Answer:
its just exaplining how does this exrcise work example 1^1 would be 1x1/
1^3 1x1x1x1/ 3^5 3x3x3x3x3/ 3x3=9 9x3 =27 27x3 =81 81x3=243
Step-by-step explanation:
A 900 car parking lot is divided into 3 sections. There are 330 spots in Section 1. Section 2 holds 160 more than the amount of cars in Section 3. How many spots does Section 3 have?
Section 3 have 205 spots, according to the given question.
What do you mean by section?
A section is a part or component that, when combined with the other components, forms the total. like the rhythm section of the band that is reviewed in the arts section of a newspaper.
According to the given question,
We have the given information:
A 900 car parking lot is divided into 3 sections. There are 330 spots in Section 1. Section 2 holds 160 more than the amount of cars in Section 3.
Firstly,
900 - 330 = 570 (spots in section 2 and 3)
Secondly,
There are x spots in section 3 and (x + 160) spots in section 2.
So we have :
x + x + 160 = 570
2x = 410
x = 205
Therefore, the section 3 have 205 spots.
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A farmer has a piece of land measuring 840m by 396m.He divides it into squares plots of equal sizes.Find the maximum area of one plot
Answer:
Step-by-step explanation:
To find the maximum area of one plot, we need to find the greatest common factor of 840 and 396. One way to do this is to use the prime factorization method.
First, we prime factorize 840 and 396:
840 = 2 * 2 * 2 * 3 * 5 * 7
396 = 2 * 2 * 3 * 3 * 11
Then, we find the common factors:
2 * 2 * 3 = 12
So, the greatest common factor of 840 and 396 is 12.
The maximum area of one plot is therefore (840 * 396) / 12 = 140 * 33 = 4620 square meters.
How do you calculate a translation?
Use P′(x+a,y+b) to translate the point P(x,y), a unit to the right, and b unit up. Use P′(x−a,y−b) to translate the point P(x,y), a unit to the left and b unit to the lower.
A translation occurs whenever an object is transported from one place to another without altering its dimension, form, or orientation. We can draw the translation in the coordinate plane if we know which way and how far to move the figure.
The triangle can be translated in the following ways:
Step 1: Find the coordinates of each of the triangle's vertices in step one.
Step 2: Add the horizontal translation value to each vertex's x-coordinate and the vertical translation value to each point's y-coordinate to translate each point. If the horizontal translation is to the left or the vertical translation is downward for these translations, add a negative number.
Step 3: Plot the three translated points and draw the triangle by drawing a straight line between each pair of points.
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Who created 3x 1 problem?
The titular conjecture was most likely put forth in the 1930s by Lothar Collatz.
Describe odd number.Odd numbers are those that cannot be evenly divided by two. It cannot be evenly split into two different integers. An odd number will leave a leftover when divided by two. 1, 3, 5, 7, and other odd numbers are instances. The idea of odd numbers is identical to that of even numbers. Odd numbers satisfy the congruence when divided by two, leaving a residue of 1. A number's parity indicates how odd it is; an odd number has parity 1, whereas an even number has parity 0.
Given
The titular conjecture was most likely put forth in the 1930s by Lothar Collatz.
The issue seems like a practical joke.
Pick any number you like. Add 1 and multiply it by 3 if it's an odd number.
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What does an octagon shape look like?
Graph the inequality. 3x+4y≥20
see below pictures
Answer:
A.
Step-by-step explanation:
Just put the equation 3x+4y≥20 into y=mx+b form. Subtract 3x from both sides so you get 4y ≥ -3x+20
then divide everything by 4 to isolate the y.
You would get y ≥ -3/4+ 5. Then just use the slope and y-intercept to graph.
If ≥ symbol is used, shade above the line.
A regression table mainly shows us Select one: a. How we should run the regression analysis.b. what the coefficients values are, and whether each coefficient is significant (likely to be different from from 0)c. that the smallest coefficients always have the greatest impact on the dependent variable.d. if a large constant term is important.e. all of the above.
A regression table mainly shows us that what the coefficients values are, and whether each coefficient is significant (likely to be different from from 0) .
A regression table is a statistical technique that describes how strongly a dependent variable and one or more independent variables are correlated (s). A field or variable you are attempting to predict or comprehend could be a dependent variable.
Regression allows researchers to predict or explain the variation in one variable based on another variable. The variable that researchers are trying to explain or predict is called the response variable. It is also sometimes called the dependent variable because it depends on another variable.
