For the given triangles ΔABC ≈ ΔADE, the measurement of angle ACB is, 87°
What is similarity of triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"
Given that,
One triangle, ΔABC
one segment DE which is intersecting sides AB & AC
ΔABC has one similar triangle inside, which is ΔADE
Triangle ΔABC and ΔADE similar,
So, we can say ΔABC ≈ ΔADE
And it is known that
for similar triangles, ratio of corresponding angles of both the triangles are equal for similar triangles
so, ∠DAE/∠AED = ∠CAB/∠ABC
⇒ 62°/(11x -2)° = 62°/(6x + 13)°
⇒ (11x -2)° = (6x + 13)°
⇒ 11x - 6x = 13 + 2
⇒ 5x = 15
⇒ x = 3
So,
∠ADE = 11x - 2 = 11 x 3 - 2 = 31° = ∠ABC
It is known that,
Sum of all the interior angles of triangle is 180°
Now,
∠ACB + ∠CAB + ∠ABC = 180°
∠ACB + 62° + 31° = 180°
∠ACB = 180° - 93°
= 87°
Hence, the angle ACB is 87°
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solve this trigonometry problem
so this how this problem is done hope you understood
12. Elmo is standing on a parade float tossing candy out to everyone. The candy is thrown with a starting velocity of 10
feet per second from a height of 3 feet modeled by the equation: h= -16t2 + 10t + 3
After how many seconds will the ball be 2 feet in the air?
a. 0. 125
b. 0. 5
c. 0. 71
d. 0. 625
The candy will be 2 feet in the air after approximately 0.19 seconds (to the nearest thousandth).
The answer closest to this value is option d, 0.625 seconds.
The equation to model the height of the candy thrown by Elmo is given by:
h = -16t^2 + 10t + 3
To find the time when the height of the candy is 2 feet,
We need to solve for t when h = 2:
2 = -16t^2 + 10t + 3
Expanding and rearranging the equation:
-16t^2 + 10t - (-1) = 0
Using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / 2a
Where a = -16, b = 10, and c = -1.
Plugging in the values:
t = (-10 ± √(10^2 - 4(-16)(-1))) / 2(-16)
t = (-10 ± √(100 + 64)) / (-32)
t = (-10 ± √(164)) / (-32)
t = (-10 ± 4) / (-32)
t = (-14 / -32) and (-6 / -32)
t = 14/32 and 6/32
The smaller value, 6/32, represents the time after which the candy will be 2 feet in the air.
Converting it to a decimal:
6/32 = 0.1875 seconds
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70:5:25 in simplest forms
Answer:
14:1:5
because of [tex]\frac{70}{5} =14\\\\\frac{5}{5}=1\\ \\\frac{25}{5}=5[/tex]
How to determine the empirical formula from percent composition?
Refer the table attached for the empirical formula calculations
What is the percentage?
It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
calculate the percentages By the atoms' relative atomic mass, divide them. The values are obtained after division. The`1 ratio that results from dividing all of the values by the value that is the least will serve as the empirical formula.
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2^x · 3^y · 108 = 2^a · 3^b. What is the sum of a and b in terms of x and y?
A. x + y + 2
B. x + y + 3
C. x + y + 4
D. x + y +5
2^x · 3^y · 108 = 2^a · 3^b. The sum of a and b in terms of x and y is option C. x + y + 4
How did we get the value?To solve for a and b, we need to determine what they equal in terms of x and y.
First, we can simplify the right side of the equation:
2^a · 3^b = 2^a · (3^2)^(b/2) = 2^a · (2^3)^(b/2) = 2^(a + 3b/2)
Next, we simplify the left side of the equation:
2^x · 3^y · 108 = 2^x · 3^y · (2^2 · 3^2) = 2^x · 3^y · (2^2)^(log3(108)/log3(2^2)) · 3^2 = 2^x · 3^(y + 2)
Comparing the two sides of the equation, we see that:
a + 3b/2 = x + (y + 2)
Solving for a and b, we get:
a = x + y
b = 2(y + 2)
So, the sum of a and b is:
a + b = x + y + 2(y + 2) = x + y + 2y + 4 = x + 3y + 4.
The answer is therefore C: x + y + 4.
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What’s the answer to this
The sequence of transformations that will map polygon JKLM onto polygon YXWZ is given as follows:
A translation by <-6, -5>, then a rotation 90º counterclockwise about the origin, and a reflection across the y-axis.
How to obtain the transformation?The vertices of polygon JKLM are given as follows:
J(-4,1), K(0,0), L(2,2) and M(0,-6).
The equivalent vertices on polygon YXWZ are given as follows:
Y(6,2), X(5,6), W(7,8), Z(-1,6).
Hence the composite rule for the y-coordinate is given as follows:
x + 6.
Which means that at some point y = x, hence there was a 90º counterclockwise rotation.
The addition to 6 means that there was a translation adding/subtracting 6 to the x-coordinate, hence the last option is correct.
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The series of transformation that maps the polygon JKLM to the polygon YXWZ are;
A rotation 90° about the origin, then a reflection about the x-axis and a translation by (5, 6)
What is a transformation of a geometric figure?A transformation involves the change in the position, size, shape of orientation of a geometric figure.
The coordinates of the vertices of the polygon JKLM are; J(-4, 1), K(0, 0), L(2, 2), and M(0, -6)
The coordinates of the vertices of the polygon YXWZ are; Y(6, 2), X(5, 6), W(7, 8), and Z(-1, 6)
Point J in JKLM corresponds to point Y in YXWZ
A rotation of point J 90° clockwise produces the image, (1, 4)
A reflection of the point (1, 4) across the x-axis produces an image at the point (1, -4)
A translation (5, 6), produces the point (6, 2)
Therefore, the series of rigid transformations that maps the image YXWZ, from the preimage JKLM are;
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How Big Is A 16 Inch Pizza? (Slices, Servings, Size, And Total Calories)
A 16-inch pizza might serve 10–12 people if you're providing a meal with sides and appetizers.
What is meant by Total Calories?A few easy calculations are needed to do this. First, double your present weight by 15, which is about how many calories per pound of body weight you need to maintain if you are moderately active.The Katch-McArdle Formula may be more accurate for persons who are slimmer and are aware of their body fat %, but the Mifflin-St. Jeor Equation is generally regarded as the most accurate equation for estimating BMR.If the food item you are consuming has 20g of protein, 35g of carbohydrates, and 15g of fat, you would multiply those amounts by 20x4, 35x4, and 15x9 to determine the number of calories each macronutrient contributes—80, 140, and 135 respectively.Therefore, the correct answer is serve.
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if event a and event b cannot occur at the same time, then events a and b are said to be a. mutually exclusive b. positively correlated c. jointly determined d. collectively exhaustive e. statistically independent
If event a and event b cannot occur at the same time, then events a and b are said to be a. mutually exclusive.
ABOUT PROBABILITYProbability and Statistics are two basic concepts in the branch of Mathematics. Probability is all about the likelihood of an event, whereas statistics is more about how we handle various data using different techniques.
By using probability and statistics, you can process complex data in a way that is very easy to understand.
Probability is one of the topics that often comes up when discussing statistics. The reason is, this one theory is commonly used when trying to predict something.
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The NC General Assembly increases minimum wage to $8.00/ hour.What is the impact of the demand for clothes?
The increase in the minimum wage to $8.00 per hour could potentially lead to an increased demand for clothes due to higher purchasing power and potential shifts in consumer preferences.
We have,
Increasing the minimum wage to $8.00 per hour can have some impact on the demand for clothes.
Here are a few potential effects to consider:
Increased purchasing power:
When the minimum wage is increased, low-wage workers have more disposable income. This extra income can lead to increased consumer spending, including on clothing.
As a result, there could be a boost in the demand for clothes as more people can afford to purchase new clothing items.
A shift in consumer preferences:
With a higher minimum wage, individuals who previously had limited resources may now have the ability to choose higher-quality clothing or purchase from more expensive brands.
This shift in consumer preferences could lead to changes in the demand for different types of clothes and potentially result in an increase in demand for higher-end or premium clothing.
