use Figure ABCDE created on your coordinate grid to find the lengths, in units, of Sides AB and AE. (4 points) Part C: What is the area of Figure ABCDE? Show your work. (5 points)
Figure ABCDE has vertices A(−3, 3), B(2, 3), C(5, −2), D(0, −3), and E(−3, −2) So the Area of figure = 36.5 sq units
To Find: Plot the points
Decompose Figure ABCDE into rectangles and triangles.
lengths of Sides AB and AE.
area of Figure ABCDE
Plot ( x , y) ( x , y)
If x is positive, start right away from the origin. If it's negative, turn left.
If +ve, move y upward; if -ve, move y downward.
Plotted and labeled points
A(−3, 3), B(2, 3), (2, 3),
AB's length is five.
A(−3, 3) E(−3, −2).
AE length is 5
two triangles and one rectangle
area of a rectangle equal 5 * 5, or 25 square units.
The right angle triangle's area is equal to (1/2) * 5 * 3 = 7.5 square units.
another triangle's area is equal to (1/2) * 8 * 1 square units.
Figure's surface area is 25 + 7.5 + 4 = 36.5 sq units.
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El departamento de teatro de la escuela está organizando una producción y planea cobrar $10 por entrada y $5 por una entrada para niños. Necesitan ganar por lo menos $3,000 cada noche para cov s. El auditorio tiene capacidad para 400 personas.
The four inequalities are a + c ≤ 400, 10a + 5c ≥ 3000, a ≥ 0 and c ≥ 0. The club must sell 200 children tickets and 200 adult tickets.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The value for one ticket is - $10
The value for one children's ticket is - $5
The total amount that need s to be earned is - $3000
The number of seats in the auditorium is - 400
Let the number of children be = c and the number of adults be = a.
Then the inequality will be -
a + c ≤ 400
10a + 5c ≥ 3000
a ≥ 0
c ≥ 0
The inequalities will have a straight line as (≤,≥) symbols are used in the inequalities.
Write the two inequalities in equation form -
a + c = 400....(1)
10a + 5c = 3000 or 2a + c = 600....(2)
Subtract equation (1) from (2) -
2a + c - (a + c) = 600 - 400
2a + c - a - c = 200
a = 200
a = 200
Substitute the value of a in equation (1) -
200 + c = 400
c = 400 - 200
c = 200
So, the intersection point is (200,200) and the number of children is 200 whereas the number of adults is 200.
Therefore, the graph is obtained.
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The school drama department is putting on a production and plans to charge $10 per ticket and $5 for a children's ticket. They need to earn at least $3,000 each night for cover the cost. The auditorium has a capacity for 400 people.
Write and graph a system of four inequalities that describe how many of each type of ticket the club must sell to meets its goal.
Sydney's Games is selling all games at a 25% discount. However, you also have a membership card at the
store, which gives you an additional 15% off. What will you end up paying for $100 worth of games?
Show your work!
The required selling price of the game after two discount is $63.75.
What is discount?The term discount designates a sum or a percentage subtracted from an item's usual selling price. Make sure you need all of the items you plan to get before waiting until after the holiday to make a purchase. A discount is a decrease in the cost of a commodity or service.
According to question:Discount = 25%,
Additional discount = 15%
Then,
Net discount is = 36.25%
We have,
Price of game = $100
Discount amount = 36.25% of $100 = $36.25
So, the selling price of the game after discount = $100 - $36.25
= $63.75
Thus, required selling price of the game is $63.75.
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You bought a fish tank in the shape of a rectangular prism. The dimensions are n, n=6, and n=18. Use the formula V=lwh to write a polynomial in standard form for the volume of the fish tank. Show all work
If the dimensions of the rectangular fish tank are n , 6 and 18 , then the polynomial in the standard form for Volume of fish tank is V = 108n .
