The probability that a student who has skipped many classes has a GPA less than 2.0 is 0.5.
To calculate this probability, we can use the data from the table given. If a student has skipped many classes, they are in the "Many Skips" category. From the table, we can see that there are 200 students in the "Many Skips" category and 100 of them have a GPA of less than 2.0. Therefore, the probability of a student with many skips having a GPA less than 2.0 is given by:
P(GPA < 2.0 | Many Skips) = 100/200 = 0.5
This means that if we randomly select a student who has skipped many classes, there is a 50% chance that their GPA will be less than 2.0. This calculation provides insight into the relationship between attendance and GPA, and it suggests that skipping many classes is associated with a lower GPA.
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At 6 a.m., the temperature was 50°F. For the next 4 hours, the temperature rose 3° per hour. The next 6
hours, it rose 2° per hour. The temperature then stayed steady until 6 p.m. For the next 2 hours, the
temperature dropped 1° per hour. The temperature then dropped steadily until the temperature was 56°F at
midnight. On the set of axes below, graph Elroy's data.
Temperature (°F)
70-
60-
4+2=4
6*2=12
6×2=0
The graph of the problem depicts the rate of the temperature change.
How to graph the temperature change?To graph temperature change, you can use a line graph. The horizontal axis represents time, while the vertical axis represents temperature. You plot points on the graph corresponding to the recorded temperature at specific times, and then connect the points to form a line.
The slope of the line represents the rate of temperature change, with a steep line indicating a rapid increase or decrease in temperature and a gentle slope indicating a slow change. The line graph helps to visually represent changes in temperature over time and can be used to analyze patterns and trends.
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Determine whether each sequence is arithmetic, geometric, or neither. Find tn.
-k^2-k+1,k+2,k^2+3k+3,2k^2+5k+4,...
The given assertion states that the sequence's nth element is -k² + (2n-3)k + 1.
What are some examples of consecutive terms?Sequential is a derivative of the Latin word consecutus, which means "following closely" without a pause. Similar to those snowstorms, which occurred back-to-back each day for five months in a succession. Additionally, consecutive numbers progress in the correct sequence or follow one another. For instance, the numerals 5, 6, 7, 8, 9, and 10 follow one another.
Looking at the differences between consecutive terms, we have:
(k+2) - (-k²-k+1) = k²+3k+3 - (k+2) = k²+2k+1 = (k+1)²
(k²+3k+3) - (k+2) = k²+2k+1 = (k+1)²
(2k²+5k+4) - (k²+3k+3) = k²+2k+1 = (k+1)²
We can see that the differences between consecutive terms are all the same, which means that the sequence is an arithmetic sequence.
To find tₙ, we need to find the common difference d. From the differences above, we have:
d = (k+1)² - (k²+k-1) = 2k
So, the nth term of the sequence is given by:
tₙ = t₁ + (n-1)d
tₙ = (-k²-k+1) + (n-1)(2k)
tₙ = -k²-k+1 + 2nk - 2k
tₙ = -k² + (2n-3)k + 1
Therefore, the nth term of the sequence is -k² + (2n-3)k + 1.
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The figure below was made with a scale of 1 unit=4ft. Draw the figure with a new scale of 1 unit=8ft. 1 unit=4fr looks like a rectangular so what woyld it look like if it was 1 unite=8ft
The new diagram with a scale factor of 1 unit = 8 feet will look the same
as each new grid now represents 8 feet.
What is a scale factor?The scale factor defines a variable in a ratio of two different measurements.
Sometimes drawings of large models are represented in a scale factor of a smaller unit.
Given, A drawing represented by a scale factor of 1 unit = 4ft,
Where every grid unit represents 4 ft.
The new drawing model will look exactly the same as now each grid unit represents 8 feet.
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Find the area of the region bounded by the line y=3x-6 and line y=-2x+8.
D: the line x=5
The area of the region bounded by the two lines is 19 square units.
How to calculate?The two lines intersect at the point where they have the same
y-coordinate, so we can set y=3x-6 equal to y=-2x+8 and solve for x:
3x - 6 = -2x + 8
5x = 14
x = 2.8
Therefore the two lines intersect at x=2.8, and the corresponding y-coordinate is y = 3(2.8) - 6 = 6.4.
We can find the coordinates of the two other corners of the region by setting x=0 and x=5:
x=0: y = 3(0) - 6 = -6
x=5: y = 3(5) - 6 = 13
So the other two points are (0, -6) and (5, 13).
We will use the Shoelace Theorem to find the area:
A = 1/2 * |(0 * 6.4) + (2.8 * 13) + (5 * -6) - (6.4 * 5) - (13 * 2.8) - (-6 * 0)|
A = 1/2 * |(0 * 6.4) + (37.4) + (30) - (32) - (36.4) - 0|
A = 1/2 * |37.4 + 30 - 32 - 36.4|
A = 1/2 * |38| = 19
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Answer:
Step-by-step explanation:
In how many ways can the seven members of a students’ council pose in a line for a yearbook photograph if the chair and vice-chair must be side by side?
Answer:
The number of ways the 7 members of the student council can pose in a line for a yearbook photograph if the chair and vice-chair must be side by side is 6!.
To see why, consider the first 6 members as a group. They can be arranged in 6! ways, since they are interchangeable. Then, the chair and vice-chair must be positioned together in the first two spots, which is only one way. So, the total number of arrangements is 6! * 1 = 720 ways.
can give brainliest if this helps ;)
Answer:
1440
Step-by-step explanation:
We should first count the chair and vice-chair as one unit i.e. one person since they have to be seated together
This means there are 6 items effectively and these 6 items can be arranged in 6! ways
6! = 720 ways
But there is more....
The chair and vice-chair have to sit together but they can sit together in two different ways:
Chair can be on the left, vice-chair can be on the right
or
Chair can be on the right, vice-chair can be on the left
So for each of the 6! combinations there are 2 ways of seating the chair and vice-chair together
Total number of ways = 6! x 2
= 720 x 2 = 1440
solve the question
in a group of 65 students 40students want to be a doctor and 20 wants to be a social worker. the number of students who want to be a doctor only and the student who wants to be a social worker only are in the ratio 3:1 by drawing venn diagram find.
1)how many students want to both?
2)how many want to be both?
Answer:To find the number of students who want to be both a doctor and a social worker, we can use the Principle of Inclusion-Exclusion (PIE). This principle states that the total number of elements in the union of two sets is equal to the sum of the number of elements in each set minus the number of elements in their intersection.
So, the number of students who want to be both a doctor and a social worker can be calculated as:
|Doctor ∩ Social worker| = |Doctor| + |Social worker| - |Doctor U Social worker|
|Doctor ∩ Social worker| = 40 + 20 - 65
|Doctor ∩ Social worker| = -5
However, this result is negative which is not possible, therefore, no students want to be both a doctor and a social worker.
To find the number of students who want to be both, we have to find the number of students who want to be both a doctor and a social worker which is 0 in this case.
Step-by-step explanation:
A theatre has n rows and m seats in each row. How many seats are in the theatre
The number of seats in the front row can be represented as: s = x - (n - 1) * (2y / n - x) / (n - 1) = x - (2y - nx) / n
Let's call the number of seats in the first row "s". Then, the number of seats in the second row is s + d, the number of seats in the third row is s + 2d, and so on. The total number of seats in the theater can be represented as:
s + (s + d) + (s + 2d) + ... + (s + (n - 1)d) = y
Expanding this equation and combining like terms, we get:
ns + (d * (n - 1) * n) / 2 = y
Now that we have an equation for the total number of seats in terms of n, d, and y, we can use the number of seats in the last row to solve for s, the number of seats in the first row:
s + (n - 1)d = x
ns + (d * (n - 1) * n) / 2 = y
Solving for s in terms of n, x, and y:
s = x - (n - 1)d
ns + (d * (n - 1) * n) / 2 = y
Substituting this expression for s into the equation for the total number of seats:
(x - (n - 1)d) + (d * (n - 1) * n) / 2 = y
Expanding and solving for d:
x + (n - 1)d = 2y / n
d = (2y / n - x) / (n - 1)
Finally, substituting this expression for d back into the equation for s:
s = x - (n - 1) * (2y / n - x) / (n - 1)
So the number of seats in the front row can be represented as:
s = x - (n - 1) * (2y / n - x) / (n - 1)
= x - (2y - nx) / n
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The complete question is:
A theater has n rows of seats, and each row has d more seats than the row in front of it. There are x seats in the last (nth) row and a total of y seats in the entire theater. How many seats are in the front row of the theater? Write your answer in terms of n, x, and y.
Y’all care to assist me lol?!
Answer:
Step-by-step explanation:
I gotchu.
Area is piR^2
= pi(70squared)
= 15393.804
Circumference is 2piR
= 2pi(70)
= 493.82
Tanner collected 360 cans. This was 40% of what Reggie collected. How many cans did Reggie collect?
Answer:
Step-by-step explanation:
Let's call the number of cans Reggie collected as "x".
According to the problem, Tanner collected 360 cans, which was 40% of what Reggie collected, so:
360 = 40/100 * x
To find the value of x, we can isolate x by dividing both sides by 40/100:
x = 360 * 100/40
x = 900
So Reggie collected 900 cans.
Answer:
900 cans
Step-by-step explanation:
We know
360 cans = 40%
We have to find 1% by taking
360 divided by 40 = 9 cans
How many cans did Reggie collect?
We take
9 x 100 = 900 cans
PLSSSS HELP IF YOU TURLY KNOW THISSS
Answer:
12
Step-by-step explanation:
[tex]\dfrac{x}{4} + 17 = 20\\\dfrac{x}{4} = 20 - 17\\\dfrac{x}{4} = 3\\x = 4 \cdot \;3 \\\\x = 12[/tex]
Answer:
x = 12
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ (x/4) + 17 = 20
Then the value of x will be,
→ (x/4) + 17 = 20
→ x/4 = 20 - 17
→ x/4 = 3
→ x = 3 × 4
→ [ x = 12 ]
Hence, the value of x is 12.
An artist plans to sell $250 of prints online each week. This week, she is within $25 of her goal. Part A: Define a variable and write an absolute value equation to represent the scenario. (4 points) Part B: Solve the equation, showing all steps. (4 points) Part C: What are the minimum and maximum amounts that the artist received for her products? (2 points)
The artist reportedly got $225 or $275 for her paintings this week, depending on the statement provided.
Using an example, describe the scenario?We might, for instance, move to the city. Most likely, he will start classes again in the fall. If we could finish the job by tomorrow, that would be perfect. In the worst-case scenario, we would have to commence the project over.
Let x become the sum the artist got this week for her works in Part A.. The situation is represented by the absolute value equation:
|250 - x| = 25
Part B: To solve the equation, we can split it into two cases:
Case 1: 250 - x = 25
Solving for x, we get:
x = 250 - 25 = 225
Case 2: 250 - x = -25
Solving for x, we get:
x = 250 + 25 = 275
Therefore, the artist received either $225 or $275 for her prints this week.
Part C: The minimum amount the artist received is $225, which is $25 less than her goal of $250. The maximum amount the artist received is $275, which is $25 more than her goal of $250.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Find the volume of the cylinder. Use 3.14 for T.
(E
34 m
drawing not to scale
27 m
The volume of the cylinder is approximately 6058.73 cubic meters.
Describe Cylinder?A cylinder is a three-dimensional geometric shape that is similar to a tube. It has two parallel bases that are circular in shape, and its lateral surface is a rectangle. The height of the cylinder is the distance between the two bases. The cylinder has a top base and a bottom base, and these are both circles with the same diameter. The volume of a cylinder can be found by multiplying the area of one of its circular bases by its height. The surface area of a cylinder can be found by adding up the areas of the two circular bases and the lateral surface. Cylinders are widely used in mathematics, engineering, and physics, and they play an important role in the study of various geometric and physical concepts.
Given the diameter of a cylinder is 34m and its height is 27m, we can find the volume of the cylinder using the formula:
Volume = π × (diameter / 2)² × height
Plugging in the values, we get:
Volume = 3.14 × (17 / 2)² × 27
Volume = 3.14 × (8.5)² × 27
Volume = 3.14 × 72.25 × 27
Volume = 6058.73 cubic meters
So, the volume of the cylinder is approximately 6058.73 cubic meters.
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Point P partitions directed segment AB in the part to part ratio of 3:4. If A(5, 5) and B(1, -2) find the y-coordinate of P.
y coordinate of point p is 2.
What is Coordinate System?Arrangement of reference lines or curves used to identify the location of points in space.
Using the section formula, if a point (x,y) divides the line joining the points
(x₁, y₁) and (x₂, y₂) in the ratio m:n then
(x, y)=(mx₂+nx₁/m+n, my₂+ny₁/m+n)
(x,y)=(3(1)+4(5)/7, 3(-2)+4(5)/7)
=(3+20/7, -6+20/7)
=(23/7, 14/7)
=(23/7, 2)
The y coordinate of point p is 2
Hence, y coordinate of point p is 2.
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Mr Sharma deposit ₹250 per month every month in a reccuring deposit account for a period of 3 Years.At the time of maturity he gets ₹ 10,110.
I. Find the of interest per annum.
ii. Find the total interest earned by Mr Sharma .
Answer:
I. 11%
II. ₹ 1110 in interest over 3 years
Step-by-step explanation:
To solve for the interest rate and the total interest earned, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where A is the maturity amount, P is the principal, r is the interest rate, n is the number of times compounded per year, t is the time in years, and
Since we know the maturity amount (A = ₹ 10,110), the principal (P = 250 * 12 * 3 = 9,000), and the time (t = 3 years), we can rearrange the formula to solve for the interest rate:
r = n * ((A/P)^(1/nt) - 1)
We'll assume that the interest is compounded monthly, so n = 12. Then:
r = 12 * ((10110/9000)^(1/36) - 1)
r ≈ 0.11
So, the interest rate is approximately 11% per year.
To find the total interest earned, we can use the formula:
Interest = A - P
Interest = 10110 - 9000
Interest = 1110
So, Mr Sharma earned ₹ 1110 in interest over 3 years.
yolonda has 7 more baseball cards than jeff. jeff has three times as many baseball cards as clara. all together, they have 21 baseball cards, how many does clara have?
As per the mentioned distribution of cards, Clara has 2 baseball cards.
Let the number of baseball cards with Clara be x. So, number of baseball cards with Jeff will be 3x. Now, the baseball cards that Yolonda has is (3x + 7). We know their sum is 21, therefore, forming the equation now -
x + 3x + 3x + 7 = 21
Performing addition on Left Hand Side of the equation
7x + 7 = 21
Dividing the whole equation by 7
x + 1 = 3
Rewriting and solving the equation for x
x = 3 - 1
Performing division on Right Hand Side of the equation
x = 2
The number of baseball cards with Clara are 2.
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Jahnay is following this recipe to make cakes. Jahnay uses 840 g of flour. How many cakes is Jahnay making? Recipe: Makes 1 Cake 150 g sugar 120 g butter 210 g flour 2 eggs
Answer:
To determine how many cakes Jahnay is making, we need to calculate the total weight of the ingredients for one cake and then divide the total amount of flour Jahnay is using by that amount.
First, let's calculate the total weight of ingredients for one cake:
150 g sugar + 120 g butter + 210 g flour + 2 eggs = 480 g
Next, let's divide the total amount of flour Jahnay is using by the total weight of ingredients for one cake:
840 g / 480 g = 1.75 cakes
So Jahnay is making 1.75 cakes.
the average expenses of a sample of 200 patients who were hospitalized at rwj hospital in new brunswick is $4400. the standard deviation of average expenses for these patients is
The standard deviation of the average expenses of 200 patients who were hospitalized at RWJ Hospital in New Brunswick cannot be determined from the information provided. The average expenses of the sample is $4400, but the standard deviation of these expenses is not given.
The standard deviation is a measure of the variability or dispersion of the data in a set and is calculated using a complete dataset of the expenses of all 200 patients. Without this dataset, it is not possible to determine the standard deviation of the average expenses.
Option A, less than $400, Option B, at least $400, and Option C, between $0 and $400, are all based on assumptions about the standard deviation that cannot be made without a complete dataset of expenses.
In conclusion, the standard deviation of the average expenses of 200 patients who were hospitalized at RWJ Hospital in New Brunswick cannot be determined from the information provided and a complete dataset of expenses would be needed to make any assumptions about the standard deviation.
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Complete Question: A sample of 200 patients who were hospitalised at the rwj hospital in New Brunswick incurred $4400 on average in costs. The patients' average monthly costs have a standard deviation of
A. less than $400.
B. $400 or more.
C. from $0 to $400
D. Unable to determine D.
Part A: Describe in words how you can find the rate of change of a bushel of corn in the current year, and find the value. (5 points) Part B: How many dollars more is the price of a bushel of corn in the current year than the price of a bushel of corn in the previous year? Show your work. (5 points) Number of Bushels
Price of Corn (dollars)
2
10
4
20
6
30
8
40
The evaluation of the possible graph and table in the question, which indicates proportional relationships are presented as follows;
Part A: The rate of change of a bushel of corn in the current year is; 8 dollars per bushel of corn
Part B: Tnhe price of a bushel of corn in the current year is three dollars ($3) more than the price in the previous year.
What is a proportional relationship?A proportional relationship is one in which the output variable of the relationship, is a multiple of the input variable and factor.
The points on the graph in the question, obtained from a similar question posted on the website are;
(0, 0), (3, 24), (6, 46), (9, 72), (12, 76), (15, 120), (18, 144)
Part A: The slope is the rate of change of the bushel of corn. Therefore, the rate of change for the current year can be found by finding the slope as follows;
The graph is a straight line graph, indicating a proportional relationship therefore, the slope of the graph is a constant, which can be found as follows;
Slope = (24 - 0)/(3 - 0) = 8
The rater of change of the bushel for the current year is; 8 dollars per bushel of corn
Part B: Whereby the values in the table for the number of bushels to the price of corn for the previous year can be presented as follows;
Number of Bushels [tex]{}[/tex] Price of Corn (dollars)
2 [tex]{}[/tex] 10
4 [tex]{}[/tex] 20
6 [tex]{}[/tex] 30
8 [tex]{}[/tex] 40
The rate of change of the price for the previous year is therefore;
Rate of change = (20 - 10)/(4 - 2) = 5
The rate of change for the previous year is therefore 5 dollars per bushel
The price of a bushel in the current year is three more dollar than the price of a bushel in the previous year.
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sin ² (θ) - cos² (θ) = 2 sin² (θ) -1
Answer:
The equation is not true.
Step-by-step explanation:
Starting with the left side,
sin²(θ) - cos²(θ) = 1 - cos²(θ) - cos²(θ) = 1 - 2cos²(θ)
The right side,
2 sin²(θ) - 1 = 2(sin²(θ) - 0.5)
Thus, in general, sin²(θ) - cos²(θ) ≠ 2 sin²(θ) -1.
quinn is baking sweet potato pies. the table shows the ratio of cups of sugar to number of pies. number of pies359 cups of sugar1 and one half2 and one half4 and one half how many cups of sugar will quinn need to make 16 pies? 8 cups 8 and one half cups 9 and one half cups 11 cups
Quinn will need 8 cups of sugar to make 16 pies based on the table that shows the ratio of pies and sugar.
Dividing and Multiplying FractionWhat we know from the question:
3 pies = 1 ½ cups of sugar
5 pies = 2 ½ cups of sugar
9 pies = 4 ½ cups of sugar
16 pies = ?
To make it easier, the answer will be explained through sentence:
First, we find out how much sugar it takes to make one pie. Use one of the ratio provided above by dividing the pie amount with the sugar’s. For example, 3 divided by 1 ½ equals ½ .
Therefore, one pie would require only ½ cups of sugar. Crosscheck with the other ratio to make sure it is correct using the same method earlier.
Second, we find out how much sugar it takes to make 16 pies. Multiply the amount of pies with the amount of sugar. So 16 x ½ equals 8.
Here are the summary
1 pies = ½ cups of sugar
16 pies = 8 cups of sugar
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Exercise 13.2 Mark the following ordered pairs of points on a graph paper and join the points as required. A(0, 3), B(5, 8), C(9, 8), D(4, 3), E(9, 6), F(4, 1), G(0, 1) on a graph paper
The ordered pairs of points on a graph is added as an attachment
How to mark and join the ordered pairs of points on a graph?From the question, we have the following parameters that can be used in our computation:
The ordered pairs
The ordered pairs are represented as
A(0, 3), B(5, 8), C(9, 8), D(4, 3), E(9, 6), F(4, 1), G(0, 1)
Next, we create a plot of the ordered pairs
When this is done, we then connect the points
See attachment for the graph of the ordered pairs
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A dog sled driver added more gear to the sled, doubling its weight. This felt too heavy, so the driver removed 20 pounds to reach the final weight of 180 pounds. Write and solve an equation to find the sled’s original weight.
Answer:
Step-by-step explanation:
x will be the original weight.
2x - 20 = 180
2x = 200
x = 100
urn i contains two red chips and four white chips: urn ii, three red and one white. a chip is drawn at random from urn i and transferred to urn ii. then a chip is drawn from urn ii. what is the probability that the chip drawn from urn ii is red?
The probability that the chip drawn from urn II is red is 4/15. Let's call the event that the chip drawn from urn I and transferred to urn II is red "R1", and the event that the chip drawn from urn II is red "R2".
The probability of event R1 is 2/6 = 1/3.
Given that event R1 has occurred, the number of red chips in urn II becomes 4, and the number of total chips becomes 4+1=5. The probability of event R2 is 4/5 = 4/5.
The probability of both events occurring is (1/3) * (4/5) = 4/15.
So, the probability that the chip drawn from urn II is red is 4/15.
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When a car slams on its brakes and starts to skid, it leaves skid marks on the road. Investigators use these marks to determine how fast a car was going when it started to brake. The car's speed,
v
v
, (in feet per second) is related to the skid mark length,
d
d
, (in feet) by the equation
v
=
√
32
f
d
v
=
32
f
d
, where
f
f
is the coefficient of friction determined by the material the car was skidding on.
Wet asphalt has a coefficient of friction of 0. 5. If a car was driving 40 miles per hour and slams on its brakes, how long of a skid mark will it leave? 1 mile = 5280 feet.
If a car was driving at a speed of 40 miles per hour and slams on its brakes the vehicle will produce a skid mark that measures around 64.2 feet.
Equation v = √(32fd), where f is the surface's coefficient of friction, relates the speed, v (in feet per second), to the length of the skid mark, d (in feet).
To begin, we may convert the car's starting speed from miles per hour to feet per second:
25 miles/hour × 5280 feet/mile / 3600 seconds/hour ≈ 36.7 feet/second
In order to solve for d, we may then enter the above numbers into the equation v = √(32fd):
36.7 = √(32 × 0.5 × d)
36.7² = 32 × 0.5 × d
d = (36.7²)/(32 × 0.5) ≈ 64.2 feet
As a result, the vehicle will produce a skid mark that measures around 64.2 feet.
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Kara, Harry, and Erin served a total of 86 orders Monday at the school cafeteria.
Henry served 10 fewer orders than Kira. Erin served 4 times as many orders as Kira.
How many orders did they each serve?
The required orders are Kara served 12.5 orders, Harry served 22.5 orders, and Erin served 50 orders.
What are conditional equation?An equation that holds true for one or more values of the variable but holds false for other values of the variable is known as a conditional equation. In Hannah's example, the equation holds true for the value of x equal to 10, but not for other values, such as 1. The equation is a conditional equation as a result.
According got question:Let we consider the number of orders Kara served as x.
Then, Harry served x + 10 orders and Erin served 4x orders.
The total number of orders they served is x + x + 10 + 4x = 86 orders.
So, 6x + 10 = 86
6x = 76
x = 12.5
Kara served 12.5 orders, Harry served 22.5 orders, and Erin served 50 orders.
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Answer:
Step-by-step explanation:
Let the orders served by Kira be k.
Orders served by Henry= 10 less than Kira
= k-10
Orders served by Erin= 4 times of Kira
= 4k
Total orders served= 86
Kira+Henry+Erin= 86
k+k-10+4k= 86
6k-10= 86
6k= 86+10
6k= 96
k= 96/6
k= 16
Kira= k= 16
Henry= k-10= 16-10= 6
Erin= 4k= 4x16= 64
∴ Kira served 16 orders, Henry served 6 orders & Erin served 64 orders
please help me on this
Answer:
x=1, y=3
Step-by-step explanation:
Answer:
x = 1, y = 3
Step-by-step explanation:
y = x + 2
y = -5x + 8
Using substitution:
x + 2 = -5x + 8
6x = 6
x = 1
y = 1 + 2
y = 3
Multiply and simplify. Correct answer will get brainliest! <3
Answer:
7, 2, 3, 4, 8, 3
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This is about the distributive property of multiplication and the product of exponents with same base.
[tex]a(b + c) = ab + ac[/tex]When you multiply exponents with same base the powers add up:
[tex]a^b*a^c=a^{b+c}[/tex]The blanks are going to be:
Blank 1: Powers of m: 3 + 4 = 7Blank 2: Powers of n: 1 + 1 = 2Blank 3: Power of m remains: 3 Blank 4: Powers of n: 1 + 3 = 4Blank 5: Powers of m: 3 + 5 = 8 Blank 6: Powers of n: 1 + 2 = 3Answer:
[tex]15m^{7}n^{2}-20m^3n^{4}+10m^{8}n^{3}[/tex]
Blank #1 : 7Blank #2 : 2Blank #3 : 3Blank #4 : 4Blank #5 : 8Blank #6 : 3Step-by-step explanation:
Given expression:
[tex]5m^3n\left(3m^4n-4n^3+2m^5n^2\right)[/tex]
Distribute:
[tex]5m^3n \cdot 3m^4n-5m^3n \cdot 4n^3+5m^3n \cdot 2m^5n^2[/tex]
Multiply the numbers:
[tex]15m^3nm^4n-20m^3nn^3+10m^3nm^5n^2[/tex]
Rearrange to collect like terms:
[tex]15m^4m^3nn-20m^3n^3n+10m^5m^3n^2n[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]15m^{4+3}n^{1+1}-20m^3n^{3+1}+10m^{5+3}n^{2+1}[/tex]
Therefore:
[tex]15m^{7}n^{2}-20m^3n^{4}+10m^{8}n^{3}[/tex]
Help……………………………………..
Manisha designed a table cloth in the shape of a square of side 54cm . She wants to decorate its boundaries by sticking a lace around it . Fing the cost of putting lace around the table cloth at the rate of ₹8.5 per meter.
At 8.5 per meter, the cost of tying lace around the tablecloth is $18.36.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10. Identity equations and conditional equations are the two types of equations. An identity holds true for all possible values of the variables. A conditional equation is valid only for certain values of the variables. An equation consists of two expressions joined by an equals sign ("=").
Here,
The perimeter of the table cloth is 4 times the length of one side, so it is 4 * 54 cm = 216 cm.
To convert from centimeters to meters, we divide by 100, so the perimeter is 216 cm / 100 = 2.16 meters.
At a rate of ₹8.5 per meter, the cost of putting lace around the table cloth is 2.16 meters * ₹8.5 per meter = ₹18.36.
The cost of putting lace around the table cloth at the rate of ₹8.5 per meter is $18.36.
To know more about equation,
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Find the value of x. 117° 94°
Answer im not sure frl but its ok
Step-by-step explanation:
Answer: 7
Step-by-step explanation: