Line ac and df are parallel they are cut by transversal Hj with your partner find the seven unknown angle measures in the diagram explain your reasoning. What do you notice about the angles with vertex B and the angles with vertex E
The measure of the unknown angles in the parallel lines AC and DF with transversal HJ are as follow,
m ∠DEH = 63° , m ∠BEF = 63° ,m ∠CBJ = 63°, m ∠CBE = 117° , m ∠FEH = 117° , m ∠BED = 117° , and m ∠ABJ = 117°.
Two lines AC and DF are parallel to each other in the attached figure
Transversal HJ cut lines AC and DF at point B and E respectively.
Measure of ∠ABE = 63°.
Using the result based on corresponding angles, alternate interior angles , and vertically opposite angles of a parallel lines we get,
Measure of ∠ABE ≅ Measure of ∠DEH ( corresponding angles)
⇒Measure of ∠DEH = 63°
Measure of ∠ABE ≅ Measure of ∠BEF ( alternate interior angles)
⇒Measure of ∠BEF = 63°
Measure of ∠ABE ≅ Measure of ∠CBJ ( vertically opposite angles)
⇒Measure of ∠CBJ = 63°
Using the result of linear pair angles,
Measure of ∠ABE + Measure of ∠CBE = 180°
⇒ Measure of ∠CBE = 180° -63°
⇒ Measure of ∠CBE = 117°
Measure of ∠CBE ≅ Measure of ∠FEH ( corresponding angles)
⇒Measure of ∠FEH = 117°
Measure of ∠CBE ≅ Measure of ∠BED ( alternate interior angles)
⇒Measure of ∠BED = 117°
Measure of ∠CBE ≅ Measure of ∠ABJ ( vertically opposite angles)
⇒Measure of ∠ABJ = 117°
Therefore, the measure of the seven unknown angles formed in the parallel line are given by m ∠DEH = 63° , m ∠BEF = 63° ,m ∠CBJ = 63°, m ∠CBE = 117° , m ∠FEH = 117° , m ∠BED = 117° , and m ∠ABJ = 117°.
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The above question is incomplete, the complete question is:
Lines AC and DF are parallel. They are cut by transversal HJ with your partner find the seven unknown angle measures in the diagram explain your reasoning. What do you notice about the angles with vertex B and the angles with vertex E.
In the attached figure.
Each triangle in the quilting square pattern shows has a base and height of 2 inches how much fabric is needed to create one quilting square
Answer:
The amount of fabric needed to create one quilting square is 8 inches.
Answer:
The amount of fabric needed to create one quilting square is 8 inches.
Step-by-step explanation:
Calculus please help
Answer:
[tex]f(x)=\dfrac{1}{20}x^5+\sinh(x)-\dfrac{1}{2}\sinh(2)x+6[/tex]
Step-by-step explanation:
Given:
[tex]\phantom{ww} \bullet\;\;\;f''(x)=x^3+\sinh(x)[/tex]
[tex]\phantom{ww} \bullet\;\;\;f(0)=6[/tex]
[tex]\phantom{ww} \bullet\;\;\;f(2)=7.6[/tex]
To find f'(x), integrate f''(x):
[tex]\begin{aligned}\displaystyle f'(x)=\int f''(x)\; \text{d}x&=\int \left(x^3+\sinh(x)\right)\; \text{d}x\\\\&=\int x^3\;\text{d}x+\int \sinh(x)\; \text{d}x\\\\&=\dfrac{1}{4}x^4+\cosh(x)+\text{K}\end{aligned}[/tex]
To find f(x), integrate f'(x):
[tex]\begin{aligned}\displaystyle f(x)=\int f'(x)\; \text{d}x&=\int \left(\dfrac{1}{4}x^4+\cosh(x)+\text{K}\right)\;\text{d}x\\\\&=\int \dfrac{1}{4}x^4\; \text{d}x+\int \cosh(x) \; \text{d}x + \int \text{K}\; \text{d}x\\\\&=\dfrac{1}{20}x^5+\sinh(x)+Kx+\text{C}\end{aligned}[/tex]
Substitute f(0) = 6 to determine the value of the constant C:
