1. The reason is that E bisects line AC and is perpendicular to line AC.
2. The reason is that the angles are alternate interior angles.
What are alternate interior angles?
Alternate interior angles are made when a transversal joins two co-planar lines. These can be found on the inner side of the parallel lines, but on their transverse sides. The transversal goes through the two co-planar lines at two separate points.
1. We are given a statement that E is the midpoint of AC.
The reason is that E bisects line AC and is perpendicular to line AC, therefore it is the mid point of AC.
2. We are given that ∠D ≅ ∠B.
The reason is that DC ║ AB. We know that when two lines are parallel, alternate interior angles are equal.
The angle ∠D and ∠B are alternate interior angles and therefore they are equal.
Hence, the required solutions have been obtained.
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The complete question has been attached below.
Find the vector projection w of u = i – 6j onto v = 2i + 7j.
Given:
\(u=i-6j\text{ }onto\text{ }v=2i+7j.\)To find:
The vector projection u onto v.
Explanation:
The vector projection u onto v formula is,
\(\frac{\vec{u}\cdot\vec{v}}{|\vec{v}|^2}\cdot\vec{v}\)Substituting the given values we get,
\(\begin{gathered} \frac{(i-6j)\cdot(2i+7j)}{|2i+7j|}(2i+7j)=\frac{(2-42)}{(\sqrt{2^2+7^2})^2}(2\imaginaryI+7j) \\ =\frac{(2-42)}{(\sqrt{4+49})^2}(2\mathrm{i}+7j) \\ =\frac{-40}{(\sqrt{53})^2}(2\mathrm{i}+7j) \\ =\frac{-40}{53}(2\mathrm{i}+7j) \end{gathered}\)Final answer:
The vector projection u onto v is,
\(\frac{-40}{53}(2\imaginaryI+7j)\)Which of the following graphs represents the relationship between
x and y if y always increases as x increases?
A. I and IV only
B. I and III only
C. III and IV only
D. I, III, and IV only
E. I, II, III, and IV
پا یا جا با
II
III
IV
The graph that could represent the relationship between x and y will be Graph E
How to explain the graphIt should be noted that in discrete mathematics, and in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". .
In this case, it should be noted that the objects correspond to mathematical abstractions called vertices and each of the related pairs of vertices.
In conclusion, the correct option is E.
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given : f(x) = x2 - 5 and g(x) = 3x - 1 Find 2g (f(-5))
The given functions are
f(x) = x^2 - 5
g(x) = 3x - 1
To find 2g(f(- 5)), we would first find f(- 5)
To find f(- 5), we would substitute x = - 5 into f(x) = x2 - 5. It becomes
f(- 5) = (- 5)^2 - 5
f(- 5) = 25 - 5
f(- 5) = 20
Then, we would substitute f(- 5) = 20 into g(x) = 3x - 1
Thus,
g(f(- 5) = 3*20 - 1
g(f(- 5) = 60 - 1
g(f(- 5) = 59
Therefore,
2g(f(- 5)) = 2 * 59 = 118
Playing golf, Mike got a + 2on the first hole and - 2 on the second hole. What is his combined score for the first two holes?
Answer:
0
Step-by-step explanation:
he had a score of 2 on the first hole and then he go a birdie i think and it subtracted 2 from that leaving 0
Bob can row 9 mph in still water. The total time to travel downstream and return upstream to the starting point is 9 hours. If the total distance downstream and back is 32 miles, determine the speed of the river (current speed).
Current Speed = ___________
Let's call the speed of the river "r". The speed of the current in the downstream direction is 9 + r mph, and the speed of the current in the upstream direction is 9 - r mph. The time it takes to travel downstream and return upstream is the same, so we can set up the following equation:
(32 miles) / (9 + r mph) + (32 miles) / (9 - r mph) = 9 hours
We can simplify this equation by converting hours to minutes and miles to feet, and then simplify further by multiplying both sides of the equation by the denominators:
32 * 60 * (9 + r) + 32 * 60 * (9 - r) = 9 * 60 * (9 + r) * (9 - r)
Expanding the right side of the equation and simplifying:
32 * 60 * (9 + r) + 32 * 60 * (9 - r) = 810 * (9 + r) * (9 - r)
Expanding the left side of the equation and simplifying:
32 * 60 * 9 + 32 * 60 * r + 32 * 60 * 9 - 32 * 60 * r = 810 * (9 + r) * (9 - r)
Combining like terms and solving for r:
32 * 60 * 9 * 2 = 810 * (9 + r) * (9 - r)
96720 = 810 * (9 + r) * (9 - r)
Dividing both sides by 810:
119 = (9 + r) * (9 - r)
Expanding the right side of the equation:
119 = 81 - r^2
Adding r^2 to both sides of the equation:
119 + r^2 = 81
Subtracting 81 from both sides of the equation:
38 + r^2 = 0
Taking the square root of both sides of the equation:
r = ± sqrt(38)
Since r is the speed of the current, it must be a positive value, so we take the positive square root:
r = sqrt(38) mph
The speed of the river (current speed) is approximately 6.17 mph.