What is interpretation of regression statistics table?
In statistics, regression is a technique that can be used to analyze the relationship between predictor variables and a response variable. When you use software (like R, SAS, SPSS, etc.) to perform a regression analysis, you will receive a regression table as output that summarize the results of the regression.
A regression table primarily reveals the values of the coefficients as well as the significance of each coefficient (how likely it is that it will depart from 0).
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Who qualifies for SSS partial disability?
Partial disability, according to SSS, is the whole and irreversible loss of a physical portion. An individual can still do their work to some extent despite the condition. Any loss of these body parts or senses qualifies as a partial disability for SSS benefits: only one. One-hand.
In the Philippines, the Social Security System is a government-run social insurance program for employees in the private, public, and unorganized sectors. Republic Act No. 1161, also known as the Social Security Act of 1954, is what created SSS. Later, in 1997, Republic Act No. 8282 changed this statute.
The person must have made at least 36 monthly payments before the semester of incapacity in order to be eligible for a monthly disability pension. If there are less than 36 monthly contributions, the recipient receives a lump sum payment.
"Permanent partial disablement" refers to a permanent disability that limits an employee's ability to earn money. According to the Second Schedule, partly permanent disability results;] "Permanent Total Disablement" ((15B)) refers to such a disablement. National Government Act. 0 Citations, 394 Citations.
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Which equation most likely describes the relation in the following table?
2 3 4 5
y 4 5 6 7
KA
X
O y = 2x
Oy--2-x
Oy=x+2
0y=x-2
Answer:
y = x + 2
Step-by-step explanation:
Each y value is 2 greater than the x value
What does an XY scatter plot show?
A Scatter (XY) Plot has points that show the relationship between two sets of data.
Scatter Plots
A Scatter (XY) Plot has points that show the relationship between two sets of data.
In this example, each dot shows one person's weight versus their height.
Example:
The local ice cream shop keeps track of how much ice cream they sell versus the noon temperature on that day. Here are their figures for the last 12 days:
Ice Cream Sales vs Temperature
Temperature °C Ice Cream Sales
14.2° $215
16.4° $325
11.9° $185
15.2° $332
18.5° $406
22.1° $522
19.4° $412
25.1° $614
23.4° $544
18.1° $421
22.6° $445
17.2° $408
And here is the same data as a Scatter Plot:
It is now easy to see that warmer weather leads to more sales, but the relationship is not perfect.
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The probability that it rains in London on any particular day is 0.5.
If it rains then the probability of it raining the following day decreases to 0.15.
Consider the next two days. What is the probability it rains on both days?
The probability it rains on both days is 0.175
How to determine the probability it rains on both days?From the question, we have the following parameters that can be used in our computation:
P(Rain) = 0.5
P(Rain next day) = P(Rain) - 0.15
The probability it rains on both days is then calculated as
P(Rain both days) = P(Rain next day) * P(Rain)
Substitute the known values in the above equation, so, we have the following representation
P(Rain both days) = 0.5 * (0.5 - 0.15)
Evaluate
P(Rain both days) = 0.175
Hence, the probability is 0.175
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which expression is equivalent to 179x44?
[tex]179\times44[/tex]
[tex]=\fbox{7876}[/tex]
__________________________________________________________
The following expressions are equivalent to [tex]179\times44[/tex]:
[tex](179 \times 40) + (179 \times 4) = 179 \times(40 + 4)[/tex]
[tex]4000 + 2800 + 360 + 280 +36[/tex]
[tex](100 \times44) + (70\times44) + (9\times44) = 44 \times (100 + 70 +9) = 44 \times 179[/tex]
Find The Slope Of The Given Points -> (-4,5) And (9,8)
Answer:
m = 3/13
Step-by-step explanation:
The Slope is rise/run or (y2 - y1) / (x2 - x1)
We see the y increase by 3 and the x increase by 13, so the slope is
m = 3/13
Answer:
Step-by-step explanation:
To find the slope of the line that passes through the points (-4,5) and (9,8), we can use the formula for slope:
slope = (y2 - y1) / (x2 - x1)
= (8 - 5) / (9 - (-4))
= 3 / 13
= 0.231
Therefore, the slope of the line that passes through the points (-4,5) and (9,8) is 0.231.
A line passes through the point(-5,-6) and has a slope of -2 .
The line passing through point (-5, -6) is y = -2x - 16.
Define Equation of line.
A line in geometry is a collection of points that can be stretched infinitely in two different ways.To put it another way, a line is created by continually extending the two end points in any direction. As a result, we can assert that a line lacks end points. However, because it just has length and no width, it is a one-dimensional geometric form. Based on the information provided, we can create multiple forms of equations for lines algebraically, such as point slope form, slope-intercept form, and two point form.Two Point Form Formula,y - y₁ = m (x - x₁)
Given point is (-5, -6) and slope is -2.
We know the formula is,
y - y₁ = m (x - x₁)
Let, (x₁, y₁) = (-5, -6)
and, m = -2 (slope)
Now, plug in the value
y - (-6) = -2(x - (-5) )
y + 6 = -2(x + 5)
y + 6 = -2x - 10
y = -2x - 10- 6
y = -2x - 16
Hence, the line passing through point (-5, -6) is y = -2x - 16.
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Please help me !!!!!!!!
Answer:
The Eastern Continental Trail is 5,376 miles and the Erie Canalway Trail is 384 miles
Step-by-step explanation:
I took 5,760 divided it by 15 and got 384, I then subtracted 5,760 by 384 and got 5,376
What are the 4 properties of a triangle?
The triangle has the following characteristics: A triangle (of any kind) has a total angle of 180 degrees. In a triangle, the lengths of the first two sides are bigger than the length of the third side. The difference between the two sides of a triangle are also smaller than the third side's length.
what is a triangle?The 3-sided polygon known as a triangle is also known as the trigon, however this term is not particularly common. There are three sides to every triangle as well as three angles, some of which may be the same.
It is one of the fundamental shapes in geometry. Triangle ABC refers to a triangle with vertices A, B, and C.
The triangle has the following characteristics: A triangle (of any kind) has a total angle of 180 degrees. In a triangle, the lengths of the first two sides are bigger than the length of the third side. The difference between the two sides of a triangle are also smaller than the third side's length.
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if there are 3 numerical predictors and one categorical variable with 4 levels, how many models with interactions do we have to consider to find the one with the lowest aic?
By using Akaike Information Criterion(AIC) to compare various models , We need to consider 16 models to find the one with lowest AIC.
What do you mean by statistics?The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data.
What is AIC and it's formula?A mathematical tool for assessing how well a model matches the data it was derived from is the Akaike information criterion (AIC).
It's formula is:
AIC=2k-2ln(L)
predictors=independent variables=3
k=independent variables+1=4
Categorical variable= 4 levels
Total number of models to be considered = 4 * 4 =16
Since, Every layer (characteristics of variable) must interact with the predictors variable to calculate AIC and find the lowest one.
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Need help ASAP!!
What is the value of the function y=2x−3 when x=−1?
1) −5
2) −1
3) 2
4) 3
Answer:
-5
Step-by-step explanation:
-2-3 is -5 :>
Answer:
y=-5
Step-by-step explanation:
A company that makes chow mix and use 138 lb of peanuts for every 2/3 lb of reasons they make 245 lb of trail mix using only peanuts and raisins. How many pounds of peanuts do they use?
The number of pounds of peanuts the company uses is 6 pounds peanuts/1 pound raisins * 33 pounds raisins = 198 pounds peanuts.
To solve this problem, you can set up a system of equations to represent the given information. The first equation represents the fact that the company uses 138 pounds of peanuts for every 2/3 pound of raisins:
138 pounds peanuts / 2/3 pound raisins = x pounds peanuts
The second equation represents the fact that the company makes 245 pounds of trail mix using only peanuts and raisins:
x pounds peanuts + y pounds raisins = 245 pounds trail mix
To solve for the number of pounds of peanuts used, you can substitute the first equation into the second equation:
(138 pounds peanuts / 2/3 pound raisins) + y pounds raisins = 245 pounds trail mix
Multiplying both sides of the equation by 2/3 to eliminate the fraction, we get:
138 pounds peanuts + (2/3)y pounds raisins = (2/3)(245 pounds trail mix)
Combining like terms, we get:
138 pounds peanuts + (2/3)y pounds raisins = (2/3)(245 pounds)
Simplifying the right side of the equation, we get:
138 pounds peanuts + (2/3)y pounds raisins = 160 pounds
Subtracting 138 pounds from both sides of the equation, we get:
(2/3)y pounds raisins = 160 pounds - 138 pounds
Simplifying the right side of the equation, we get:
(2/3)y pounds raisins = 22 pounds
Dividing both sides of the equation by 2/3, we get:
y pounds raisins = (3/2)(22 pounds)
Simplifying the right side of the equation, we get:
y pounds raisins = 33 pounds
Substituting this value into the first equation, we get:
138 pounds peanuts / 2/3 pound raisins = 33 pounds raisins
Multiplying both sides of the equation by 2/3, we get:
138 pounds peanuts / (2/3)(33 pounds raisins) = 33 pounds raisins
Simplifying the right side of the equation, we get:
138 pounds peanuts / 22 pounds raisins = 33 pounds raisins
Dividing both sides of the equation by 22 pounds raisins, we get:
138 pounds peanuts / 22 pounds raisins / 33 pounds raisins = 33 pounds raisins / 22 pounds raisins
Simplifying the equation, we get:
6 pounds peanuts / 1 pound raisins = 33 pounds raisins / 22 pounds raisins
This equation shows that for every 1 pound of raisins the company uses, they use 6 pounds of peanuts.
Therefore, the number of pounds of peanuts the company uses is 6 pounds peanuts/1 pound raisins * 33 pounds raisins = 198 pounds peanuts.
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138 pounds peanuts / 2/3 pound raisins = x pounds peanuts
The second equation represents the fact that the company makes 245 pounds of trail mix using only peanuts and raisins:
x pounds peanuts + y pounds raisins = 245 pounds trail mix
(138 pounds peanuts / 2/3 pound raisins) + y pounds raisins = 245 pounds trail mix
138 pounds peanuts + (2/3)y pounds raisins = (2/3)(245 pounds trail mix)
138 pounds peanuts + (2/3)y pounds raisins = (2/3)(245 pounds)
138 pounds peanuts + (2/3)y pounds raisins = 160 pounds
(2/3)y pounds raisins = 160 pounds - 138 pounds
(2/3)y pounds raisins = 22 pounds
y pounds raisins = (3/2)(22 pounds)
y pounds raisins = 33 pounds
138 pounds peanuts / 2/3 pound raisins = 33 pounds raisins
138 pounds peanuts / (2/3)(33 pounds raisins) = 33 pounds raisins
138 pounds peanuts / 22 pounds raisins = 33 pounds raisins
138 pounds peanuts / 22 pounds raisins / 33 pounds raisins = 33 pounds raisins / 22 pounds raisins
6 pounds peanuts / 1 pound raisins = 33 pounds raisins / 22 pounds raisins
This equation shows that for every 1 pound of raisins the company uses, they use 6 pounds of peanuts.
Therefore, the number of pounds of peanuts the company uses is 6 pounds peanuts/1 pound raisins * 33 pounds raisins = 198 pounds peanuts.
Construct The Cumulative Frequency Distribution For The Given Data. Construct The Cumulative Frequency Distribution.
The cumulative frequency distribution is a type of statistical representation that shows the total number of data points in a sample that are less than or equal to a given value. It is often used to understand the distribution of data within a sample and to identify patterns or trends.
To construct a cumulative frequency distribution for given data, follow these steps:
Sort the data in numerical order from lowest to highest.Determine the number of data points in the sample. This is the total frequency for the distribution.Calculate the cumulative frequency for each data point by adding the frequency of that point to the cumulative frequencies of all previous points.Create a table or graph with the data points as the x-axis and the cumulative frequencies as the y-axis.For example, given the following data:
[tex]10, 15, 20, 25, 30, 35, 40, 45[/tex]The cumulative frequency distribution would be:
Data Point | Frequency | Cumulative Frequency
10 | 1 | 1
15 | 1 | 2
20 | 1 | 3
25 | 1 | 4
30 | 1 | 5
35 | 1 | 6
40 | 1 | 7
45 | 1 | 8
This distribution could be represented in a graph by plotting the data points on the x-axis and the cumulative frequencies on the y-axis and connecting the points with a line.
The answer is general since the data is not provided.
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Darnell rents some tables for $362 and some chairs for $3 each for a party. He spends a total of $500.
Answer: 46 chairs
Step-by-step explanation:
First, we have to find the amount of money Darnell spent to rent the chairs by taking
500 - 362 = $138
Then take $138 divided by $3 = 46 chairs
So he rent 1 table and 46 chairs
Answer:
let x - chairs
Darnell rents some tables for $362 and some chairs for $3 each for a party. He spends a total of $500.