[tex]\begin{aligned}f(0)=\dfrac{1}{20}(0)^5+\sinh(0)+K(0)+\text{C}&=6\\\\0+0+0+\text{C}&=6\\\\\text{C}&=6\end{aligned}[/tex]
Substitute f(2) = 7.6 and C = 6 to determine the value of the constant K:
[tex]\begin{aligned}f(2)=\dfrac{1}{20}(2)^5+\sinh(2)+K(2)+6&=7.6\\\\1.6+\sinh(2)+2K+6&=7.6\\\\\sinh(2)+2K&=0\\\\2K&=-\sinh(2)\\\\K&=-\dfrac{1}{2}\sinh(2)\end{aligned}[/tex]
Therefore, function f(x) is:
[tex]\boxed{f(x)=\dfrac{1}{20}x^5+\sinh(x)-\dfrac{1}{2}\sinh(2)x+6}[/tex]
[tex]\textsf{As}\;\;\sinh(2)=\dfrac{e^4-1}{2e^2},\;\textsf{we can also write the equation as:}[/tex]
[tex]f(x)=\dfrac{1}{20}x^5+\sinh(x)-\dfrac{1}{2}\left(\dfrac{e^4-1}{2e^2}\right)x+6[/tex]
[tex]f(x)=\dfrac{1}{20}x^5+\sinh(x)-\left(\dfrac{e^4-1}{4e^2}\right)x+6[/tex]
The area of a square table top can be represented by (9x^2-30x+25) square feet. The perimeter of the table top is 34 feet. What is the value of x? Explain ow you solved this problem.
The requried value of x that satisfies the problem is 4.5,
Let's start by finding the side length of the square tabletop, which is equal to the square root of its area. We have:
Area = 9x² - 30x + 25
Side length = √(Area) = √(9x² - 30x + 25)
To find x, we need to use the fact that the perimeter of the table top is 34 feet. The perimeter of a square is given by 4 times the length of one of its sides, so we can write:
Perimeter = 4 * Side length
34 = 4 * √(9x² - 30x + 25)
8.5 = √(9x² - 30x + 25)
9x² - 30x - 47.25 = 0
We can solve this quadratic equation by using the quadratic formula gives,
x = 4.5 and -1.16
Therefore, the value of x that satisfies the problem is approximately 4.5, since the other solution is negative and not meaningful in this context.
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Select all of the figures that show axis symmetry.
Answer: All of them
Step-by-step explanation:
All of them can be divided into two equal halves.
The figures that show axis symmetry are 1, 2, and 3.
What is the axis of symmetry?The axis of symmetry is a line, plane, or other axis that divides a geometric figure into two mirror-image halves that are congruent to each other.
A figure has axis symmetry if it looks the same after being rotated around an axis.
Out of the given figures, the ones that have axis symmetry are:
Sphere (has infinite axis symmetry)Cone (has rotational symmetry around its central axis)Cylinder (has rotational symmetry around its central axis)The figures that do not have axis symmetry are:
Cube (has only point symmetry)Rectangular cone (has no rotational symmetry)So, the figures that show axis symmetry are 1, 2, and 3.
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5a-3b=7b find the ratio of a:b
(i need answers quick)
The ratio of a:b in 5a-3b=7b is 4:5.
We know that,
A ratio is an ordered pair of numbers a and b, written as a/b where b does not equal 0. A proportion is an equation in which two ratios are equal to each other. For example, if there are 2 boys and 6 girls, you can write the ratio as: 1 : 3 (for every boy there are 3 girls).
Ratios compare two numbers obtained by dividing. If one data point (A) is compared to another data point (B), it is expressed as A/B. It means that we are partitioning information A from information B. For example, if A is five and B is 10, your ratio would be 5/10, or 1/2.
