9514 1404 393
Answer:
A) 1
Step-by-step explanation:
Let the distance from A to BC be represented by y, and the distance DE be represented by x. We can write some relations using the definition of the tangent of an angle, and the double-angle formula for tangent. The double-angles are complementary
Left angles
Call the smaller angle α. Then the larger angle is 2α.
tan(α) = x/2
tan(2α) = 2tan(α)/(1 -tan(α)²) = 2(x/2)/(1 -(x/2)²) = 4x/(4 -x²)
Right angles
tan(β) = x/3
tan(2β) = 2tan(β)/(1 -tan(β)²) = 2(x/3)/(1 -(x/3)²) = 6x/(9 -x²)
__
Angles 2α and 2β are complementary, so the product of their tangents is 1.
(4x/(4 -x²))(6x/(9 -x²)) = 1
24x² = (4 -x²)(9 -x²) . . . . multiply by the product of denominators
x⁴ -37x² +36 = 0 . . . . . put in standard form
(x² -36)(x² -1) = 0 . . . . . factor
Solutions to this equation are x = ±1 and x = ±6. Only positive values less than 1.25 can possibly satisfy the geometry. Hence x = DE = 1.
The length of DE is 1.
Find the equation of the line that passes through (-4, 2) and is perpendicular to the line that goes through (-4, 6) and (5, 2).
Answer:
9x -4y = -44
Step-by-step explanation:
You want the equation of the line through (-4, 2) and perpendicular to the line through (-4, 6) and (5, 2).
Equation of a LineThe equation of a line through (h, k) and perpendicular to the line through (x1, y1) and (x2, y2) can be written as ...
(x2 -x1)(x -h) +(y2 -y1)(y -k) = 0
Using the given points, this becomes ...
(5 -(-4))(x -(-4)) +(2 -6)(y -2) = 0
9(x +4) -4(y -2) = 0
Expanding this gives the general form equation:
9x -4y +44 = 0
Subtracting the constant gives the standard form equation:
9x -4y = -44
7 large tanks and 40 fish in each tanks how many fish on display
Answer:
280
Step-by-step explanation:
All you have to do is 7x4 and look for how many 0's there are in the equation and add them on.
In this diagram below AC=3x-15 and DE=6Solve for the value of X.
ANSWER
x = 9
EXPLANATION
From the question, we see that DE is the midsegment of the triangle ABC.
According to the Midsegment Theorem:
DE = 1/2 * AC
=> AC = 2DE
Therefore, we have that:
3x - 15 = 2 * 6
3x - 15 = 12
Collect like terms:
3x = 15 + 12
3x = 27
Divide through by 3:
x = 27 / 3
x = 9
That is the value of x.
6/10 + 5/100
is it
65/100 or 65/110 or 56/100 or 56/110
Answer:
65/100 that is the answer to this question
What?
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Suppose X is a random variable with mean X and standard deviation oXSuppose Y is a random variable with mean Y and standard deviation oY. The mean of X + Y is: O a. MX+MY O b.uX/oX) + (Y /oY). O c. 1X+uY, but only if X and Y are independent.O d (uX/oX) + (Y/oY), but only if X and Y are independent.
The correct option regarding the mean of X + Y is given as follows:
a. MX+MY.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.
Hence, when two variables are added, we can add their means, as we add all the observations and divide by the number of observations, considering the two variables.
This means that the correct option is given by option A.
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If 15 is equal to 20% how much is 100%???
Answer:
75=100%
Step-by-step explanation:
15=20%
30=50%
75=100%
A person must pay
5 to play a certain game at the casino. Each player has a probability of 0.13 of winning
15. Each player has a probability of 0.87 of losing the game and winning nothing.
What is the Expected Value for the player? If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer with two decimal places.
Expected Value = $
If a person plays this game a very large number of times over the years, do we expect him/her to come out financially ahead or behind?
behind
ahead
The Expected Value for the player is -$2.40, which is negative. This means that on average, the player can expect to lose $\(2.40\) for each game played.
What is the probability of losing by the amount paid?To calculate the Expected Value for the player, we can multiply the probability of winning by the amount won, and subtract the probability of losing by the amount paid.
Expected Value = (Probability of Winning * Amount Won) - (Probability of Losing * Amount Paid)
Given the following information:
Probability of winning \(= 0.13\)
Amount won = $15
Probability of losing \(= 0.87\)
Amount paid = $5
Plugging these values into the formula:
Expected Value \(= (0.13 \times $15) - (0.87 times $5)\)
Expected Value \(= $1.95 - $4.35\)
Expected Value = \(-$2.40\)
If a person plays this game a very large number of times over the years, we expect them to come out financially behind, as the Expected Value is negative. This indicates that, on average, the player will lose money over time by playing this game repeatedly.
Therefore, The Expected Value for the player is -$2.40, which is negative. This means that on average, the player can expect to lose $2.40 for each game played.