Questlon 3 of 10
2 Points
The volume of a cube depends on the length of its sides. This can be written
in function notation as (s). What is the best interpretation of (4) = 64?
O A. 4 sides of the cube have a total length of 64 feet.
B. A cube with side lengths of 4 feet has a volume of 64 cubic feet.
C. A cube with a volume of 4 cubic feet has side lengths of 64 feet.
O D. 4 of these cubes will have a total volume of 64 cubic feet.
SUBMIT
Answer:
b)A cube with side lengths of 4 feet has a volume of 64cubic feet
Step-by-step explanation:
volume=length×width×height
=4×4×4
=64feet³
What is the total square inches
Square Area = side x side = 3x3 = 9
Rectangle Area = side x side= 7x3= 21
9 + 21 = 30 square inches
Answer:
30 square inches
Step-by-step explanation:
\(\boxed{\text{\bf Area of rectangle = length *width}}\)
Rectangle1:
Area = 6 * 3
= 18 square inches
Rectangle2:
Area = 4 * 3
= 12 square inches
Area of the figure = area of rectangle1 + area of rectangle2
= 18 + 12
= 30 square inches
A college offers shuttle service from Ball Hall or Lot A to its campus quad. Both shuttles first depart their locations at 9:25 A.M. They run from each location to campus and back at the intervals shown. When is the next time both shuttles will depart for campus at the same time? Explain.
Ball Hall: 30 minutes
Lot A: 20 minutes
Using the lowest common factor of the shuttles' run times, they will depart again for the campus simultaneously at 10.25 A.M.
How is the time determined?We can use the lowest common factor (LCM) of their run time to determine when they depart again for the campus.
The lowest common factor of 30 and 20 is 60 because both 30 and 20 can divide 60 evenly without a remainder, showing that it takes 60 minutes for the two shuttles to depart for the campus at the same time.
We can conclude that every 60 minutes or hour, the two shuttles simultaneously depart for the campus. Every hour, the shuttle departing from Ball Hall completes 2 runs, while the shuttle departing from Lot A completes 3 runs.
Thus, using the lowest common factor, the next time both shuttles will depart for the campus at the same time is 10:25 A.M.
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Algebra Question
Let v = (-7,6,-6) and w = (-5,-3,-6) be vectors in R^3. Find the orthogonal projection of v onto w.
Answer:
Projection on w: (-54/14, -159/70, -159/35)
I have the correct answer but I don't know how they got it.
The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).
To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:
proj_w(v) = (v⋅w) / (w⋅w) * w
where ⋅ denotes the dot product.
Calculating the dot product of v and w:
v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53
Calculating the dot product of w with itself:
w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70
Now, substituting these values into the formula, we have:
proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)
Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).
In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.
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1 way ANOVA analysis was used to test the effectiveness of 3 kinds of headache medicines (Advil, Tylenol, and Excedrin). The analysis involved 21 people (7 per group), and used an alpha level of 0.01. What is the Critical Value
Answer:
The critical region is F >F ₀.₀₁ (2,18) = 6.01
Step-by-step explanation:
For 1 way ANOVA the degrees of freedom Between Samples would 2 and within Samples would be 18 .
Alpha is given to be = 0.01
v1 = k-1 and v2 = n-k
Where k is the number of rows and n is the total number of values
v1= 3-1= 2 and v2 = 21-3= 18
So if we look up the table we find the values of the critical region to be 6.01
Hence the critical region is less and equal to 6.01
The critical region is F >F ₀.₀₁ (2,18) = 6.01
She borrows $25.63 from her sister to help pay for the dress. Then Jenny earns $16.33 helping her dad organize his home office. If she gives all the earnings to her sister, Jenny will still owe her sister $
.
A movie theater can seat a maximum of 25 people. Let p represent the total number of people. Which inequality represents p, the number of people the theater can seat?