500 = 362 + 3x
500 - 362 = 3x
138 = 3x
x = 46
46 chairsCHECKING:500 = 362 + 3(46)
500 = 362 + 138
500 = 500
Therefore, Darnell rents 46 chairs.
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Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-4. Which graph best represents the equation that has the roots x
Answer:
B
Step-by-step explanation:
this just means that the graph has to have x-intercepts (y = 0) at these x-values.
so, which graph intersects the x-axis at x = -7/3 and x = 1/2 ?
only B does that.
the others have other x-intercept points.
Which expression is equivalent to 2x² 4 3x² 2x 7?
The equivalent expression to 2x² + 4 + 3x² + 2x + 7 is 8x² + 2x + 11.
What is equivalent equation?An equivalent equation is an equation that has the same solution set as another equation. It is a mathematical expression that is equal in value to another expression. The two equations can often be solved using the same methods and yield the same result. Equivalent equations are useful in solving complex mathematical problems by breaking them down into simpler equations.
This is obtained by combining the like terms such as 2x² and 3x², which results in 5x², and 4 and 7 resulting in 11. The expression can be written as 5x² + 2x + 11. The final result can be obtained by multiplying 5x² with 2, which results in 8x². Hence, the equivalent expression is 8x² + 2x + 11.
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Find area of the fig.
The area of the composite figures are as follows;
10. Area of the trapezoids are; 96 cm², 80 cm², 96 cm², 80 cm²
Area of the rectangle at the center = 320 cm²
11. Area of the field on the left is 18,600 m²
Area of the field on the right is 11,000 m²
What is a composite figure?A composite figure is a figure that consists of two or more regular shapes.
10. The width of each trapezoid are;
(28 - 20)/2 = 4
(24 - 16)/2 = 4
The area of each trapezoid are;
The area of each of the left and right trapezoid = 4 × (20 cm + 28 cm)/2 = 96 cm²
Area of the top and bottom trapezoid = 4 × (16 cm + 24 cm)/2 = 80 cm²
Area of the rectangle at the center = 16 cm × 20 cm = 320 cm²
11. Area of ΔDEI = 0.5 × 80 m × 60 m = 2400 m²
Area of trapezoid EIGF = 0.5 × (60 m + 50 m) × (60 m + 20 m) = 4400 m²
Area of the triangle ΔAGF = 0.5 × 50 m × 80 m = 2000 m²
Area of ΔAHC = 0.5 × 40 m × (20 m + 80 m) = 2000 m²
Area of ΔABC = 0.5 × 30 m × (20 m + 80 m) = 1500 m²
Area of quadrilateral AHCB = 2000 m² + 1500 m² = 3500 m²
Area of triangle ΔCDH = 0.5 × 40 m × (80 m + 60 m) = 2800 m²
Adding together, we get;
2400 + 4400 + 2000 + 2000 + 1500 + 3500 + 2800 = 18,600
The area of composite figure is 18,600 m²\
Area of ΔEFH = 0.5 × 20 m × 40 m = 400 m²
Area of trapezoid GFHJ = 0.5 × (20 m + 40 m) (40 m + 40 m) = 2400 m²
Area of triangle ΔAGJ = 0.5 × 40 m ×(20 m + 60 m) = 1600 m²
Area of triangle ΔABK = 0.5 × 30 m × 60 m = 900 m²
Area of trapezoid BCF_K = 0.5 × (40 m + 30 m) × (40 m + 20 m) = 2100 m²
Area of triangle ΔCIE = 0.5 × 40 m × (40 m + 40 m) = 1600 m²
Area of triangle ΔCDE = 0.5 × 50 m × (40 m × 40 m) = 2000 m²
Adding the areas together, we get;
400 + 2400 + 1600 + 900 + 2100 + 1600 + 2000 = 11000
The area of the field is 11,000 m²
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Consider the mathematical sentence 2 = 2.
Is there any variable or constant that you could add to or subtract from both sides, or multiply or divide both sides by using the Properties of Equality to make this true sentence false? Choose variables and constants to create new mathematical sentences to justify your conclusion.
Answer: There is no variable or constant that you can add, subtract, multiply, or divide between the two sides of the sentence to make the sentence false by adding, subtracting, multiplying, or dividing each side of the sentence by the variable x x x and the constant 3.
Answer: No. Adding, subtracting, multiplying, and dividing both sides by the variable x x x and the constant 3 gives a true statement for each operation so there is no variable or constant that you can add, subtract, multiply, or divide to both sides to make the sentence false.
Step-by-step explanation:
What do 14 and 18 have in common?
The grade point average6of 20 college enior elected at random from a graduating cla are a
The mean of grade-point averages of 20 college seniors selected at random from a graduating class is 2.50.
What is Mean?Mean is the average of all numbers in the data set. The average can be found by dividing the sum of all numbers in the observed data by the number of data observations. This helps researchers, statisticians, etc. to find mean values in datasets. The formula for calculating the
average is:
mean = sum of values / number of values
It is denoted by X-bar.
We have the grade-point averages of 20 college seniors. The the random sample of graduating class as :
2.2, 1.6 ,2.7, 2.2, 2.4, 2.6, 3.8, 3.0, 2.5, 3.3, 1.8, 2.3, 3.3, 2.8, 2.0, 3.2, 2.1, 2.0, 2.9, 1.3
The Sum of grade point averages of 20 college seniors is calculated as follows,
∑ x = 2.2 + 1.6 + 2.7 + 2.2 + 2.4 + 2.6+ 3.8 + 3.0 + 2.5 + 3.3 + 1.8 + 2.3 + 3.3 + 2.8 + 2.0 + 3.2 + 2.1 + 2.0 + 2.9 + 1.3
∑x = 50
Total number of colleges , n = 20
Mean of distribution is calculated as follows,
X- bar = ∑x / n
where n is number of observations
X- bar = 50/20
=> X-bar = 2.5
Hence, required mean is 2.5 ..
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Complete question:
The grade-point averages of 20 college seniors selected at random from a graduating class are as follows:
2.2, 1.6 ,2.7, 2.2, 2.4, 2.6, 3.8, 3.0, 2.5, 3.3, 1.8, 2.3, 3.3, 2.8, 2.0, 3.2, 2.1, 2.0, 2.9, 1.3 Calculate the mean?
Can anyone help me with this question?
Given that X = [3, 5) and Y = (4, 9). Find A ∪ B
Answer:
A ∪ B = [3, 9)
Step-by-step explanation:
Set X is 3, and all number greater than 3 up, but not including, 5.
Set Y is all numbers from 4 to 9, but not including 4 or 9.
The union of the sets is all numbers from 3 up to 9, including 3 but not including 9.
A ∪ B = [3, 9)
What does translation of a triangle mean?
A translation occurs whenever an object is transported from one place to another without altering its dimension, form, or orientation.
A translation occurs whenever an object is transported from one place to another without altering its dimension, form, or orientation. We can draw the translation in the coordinate plane if we know which way and how far to move the figure.
The triangle can be translated in the following ways:
Step 1: In the first step, determine the coordinates of each vertex of the triangle.
Step 2: To translate each point, add the horizontal translation value to the x-coordinate of each vertex and the vertical translation value to the y-coordinate of each point. Add a negative number if either the vertical or horizontal translation for these translations is downhill or to the left.
Step 3: Plot the three translated points and draw the triangle by drawing a straight line between each pair of points.
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Please help ASAP. I don’t understand the question.
Answer:
Senior citizen ticket: $9
Child ticket: $13
Step-by-step explanation:
This can be solved by creating a system of equations:
[tex]f(x)=7x+5y=128[/tex]
and
[tex]g(x)=8x+10y=202[/tex]
where x is the cost of a senior citizen ticket and y is the cost of a child ticket.
Solve equation 2 for 5y:
[tex]8x+10y=202\\10y=202-8x\\\frac{10y}{x}=\frac{202-8x}{2}\\5y=101-4x[/tex]
Substitute (101-4x) for 5y in equation 1:
[tex]7x+(101-4x)=128\\3x+101=128\\(3x+101)-101=(128)-101\\3x=27\\\frac{3x}{3}=\frac{27}{3}\\x=9[/tex]
Substitute 9 for x in equation 2:
[tex]8(9)+10y=202\\72+10y=202\\(72+10y)-72=(202)-72\\10y=130\\\frac{10y}{10}=\frac{130}{10}\\y=13[/tex]
A senior citizen ticket costs $9 and a child's ticket costs $13.
To check these values, insert them into the equations:
[tex]128=7(9)+5(13)\\128=63+65\\128=128[/tex]
and
[tex]202=8(9)+10(13)\\202=72+130\\202=202[/tex]