The dimensions of the fish tank in shape of rectangular prism re :
length = n , width = 6 and height = 18 ;
the formula to be used to calculate the volume of rectangular fish tank is written as : Volume = length × Width × Height ;
substituting the values in the volume formula ,
we get ;
Volume of tank = n × 6 × 18 ;
= n × 108 ;
= 108n .
Therefore , the polynomial in the standard form can be written as V = 108n .
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Which system of equations has a solution of (3/5,-13/10)?
A value we can put in place of a variable (such as x) that makes the equation true and the answer is 13/-10
What is meant by variable ?A number that is capable of taking on any one of a range of values.
A variable's symbolic representation.
Something which can change.
A variable that could alter in a scientific experiment.
A property that can be measured and given varied values is known as a variable.
Variables include things like height, age, income, province of birth, school grades, and kind of dwelling.
Independent, dependent, and controlled variables make up the three primary variables. A automobile driving down various surfaces is one example.
A variable in programming is a value that can change based on external factors or data that has been supplied to the program.
3x+5y
= 0x+5y
=-3x+y
=-3/5x + y
= 3/5 13x + 10y
=0x + 10y
=13x+y
=13/- 10
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what is the length of a rectangle that has a perimeter of 48 inches and a width of 18 inches
Answer:
x+x+18+18=48inches
2x+36 = 48 inches
2x = (48-36) inches
2x = 12 inches
x = 6 inches
I need help asap with this question
In the right-angle triangle RQS the measure of m∠R = 90°, m∠Q = 59° and m∠S = 31°.
What is a right-angled triangle?
Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.
A right-angled triangle RQS is given.
The measure of ∠R is given as = 90°.
The measure of ∠Q is given as = (2x + 33)°.
The measure of ∠S is given as = (5x - 34)°.
According to the properties of the triangle, the sum of all angles of a triangle equals 180°.
So, the equation will be -
∠R + ∠Q + ∠S = 180°
Substituting the values into the equation -
90° + (2x + 33)° + (5x - 34)° = 180°
Combining the like terms -
90° + 2x + 33° + 5x - 34° = 180°
7x + 89° = 180°
7x = 180° - 89°
7x = 91°
x = 13°
The measure of ∠Q - (2x + 33)°
∠Q = 2(13°) + 33°
∠Q = 26° + 33°
∠Q = 59°
The measure of ∠S - (5x - 34)°
∠S = 5(13°) - 34°
∠S = 65° - 34°
∠S = 31°
Therefore, the measures of angles are 90°, 59° and 31°.
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Read the passage and examine the text in bold. Then, answer the question.
I always loved my grandfather's explanations of our seasons, "This is the country of three seasons. From June on to November, it lies hot, still, and unbearable, sick with violent and unrelenting storms; then on until April, it is chill, quiet, and drinks its scant rain and scanter snows. From April to the hot season again, it is blossoming, radiant, and a seductress." His months were only approximate, later or earlier the rain-laden wind may drive up the water gate of the Colorado River from the Gulf and bring to us our heat, chill, or radiance. In the desert, we see the land set its seasons by the rain.
Does the bolded portion contain an error? Choose the correction if one is needed.
A. and drank its scant rain
B. and thirsty for its scant rain
C. and, drinks its scant rain
D. No correction is needed
The context clues show that the bolded portion contain doesn't contain an error. Therefore, D. No correction is needed
What are context clues?When determining a word's meaning, context clues take into account the words that immediately precede the unknown word and lead us to infer its meaning.
These words, also known as visual indices, are explained or defined by other words that are used in the same sentence.
From June on to November, it lies hot, still, and unbearable, sick with violent and unrelenting storms; then on until April, it is chill, quiet, and drinks its scant rain and scanter snows. From April to the hot season again, it is blossoming, radiant, and a seductress.
In this case, it is grammatically correct. The correct option is D.
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• Kwan is planting a garden. He plants vegetables in
1
of the garden. He uses
2
of the
5
vegetable garden for radishes. Kwan wants to know how much of the whole garden
he is using to plant radishes.