The inequality that represents p, the number of people the theater can seat is p ≤ 25
Which inequality represents p, the number of people the theater can seat?From the question, we have the following parameters that can be used in our computation:
A movie theater can seat a maximum of 25 people
This means that
Maximum = 25 people
In other words, the movie theatre can allow 25 or less people to attend a movie
In inequality, 25 or less means less than or equal to 25
When represented as an inequality expression, we have
≤ 25
Using the variable p, we have
p ≤ 25
Hence, the inequality is p ≤ 25
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A desk is 39 inches wide. What is the width in yards
Answer:
1.0833 yd
Step-by-step explanation:
Inches Yards
37" 1.0278 yd
38" 1.0556 yd
39" 1.0833 yd
40" 1.1111 yd
Have a great day! :D
select “equivalent” or “not equivalent” to indicate whether the expression above is equivalent or not equivalent to the values or expressions in the last column
9514 1404 393
Answer:
EquivalentNot EquivalentEquivalentNot EquivalentStep-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
__
The left-side expressions (all the same) can be simplified to ...
(7^(1/5))·(49^(7/5)) = (7^(1/5))·((7^2)^(7/5))
= (7^(1/5))·(7^(14/5)) . . . . . . matches 3rd right-side expression
= 7^(1/5 +14/5) = 7^(15/5) = 7^3
= 343 . . . . . . . . . . . . . . . . . . matches 1st right-side expression
__
49 is obviously not equivalent to 343.
49^(2/10) is obviously not equivalent to 49^(7/5).
What I explain how to solve the equation 3/4 x + 5=11
Answer:
x = 8
Step-by-step explanation:
3/4x + 5 = 11
3/4x = 6
12/4 = 3x = 24
3x = 24
x = 8
Answer:
x = 8
Step-by-step explanation:
\(\frac{3}{4}\) x + 5 = 11
\(\frac{3}{4}\) x = 6
x = \(\frac{4}{3}\) (6)
x = 8
Simplify the following: *
-4– (-5)
What number must be multiplied by 3/4 to create a product of 1 and explain why.
What number must be multiplied by 1 2/5 to create a product of 1 and explain why.
I need these answers quick
Answer:
1.3------ something
Step-by-step explanation:
this is a unit test right answers only pls
Answer:
d
Step-by-step explanation:
took da test
100 points PLEASE ANSWER
ASAP thank you so much
Show work
Answer:
See below
Step-by-step explanation:
L = length
W = 2 feet less than L = L-2
Area = L x W
20 = L * (L-2)
20 = L^2 - 2L
0 = L^2 - 2L - 20
Use Quadratic Formula a = 1 b = -2 c = -20
L = [-b ± sqrt(b^2-4ac) ]/2a
to calculate L = 5.5826 ft then W = L-2 = 3.5826 ft
Let's Length be x and width be x-2
So
Area=20x(x-2)=20x²-2x=20x²-2x-20=0On solving
x=5.6ftL=5.6
W=5.6-2=3.6ft
Please i nedd help with this i will give brainliest
Answer:
1) 1 hour
2) 1 hour
3) 2 hours
Step-by-step explanation:
1 hour = 60 minutes
Therefore,
7/8 of an hour implies 7/8 of 60 minutes
7/8 * 60 = 420/8 = 52.5 Mins
52.5 is closest to an hour
5/6 of an hour implies 5/6 of 60 minutes
5/6 * 60 = 50 = 50 Mins
50 is closest to an hour
An hour + Anhour = 2 hours
Total: 2 hours
If 6 cubic inches of flavored ice is equal to 1 ounce, how many ounces of shaved ice is that?
Answer:
0
Step-by-step explanation:
i see 0 cubic inches so that means there will be 0 ounces
tell me what you see and i will try to help
BRAINLIEST+ STARS!!
A rectangular block of copper metal weighs 1890 g. The dimensions
of the block are 8 cm x 5 cm x 5 cm. From this data, what is the
density of copper?
A. 9.45 g/cm3
B. 1,690 g/cm3
C. 2,090 g/cm3
D. 0.106 g/cm3
E. 10.98 g/cm3
To find the density:
⇒ must find the relationship between the density, mass, and volume
⇒ \(Density = \frac{mass}{volume}\)
Let's examine the information given:
weight: 1890gdimensions: 8cm * 5cm* 5cmLet's first find the volume:
⇒ the volume is the dimensions multiplied together
\(Volume = 8cm * 5cm * 5cm = 200cm^3\)
LEt's calculate the density now:
\(Density = \frac{1890g}{200cm^3} =9.45g/cm^3\)
Answer: The density of the copper is 9.45g/cm^3 or Choice (A)
Hope that helps!
a simple random sample of size n is obtained from a population whose size is and whose population proportion with a specified characteristic is describe the sampling distribution of . round the standard deviation of the sampling distribution to three decimal places.
The sampling distribution of is a binomial distribution with parameters n and p, where n is the sample size and p is the population proportion of the specified characteristic.
The mean of the sampling distribution is np and the standard deviation is \($\sqrt{np(1-p)}$\).
