The correct option is D. Inequality. The expression -9 > 2x is an inequality, meaning it shows a relationship between two values that are not necessarily equal.
In this case, it indicates that -9 is greater than 2 times x. To solve the inequality, we would need to isolate x on one side of the inequality symbol. We can start by dividing both sides by 2, which gives us -4.5 > x. This means that any value of x that is less than -4.5 would satisfy the inequality. Therefore, the solution set for this inequality is all real numbers less than -4.5.
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Full question:
Which word BEST describes 9(2x+6y)
A Constant
B. Equation
c. Expression
D. Inequality
What is the x-coordinate of the midpoint of line segment AB with points A(21, 5) and B(-9, -13).
Answer:
6
Step-by-step explanation:
You want the x-coordinate of the midpoint of segment AB with endpoint coordinates A(21, 5) and B(-9, -13).
MidpointThe midpoint of a line segment has coordinates that are the average of the endpoint coordinates:
M = (A +B)/2
M = ((21, 5) +(-9, -13))/2 = (12, -8)/2
M = (6, -4)
The midpoint of AB is (6, -4).
The x-coordinate of the midpoint is 6.
A square on the coordinate plane has vertices at (−5, 5), (5, 5), (5, −5), and (−5, −5). A dilation of the square has vertices at (−10, 10), (10, 10), (10, −10), and (−10, −10). Find the scale factor and the perimeter of each square
the perimeter of the original square is 40 units, and the perimeter of the dilated square is 80 units.
To find the scale factor of the dilation, we can compare the corresponding side lengths of the two squares. The distance between the points (-5,5) and (5,5) is 10 units, which is also the length of the side of the original square. The distance between the points (-10,10) and (10,10) is 20 units, which is the length of the side of the dilated square. Therefore, the scale factor is:
Scale factor = Length of dilated square side / Length of original square side = 20 / 10 = 2
This means that the dilated square is twice as large as the original square.
To find the perimeter of the original square, we can add up the length of each side. Each side of the square has a length of 10 units, so the perimeter is:
Perimeter of original square = 4 × length of one side = 4 × 10 = 40 units
To find the perimeter of the dilated square, we can use the same method. Each side of the dilated square has a length of 20 units, so the perimeter is:
Perimeter of dilated square = 4 × length of one side = 4 × 20 = 80 units
Therefore, the perimeter of the original square is 40 units, and the perimeter of the dilated square is 80 units.
Dilation is a transformation that changes the size of an object but leaves its shape unchanged. In this case, the dilation of the square resulted in a larger square that was similar to the original square, meaning that the corresponding angles in the two squares were equal. The scale factor of the dilation determined the ratio of the side lengths of the two squares, and the perimeter of each square was proportional to its side length. Dilations are used in geometry to create similar figures and to scale up or down an object in size.
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−
2
x
+
2
y
=
8
6
x
+
y
=
11
If
(
x
,
y
)
is the solution to the system of equations above, what is the value of
7
y
?
Answer:
7y=-91
Step-by-step explanation:
-2x + 2y = 8 (multiply the second equation by 2)
12x + 2y = 22
Adding the two equations, we get:
10x = 30
Therefore, x = 3.
Substituting x = 3 into the second equation, we get:
6(3) + y = 11
Simplifying, we get:
y = -13
Finally, we can find the value of 7y:
7y = 7(-13) = -91
Graph f(x) = -x. Click on the graph until the graph of f(x) = -x appears.
The graph of f(x) = -x is attached.
What is the x-intercept?The intersection of a function or equation's graph with the x axis is known as the x intercept. This can be compared to a point having a value of 0.
For any given curve, the x-intercept is a coordinate that is plotted on the x-axis. To put it another way, the x-intercept is the value of the x coordinate at the point where the graph crosses the x-axis, or we can say that it is the value of the x coordinate at a point where the value of the y coordinate equals zero.
f(x) = -x ----------(1)
Equation (1) can be written as f(x) = -x+0
This is in the form of f(x)=mx+b,
where , m= -1, b=0
this represents a line
Find the x and y-intercepts: ( consider f(x)=y)
Find x-intercept when y=0
=> 0=-x
=> x=0
Thus, x-intercept is (0,0)
Find y-intercept when x=0
=> y=-0 = 0
Thus, y-intercept is (0,0)
We need another point, because both intercepts are same
When x= 1, y= -1
The point is (1,-1)
Plot these points and join them with a line.