Kwan is utilizing 8% of the entire garden to plant radishes.
Kwan is planting a garden and he is utilizing 1/5 of the garden to plant vegetables. That implies that 1 out of 5 pieces of the garden is being utilized to grow vegetables.
He then, at that point, expresses that he utilizes 2/5 of that 1/5 region for radishes. That implies that 2/5 of the area utilized for vegetables is being utilized to grow radishes.
To find the fraction of the entire garden that is being utilized for radishes, we want to join the two fractions. We can do this by multiplying them together.
At the point when we multiply 1/5 by 2/5, we get 2/25. This fraction can likewise be communicated as a rate by multiplying it by 100.
2/25 * 100 = 8%
So, Kwan is utilizing 8% of the entire garden to plant radishes.
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Graph y= 1/3x-3 .I just need to know the plots
Answer: Points: (0, -3), and (9, 0)
Step-by-step explanation:
In order to graph an equation, you find 2 pairs of points and then just connect them into a line. (The x intercepts and the y intercepts are helpful)
One pair: (x, y) = (0, -3)
Another pair: (x, y) = (9, 0)
Now just connect them to get the line :>
White Oak is 15 miles from River City. What would its distance be on the map? WHOEVER ANSWERS GETS 30 POINTS
When White Oak is 15 miles from River City and the scale is 1 in.=3 mi, the distance in the map is 5 inches.
How to explain the scale?The ratio that describes the relationship between the actual figure and its model is called the scale. It serves as a representation of the actual figures in smaller units on maps. A scale of 1:5, for instance, means that 1 on the map is equivalent to the size of 5 in the real world.
A scale of 1:5, for instance, means that the size of 1 unit in the drawing corresponds to the size of 5 units in the real world. A scale of 1:5 is evident, for instance, if a giraffe that stands 150 inches tall in real life is depicted on the drawing as 30 inches tall.
In this case, when White Oak is 15 miles from River City and the scale is 1 in.=3 mi, the distance in the map is:
= 15 / 3
= 5 inches.
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The polygon in the diagram is a square with center P. The answer options are below:
144.0in
72.0in
24.0in
36.0in
Refer to image for other info
The area of square = 72.0 in The surface area of a shape is measured using the area.use square units for area when you can multiply the length to determine the area .
Option B is correct.
What is area of square?The quantity of square units required to completely fill a square is known as the area of a square. The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area. The measurement is made using square units, with square metres serving as the standard unit (m²).
Area of square = Side ²
side=6√2
Area=?
Area of square = ( 6√2)²
72 .0 inches.
Why square units for area?This is because the sum of two lengths is used to calculate an area. If those are, for instance, measured in meters, you would multiply some meters by others. Consequently, the expression for the area in square meters. Similar to volume: You divide three lengths by.
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James has x quarters. His brother has 4 times as many quarters as James has. How may quarters do they have altogether?
The total number of quarters James and his brother will be 5x
Addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
James has x quarters while his brother has 4 times as many quarters as James.
So, for determining the value of the total number of quarters James's brother have we will multiply the value of the total number of quarter James have by 4.
So, the value of the total quarter James's brother has = 4*x = 4x
Now for determining the total number of quarters of James and his brother we will add both values.
The total number of quarters James and his brother will be= x+4x = 5x
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3 ( � − 2 ) + � − 1 = 3(x−2)+x−1= 5 5
Answer: The equation provided is already solved, on the left side of the equation it shows the step by step solution of the equation:
3(x-2)+x-1 = 3(x-2) + x - 1 = 5
3x - 6 + x - 1 = 5
Combining like terms
4x - 7 = 5
Adding 7 to both sides
4x = 12
Dividing both sides by 4
x = 3
So the value of x that makes the equation true is x = 3
Step-by-step explanation:
To the nearest hundredth find the value of x
Answer:
x = 14.83 (to the nearest hundredth)
Step-by-step explanation:
Following the Pythagoras' Theorem,
a² + b² = c²
x² + 6² = 16²
x² = 220
∴ x = 14.83 (to the nearest hundredth)
Rewrite one fourteenthx3y + eight fourteenthsxy2 using a common factor.
one seventhxy(2x2 + 8y)
one seventhx2y(2x + 8y)
one fourteenthxy(x2 + 8y)
one fourteenthx3y2(y + 8)
The expression 1/14 x³y + 8/14 xy² can be rewritten as one fourteenth xy (x² + 8y).