For above information,
5a - 3b = 7b
5a = 7b- 3b
5a= 4b
So, a/b= 4/5
a:b is 4:5
Thus, the ratio of a:b in 5a-3b=7b is 4:5.
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Name 2 other categories of data you could use to better understand the physical fitness levels of these students.
Two other categories of data that could be used to better understand the physical fitness levels of students are:
Body composition data:
Cardiovascular fitness data:
We have,
Two other categories of data that could be used to better understand the physical fitness levels of students are:
Body composition data:
This data can include measurements such as body mass index (BMI), body fat percentage, and waist circumference.
By collecting body composition data for students, we can better understand their overall physical health and identify potential risk factors for chronic diseases related to physical fitness.
Cardiovascular fitness data:
This data can include measurements such as resting heart rate, maximal oxygen uptake (VO2 max), and cardiovascular endurance test results.
By collecting cardiovascular fitness data for students, we can better understand their cardiovascular health and fitness levels, as well as identify potential risk factors for heart disease and other related conditions.
Thus,
Two other categories of data that could be used to better understand the physical fitness levels of students are:
Body composition data:
Cardiovascular fitness data:
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Help me please and thank you very much! :)
Answer:
2700
Step-by-step explanation:
20 inches x 15 inches x 9 inches! <3
also get some sleep lol
johnathannes brahms destoryed or left many because of his work unplublished because
A. He didnt want to be sucessful
B. He thought they were too good to publish
C. He was a perfectionist and was never satisfied with them.
Answer asap for brainlist
Mary has the qualities of being a team leader.
Here, we have,
Team leaders upload any other stage of control. They’re employed to persuade and construct relationships, to make matters happen. Team chief’s to-do lists may be vast, however through categorizing them, it’ll come up with readability approximately the reason of your job.
A group chief has an outline of a set of humans, motivates, offers guidance and video display units performance. It is probably an professional identify alternate or a delegation exercising out of your management, however both way, being a group chief separates you out of your friends as a depended on individual to manipulate a assignment or institution of humans.
Team leaders and executives have exceptional responsibilities. Unlike managers, group leaders won’t have the authority to direct, alternate plans, put in force or construct their groups via hiring and firing. Their position is mostly a motivational and inspirational one inside an organization. They’re professional dating developers and mediators, liaising among the humans and management.
Thus this are the qualities of team leader.
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complete question;
Mary is a perfectionist . She loves participating on teams and often takes on too many tasks because she wants to ensure that they are done on time and on budget.
Triangle ABC and triangle DEF are similar. What is the measure
of side DF?
B
E
9 cm
15 cm
D
с
? cm
25 cm
F
The measure of side DF is 15cm
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. For two traingles to be similar, the corresponding angles of the triangles must be equal.
And also, the ratio of corresponding sides of Similar triangles are equal
This means;
15 /25 = 9/DF
representing DF by x
15/25 = 9/x
15x = 25×9
15x = 225
divide both sides by 15
x = 225/15
x = 15cm
Therefore the measure of DF is 15cm
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An urn contains 6 red and 8 black balls. Five balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 5 balls drawn from the urn are black? Round your answer to three decimal places.
A. Roel organized his students' scores on the following line plot.
Students' Scores
00000
60
65
70
75
80
85
90
95
100
Based on this information, which of the following BEST describes the median student
score?
A 35
B. 80
C. 85
D. 90
Answer: - None of the above.
Step-by-step explanation:
The median is the middle value of the data set when arranged in order. In this case, we have an even number of values, so we need to take the average of the middle two values to find the median. The middle two values are 80 and 85. Therefore, the median student score is: (80 + 85) / 2 = 82.5
The closest answer choice to this value is C. 85, but it is not the correct answer. Therefore, the correct answer is none of the above.