Price sensitivity:
While an increase in the minimum wage may provide workers with more spending power, some individuals may still be price-sensitive and prefer more affordable clothing options.
As a result, there may be continued demand for lower-priced clothing items or a preference for sales and discounts.
Employment and production costs:
An increase in the minimum wage could potentially lead to higher labor costs for clothing manufacturers and retailers.
To mitigate these increased costs, businesses may take steps such as adjusting their pricing strategies, implementing cost-saving measures, or exploring more efficient production methods.
These factors could impact the overall supply of clothes and potentially influence prices.
Thus,
The increase in the minimum wage to $8.00 per hour could potentially lead to an increased demand for clothes due to higher purchasing power and potential shifts in consumer preferences.
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an 80-kg baseball player slides into third base. he experiences 60 n of friction force over a distance of 1.2 m. the amount of work done by friction is ______ joule.
The amount of work done by friction is 72 Joules (60 N x 1.2 m = 72 J).
The amount of work done by friction can be determined using the equation W = Fd, where W is work, F is force, and d is distance. In this case, the friction force is 60 N, and the distance is 1.2 m. Therefore, the amount of work done by friction is 72 Joules (60 N x 1.2 m = 72 J).
The amount of work done by friction can be thought of as the energy required to overcome the friction between the baseball player and the third base. The friction force acts in the opposite direction of the player's motion, opposing their forward momentum. As the player slides into third base, they must do work to overcome the friction force and move forward. The work done by friction is equal to the amount of energy that the player must expend to complete the motion.
In this case, the player must do 72 Joules of work to overcome the friction force and slide into third base. This is equal to the friction force (60 N) multiplied by the distance (1.2 m). As the player slides over the surface of the base, they must do this amount of work to complete the motion.
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quires 2 1/2 feet of wood. She has a total of 13 feet of wood. What is the greatest number of birdhouses could
The required number of birdhouses can be made through the 13 feet of wood are 5 birdhouses.
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
A birdhouse consists of 2 1/2 feet of wood,
he has a total of 13 feet of wood.
Number of birdhouses
= ratio of wood total length / used to build one birdhouse
= 13 / [2 /1/2]
= 5.2
≈ 5
Thus, the required number of birdhouses can be made through the 13 feet of wood are 5 birdhouses.
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help me with this math problem please
The Answer Is Underneath This Sentence.
Step-by-step explanation:
Its The First One.
Hang Yo bought a treadmill for $875. He made a 10% down payment and financed the rest over 36 months. Find the monthly payment if the finance charge was 4% of the amount financed. Round the answer to the nearest cent. The monthly payment for the treadmill was $
The monthly payment is $48.56.
What is the down payment?
A down payment is a payment made by a borrower to a lender in advance of a loan in order to reduce the amount to be borrowed. It is usually a percentage of the purchase price of an item, such as a house or a car, and is paid when the loan is being taken out.
The amount of the down payment made by Hang Yo is $925 * 10% = $92.50.
The amount financed is $925 - $92.50 = $832.50.
The finance charge is 5% of the amount financed, or $832.50 * 5% = $41.63.
The total amount to be paid back over 18 months is $832.50 + $41.63 = $874.13.
the monthly payment is $874.13 / 18 months = $48.56 (rounded to the nearest cent).
Hence, the monthly payment is $48.56.
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A cyclilit rode a contant peed of 21 mph for 3 hour then he decreaed her rate of peed to 17 mph for 4 hour how far did the cycilit ride in 7 hour
The cyclist rode 131 miles in 7 hour
What is velocity?It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).
The cyclist rode at a constant velocity of 21mph for 3 hours.
21 x 3 = 63 miles
Then she decreased the rate of velocity to 17mph for 4hours.
63 + (17 x 4) = 63 + 68 = 131 miles
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Correctly written question:
A cyclist rode at constant speed of 21 mph for 3 hours. Then, she decreased her rate of speed to 17 mph for 4 hours. How far did the cyclist ride in 7 hours?
point D is the centroid of triangle ABC, BD=3x-2 and BF=3x. find the value of x. HELP ASAP PLS!!!!
Answer:
Step-by-step explanation:
hope this helps
a positive point charge q is at the center of a spherical shell of radius r carrying charge 2q distributed uniformly over its surface. (A) Write an expression for the electric field strength at 1/2 R.
(B) Write an expression for the electric field strength at 2R.
The expression for the electric field strength at 1/2 R is E = [tex]\frac{8 \times \pi\times k \times q \times r^2 }{(1/2R)^2}[/tex], and the expression for the electric field strength at 2R is E = [tex]\dfrac{ 2 \times \pi \times k \times q \times r^2 }{(2R)^2}[/tex]
The spherical shell is what?A spherical shell in geometry is a three-dimensional version of an annulus. It is the area of a ball that lies between two concentric spheres with various radii.
(A) The equation E = k × q / r2 can be used to determine the electric field strength at a point P outside of a uniformly charged sphere, where k is the Coulomb constant, q is the charge, and r is the distance between the point P and the sphere's centre.
For a spherical shell of radius r carrying charge 2q, the total charge on the shell can be considered as 2 × 4 × π × r² × q, where q is the surface charge density on the shell.
The electric field strength at 1/2R can be calculated using this formula as follows:
E = [tex]\dfrac{k \times (2 \times 4 \times \pi \times (r^2) \times q)}{((1/2R)^2)}[/tex]
[tex]= \dfrac{8 \times \pi\times k \times q \times r^2 }{(1/2R)^2}[/tex]
(B) Similarly, the electric field strength at 2R can be calculated as:
E = [tex]\dfrac{k \times (2 \times 4 \times \pi \times (r^2) \times q)}{(2R)^2}[/tex]
[tex]= \dfrac{ 2 \times \pi \times k \times q \times r^2 }{(2R)^2}[/tex]
Hence, the expression for the electric field strength at 1/2 R is E = [tex]\frac{8 \times \pi\times k \times q \times r^2 }{(1/2R)^2}[/tex], and the expression for the electric field strength at 2R is E = [tex]\dfrac{ 2 \times \pi \times k \times q \times r^2 }{(2R)^2}[/tex]
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Please help Simplify: (pic att)
5x
x+_−x+1
x² + 3x - 4
[?]x² - [
[ ]x - [
x² +
Answer:
The simplified expression is 5x² + 2x - 4.
Step-by-step explanation:
pls this is urgent hurryyy
Answer:
Step-by-step explanation:
Thats true
need help with homework lines and transversal
Measure of all the angles shown in diagram are, 124°.
What are Parallel lines?Parallel lines are those lines that are equidistance from each other and never intersect each other.
We have to given that;
Angles shown in figure.
Now, By definition of alternate angles of parallel lines we get;
⇒ 10x + 14 = 15x - 41
Solve for x;
⇒ 14 + 41 = 15x - 10x
⇒ 55 = 5x
⇒ x = 55/5
⇒ x = 11
Thus, Measure of angles are,
⇒ 10x + 14 = 10 × 11 + 14
= 110 + 14
= 124
⇒ 15x - 41 = 15 × 11 - 41
= 165 - 41
= 124
Thus, Measure of all the angles shown in diagram are, 124°.
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(0)
Consider the following two probability distributions: Distribution A Distribution
B x P(x) x P(x)
0 0.20 0 0.01
1 0.20 1 0.02
2 0.20 2 0.94
3 0.20 3 0.02
4 0.20 4 0.01
Which of the following is an accurate statement regarding these two distributions?
a. Distribution A has a higher variance.
b. Distribution B has a higher variance.
c. Both distributions are positively skewed.
d. Both distributions are uniform.
b. Distribution B has a higher variance is an accurate statement regarding these two distributions.
Variance is a measure of the spread of a probability distribution. It tells us how far away from the mean values in the distribution are. The higher the variance, the more spread out the values are.
In this case, Distribution B has a higher variance than Distribution A. To calculate the variance of a distribution, we use the formula:
[tex]$$\sigma^2 = \sum_{i=1}^{n} (x_i - \mu)^2 \cdot P(x_i)$$[/tex]
Where [tex]$x_i$[/tex] is a possible value, [tex]$P(x_i)$[/tex] is the probability of that value, and [tex]$\mu$[/tex] is the mean of the distribution. If we use this formula to calculate the variance of each distribution, we'll find that the variance of Distribution B is larger than the variance of Distribution A.
This means that the values in Distribution B are more spread out and less consistent than the values in Distribution A, making Distribution B have a higher variance.
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Help!!
The pentagon in Washington, D.C.,is shaped like a regular pentagon.Find the measure of each interior angle.
Each interior angle in the pentagon in Washington, D.C., measures 108 degrees.
What is pentagon and how to measure its interior angle?A pentagon is a polygon with five straight sides and five interior angles. It is a geometric shape with five vertices and five sides that are all straight lines.The measure of each interior angle in a regular pentagon can be found using the formula:$180(n-2)/n$where n is the number of sides in the polygon. In this case, n = 5, so the formula becomes:$180(5-2)/5 = 180(3)/5 = 108^\circ$So each interior angle in the pentagon in Washington, D.C., measures 108 degrees.
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Select the quadratic inequality that represents the graph.
The quadratic inequality that represents the graphs is
A. y ≥ 2/3 (x + 3)² - 23How to find the quadratic inequality of the graphThe line in the graph is a solid line hence the equation will have a greater than or equal to or les than or equal to
For shading above the curve the is greater than or equal to.
comparing with the equation
y = a(x - h)² + k
where
h and k are the coordinates at the vertex
For a graph opening upward "a" is positive
The first option matches the conditions
y ≥ 2/3 (x + 3)² - 23
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Question 2 (1 point)
Which of the following statements describes a correct method for solving this equation?
3+2x = 5
A.Divide both sides of the equation by 5, and then add 2 to both sides.
B.Divide both sides of the equation by 5, and then subtract 2 from both sides.
C.Subtract 3 from both sides of the equation, and then divide both sides by 2.
D.Add 3 to both sides of the equation, and then divide both sides by 2.
Answer:
Answer is (C) .....
Subtract 3 from both sides of the equation, and then divide both sides by 2.
question 7 what function creates a scatterplot and then adds a small amount of random noise to each point in the plot to make the points easier to find? 1 point the geom point() function the geom jitter() function the geom bar() function the geom smooth() function
The correct option is (C) The geom_jitter() function.
The jitter geom is a convenient shortcut for geom_point(position = "jitter"). It adds a small amount of random variation to the location of each point, and is a useful way of handling overplotting caused by discreteness in smaller datasets.
geom_jitter(mapping = NULL, data = NULL, stat = "identity",
position = "jitter", ..., width = NULL, height = NULL, na.rm = FALSE,
show.legend = NA, inherit.aes = TRUE)
Since we want points to be jittered and dodged, we can use geom_point with position_jitterdodge (). Make sure to specify the "group" variable: this graph specifies three potential grouping variables (cluster, region, cd_code), and position_jitterdodge can't tell which two to use unless specified.
The geom_jitter() function creates a scatterplot and then adds a small amount of random noise to each point in the plot to make the points easier to find.
Thus, the correct option is (C) The geom_jitter() function.
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The correct option is (C) The geom_jitter() function.
The jitter geom is a convenient shortcut for geom_point(position = "jitter"). It adds a small amount of random variation to the location of each point, and is a useful way of handling overplotting caused by discreteness in smaller datasets.
geom_jitter(mapping = NULL, data = NULL, stat = "identity",
position = "jitter", ..., width = NULL, height = NULL, na.rm = FALSE,
show.legend = NA, inherit.aes = TRUE)
Since we want points to be jittered and dodged, we can use geom_point with position_jitterdodge (). Make sure to specify the "group" variable: this graph specifies three potential grouping variables (cluster, region, cd_code), and position_jitterdodge can't tell which two to use unless specified.
The geom_jitter() function creates a scatterplot and then adds a small amount of random noise to each point in the plot to make the points easier to find.
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what is the answer for this maths watch question?
Answer:
3.814697266x10
Step-by-step explanation:
a scatterplot includes data showing the relationship between the value of a painting and the age of the painting. which graph displays the line of best fit for the data?
The scatterplot that displays the line of best fit for the data would be the scatterplot that includes the calculated line of best fit plotted on the graph along with the data points.
A line of best fit, also known as a regression line, is a line that represents the relationship between two variables in a scatterplot. The line of best fit is used to describe the overall trend in the data and can be used to make predictions about one variable based on the values of the other variable.
The line of best fit in a scatterplot can be represented as a straight line, a polynomial, or another type of mathematical function, depending on the relationship between the variables. To find the line of best fit, the student would need to use statistical techniques such as linear regression or polynomial regression to calculate the equation of the line that best represents the data.
The line of best fit is then plotted on the scatterplot along with the data points, creating a visual representation of the relationship between the two variables. The line of best fit can be used to make predictions about one variable based on the values of the other variable, and to determine the strength and direction of the relationship between the two variables.
Thus, In conclusion, the scatterplot that displays the line of best fit for the data would be the scatterplot that includes the calculated line of best fit plotted on the graph along with the data points.
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The scatterplot that displays the line of best fit for the data is the scatterplot that includes the computed line of best fit drawn on the graph with the data points.
The scatterplot that includes the computed line of best fit shown on the graph with the data points is the scatterplot that displays the line of best fit for the data.
A line of best fit, also known as a regression line, is a line in a scatterplot that illustrates the connection between two variables. The line of best fit is used to depict the general trend in the data and may be used to forecast one variable based on the values of another.
Depending on the relationship between the variables, the line of best fit in a scatterplot can be depicted as a straight line, a polynomial, or another sort of mathematical function. The learner would need to apply statistical techniques such as linear regression or polynomial regression to derive the equation of the line that best represents the data in order to obtain the line of best fit.
The line of best fit is then drawn alongside the data points on the scatterplot, producing a visual depiction of the connection between the two variables. The line of best fit may be used to anticipate the value of one variable based on the value of another variable, as well as to identify the strength and direction
To summarize, the scatterplot that displays the line of best fit for the data is the scatterplot that includes the computed line of best fit drawn on the graph with the data points.
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Given the graph of the function F(x) below, what happens to F(x) when x goes from 0 to 1?   A. F(x) is a negative number with a small absolute value.  B. F(x) is a negative number with a large absolute value.  C. F(x) is a very small positive number.  D. F(x) is a very large positive number. ASAP PLEASE TIMED TESR
Answer:
I think that b or c I believe
Name one particular solution for 8x-3y≤12
Answer:
y ≤ 4
Step-by-step explanation:
you are given an array[] of size n. you have to convert the array into non decreasing array
We can use a sorting algorithm such as Insertion Sort, Selection Sort, Merge Sort, or Quick Sort to sort the array in increasing order. This will convert the array into a non decreasing array.
1. Initialize a sorting algorithm of your choice.
2. Compare two adjacent elements and swap them if they are not in the desired order.
3. Repeat step 2 until the array is sorted.
4. After sorting, the array will be in non decreasing order.
We can use a sorting algorithm such as Insertion Sort, Selection Sort, Merge Sort, or Quick Sort to sort the array in increasing order. This will convert the array into a non decreasing array.
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Cameron baked two pans of brownies for the school bake sale. She couldn't wait and ended up eating 1/6 of a pan. How many brownies does she have left
Cameron is left with 11/6 of a pan by using mathematical operation known as subtraction.
Given,
Total number of brownies = 2 pans
Cameron ate = 1/6 of a pan
In this question we will be using mathematical operation known as subtraction.
Subtraction is an arithmetic operation that involves finding the difference between two numbers. In other words, it is the process of removing a quantity from another. It is a fundamental mathematical concept that is widely used in everyday life, from calculating the change from a purchase to determining the difference between two quantities. Subtraction can be performed with whole numbers, decimals, fractions, and even with negative numbers. In all cases, the process of subtraction involves aligning the numbers to be subtracted, either vertically or horizontally, and then subtracting the smaller quantity from the larger one.
Brownies left = 2 pans - 1/6 of pan
= 12/6 -1/6
= 11/6 pan
Hence, she is left with 11/6 of a pan to eat.
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