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
The given expression is [tex]\frac{1}{14}[/tex] x³y + [tex]\frac{8}{14}[/tex] xy².
We have to take the common factor of both the terms [tex]\frac{1}{14}[/tex] x³y and [tex]\frac{8}{14}[/tex] xy² outside.
The common factor of both terms is [tex]\frac{1}{14}[/tex] xy.
[tex]\frac{1}{14}[/tex] x³y + [tex]\frac{8}{14}[/tex] xy² = [tex]\frac{1}{14}[/tex] xy (x² + 8y)
Hence the given expression can be rewritten as [tex]\frac{1}{14}[/tex] xy (x² + 8y).
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Iman ate 1/3 of a bag of popcorn.
His 4 friends ate equal shares of the remaining popcorn.
Which expression represents the popcorn that each friend ate?
Answer: 1/3 per friend.
Step-by-step explanation:1/3 1/6*4= 3/3 or 1 whole bag. to find the 1/6, 2/3 multiply by 1/4= 2/12 or 1/6 of popcorn per friend
Mrs. Cooper paid more than $22 for a pack of hand towels. Each towel cost $2.85. The hand towels were available in packs of 4, 5, 6, and 8. Use the inequality to find the minimum number of towels, t, in the pack.
Using inequality, the minimum number of towels in the pack is t = 6.
How to Find Minimum Number Using Inequality?We can start by using the inequality 2.85t > 22, where t is the number of towels in the pack.
To find the minimum number of towels, we can use the smallest possible value for t that satisfies the inequality. Since the hand towels were available in packs of 4, 5, 6, and 8, we can use t = 4 in the inequality:
2.85(4) > 22
Simplifying the left side of the inequality gives:
11.4 > 22
This is not true, so t = 4 does not satisfy the inequality.
Next, we can use t = 5:
2.85(5) > 22
Simplifying the left side of the inequality gives:
14.25 > 22
This is also not true, so t = 5 does not satisfy the inequality.
We can keep doing this for t = 6, and t = 8, we will find out t=6 is the minimum value of t that satisfies the inequality.
2.85(6) > 22
Simplifying the left side of the inequality gives:
17.1 > 22
This is true, so t = 6 is the minimum number of towels in the pack.
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how many ways are there to list the digits { 1 , 2 , 2 , 3 , 4 , 5 , 6 } so that identical digits are not in consecutive positions?
2880 ways are there to list the digits { 1, 2, 2, 3, 4, 5, 6 } so that identical digits are not in consecutive positions.
The list of the digits is: { 1, 2, 2, 3, 4, 5, 6 }
Here we have to determine how many ways are there to list the digits { 1, 2, 2, 3, 4, 5, 6 } so that identical digits are not in consecutive positions
We have one number in consecutive positions in this question
That is: (2, 2)
Number of ways that (2,2) are in consecutive positions = [tex]$\frac{6!}{2!}[/tex] = 360
The permutation of 1, (2, 2), 3, 4, 5, 6 = 6!
6! = 720
To get the total number of permutations
= [tex]$\frac{7!}{2!}[/tex]
= [tex]$\frac{5040}{2}[/tex]
= 2520
The number of ways that 2 identical digits are not consecutively positioned
= 2520 - 360 + 720
= 2880
There are 2880 ways to list the digits { 1, 2, 2, 3, 4, 5, 6 }.
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