A swimming pool is shaped like the figure below. Each end is a semicircle, and the length and width of the rectangle are 60 feet and 30 feet, respectively.
The area of the border is 105.53 feet².
We have,
The swimming pool is a combination of two shapes.
Rectangle:
Length = 60 feet
Width = 30 feet
Area = 60 x 30 = 1800 feet²
Semicircle:
Diameter = 30 feet
Radius = 15 feet
Area = π/2 r² = 1/2 x 3.14 x 15 x 15 = 353.25 feet².
Now,
The area of the swimming pool.
= 1800 + 353.25
= 2153.25 feet²
Now,
Without the border.
Area of the swimming pool.
= rectangle area + semicircle area
= 60 x (30 - 1) + 1/2 x π x (15 - 1)²
= 60 x 29 + 1/2 x 3.14 x 14 x 14
= 1740 + 307.72
= 2047.72 feet²
Now,
The area of the border.
= 2153.25 - 2047.72
= 105.53 feet²
Thus,
The area of the border is 105.53 feet².
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I need help with solving and graph each of the following inequalities
The solution and graph of each of the inequalities is shown below:
k ≥ 4v < 17x ≤ 6y > 8g > 3.9w > -7What is an inequality?In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).Next, we would determine the solution for each of the inequalities as follows;
k + 7 ≥ 11
k ≥ 11 - 7
k ≥ 4
5 > v - 12
5 + 12 > v
17 > v
v < 17 (flip).
-5x ≤ -30
x ≤ 6
y/4 > 2
y > 2(4)
y > 8
10g + 19 > 49
10g > 49 - 19
10g > 39
g > 3.9
-w - 7 > 0
-w > 7
w > -7
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4,12,44,176,890
which is odd one ?
Answer:
If we are looking at 100th it is 176 if it's tens look at 7 and 9
The distance between (2,2) and (8,2) is 6 units on a coordinate plane. Select all of the pairs of points that are 6 units apart.
The points are not at a distance of 6 units from each other.
Given that the distance between point (2, 2) and point (8, 2) is 6 units a coordinate plane.
We need to find which other pairs of points are also 6 units apart.
The distance between two points (x₁, y₁), (x₂, y₂) are 6 if and only if either
( x₂ - x₁ = 6 and y₂ = y₁ )or ( x₂ = x₁ and y₂ - y₁ = 6 ).
If either of the conditions is satisfied, then only we can say that the two points has distance of 6 units between them.
Now, As given
Let (x₁, y₁) = ( 2, 2) , (x₂, y₂) = (8, 2)
Check whether the conditions are satisfied or not .
Here x₁ = 2 , x₂ = 8, y₁ = 2, y₂ = 2
Now,
x₂ - x₁ = 8 - 2 = 6 , y₂ - y₁ = 2 - 2 = 0
∴ we get
1st condition is satisfied, So the points have a distance of 6 units between them.
Now,
Let us suppose another point (x₁, y₁) = ( 4, 3) , (x₂, y₂) = (3, 3)
Here x₁ = 4 , x₂ = 3, y₁ = 3, y₂ = 3
Now,
x₂ - x₁ = 4 - 3 = 1 , y₂ - y₁ = 3 - 3 = 0
Here neither of the conditions are satisfied.
So, the points are not at a distance of 6 units from each other.
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Amelia gathered data about the heights of students at her school. Based on the displays, what inferences can you make about each sample?
Amelia can make inferences by using
The range of heightsThe shape/mean of the distributionThe presence of outliers, etc.What is the inferences about?Inferences from data on student heights include range determination based on minimum and maximum values, indicating greater variability with a larger range.
The average height of students can be determined using measures like mean, median, and mode. The distribution's shape can be determined by the histogram or box plot, indicating how the heights are distributed. inferences can be made by the use of height samples to gain insight into school population.