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Complete Question:
Which of the following is the graph of f(x) = x2?
Click on the graph until the correct graph appears.
Eighteen individuals are scheduled to take a driving test at a particular DMV office on a certain day, eight of whom will be taking the test for the first time. Suppose that six of these individuals are randomly assigned to a particular examiner, and let X be the number among the six who are taking the test for the first time. a. What kind of a distribution does X have (name and values of all parameters)?
b. Compute c. Calculate the mean value and standard deviation of X.
The distribution of X is a hypergeometric distribution, he probability that exactly 2 of the 6 individuals assigned to the examiner are taking the test for the first time is 0.317 and the mean value of hypergeometric distribution is 1.187.
a. The distribution of X is a hypergeometric distribution with the following parameters:
N = 18 (total number of individuals)
K = 8 (number of individuals taking the test for the first time)
n = 6 (number of individuals randomly assigned to a particular examiner)
b. The probability mass function of a hypergeometric distribution is given by:
P(X = x) = (K choose x) * ((N-K) choose (n-x)) / (N choose n)
So, for example, the probability that exactly 2 of the 6 individuals assigned to the examiner are taking the test for the first time is:
P(X = 2) = (8 choose 2) * (10 choose 4) / (18 choose 6) = 28 * 210 / 18564 = 0.317
c. The mean value of a hypergeometric distribution is given by:
E(X) = n * (K/N) = 6 * (8/18) = 2.667
The standard deviation of a hypergeometric distribution is given by:
SD(X) = sqrt(n * (K/N) * ((N-K)/N) * ((N-n)/(N-1))) = sqrt(6 * (8/18) * (10/18) * (12/17)) = 1.187
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MNPQ is a rectangle. Find the value of x.
*
Trey and matt each have a rectangular prism the base if treys is 4 by 7 by 12 the base of matts prism is 6 by 10 by 3 whose rectangular prism will require more material to construct
Trey's rectangular prism will require more material to be constructed.
To determine which rectangular prism will require more material to construct, we need to calculate the surface area of each prism.
The surface area of a rectangular prism is given by the formula,
SA = 2×l×w + 2×l×h + 2×w×h
where l, w, and h are the length, width, and height of the prism, respectively.
For Trey's prism, the length is 12, the width is 7, and the height is 4. Therefore, the surface area of Trey's prism is:
SA of Trey = 2(12 x 7) + 2(12 x 4) + 2(7 x 4) = 336
For Matt's prism, the length is 10, the width is 6, and the height is 3. Therefore, the surface area of Matt's prism is,
SA of Matt = 2(10 x 6) + 2(10 x 3) + 2(6 x 3) = 192
Comparing the surface areas, we see that Trey's prism requires more material to construct since its surface area is larger than Matt's prism. Therefore, Trey's rectangular prism requires more material to construct than Matt's rectangular prism.
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In the table below, find the slope, y-intercept, and equation for each racer.
Hint: Time is going to be your independent x / the x-axis. Distance is going to be your dependent y / the y-axis.
Therefore , the solution of the given problem of slope comes out to be y = 15x + 10.
Explain slope.A line's steepness is determined by its slope. In gradient based equations, a situation known as gradient overflow can happen. One can determine the slope by dividing the sum of a run (width differential) and rise (climbing distinction) between two places. The equation with the hill variation, y = mx + b, is used to model the fixed path issue. where grade is mm, a = bc, and the line's y-intercept is situated; (0, b).
Here,
A racer:
Due to the fact that the race begins at the beginning, the y-intercept
is 0.
We can select any two locations from the table and use the following formula to determine the slope:
=> Slope Equals (Distance Change) / (change in time)
As an illustration, if we select the coordinates (1, 10) and (3, 40), we obtain:
=> slope = (40 - 10) / (3 - 1) = 30 / 2 = 15
As a result, Racer A's calculation is:
=> y = 15x
Runner B:
As an illustration, if we select the coordinates (1, 25) and (3, 55), we obtain:
=> slope = (55 - 25) / (3 - 1) = 30 / 2 = 15
As a result, Racer B's calculation is:
=> y = 15x + 20
Runner B
The race begins at a distance of 10 feet, so the y-intercept is 10.
We can select any two locations from the table and use the following formula to determine the slope:
Slope Equals (Distance Change) / (change in time)
As an illustration, if we select the coordinates (1, 35) and (3, 65), we obtain:
=> slope = (65 - 35) / (3 - 1) = 30 / 2 = 15
As a result, Racer C's equation is:
=> y = 15x + 10
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URGENT!!
3. Suppose ABC=EFG, and EG=7x-11, AB 5x -9. GF=3x-1 and AC=2x+4 . Find the value of x and the lengths of the sides of EFG.
Part I: Sketch the triangles below.
Part II: Use measures for AC and EG to find the value of x. Show your work.
Part III: Find the lengths of the sides of EFG. Show your work.
Part IV: Explain how to find the lengths of the sides of ABC.
Part II: Value of x=0
Part III: the lengths of the sides of EFG as EF = G = 11 and EG = -11.
Part IV: the lengths of the sides of ABC as AB = -9, GF = -1, and AC = 4.
What is value?Value can be used to find the solution to an equation or to compare two or more values.
Part II: To find the value of x, we need to use measures for AC and EG. We can use the equation AC = 2x + 4 to solve for x.
We can rearrange the equation to 2x = AC - 4, and then substitute in the value of AC, which is 2x + 4.
This gives us 2x = 2x + 4 - 4, or 0 = 0
x = 0.
Part III: To find the lengths of the sides of EFG, we can use the equation EF = G + 7x - 11.
Substituting in the value of x, which is 0, we get
EF = G + 7 * 0 - 11,
or EF = G - 11.
Since EG = 7x - 11, substituting in the value of x gives us
EG = 7 * 0 - 11,
or EG = -11.
So EF = G and EG = -11
Part IV: To find the lengths of the sides of ABC, we can use the equation AB = 5x - 9, substituting in the value of x as 0.
This gives us AB = 5 * 0 - 9,
or AB = -9.
Since GF = 3x - 1 and AC = 2x + 4, substituting in the value of x gives us GF = 3 * 0 - 1,
or GF = -1,
and AC = 2 * 0 + 4
or AC = 4.
So AB = -9, GF = -1, and AC = 4, giving us the lengths of the sides of ABC as AB = -9, GF = -1, and AC = 4.
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ALGEBRA 2 HELP
(Please show work!)
A student wrote the arithmetic series 8 + 11 + ... + 29 in summation notation as (picture below)
a. Describe and correct the error in the notation.
b. Evaluate the corrected summation of the arithmetic series above.
[tex]S_8=[/tex]
c. Write the explicit and recursive formulas for the arithmetic series above,
Explicit:
[tex]a_n=[/tex]
Recursive:
If [tex]a_1=[/tex]
Then for n > 1
[tex]a_n=[/tex]
Step-by-step explanation:
ALGEBRA 2 HELP
(Please show work!)
A student wrote the arithmetic series 8 + 11 + ... + 29 in summation notation as (picture below)
a. Describe and correct the error in the notation.
b. Evaluate the corrected summation of the arithmetic series above.
�
8
=
S
8
=
c. Write the explicit and recursive formulas for the arithmetic series above,
Explicit:
�
�
=
a
n
=
Recursive:
If
�
1
=
a
1
=
Then for n > 1
�
�
=
a
n
=
Find the Primeter and area
For rectangle type books, the difference in the heights of their stacks of books is 15 3/4 inches.
What exactly is a rectangle?
A rectangle is a type of quadrilateral (a four-sided polygon) that has four straight sides and four right angles. It is a two-dimensional shape, meaning it lies flat in a plane, and is defined by its two sets of parallel sides, each pair of which are equal in length.