Sampling Distribution of a Simple Random SampleRound the standard deviation to three decimal places, it is \($\sqrt{np(1-p)}$ = $\sqrt{n \cdot p \cdot (1-p)} \approx \sqrt{n \cdot p \cdot 0.99}$\).
The sampling distribution of is a binomial distribution with parameters n and p, where n is the sample size and p is the population proportion of the specified characteristic. The mean of the sampling distribution is np and the standard deviation is \($\sqrt{np(1-p)}$\). This means that for a given sample size n and population proportion p, the standard deviation of the sampling distribution can be calculated by taking the square root of the product of n, p, and (1-p).
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A bag of baseballs costs $12. There are 15 balls in the bag. Another bag of baseballs costs $15 for 20 balls. Which bag prices individual baseballs lower?
Answer:
Step-by-step explanation:
For the first bag:
Price of the bag = $12
Number of balls in the bag = 15
Price per ball = Price of the bag / Number of balls
Price per ball for the first bag = $12 / 15 = $0.8
For the second bag:
Price of the bag = $15
Number of balls in the bag = 20
Price per ball = Price of the bag / Number of balls
Price per ball for the second bag = $15 / 20 = $0.75
Comparing the prices per ball, we find that the second bag has a lower price per baseball. Therefore, the second bag offers a better price for individual baseballs compared to the first bag.
Answer:
Step-by-step explanation:
To find out which bag prices individual baseballs lower, we can divide the total cost of each bag by the number of balls in the bag. This will give us the price per ball for each bag.
For the first bag, the price per ball is $12 / 15 = $0.80.
For the second bag, the price per ball is $15 / 20 = $0.75.
Therefore, the second bag prices individual baseballs lower.
TRY IT Solve and support your thinking
A grasshopper weighs of an ounce. A beetle weighs
of an ounce. Which weighs more?
100
10
Answer:
45 hihihihihihihihihihihihih
Step-by-step explanation:
Answer:
Your answer doesnt say how much the beetle wighs, probably the grasshopper though
Step-by-step explanation:
the number of hours per week that the television is turned on is determined for each family in a sample. the mean of the data is 32 hours and the median is 28.2 hours. twenty-four of the families in the sample turned on the television for 17 hours or less for the week. the 8th percentile of the data is 17 hours. step 1 of 5 : based on the given information, determine if the following statement is true or false. the 55th percentile is less than 27 hours.
The given statement "The 55th percentile is less than 27 hours" is false.
What is arithmetic mean?The arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.
The data is given in the question, as follows:
Mean = 32 hours
Median = 28.2 hours
8th percentile = 17 hours
Number of families who turned on the television for 17 hours or less = 24
The given information to estimate the 55th percentile as follows:
Half the families in the sample turned on the television for 28.2 hours or less (since this is the median).
Of the remaining half, 8% turned on the television for 17 hours or less (since this is the 8th percentile), which leaves 42% of the families who turned on the television for more than 28.2 hours but less than 17 hours.
Therefore, we can estimate the 55th percentile to be around the middle of this range, which is approximately 28.2 + 0.42(32-28.2) = 30.56 hours.
Since 30.56 hours is greater than 27 hours, we can conclude that the statement "The 55th percentile is less than 27 hours" is false.
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Graph the equation
3x + 4y = 12
6
5
4
d
3
2
1
-7-6
-5 4 3 -2 -1
3
4
5
6
7
-2.
-3
4
-6
Clear All Draw
There ya go, good luck,,,,
I am lost on this question i found both but it keeps on telling me i am incorrect
Answer:
I have completed the answers and attached them to the explanation.
Step-by-step explanation:
Answer:
Step-by-step explanation:
The question asks for a subtraction expression:
length is always a positive number so bigger number first here.
OB = 4-(-1) >only moves in x direction so subtract x's
AB = 4-(-2) >only moves in y direction so subtract y's
Need help solving for relative frequency please!
Answer:
Kindly check explanation
Step-by-step explanation:
Given :
Relative frequency = frequency / total frequency
Total frequency = 389+335+975+351+72 = 2122
Response ________ Frequency __ R/ frequency
Never ____________ 389 _ 389/2122 = 0.180
Rarely ____________ 335 _ 335/2122 = 0.158
Sometimes _________975 _975/2122 = 0.459
Most of the time _____ 351 _ 351/2122 = 0.165
Always ____________ 72 __ 72/2122 = 0.034
.The rate of income tax increases from 15.2% to 20.9%.due to this Gaurav had to pay
5.55% more tax than previous year. but simultaneously income of Gaurav also decreases
by 18400 Rs. find income of Gaurav last year
Answer:
Step-by-step explanation: