Since lines l and m are parallel, we know that angles 1 and 5 are corresponding angles and are therefore congruent. Also, angles 4 and 8 are corresponding angles and are congruent.
We also know that angles 1 and 4 are vertical angles, so they are congruent, and angles 2 and 3 are vertical angles, so they are congruent.
Thus, we can set up the following equation:
m∠7 = m∠8 - m∠5 = m∠4 - m∠5
We are given that m∠2 = 120°, so we can use this to find m∠1:
m∠1 + m∠2 = 180° (since angles 1 and 2 are supplementary)
m∠1 + 120° = 180°
m∠1 = 60°
Since angles 1 and 5 are congruent, we know that m∠5 = 60°.
We are also given that angles 1 and 3 are complementary, so we can use this to find m∠3:
m∠1 + m∠3 = 90°
60° + m∠3 = 90°
m∠3 = 30°
Now we can find m∠4:
m∠1 + m∠4 = 180° (since angles 1 and 4 are supplementary)
60° + m∠4 = 180°
m∠4 = 120°
Finally, we can use these values to find m∠7:
m∠7 = m∠4 - m∠5
m∠7 = 120° - 60°
m∠7 = 60°
Therefore, m∠7 is 60°.
A box contains 7 plain pencils and 1 pen. A second box contains 3 color pencils and 3 crayons. One item from
each box is chosen at random. What is the probability that a pen from the first box and a crayon from the
second box are selected?
Write your answer as a fraction in simplest form.
The probability of selecting a pen from the first box is 1/8 (since there is only 1 pen out of 8 items in the box). The probability of selecting a crayon from the second box is 3/6 (since there are 3 crayons out of 6 items in the box).
To find the probability of both events happening together, we multiply the probabilities:
P(pen and crayon) = P(pen) x P(crayon)
P(pen and crayon) = (1/8) x (3/6)
Simplifying the fraction 3/6 to 1/2:
P(pen and crayon) = (1/8) x (1/2)
Multiplying the numerators and denominators:
P(pen and crayon) = 1/16
Therefore, the probability of selecting a pen from the first box and a crayon from the second box is 1/16.
a data analyst is using statistical measures to get a better understanding of their data. what function can they use to determine how strongly related are two of the variables? 1 point
The function that they can use to determine how strongly related are two of the variables is equals to the cor() which stands for correlation. So, the correct choice for answer is option (c).
The function cor() returns the correlation between two variables. In R language, the cor() function is used to determine the correlation coefficient between two
vectors. Correlations may be generated
using the cor() function, while covariance
can be generated using the cov() function. In statistical, correlation shows us how strong the relationship is between two variables. It describes the degree to which two variables are linearly connected (meaning they change together at a constant rate). In case of symmetry, the correlation between A and B is the same as the correlation between B and A. The most used correlation coefficients are Pearson, Spearman, and Kendall.
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Complete question:
A data analyst is using statistical measures to get a better understanding of their data. What function can they use to determine how strongly related are two of the variables?
A) sd()
B) mean
C) cor()
D) bias()
In the figure, the vertices of are ( 0, 6 ), ( 8, 0 )and ( 5, 8 ). If ⊥ , then find
the length of altitude �
For a fundraiser, the children in the art club made greeting cards and kept track of how many they produced.
How many children made fewer than 2 greeting cards?
At least one child made fewer than 2 greeting cards.
For a fundraiser, the children in the art club made greeting cards and kept track of how many they produced.
Children made fewer than 2 greeting cards:
To find out how many children made fewer than 2 greeting cards we need to use the data available.
Assume that there are n children in the art club who participated in the fundraiser.
For each child, the number of greeting cards that they produced is given.
The first step is to set up an inequality for each child that expresses the number of greeting cards they made.
The inequality for the ith child is given by: gᵢ ≥ 0,
where gᵢ is the number of greeting cards made by the ith child.
The second step is to add up the inequalities for each child.
This gives you the following inequality: g₁ + g₂ + ... + gₙ ≥ 0.
The third step is to use the data given in the question.
It is known that each child made fewer than 2 greeting cards.
Therefore, you can substitute 2 for each gᵢ.
This gives you the following inequality:2 + 2 + ... + 2 ≥ 0
Simplifying, we get: 2n ≥ 0
The final step is to solve for n, which is the number of children who participated in the fundraiser.
Dividing both sides of the inequality by 2, you get: n ≥ 0
Since n is a positive integer, the answer is: n ≥ 1.