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Pls pls help I’ll mark u brainliestttt
convert this into a standard number
\(10^{12}\)
10^12 in standard number is 1000000000000
How to convert the number?The number is given as:
\(10^{12\)
Expand the expression
\(10^{12} = 10 * 10 * 10 * 10 *10 * 10 * 10 * 10*10 * 10 * 10 * 10\)
Evaluate the product
\(10^{12} = 1000000000000\)
Hence, 10^12 in standard number is 1000000000000
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Find the values of x and y
Answer:
x=45 y=137.5
Step-by-step explanation:
2x=90
x=45
One angle is 45. Another angle is 90.
The total angle sum would be 360
So
45+90+y+(y-50)=360
135+y+y-50=360
85+2y=360
2y=275
y=137.5
Since the two lines with red arrows are parallel, that means the two angles on the left are both 90º angles.
2x = 90
or x = 45
Now, 2x + 90 + y + (y-50) = 360, since this is a quadrilateral and we know 2x=90.
So 90 + 90 + y + y-50 = 360
or 2y + 130 = 360
or 2y = 230
or y = 115
To check, add up the angles to make sure it adds to 360:
90 + 90 + 115 + 65 = 360.
00:00
Brandy made 7 batches of cookies. Each batch contained 12 cookies.
She put the same number of cookies in each of 5 bags. How many cookies were NOT put in bags?
16 cookies
12 cookies
4 cookies
2 cookies
Answer:
4 cookies
Step-by-step explanation:
The remainder of (7x12)/5 is your answer.
If the mean of a positively skewed distribution is 70, which of these values
could be the median of the distribution?
Answer:
65
Step-by-step explanation:
just took the quiz.com
Over the last semester, Mr. Finch kept track of the number of student
absences, Now that the semester is over, he wants to see if there is a linear
relationship between the number of absences and a student's grade for the
semester. The data he collected are given in the table.
A scatter plot of the data is shown in the image attached below.
An equation for the least squares regression line (trend line) is y = -3.49x + 93.14
How to determine a line of best fit for the data?In order to determine a linear equation for the least squares regression line (trend line) that models the data points contained in the table (see attachment), we would have to use a scatter plot.
In this scenario, the number of absences would be plotted on the x-axis of the scatter plot while the algebra grade would be plotted on the y-axis of the scatter plot.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the trend line on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the number of absences and algebra grade in the table, a linear equation for the least squares regression line (trend line) in terms of the problem is given by:
y = -3.49x + 93.14
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There are 50 students in a class. If 14% are absent on a particular day, Find the number of students in the class on that day.
find ML
K 2x+5
M 5x-4
The figure labelled JKLM is a kite and the length ML is equal to 11.
What is a kiteA kite is a quadrilateral that have two pairs of equal length of sides and these sides are adjacent to each other. It can be viewed as a pair of congruent triangles with a common base.
The line JM bisects the kite into two congruent triangles, and thus;
the lengths ML and MK are equal.
ML = 5x - 4 and MK = 2x + 5 so;
5x - 4 = 2x + 5 {collect like terms}
5x - 2x = 5 + 4
3x = 9
x = 9/3 {divide through by 3}
x = 3
we substitute 3 for x;
ML = 5(3) - 4
ML = 15 - 4
ML = 11
Therefore, the value of length ML for the kite is equal to 11.
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PLEASE PLEASE PLEASE HELPPPPPPPPPPPPP
Answer:
1) B
2) B
Step-by-step explanation:
1) funtion 1 slope is 4
function 2 we use y2-y1/x2-x1
10-6/3-1
4/2
2 is the slope of function 2
so function 1 is bigger
1) only b is correct because it lands on the same line of y=x
hopes this helps please mark brainliest
The area of a square is 36 sq.cm, then its perimeter is a) 24 cm b) 6 cm c) 144 cm d) 36 cm
Answer:
Step-by-step explanation:
3.6*
It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2
For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.
We get
36 = s^2
Now, we need to get the square root of both sides, which gives us
s = √36 s = 6 cm
Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.
Therefore, the perimeter of the square is 24 cm.
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Given: m || n
What is the value of x?
x =
X = y-2
2x-y=2
X=
Y=
Answer:
y =4 and x=6 hope it may help u
Peggy invests $8, 400 at 6 1/2% interest for 10 years compounded semiannually. Find the amount of money in the account at the end of the term.
Answer:1200
Step-by-step explanation:1200
What is the volume, in cubic meters, of a cylinder with a height of 3 meters and a base radius of 4 meters, to the nearest tenths place?
Answer: If I did it correctly it should be 150.8
Step-by-step explanation:
The formula for the volume of a cylinder is height x π x (diameter / 2)2, where (diameter / 2) is the radius of the base (d = 2 x r), so another way to write it is height x π x radius2.
Hope this helps!
A gardener has seven identical-looking tulip
bulbs, of which each will produce a different
color tulip. Four of the colors are unknown,
however one will become white, one will
become yellow, and one will become pink. He
plants them abitrarily in a row. When the
flowers start to bloom, what is the probability
that the yellow one is first in the row, the white
one is second, and the pink one is at the end of
the row?
Solution
Step-by-step explanation:
Given
There are 7 bulbs out of which 1 is Yellow and 1 is Pink and 1 is white
If a gardener randomly select 6 bulbs
Then the Probability of selecting yellow = 1/7
probability of selecting white = 1/7
and the probability of selecting pink = 1
\(\text{probability = }\frac{1}{7}\times\frac{1}{6}\times1=\frac{1}{42}=0.0238\)Therefore the correct answer is 0.0238
Write 1 11/20 as a decimal.
First, we transform the mixed fraction into an improper fraction:
\(1\frac{11}{20}=\frac{20}{20}+\frac{11}{20}=\frac{32}{20}.\)Now, we divide 32 and 20 and get:
\(\frac{32}{20}=1.6.\)Answer: 1.6
1. What is the value of the 7th term in (2x + y)'?
Answer:
n/a
Step-by-step explanation:
The equation -2(3y+7)=28 is solved in several steps below. For each step, choose the reason that best justifies it
The value of the expression is -7.
We have,
-2 (3y + 7) = 28
(given)
-6y - 14 = 28
(distributive property)
-6 - 14 + 14 = 28 + 14
(addition property of equality)
-6y = 42
(simplifying)
-6y/-6 = 42/-6
(Division property of equality)
y = -7
Thus,
The value of the expression is -7.
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a right cylinder with radius 4 cm and height 3 cm 314 cu cm a cone with radius 5 cm and height 12 cm. what is the volume
The volume of the cylinder is 150.72 cm³ ⇒ last answer
The volume of the cone is 314 cm³ ⇒ 1st answer
The volume of the pyramid is 160 cm³ ⇒ 2nd answer
The volume of the pyramid is 48 cm³ ⇒ 3rd answer
Step-by-step explanation:
* Let's revise the volumes of some shapes
- The volume of the cylinder of radius r and height h is:
V = π r² h
- The volume of the cone of radius r and height h is:
V = 1/3 π r² h
- The volume of the pyramid is:
V = 1/3 × its base area × its height
* Lets solve the problem
# A cylinder with radius 4 cm and height 3 cm
∵ V = π r² h
∵ π = 3.14
∵ r = 4 cm , h = 3 cm
∴ v = 3.14 (4)² (3) = 150.72 cm³
* The volume of the cylinder is 150.72 cm³
# A cone with radius 5 cm and height 12 cm
∵ V = 1/3 π r² h
∵ π = 3.14
∵ r = 5 cm , h = 12 cm
∴ V = 1/3 (3.14) (5)² (12) = 314 cm³
* The volume of the cone is 314 cm³
# A pyramid with base area 16 cm² and height 30 cm
∵ V = 1/3 × its base area × its height
∵ The area of the base is 16 cm²
∵ The height = 30 cm
∴ V = 1/3 (16) (30) = 160 cm³
* The volume of the pyramid is 160 cm³
# A pyramid with square base of length 3 cm and height 16 cm
∵ V = 1/3 × its base area × its height
∵ The area of the square = s²
∵ The area of the base = 3² = 9 cm²
∵ The height = 16 cm
∴ V = 1/3 (9) (16) = 48 cm³
* The volume of the pyramid is 48 cm³.
expand using algebric
identity
1) (2xy+5y)2
Step-by-step explanation:
(2xy + 5y)2 = 4xy + 10y
Topic: algebraic manipulation
If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!
Answer:
4xy+10y
Step-by-step explanation:
(2xy+5y)2
4xy+10y
a jet plane travels 1,290 in 3 hours Assuming its speed is constant, how long will it take to travel 5,160 Miles?
The time it takes is 12 hours to travel 5,160 Miles.
The time is take can be calculated as follows?
The first is calculate the speed of jet plane in miles/hour (mph)
= 1,290 / 3
= 430 mph
Next is to calculate the time is take to travel 5,160 by dividing the distance by the speed
= 5,160 / 430
= 12 hours
Thus, the time it takes is 12 hours.
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You make $12 an hour, plus time and a half for each hour over 40 hours that you work in a week. How many hours do yo need to work to earn $606?
Answer:
47 hours
Step-by-step explanation:
[606 -(12×40)]/(1½×12) =
(606-480)/(18) =
126/18 = 7
the total working hours = 40+7 = 47 hours
Answer:
47 hours
Step-by-step explanation:
First, we do 12 times 40, the answer we get is 480 dollars.
Then, we do 606 minus 480, the answer we get is 126.
Next, we do 126 divided by 18, and we get 7
Therefore, the total hours is 47 hours.