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If the rate of inflation is 2.6% per year, the future price p (1) (in dollars) of a certain item can be modeled by the following exponential function, where t is the
number of years from today.
p(t)=1200 (1.026)
Find the current price of the item and the price 8 years from today.
Round your answers to the nearest dollar as necessary.
Current price ?$
Price 8 years from today?$
a) Based on the exponential function, p(t)=1200 (1.026)^t, the item's current price with a rate of inflation of 2.6% per year is $1,200.
b) In 8 years, the future price of the item would be $1,473.53.
What is an exponential function?An exponential function is a mathematical equation depicting the relationship between one variable and another with a periodic constant rate of growth or decline.
Exponential functions are classified into two:
Exponential growth functionExponential decay function.Let the number of years from today = t
Annual inflation rate = 2.6%
Current price = $1,200
Time in years = 8 years
Exponential function:p(t)=1200 (1.026)^t
p(8) = 1,200(1.026)^8
= $1,473.53
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Claire got 17 out of 20 questions correct on her vocabulary quiz. What percent of the questions did she get wrong?
The percentage of the questions she got wrong is 15%
What is a Percentage?
Percentage is a number or ratio by dividing the value by the total value and then multiplying the result by 100.
How to determine this
Out of 20 questions, Claire got 17 questions
i.e the questions she got right = 17
The questions she got wrong = 20 - 17 = 3
To get the percentage she got wrong
= 3/20 *100%
= 300/20%
= 15%
Therefore, the percentage she got wrong is 15%
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3cm
7 cm
2 cm
Surface area of the prism
The surface area of the rectangular prism is 82 square cm.
Given that:
Length, L = 3 cm
Width, W = 7 cm
Height, H = 2 cm
Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as,
SA = 2(LW + WH + HL)
The surface area of the rectangular prism is calculated as,
SA = 2 x (3 x 7 + 7 x 2 + 2 x 3)
SA = 2 x (21 + 14 + 6)
SA = 2 x 41
SA = 82 square cm
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Chantel is deciding which of two similar wallets she will buy. Both are rectangular, but she wants the one that will best fit in her purse. The larger wallet is 18 centimeters long and the smaller one is 10 centimeters long. What is the area of the larger wallet if the area of the smaller one is 60 square centimeters?
The requried area of the larger wallet is 194.4 square centimeters.
Since the two wallets are similar, their corresponding sides are proportional. Let x be the width of the smaller wallet, then the width of the larger wallet is 18/10 times x, or 9/5 times x. Therefore, the dimensions of the larger wallet are 9/5 times the dimensions of the smaller wallet.
The area of the smaller wallet is x times 10 (length times width), or 10x square centimeters. We are given that this area is 60 square centimeters, so:
10x = 60
x = 6
Therefore, the width of the smaller wallet is 6 centimeters. The width of the larger wallet is 9/5 times 6, or 10.8 centimeters. The length of the larger wallet is 18 centimeters.
The area of the larger wallet is 10.8 times 18, or 194.4 square centimeters. Therefore, the area of the larger wallet is 194.4 square centimeters.
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help
A grocery store clerk is placing cans of soup on an 8-ft long shelf. If the cans are lined up in a row, how many more of the smaller cans will fit on the shelf than the larger cans? Round to the nearest whole number.
There is 1 smaller can that will be put on the shelve.
Given that, a clerk is placing cans of soup on an 8-ft long shelf, we need to find how many more of the smaller cans will fit on the shelf than the larger cans,
Volume of small cans = 127.2 in³
Therefore,
127.2 = 3.14 × 4.5 × r²
r² = 127.2 / 14.13
r² = 9
r = 3
Similarly, the volume of the large can = 301.6 in³
301.6 = 3.14 × 6 × r²
r² = 16
r = 4
The number of small cans that can be out on the shelve = 8/3 ≈ 9
The number of larger cans that can be out on the shelve = 8/4 = 2
Hence, there is 1 smaller can that will be put on the shelve.
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What is the value of c in the equation?