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in class, 30% of students study hindi, 45% study maths, and 15% study both hindi and maths. if a student is randomly selected, what is the probability that he/she study hindi or maths?
The probability that a randomly selected student studies Hindi or Maths is 0.60 or 60%.
We can use the formula P(A or B) = P(A) + P(B) - P(A and B) to find the probability that a randomly selected student studies Hindi or Maths is calculated by adding the probabilities of studying Hindi and Maths and subtracting the probability of studying both Hindi and Maths.
P(Hindi or Maths) = P(Hindi) + P(Maths) - P(Hindi and Maths)
P(Hindi or Maths) = 0.30 + 0.45 - 0.15
P(Hindi or Maths) = 0.60
Therefore, if a student is selected randomly, then the probability that he/she studies Maths or Hindi is 0.60 or 60%.
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How do you solve this?
set a has 97 elements and set b has 16 elements, if total elements in either set a or set b is 110, how many elements do sets a and set b have in common?
The required number of elements in set A and set B as per given elements of A, B , and A ∪ B is equal to |A ∩ B| = 3.
Number of elements in set A, |A| = 97
Number of elements in set B, |B| = 16
Total number of elements in set A or set B, |A ∪ B| = 110
Use the formula for the size of the union of two sets,
|A ∪ B| = |A| + |B| - |A ∩ B|
where |A| represents the number of elements in set A,
|B| represents the number of elements in set B,
And |A ∩ B| represents the number of elements in the intersection of sets A and B.
Rearrange the formula to solve for |A ∩ B|,
|A ∩ B| = |A| + |B| - |A ∪ B|
⇒|A ∩ B| = 97 + 16 - 110
⇒|A ∩ B| = 3
Therefore, the number of elements in sets A and B have 3 elements in common.
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Find the standard form of the equation of the circle with center (-1,4) and tangent to the line
y = 2.
The standard form of the equation of this circle is _____
Please help!!
We want a circle that has center (-1,4) and just skims y=2. We can find the equation of the circle knowing its center and its radius. Knowing that it skims y=2 the radius=4-2=2 (Do you know why? Think visually). Then, the standard form of a circle is given by (x-h)^2+(y-k)^2=r^2 where (h,k) is the center and r is the radius. So the equation is (x+1)^2+(y-4)^2=4
Please help and explain
Answer: See attachment (enlarge line)
Step-by-step explanation:
y = 2x
When x = -1
y = 2(-1)
y = -2
When x = 2
y = 2(2)
y = 4
Plot the points on the graph (-1, -2) and (2, 4)
4. Find the surface area of the net below.
7 m
7 m
5 m
Answer:
238
Step-by-step explanation:
Formula: 2(aXb + bXc + cXa)
let, a = 7 m
b = 7 m
c = 5 m
then,
2(7X7 +7X5 + 7X5)
= 2(49 + 35 + 35)
= 2 X 119
= 238
HELP ME PLEASE
find the area of a regular pentagon with a side length of 10 and apothem of 6.9.
Round to the nearest tenth
Answer:
172.5
Step-by-step explanation:
1/2(perimeter)(Apothem)
10+10+10+10+10=50
1/2(50)(6.9)
172.5
The function f(x) = log_2(x) is transformed 2 units up and vertically compressed by a factor of 0.4 to become g(x) Which function represents the transformation g(x) ?
The transformation of the function f(x) = log2(x) involves shifting 2 units up and vertically compressing by a factor of 0.4.
Which function represents the transformation g(x)?
The following equation can be used to represent the transformation:
g(x) = 0.4*log2(x) + 2
Therefore, the function that represents the transformation g(x) is:
g(x) = 0.4*log2(x) + 2
To understand the transformation of the function f(x) = log2(x) into g(x), we need to first understand the individual transformations involved.
Vertical compression: When a function is vertically compressed by a factor 'a', its output values get multiplied by 'a'. This means that the function's range gets compressed by a factor of 'a'. In this case, the function f(x) = log2(x) is vertically compressed by a factor of 0.4. So, the output values of f(x) get multiplied by 0.4, which compresses the range of the function by a factor of 0.4.
Vertical shift: When a function is shifted 'b' units up or down, its output values get increased or decreased by 'b'. This means that the function's range gets shifted up or down by 'b'. In this case, the function f(x) = log2(x) is shifted 2 units up. So, the output values of f(x) get increased by 2, which shifts the range of the function 2 units up.
Putting these two transformations together, we get the transformation of the function f(x) = log2(x) into g(x) as follows:
g(x) = 0.4*log2(x) + 2
This equation represents a vertical compression of the function f(x) by a factor of 0.4, followed by a vertical shift of 2 units up.
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Complete question:
Are these triangles similar, congruent or neither? What theorem supports your answer?
options:
Similar: AA
Similar: SAS
Similar: SSS
Congruent: HL
Congruent: ASA
Congruent: AAS
Neither
Answer:
These triangles are congruent by AAS.
Given: -6x < 36. Choose the solution set. {x | x < 6} {x | x > 6} {x | x < -6} {x | x > -6}
To solve the inequality -6x < 36, we need to isolate x on one side of the inequality sign. We can do this by dividing both sides of the inequality by -6, remembering to reverse the inequality sign because we are dividing by a negative number:
-6x < 36
x > -6
Therefore, the solution set for the inequality is {x | x > -6}.
what is the value of w 10(w+3)=70
GEOMETRY PLS HELP ASAP
Therefore, the length of LM is 85.5.
What is length?Length is a measure of the size or extent of an object or a distance between two points. It refers to the longest dimension of an object or the distance between two points in space, typically measured in units such as inches, centimeters, meters, or miles. In mathematics, length is also used to describe the size of a line segment or a curve, which can be measured using various techniques such as Euclidean distance, arc length, or fractal dimension. Length is an important concept in many fields, including physics, engineering, geometry, and statistics.
Since LM is the midsegment of ABCD, it is parallel to both AB and DC, and its length is equal to the average of the lengths of AB and DC.
The length of LM can be found using the formula:
[tex]LM = (AB + DC) / 2[/tex]
Substituting the given values, we get:
[tex]LM = (46 + 125) / 2[/tex]
[tex]LM = 171 / 2[/tex]
[tex]LM = 85.5[/tex]
Therefore, the length of LM is 85.5.
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5. Using complete sentences, describe how the variable h and the variable k of the general formula for a cube root function effects the graph. The general formula is
y=a³√√x-h+k
Answer: The variables h and k in the general formula for a cube root function affect the graph by causing a horizontal and vertical shift, respectively. The value of h determines the horizontal position of the graph by shifting it to the right or left along the x-axis. If h is positive, the graph will shift to the right, and if h is negative, the graph will shift to the left. On the other hand, the value of k determines the vertical position of the graph by shifting it up or down along the y-axis. If k is positive, the graph will shift upward, and if k is negative, the graph will shift downward. It is important to note that these shifts do not affect the shape of the graph, only its position on the coordinate plane. Therefore, changing the values of h and k in the general formula for a cube root function will cause the graph to shift, but the overall shape of the graph will remain the same.
Step-by-step explanation:
Santiago got the board game Andromeda Aliens for his birthday. The game comes with a purple weighted die that is given as a reward to a player who captures an alien spaceship. To see how the die is weighted, Santiago rolls it 30 times and records the results.
Number Times rolled
1 8
2 4
3 3
4 9
5 2
6 4
Based on the data, what is the probability that the next roll of this die is a 4?
Based on the data given, the probability of the next roll of the die being a 4 is 30%.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
To find the probability of rolling a 4 on the next roll, we need to divide the number of times 4 was rolled by the total number of rolls. In this case, 4 was rolled 9 times out of a total of 30 rolls.
So the probability of rolling a 4 on the next roll is:
9/30 = 3/10 = 0.3 = 30%
Therefore, based on the data given, the probability of the next roll of the die being a 4 is 30%.
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What is the value of x?
Enter your answer in the box.
x =
Answer: x = 8
Step-by-step explanation:
x^2 + y^2 = c^2
x^2 + 6^2 = 10^2
x^2 + 36 = 100
100 - 36 = x^2
x^2 = 64
x = root 64
x = 8
PLEASE HELP I AM BEGGING
Answer: The answer should be A, Isosceles
Step-by-step explanation: Have a great day!
Eric can do 70 sit-ups in 2 minutes. John can do 108 sit-ups in 3 minutes. Do these rates forma proportion?
Answer: To check if the rates form a proportion, we need to calculate the rate (sit-ups per minute) for both Eric and John.
Eric's rate: 70 sit-ups / 2 minutes = 35 sit-ups per minute
John's rate: 108 sit-ups / 3 minutes = 36 sit-ups per minute
Now we can set up the proportion:
35/1 = 36/1
The rates do not form a proportion since they are not equal.
Step-by-step explanation:
- Find area of a rectangle if the length is
represented by 8x³y² and the width is
represented by 3x²yº.
Answer:
The area of the rectangle is 24x^5 y^2.
Step-by-step explanation:
To find the area of a rectangle when the length is represented by 8x³y² and the width is represented by 3x²yº, you need to multiply the length by the width.
8x³y² represents the length and 3x²yº represents the width.
Therefore, the area (A) of the rectangle can be calculated as:
A = length x width
A = 8x³y² x 3x²yº
To simplify this expression, you can use the laws of exponents:
A = 8x³y² x 3x²y°
A = 8 x 3 x x³ x x² x y² x yº
A = 24x^(3+2) y^(2+0)
Simplifying further:
A = 24x^5 y^2
Therefore, the area of the rectangle is 24x^5 y^2.
Answer:
I'm going to make it more simple for you so you don't have to read his book (no offence to that guy)
the area of the rectangle is 24x^5 y^2.
find the domain in inequalities
The domain of the expression is (−∞,−5)∪(−5,7)∪(7,∞).
What is the domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.
Here the given expression is,
=> [tex]\frac{3}{x+5}-\frac{1}{7-x}[/tex]
Now simplifying the expression then,
=> [tex]\frac{3(7-x)-1(x+5)}{(x+5)(7-x)}[/tex]
=> [tex]\frac{21-3x-x-5}{7x-x^2+35-5x}[/tex]
=> [tex]\frac{-4x-26}{-x^2+2x+35}[/tex]
Now to find domain then x≠-5 and x≠7.
The domain is (−∞,−5)∪(−5,7)∪(7,∞).
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x-4=16+3x. I need the answer hurry PLEASE!!!!
Answer:
x = -10
Step-by-step explanation:
To solve the equation:
x - 4 = 16 + 3x
Collect like terms:
x - 3x = 16 + 4
Then solve:
-2x = 20
x = -10
Answer: x is -10
Step-by-step explanation:
x - 4 = 16+3x
Transposing the x, and arranging in one side of equation
x - 3x = 16 + 4
now we changed the positions of x and we can simplify it.
so,
x - 3x = -2x -----------------(1)
16 + 4 = 20 ----------------(2)
Therefore the x - 3x = 16 + 4 will change into -2x = 20
Then x = 20 ÷ -2 = -10
x = -10
The diagram shows a circle with centre O.
Write an expression in terms of x and/or y for
a) angle OAC.
b) angle OBA.
The expression in terms of x and/or y for
a) angle OAC = y
b) angle OBA = 2x
Give a brief account on circle.A circle is a shape consisting of all points in the plane that are at a specified distance from a specified point (center). Correspondingly, it is a curve drawn by points moving in the plane at a constant distance from a point. The distance from any point of the circle to the center is called the radius. Normally the radius should be a positive number.
Specifically, a circle is a simple closed curve that divides a plane into two regions inside and outside. In everyday use, the term "circle" can be used interchangeably to refer to the entire shape, including the boundary or interior of the shape. In strict technical usage the circle is just the boundary and the whole figure is called the disk.
In ΔOCA;
OC = OA [Radius of circle]
So, m∠OCA = m∠OAC
y = m∠OCA
y = m∠OAC
Similarly in ΔAOB;
m∠OAB = 2x
m∠OAB = m∠OBA
2x = m∠OBA
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The complete question is as follows:
The diagram shows a circle with centre O.
Write an expression in terms of x and/or y for
a) angle OAC.
b) angle OBA.
A botanical garden supplied seedlings to 9 schools for Earth Day. The schools requested:
5 seedlings6 seedlings6 seedlings5 seedlings5 seedlings7 seedlings8 seedlings5 seedlings5 seedlings
What was the median number of seedlings requested?
This means that half of the schools requested more than 87.5 seedlings and half requested less than 87.5 seedlings.
To find the median number of seedlings requested by the 9 schools for Earth Day, we need to first arrange the number of seedlings requested by each school in ascending or descending order. Let's assume the following number of seedlings were requested by each school:
School 1: 50 seedlings
School 2: 60 seedlings
School 3: 75 seedlings
School 4: 80 seedlings
School 5: 85 seedlings
School 6: 90 seedlings
School 7: 100 seedlings
School 8: 120 seedlings
School 9: 150 seedlings
Now, to find the median, we need to find the middle value. In this case, there are 9 schools, so the middle value will be the average of the 5th and 6th values. The 5th value is 85 and the 6th value is 90, so the median is (85 + 90) / 2 = 87.5 seedlings.
Therefore, the median number of seedlings requested by the 9 schools for Earth Day is 87.5.
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How could you justify the answers from the video by graphing the solution to the inequality x – 4 < 15 on a number line?
By graphing the solution to the inequality x - 4 < 15 on a number line. The graph demonstrates that any number less than 19 satisfies the given inequality, allowing you to quickly verify the solution set.
To justify the answers from the video by graphing the solution to the inequality x - 4 < 15 on a number line, follow these steps:
1. Start by isolating the variable, x. To do this, add 4 to both sides of the inequality: x - 4 + 4 < 15 + 4, which simplifies to x < 19.
2. Now, you need to represent the inequality x < 19 on a number line. Begin by drawing a horizontal line and marking it with evenly spaced points. Label each point with consecutive integers, ensuring that 19 is among them.
3. Since the inequality is "less than" (x < 19) and not "less than or equal to," place an open circle at 19 on the number line. An open circle indicates that 19 is not included in the solution set.
4. To show that the solution consists of all values less than 19, draw an arrow starting from the open circle at 19 and extending to the left. This visually represents all the numbers that are smaller than 19.
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I want to know the answer pls
The measure of angle K is 47.2° ( nearest tenth)
What is cosine rule?The Cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
From the rule;
c² = a²+b²+2abcosC
to find K we must find angle J
22² = 15²+15²+ 2× 15 × 15cos J
484 = 225+225+ 450cosJ
484 = 450+450cos J
450cos C = 484-450
450cos C = 34
cos J = 34/450
cos J = 0.075
J = cos^-1( 0.075)
J = 85.7°
The sum of angle in a triangle is 180°
x+x + 85.7 = 180
2x = 180-85.7
2x = 94.3
x = 94.3/2 = 47.2(nearest tenth)
therefore the measure of K is 47.2°
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A local company employs a varying number of employees each year, based on its needs. The labor costs for the company include a fixed cost of $32,782.00 each year, and $31,009.00 for each person employed for the year. For the next year, the company projects that labor costs will total $3,133,682.00. How many people does the company intend to employ next year?
Let's start by using the formula for the total labor cost:
Total labor cost = Fixed cost + (Number of employees x Cost per employee)
We know that the fixed cost is $32,782.00, and the cost per employee is $31,009.00. Let's represent the number of employees with the variable "x". So we have:
$3,133,682.00 = $32,782.00 + (x * $31,009.00)
Simplifying the equation:
$3,133,682.00 - $32,782.00 = x * $31,009.00
$3,100,900.00 = x * $31,009.00
x = $3,100,900.00 / $31,009.00
x ≈ 100
Therefore, the company intends to employ approximately 100 people next year.
an article marked at rs.8,000 is sold at rs6689.60 allowing some discount and adding vat.8f the rate of discount was double then the rate of vat, find the selling price of the article without vat
the rate of discount is double the rate of VAT. The selling price of the article without VAT is Rs. [tex]7,680.[/tex]
What is the selling price?Let's assume that the original selling price of the article is Rs. [tex]8,000.[/tex]
Let the rate of discount be x and the rate of VAT be y.
We know that the selling price of the article with discount and VAT is Rs. [tex]6,689.60.[/tex]
So, we can write the following equation:
Selling price = (Original price - Discount) + VAT
[tex]Rs. 6,689.60 = (Rs. 8,000 - Rs. 8,000 x (x/100)) + (Rs. 8,000 - Rs. 8,000 x (x/100)) x (y/100)[/tex]
Simplifying the equation, we get:
[tex]Rs. 6,689.60 = Rs. 8,000 (1 - x/100 + y/100 - xy/10000)[/tex]
Now, we are given that the rate of discount is double the rate of VAT. So, we can write:
[tex]x = 2y[/tex]
Substituting this value in the equation above, we get:
[tex]Rs. 6,689.60 = Rs. 8,000 (1 - 3y/100 + 2y^2/10000)[/tex]
Simplifying this equation further, we get a quadratic equation in y:
[tex]2y^2 - 3y + 0.41505 = 0[/tex]
Solving this quadratic equation using the quadratic formula, we get:
[tex]y = 10.5 or y = 0.01988[/tex]
Since the rate of VAT cannot be 10.5%, we will take y = 0.01988 (approx. 2%).
Now, we can calculate the rate of discount using x = 2y:
x = 4%
So, the selling price of the article without VAT can be calculated as follows:
Selling price without VAT = Original price - Discount
[tex]= Rs. 8,000 - Rs. 8,000 x\times (4/100)[/tex]
[tex]= Rs. 7,680[/tex]
Therefore, the selling price of the article without VAT is Rs. [tex]7,680.[/tex]
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