In a rectangle, opposite sides are parallel and congruent (equal in length), and adjacent sides are perpendicular (meet at a right angle). The diagonals of a rectangle bisect each other (divide each other into two equal parts) and are congruent.
The area of a rectangle is calculated by multiplying its length and width, while its perimeter is found by adding the lengths of all its sides. The area of a rectangle is A = l x w, where A is the area, l is the length, and w is the width.
Now,
To solve this problem, we need to first find out the height of Rick's stack of books. We know that his stack is 3 times as tall as Trevor's stack, so:
Rick's stack = 3 x Trevor's stack
Rick's stack = 3 x 7 7/8 inches
Rick's stack = 23 5/8 inches
Now that we know the height of both stacks, we can find the difference between them:
Difference = Rick's stack - Trevor's stack
Difference = 23 5/8 inches - 7 7/8 inches
Difference = 15 6/8 inches
Difference = 15 3/4 inches
Therefore, the difference in the heights of their stacks of books is 15 3/4 inches.
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Q27) A retailer receives some products from three suppliers - $1, S2 and S3. The probability of successfully delivering the products in time by the suppliers are 0.85 for S1, 0.82 for S2 and 0.91 for S3. No supplier's delivery is impacted by any other supplier's delivery. The manufacturer orders 500 units of a raw material from $1, 120 units from S2 and 156 units from S3. What is the expected loss for the retailer given that failure to receive the materials in time will cost the manufacturer $20 per unit for the product supplied by $1, $30 for the product supplied by 52 and $10 for the product supplied by S3.
Expected loss for the retailer is $2288.4
There are three suppliers named S1, S2, and S3 who provide raw materials to a retailer. The probability of supplying the raw materials on time for S1, S2, and S3 are 0.85, 0.82, and 0.91 respectively. Let’s suppose that the retailer orders 500 units of raw material from S1, 120 units from S2, and 156 units from S3. The loss for the retailer is $20, $30, and $10 respectively for S1, S2, and S3. To find out the expected loss for the retailer, we can use the formula given below:Expected loss = (probability of loss) × (value of loss) + (probability of no loss) × (value of no loss)Let’s calculate the expected loss for each supplier separately.Supplier S1: The probability of not receiving raw material on time from S1 is 1 - 0.85 = 0.15. The expected loss due to S1 can be calculated as follows:Expected loss for S1 = (0.15) × (500 units) × ($20 per unit) = $1500Supplier S2: The probability of not receiving raw material on time from S2 is 1 - 0.82 = 0.18. The expected loss due to S2 can be calculated as follows:Expected loss for S2 = (0.18) × (120 units) × ($30 per unit) = $648Supplier S3: The probability of not receiving raw material on time from S3 is 1 - 0.91 = 0.09. The expected loss due to S3 can be calculated as follows:Expected loss for S3 = (0.09) × (156 units) × ($10 per unit) = $140.4Therefore, the total expected loss for the retailer can be calculated by adding the losses from all three suppliers.Total expected loss = $1500 + $648 + $140.4 = $2288.4Thus, the expected loss for the retailer is $2288.4.
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Giving Brainliest!!!
Answer:294
Step-by-step explanation:
Answer:
[tex]294m^2[/tex]
Step-by-step explanation:
Volume of a cube is side x side x side or [tex]s^3[/tex]
now we find the value of one side
[tex]s^3 = 343m^3\\s = \sqrt[3]{343m^3} \\s = 7m\\[/tex]
Now we have a side value we can find the surface area of this cube which is
Surface area = [tex]6 * s^2[/tex]
= [tex]6 * (7m)^2[/tex]
= [tex]6 * 49m^2[/tex]
= [tex]294 m^2[/tex]
Hope this helps!
Brainliest and a like is much appreciated!
enter your answer and show all the steps that you use to solve this in the space provided.
find the surface area of the cone. Use 3.14 for π height 7in diameter 8in and below it says drawing not to scale??
The surface area of the cone is 305.30 inches squared.