15.3 = StartFraction c Over 2.1 EndFraction
13.2
17.4
32.13
321.3
Answer:
32.13
Step-by-step explanation:
The value of c in the equation 15.3 = c/2.1 is 32.13. To solve for c, you can cross-multiply and simplify the equation to c = 15.3 x 2.1 = 32.13.
The solution to the equation "the quotient of a number and 8 is 16" is 128. To solve for the number, you can multiply both sides by 8 to get "the number is 16 x 8 = 128."
To translate the sentence "the quotient of a number and 8 is 16" into an equation, you can use "x" to represent the number and write x/8 = 16.
Answer:
c or a
Step-by-step explanation:
i thing a
graphing transformations
Each of the graphs should be matched with the appropriate function as follows;
Graph 1: D. f(x) = (x - 2)² + 3
Graph 2: C. f(x) = -(x - 2)² - 3
Graph 3: B. f(x) = -(x - 3)² - 2
Graph 4: C. f(x) = (x - 3)² + 2
What is the general form of a quadratic function?In Mathematics and Geometry, the standard or general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Mathematically, the vertex form of a quadratic function is modeled by this equation:
f(x) = a(x - h)² + k
Where:
h and k represents vertex of the graph.a represents leading coefficient.In conclusion, we can logically deduce that each of the given quadratic function were either vertically translated or horizontally translated.
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Please help with this simple question (Large reward)
Answer:
H
Step-by-step explanation:
Firstly, G and J cannot be the answers because the beginning numbers are too big. If you look at the fractions, you can see 2 and 7/8 because 2 is the smallest of all of them. Now the answer is between F and H.
In F, the second number is 3 and 1/2.
In H, the second number is 3 and 1/4.
If you want to make it an improper fraction to visualize better, it would be 7/2 and 12/4=6/2. Or you can just compare to see which is smaller, 1/2 or 1/4. In this case, 3 and 1/4 is smaller. Therefore the answer is H.
The table shows the results of rolling a die several times. Outcome 1 2 3 4 5 6 Number of times outcome occurred 7 4 4 5 6 4 To the nearest percent, what is the experimental probability of rolling a 6? Question 1 options: 17% 20% 13% 67%
The experimental probability of the rolling a 6 is 13%.
How to find the experimental probability of rolling a 6?Probability is the likelihood of a desired event happening. Experimental probability is a probability that relies mainly on a series of experiments.
From the table:
The total number of times all the numbers appear is:
total number of times = 7 + 4 + 4 + 5 + 6 + 4 = 30
The number six (6) occurred 4 times.
Experimental probability = (occurrence of 6 / total number of times)
Experimental probability = 4/30 * 100
Experimental probability = 13%
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URGENT! Can someone please help?
a. The missing values of the logarithm expression is log₃(40).
b. The missing values of the logarithm expression is log₅(8).
c. The missing values of the logarithm expression is log₂(1/25).
What is the missing of the logarithm expression?The missing values of the logarithm expression is calculated as follows;
(a). log₃5 + log₃8, the expression is simplified as follows;
log₃5 + log₃8 = log₃(5 x 8) = log₃(40)
(b). The log expression is simplified as;
log₅3 - log₅X = log₅3/8
log₅X = log₅8
X = 8
(c). The log expression is simplified as;
-2log₂5 = log₂Y
log₂5⁻² = log₂Y
5⁻² = Y
1/25 = Y
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HELP FASTER WILL GIVE BRAINLIEST!!!!!!!!! NOTICE ITS + AND THEN - IN EQUATION NOT TWO +, SO D ISNT CORRECT!!!!!!
Identify the correct graph of the system of equations.
3x + y = 12
x − 4y = 4
The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 12.
The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.
The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 12.
The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.
The correct graph of the system of equations 3x + y = 12 and x - 4y = 4 is:
The graph shows a line with an x-intercept at (4, 0) and a y-intercept at
(0, -1). There is a second line with an x-intercept at (4, 0) and a y-intercept at (0, 12).
We have,
To graph the system of equations 3x + y = 12 and x − 4y = 4, we first need to rearrange them in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept:
3x + y = 12 => y = -3x + 12
x - 4y = 4 => y = (1/4)x - 1
Now we can see that the first equation has a slope of -3 and a y-intercept of 12, while the second equation has a slope of 1/4 and a y-intercept of -1.
Now,
The x-intercept is when y = 0.
So,
3x + y = 12
3x = 12
x = 4
And,
x - 4y = 4
x = 4
Thus,
The correct graph of the system of equations 3x + y = 12 and x - 4y = 4 is:
The graph shows a line with an x-intercept at (4, 0) and a y-intercept at
(0, -1). There is a second line with an x-intercept at (4, 0) and a y-intercept at (0, 12).
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The volume in a set of wine bottles is known to follow a normal distribution with mean μ ounces and standard deviation of σ = 0.5 ounces. You take a sample of the bottles and measure their volumes. How many bottles do you need to sample to construct a 90% confidence interval for μ with a margin of error at most 0.1 ounces?
We need to sample at least 18 wine bottles to construct a 90% confidence interval for the mean volume of the population, with a margin of error of at most 0.1 ounces.
To determine the sample size required for a given confidence interval and margin of error, we need to use the following formula:
[tex]n = (Z^2 * \sigma^2) / E^2[/tex]
Where:
n = sample size
Z = the z-score associated with the desired confidence interval (for 90% confidence, Z = 1.645)
σ = the standard deviation of the population (0.5 ounces in this case)
E = the desired margin of error (0.1 ounces in this case)
Plugging in the values, we get:
[tex]n = (1.645^2 * 0.5^2) / 0.1^2[/tex]
n = 17.1
Thus, we need to sample at least 18 wine bottles to create a 90% confidence interval for the population's mean volume, with a margin of error of no more than 0.1 ounces.
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We need to sample at least 69 bottles to construct a 90% confidence interval for the mean volume of the wine bottles with a margin of error at most 0.1 ounces.
We have,
To construct a confidence interval for the mean volume of the wine bottles, we need to use the formula:
Confidence interval = sample mean ± margin of error
Where,
Margin of error = z (σ/√(n))
Here, we want to construct a 90% confidence interval with a margin of error at most 0.1 ounces.
This means that the margin of error should be less than or equal to 0.1, and the confidence level is 90%, so the critical value of z is 1.645
(using a standard normal table or calculator).
We are given that the standard deviation is σ = 0.5 ounces.
We don't know the sample mean or the sample size (number of bottles), so we'll use the worst-case scenario to find the sample size that gives the largest margin of error.
The worst-case scenario is when the sample mean is equal to the population mean (μ) plus the margin of error (0.1 ounces), and the sample size is as small as possible (which gives the largest margin of error).
So, we have:
0.1 = 1.645 x (0.5/sqrt(n))
Solving for n, we get:
n = (1.645 x 0.5/0.1)²
n = 68.225
Rounding up to the nearest whole number, we get:
n = 69
Therefore,
We need to sample at least 69 bottles to construct a 90% confidence interval for the mean volume of the wine bottles with a margin of error at most 0.1 ounces.
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(c) log12-(1/2log 9+1/3 log8) write a single form equation
The log expression in single equation is log 12 - log 3 + log 2.
What is the solution of the log equation?
The solution of the log equation is calculated by applying the following method.
log 12 - ¹/₂log 9 + ¹/₃log 8
we can simplify the equation as follows;
log 12 - log 3 ⁽² ˣ ¹/₂⁾ + log 2 ⁽³ ˣ ¹/₃⁾
= log 12 - log 3¹ + log 2¹
= log 12 - log 3 + log 2
Thus, the log equation or expression has been simplified in the form of single equation.
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