How to find the surface area of a cone?The height of the cone is 7 inches and the diameter of the cone is 8 inches. Therefore, let's find the surface area of the cone as follows:
surface area of the cone = πr(r + l)
where
r = radiusl = slant heightHence,
r = 8 / 2 = 4 inches
l² = 7² + 4²
l = √49 + 16
l = √65
l = 8.0622577483
l = 8.06 inches
Therefore,
surface area of the cone = 3.14 × 8.06(4 + 8.06)
surface area of the cone = 25.3154893297(12.06)
surface area of the cone = 305.304801316
surface area of the cone = 305.30 inches squared
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These triangles are similar. I need to know what x is.
The value of x as per the similarity of triangles is = 7.1.
What is similarity of triangles?If two triangles' sides have the same ratio or proportion and their angles are the same (corresponding angles), then the triangles will resemble one another (corresponding sides).
Similar triangles may have varied side lengths when compared individually, but they must all have the same ratio of their side lengths and equal angles.
Now in the figure, the triangles are similar.
So, sides of the triangles will be proportional to each other.
Now, 9/15 = 4.3/x
⇒ x = (4.3 × 15)/ 9
⇒ x = 7.1
Therefore, the value of x as per the similarity of triangles is = 7.1.
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*See image *The number of foxes in a forest increases
by 20% each year.
This year, there are 500 foxes in the
forest.
Calculate the number of foxes that there
will be in the forest
a) after 1 year.
b) after 2 years.
Answer:
a) 600 foxes
b) 720 foxes
Step-by-step explanation:
See attached spreadsheet.
The rate of population increase is 20% each year. To find a new year's population, multiply the previous year's population by 0.20 (20%) and add that to the previous year. Year 1 would be (500)*(0.20) = 100 new foxes which are added to the year 0 population of 500, which means there are (500+100) or 600 foxes in year 1.
Year 2: (0.20)*(600) = 120 new foxes
Add 120 to the existing 600 to find 720 foxes in year 2,
============
A formula that can be used to predict the fox population for any year, n, would be:
P(n) = 500*(1+0.20)^n
where P(n) is the popluation at year n. The 500 is the population at year 0 (the starting population). (1+0.20) is the growth for each year (120%, which means the original population plus 20%). That is raised to the year of interest, n. [When n=0, (1+0.20)^0 = 1]
When women were allowed to become pilots of fighter jets, engineers needed to redesign the ejection seats because they had been originally designed for men only. The ACES-II ejection seats were designed for men weighing between 140LB and 211LB. Weights of women are now normally distributed with a mean of 165LB and a standard deviation of 45.6LB
a. If 1 woman is randomly selected, find the probability that her weight is between 140LB and 211LB
b. If 36 different women are randomly selected, find the probability that their mean weight is between 140LB and 211LB
The probability that the mean weight of 36 different women is between 140LB and 211LB is approximately 0.9874.
Is it possible for a random variable to have 0 probability across the board?There can only be one value for a random variable. A random variable's value could be zero with a probability of zero. A probability distribution's total probabilities are always equal to one.
a. We must convert the weight to a typical normal distribution using the following formula in order to determine the likelihood that a randomly chosen woman weighs between 140LB and 211LB.
z = (x - μ) / σ
If the weight x, the mean weight, and the standard deviation are all given. The probability can then be determined using a calculator or a typical normal table.
When x=140LB, we get:
z = (140 - 165) / 45.6 = -0.5461
x = 211LB results in:
z = (211 - 165) / 45.6 = 1.0096
The area under the standard normal curve between z = -0.5461 and z = 1.0096 is found to be roughly 0.6267 using a typical normal table or calculator.
Hence, the likelihood that a lady chosen at random weighs between 140LB and 211LB is roughly 0.6267.
b. We must normalise the sample mean to a standard normal distribution using the following method in order to determine the likelihood that the mean weight of 36 individual women is between 140LB and 211LB.
z is equal to (x - ) / (n / sqrt(n)).
When n is the sample size, x is the sample mean weight, is the mean weight, and is the standard deviation. The probability can then be determined using a calculator or a typical normal table.
To solve this issue, we have:
μ = 165LB
σ = 45.6LB
n = 36
If x = 140 LB, we get:
z = (140 - 165) / (45.6 / sqrt(36)) = -2.4994
With x = 211LB, we get:
z = (211 - 165) / (45.6 / sqrt(36)) = 2.4994
The area under the standard normal curve between z = -2.4994 and z = 2.4994 is found to be around 0.9874 using a standard normal table or calculator.
Hence, there is a roughly 0.9874 percent chance that the average weight of 36 individual women falls between 140LB and 211LB.
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Do what the picture says and right answer gets brainilest!!!
Answer:
Below
Step-by-step explanation:
See image attached
5(x-y)+4=7 what is the value of x-y
Step-by-step explanation:
We can solve for x-y by isolating the term on one side of the equation and simplifying:
5(x-y) + 4 = 7
5(x-y) = 7 - 4
5(x-y) = 3
Next, we can divide both sides by 5:
x - y = 3/5
Therefore, the value of x-y is 3/5.
A bank offers two interest account plans. Plan A gives you 6% interest compounded annually. Plan B gives you 13% annual simple interest. You plan to invest $2,000 for the next 4 years. Which account earns you the most interest (in dollars) after 4 years? How much will you have earned?
Answer:
Plan A
The formula is
A=p (1+r)^t
A=2,000×(1+0.06)^(4)
A=2,524.95 ( future value )
Interest earned=A-p
Interest earned=2524.95-2000
Interest earned=524.95
Plan B
Use the simple interest formula
I=prt
I interest earned?
P principle 2000
R interest rate 0.13
T time 4years
I=2,000×0.13×4
I=1,040
The Answer is
Plan B; $1,040
Step-by-step explanation:
Find the probability of obtaining exactly four tails when flipping four coins. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth
The probability of obtaining exactly four tails {( T,T,T,T)}, when flipping four coins is equals to the 1/16 = 0.0625.
Independent Events : If the result of one event does not influence the result of another event, then the events are referred to as independent. In other words, it can be said that both events can happen simultaneously without interference. Probability is defined as a chance of occurrence of an event. Let E be the event that exactly four tails when flipping four coins. As we know that, when One coin is flip, total outcomes = 2 = { H,T}
So, 4 coins flipped, total possible outcomes = 16
Probability of getting tail on flipping one coin = 1/2
That is exactly four tails when flipping four coins are independent events. Therefore, the probability of obtaining four tails in a row in 4 flips of a coin is the product of probability in 4 flips. Since each flipping of a coin is independent, so
the probability of obtaining exactly four tails when flipping four coins = P(X = 4)
=( 1/2)(1/2)(1/2)(1/2) = (1/2)⁴
= 0.0625
Hence, required probability is 0.0625.
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What point on the number line is one fourth of the way from the point 0 to the point −3? −0.25 −0.5 −0.75 −1
Answer: 0.75
Step-by-step explanation: Hope this helps :D
Answer: -0.75
Step-by-step explanation:
1/4th of the way to point 0,-3 from 0
-3/4=-0.75, therefore, the answer is C, -0.75.
Hi. I need to know the answer because one of my friends wanted to know the answer and I knew the answer, but not how to explain it well enough: Adrienne and Evelyn have a pet cat. When they got it as a kitten, as much as it it weighed 0.6 kilograms. Now it weighs 7.3 times did when it was a kitten. How much does their cat weigh now?
So their cat weighs 4.38 kilograms now.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.
Algebraic expressions can take many different forms, but some common examples include:
3x + 7
2a^2 + 5ab - 3b^2
(x + 2)(x - 5)
4x^2 - 9.
Let's start by figuring out how much the cat weighs now. We know that the cat weighs 7.3 times what it did when it was a kitten, and it weighed 0.6 kilograms when it was a kitten.
To find out how much the cat weighs now, we can multiply its original weight by 7.3:
0.6 kilograms x 7.3 = 4.38 kilograms
Therefore, So their cat weighs 4.38 kilograms now.
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Mrs. Smitherman is coordinating the third- and fourth-grade program. She wishes to arrange the children to the fewest number of rows that contain the same number of children. She also does not wish to mix be classes within a row. If there are 60 third graders and 48 fourth graders, how many children should be aced in each row? How many rows will be needed?
Answer:
Number of students in each row = 12
Total number of rows = 9
Step-by-step explanation:
We have to assume that each row can seat the same number of students
Find the GCF(greatest common factor) of 60 and 48 to find the number of students in each row
60 = 12 x 5
48 = 12 x 4
The GCF = 12
So there are 12 students per row
If there are 60 third-grade students they will occupy 60/12 = 5 rows
48 fourth grade students will occupy 48/12 = 4 rows
Therefore the total number of rows = 5 + 4 = 9 rows
(x + 2y ) 2 some one answer this please I need help
Answer:
x² + 4xy + 4y²
Step-by-step explanation:
(x + 2y )²
= (x + 2y) (x + 2y)
= x² + 2xy + 2xy + 4y²
= x² + 4xy + 4y²
So, the answer is x² + 4xy + 4y²
help please i really appreciate it
Answer:
B
Step-by-step explanation:
for the next olympic winter games, the organizers wish to expand the number of teams competing in curling. they wish to have teams enter, divided into two pools of seven teams each. right now, they're thinking of requiring that in preliminary play each team will play seven games against distinct opponents. five of the opponents will come from their own pool and two of the opponents will come from the other pool. they're having trouble setting up such a schedule, so they've come to you. by using an appropriate graph-theoretic model, either argue that they cannot use their current plan or devise a way for them to do so.
The organizers can use their current plan and have each team play 7 games against distinct opponents, with 5 of the opponents from their own pool and 2 of the opponents from the other pool.
To answer this question, we can use a bipartite graph as a model. A bipartite graph is a graph that has two sets of vertices, X and Y, with edges only between vertices from different sets. In this case, we can have one set of vertices representing the teams in one pool and the other set of vertices representing the teams in the other pool.
We can start by drawing a bipartite graph with 14 vertices, 7 in each set. Each vertex represents a team, and we can label them as T1, T2, ..., T14. Now, we need to add edges to represent the games that each team will play.
For each team in one pool, we can add 5 edges to connect it to 5 different teams in the same pool, and 2 edges to connect it to 2 different teams in the other pool.
After adding all the edges, we can see that each team has 7 edges connected to it, representing the 7 games that it will play. However, we also need to make sure that each team plays against distinct opponents. To do this, we can check if there are any duplicate edges in the graph.
If there are no duplicate edges, then the schedule can be used as it is. But if there are duplicate edges, then the schedule cannot be used and the organizers need to come up with a different plan.
In this case, we can see that there are no duplicate edges in the graph, which means that the schedule can be used as it is. Therefore, the organizers can use their current plan and have each team play 7 games against distinct opponents, with 5 of the opponents from their own pool and 2 of the opponents from the other pool.
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HEELLPPPP!!!! quickly im being timed.
A curve has the equation y= x² + ax + b, where a and b are numbers. The turning point of the curve is (5, 4). Work out the values of a and b.
The values of a and b are -10 and 29, respectively of the curve.
What do you mean by turning point of a quadratic curve ?
The turning point of a quadratic curve is the point at which the curve changes direction from going up to going down, or vice versa. It is also known as the vertex of the parabola. The x-coordinate of the turning point is given by -b/2a, and the y-coordinate is the value of the function at that point.
Finding the values of a and b :
Given that the turning point of the curve is (5,4), we can write the following equations:
[tex]4 = 5^2 + 5a + b[/tex] (since the turning point lies on the curve)
[tex]0 = 2(5) + a[/tex] (since the derivative of the curve at the turning point is 0)
Simplifying the second equation gives us:
[tex]a = -10[/tex]
Substituting this value of a in the first equation, we get:
[tex]4 = 5^2 - 50 + b[/tex]
[tex]b = 29[/tex]
Therefore, the values of a and b are -10 and 29, respectively.
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PLEASE HELPP!!
Given the Following hexagon
Calculate the missing angles.