What is the location of point F, which partitions the directed line segment from D to E into a 5:6 ratio?
-1/11
1/11
2/15
15/2
Answers
The correct answer is b
F is a point which is greater than zero and F must be in the location of 1/11 and it can be determine by using arithmetic operations.
Given :
F partitions the directed line segment from D to E into a 5:6 ratio.
Given that F partitions the directed line segment from D to E into a 5:6 ratio therefore, total segments is (5 + 6 = 11).
From point D to E in the given line segment there are 9 units. To divide the line segment of 9 unit into 11 unit, first find the distance between two units, that is:
[tex]\dfrac{9}{11}=0.82[/tex]
[tex]0.82\times 5 = 4.1[/tex]
Now, it can be say that F is a point which is greater than zero and F must be in the location of 1/11.
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Related Questions
Sixty-five percent of men consider themselves knowledgeable football fans. if 12 men are randomly selected, find the probability that exactly four of them will consider themselves knowledgeable fans.
Answers
Answer:
P(x)= 0.0198
Step-by-step explanation:
Given : 65% men are knowledgeable football fans, 12 are randomly selected ,
To find : Probability that exactly four of them will consider themselves knowledgeable fans.
Solution : Let P is the success rate = 65% = 0.65
Let Q is the failure rate = 100-65= 35%= 0.35
Let n be the total number of fans selected = 12
Let r be the probability of getting exactly four = 4
Formula used : The binomial probability
[tex]P(x)= \frac{n!}{(n-r)!r!}P^rQ^{n-r}[/tex]
putting values in the formula we get ,
[tex]P(x)= \frac{12!}{(12-4)!4!}(0.65)^4(0.35)^{12-4}[/tex]
[tex]P(x)= (495)(0.1785)(o.ooo22 )[/tex]
P(x)= 0.0198
The probability that exactly four out of the twelve randomly selected men will consider themselves knowledgeable football fans is approximately 0.236 or 23.6%.
Step 1: Model Selection (Binomial Distribution)
This scenario can be modeled using the binomial distribution if the following conditions are met:
Fixed number of trials (n): In this case, we have a fixed number of men being selected (n = 12).Binary outcome: Each man can be classified into two categories: either a "knowledgeable fan" (success) or a "not knowledgeable fan" (failure).Independent trials: The knowledge level of one man doesn't affect the selection of another.Constant probability (p): The probability (p) of a man being a knowledgeable fan remains constant throughout the random selection (given as 65%).Since these conditions seem reasonable, the binomial distribution is a suitable model for this scenario.
Step 2: Formula and Values
The probability (P(x)) of exactly x successes (knowledgeable fans) in n trials (men selected) with probability p of success (knowledgeable fan) can be calculated using the binomial probability formula:
P(x) = nCx * p^x * (1 - p)^(n-x)
where:
n = number of trials (12 men)x = number of successes (4 knowledgeable fans - what we're interested in)p = probability of success (knowledgeable fan - 65% converted to decimal: 0.65)(1 - p) = probability of failure (not knowledgeable fan)Step 3: Apply the Formula
We are interested in the probability of exactly 4 men being knowledgeable fans (x = 4). Substitute the known values into the formula:P(4) = 12C4 * 0.65 ^ 4 * (1 - 0.65) ^ (12 - 4)Step 4: Calculate Using Calculator or Software
While it's possible to calculate 12C4 (combinations of 12 choosing 4) by hand, using a calculator or statistical software is often easier.12C4 = 495 (combinations of 12 elements taken 4 at a time)Step 5: Complete the Calculation
Now you have all the values to complete the calculation:P(4) = 495 * 0.65 ^ 4 * (1 - 0.65) ^ 8Using a calculator or software, evaluate the expression. You'll get an answer around 0.236. How many radians are contained in the angle AOT in the figure? Round your answer to three decimal places.
A. 0.459 radian
B. 2.178 radians
C. 1.047 radians
D. 0.955 radian
Answers
60 ÷ 57.3 = 1.047
correct answer: C
Answer:
Option C. 1.047 radians
Step-by-step explanation:
We have to find the measure of angle AOT in radians.
To convert measure of an angle from degree to radians we use the formula
[tex]\text{radians}=\frac{\pi(\text{degrees})}{180}[/tex]
= [tex]\frac{\pi(60)}{180}=\frac{\pi }{3}[/tex]
(Since measure of angle AOT is 60°)
= [tex]\frac{3.14}{3}[/tex] (since π = 3.14)
= 1.047 radians
Therefore, option C. 1.047 radians is the correct option.
Find the selling price of an item listed at $400 subject to a discounted series of $25%, 10%, and 5%
A. $256.50
B. $270.00
C. $225.00
D. $300.00
Answers
$300 - ($300 x 0.10) = $270
$270 - ($270 x 0.05) = $256.50
answer
A. $256.50
Answer:
Selling price of an item is $256.50 (A).
Step-by-step explanation:
Given : WE have given an item listed at $400 subject to a discounted series of $25%, 10%, and 5% .
To find : Find the selling price of an item.
Formula used : Selling price = marked price - discount.
Solution : We have an item listed at = $400.
Discount percentage = $25% , $10% , $5.
Discount 1 = $400 ×[tex]\frac{25}{100}[/tex] = $100.
Selling price = $400-100 = $300.
Discount 2 = $300 ×[tex]\frac{10}{100}[/tex] = $30.
Selling price = $300-30 = $270.
Discount 3 = $270 ×[tex]\frac{5}{100}[/tex] = $13.50.
Final selling price = $270-13.50 = $256.50.
Therefore, Selling price of an item is $256.50 (A).
Write a segment addition problem using three points that asks the student to solve for x but has a solution x = 20
Answers
The segment addition problem was given below which gives the value of x as 20.
Segment addition problem:
Consider three points on a line: A, B, and C. Point B is located between points A and C.
The lengths of the line segments are as follows:
Length of segment AB: 12
Length of segment BC: x
Length of segment AC: 32
Find the value of x.
We have the equation for segment addition: AB + BC = AC
Substitute the given values:
12 + x = 32
Now, solve for x:
x = 32 - 12
x = 20
Therefore, the value of x is indeed 20, and the lengths of the segments satisfy the segment addition property.
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To construct a segment addition problem with a solution of x = 20, use three collinear points A, B, and C and set AB = x and BC = 20 - x, with the entire segment AC being 20 units. Solving the equation x + (20 - x) = 20 confirms that x = 20 is the solution.
Explanation:To write a segment addition problem that solves for x where the solution is x = 20, let’s use three collinear points A, B, and C with point B between A and C. We can then express the lengths of segments AB and BC in terms of x. For instance, if AB is x units long and BC is 20 - x units long, the total length of AC would be 20 units. We can write an equation based on this:
AB + BC = AC
x + (20 - x) = 20
By simplifying, x cancels out on the left-hand side, leaving 20 = 20, which is true for x = 20. Therefore, this is a valid segment addition problem where solving for x yields 20 as the solution.
Here is the step-by-step problem phrased as a question:
Let points A, B, and C be collinear with B between A and C.If AB = x and BC = 20 - x, and AC = 20, find the value of x.The three sides of a triangle are consecutive odd integers. If the perimeter of the triangle is 39 inches find the lengths of the sides of the triangle
Answers
Jessica attains a height of 4.7 feet above the launch and landing ramps after 1 second. Her initial velocity is 25 feet per second. Find the angle of her launch. a. Which equation can you use with the given information to solve for ?
Answers
Height = 4.7 ft x (1 m/ 3.28 ft) = 1.43 m
Velocity = 25 ft / s x (1 m / 3.28 ft) = 7.62 m/s
The maximum height that can be attained by an object following a projectile path is calculated through the equation,
H = (v₀²)(sin²θ) / 2g
where v₀ is the initial velocity, H is the maximum height and g is the acceleration due to gravity.
Transforming the equation to calculate for θ,
sinθ = sqrt ((H)(2g) /(v₀²))
sinθ = sqrt ((1.43)(2)(9.8)) / (7.62²))
sinθ = 0.76
We calculate for the angle by getting the arcsin.
sin⁻¹ (0.76) = 49.46°
ANSWER: 49.46°
Hey there! I would like some help please :) Thanks!
Answers
Congruent triangles have exactly the same three angles, so ∠D = ∠B.
Find an exact value. sin(17pi/12)
a. √6 - √2 / 4
b. -√6 - √2 / 4
c. √6 + √2 / 4
d. √2 - √6 / 4
Answers
feel free to ask if you have any doubts.
The required exact value of the given trigonometric function is sin(17π/12) = (√6 + √2)/4
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
The trigonometric function is given in the question, as follows:
sin(17π/12)
To find the value of sin(17π/12), we can use the following trigonometric identity:
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
In this case, we can write:
sin(17π/12) = sin(π/3 + π/4)
We know that sin(π/3) = √3/2 and cos(π/3) = 1/2, and sin(π/4) = cos(π/4) = √2/2.
Therefore, we can use the above identity to get:
sin(17π/12) = sin(π/3)cos(π/4) + cos(π/3)sin(π/4)
= (√3/2)(√2/2) + (1/2)(√2/2)
= (√6/4) + (√2/4)
= (√6 + √2)/4
So the answer is option (c): √6 + √2 / 4.
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True or false an inscribed angle is formed by two radii that share an endpoint
Answers
True or false an inscribed angle is formed by two radii that share an endpoint
the correct answer is : FALSE
Answer:
The given statement : an inscribed angle is formed by two radii that share an endpoint is an FALSE statement.
Step-by-step explanation:
Inscribed angle is a angle which is formed inside the circle by joining of two intersecting chords inside a circle.
The inscribed angle is explained with the help of a diagram below :
In the diagram attached below, ∠ABC is an inscribed angle with an intercepted minor arc from A to C.
Thus, the inscribed angle is not formed with the help of radii that share a common end point.
Hence, The given statement : an inscribed angle is formed by two radii that share an endpoint is an FALSE statement.
A sports recreation company plans to manufacture a beach ball with a surface area of 7238 in.2 find the radius of the beach ball. use the formula , where a is the surface area and r is the radius of the sphere. 576 in. 48 in. 75 in. 24 in.
Answers
The given problem supplies as with the surface area of the beach ball and we are to look for the required radius. Assuming that the beach ball is perfectly shaped in the form of a sphere, then the formula for calculating the surface area of a sphere is given as:
SA = 4 π r^2
where r is the radius of the sphere and SA is the surface area which is given to be 7238 in^2
Rewriting the formula in terms of r:
r^2 = SA / 4 π
r = sqrt (SA / 4 π)
Solving for r:
r = sqrt (7238 in^2 / 4 π)
r = 24 in
Answer:
24 inches
slope of -8 and Y intercept of (0, 12) in slope intercept form.
Answers
Line segment LM is dilated to create L'M' using point Q as the center of dilation and a scale factor of 2.
What is the length of segment QM'?
Answers
Answer: 6 units
Step-by-step explanation:
Given: Line segment LM is dilated to create L'M' using point Q as the center of dilation and a scale factor of 2.
Since in dilation , to calculate the distance of a point on image from center point we need to multiply scale factor to the distance of corresponding point on pre-image from center point .
Thus we have,
[tex]QM'=2\times QM\\\\\Rightarrow QM'=2\times3\\\\\Rightarrow QM'=6[/tex]
Hence, the length of segment QM' = 6 units.
Answer:
6 units
Step-by-step explanation:
Find the slopes of the asymptotes of the hyperbola with the following equation.
36 = 9x ^{2} - 4y^{2}
Answers
The given equation is a hyperbola, and by converting it to standard form we find a = 2 and b = 3. Therefore, the slopes of the asymptotes are ±3/2.
Explanation:The equation given is in the form of a hyperbola equation which could be written as [tex]x^2/a^2 - y^2/b^2 = 1.[/tex] This suggests that the transverse axis is horizontal meaning the hyperbola opens to the left and right. The slopes of the asymptotes for hyperbola is given by ±b/a.
First, we need to rewrite our equation in standard form. The equation given is [tex]36 = 9x^{2} - 4y^{2}.[/tex] To convert it into the standard form, we divide whole equation by 36 to isolate 1 on one side. This yields [tex](x^2/4) - (y^2/9) = 1.[/tex] Now, it is in the standard form of hyperbola.
By comparing it with the standard equation, we see that [tex]a^2 = 4 \ and\ b^2 = 9[/tex]which gives a = 2 and b = 3. Based on these, we can now find the slope of the asymptotes which is ±b/a = ±3/2.
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Which graph represents the solution to the system of inequalities? x + y ≥ 4 2x + 3y < 12
Answers
x + y ≥ 4
2x + 3y < 12
For the first step, let's disregard the inequality symbols and take it like any conventional algebraic equation. This is to be able to graph the lines on a Cartesian planes first.
For the first equation, x+y=4. To find the x- and y-intercepts, let the other variable be 0. For example,
x-intercept:
x+0=4
x=4
y-intercept:
0+y=4
y=4
Therefore, you can graph the equation line by plotting the intercepts (4,0) and (0,4) and connecting them together. The same thing is done to the second equation:
x-intercept:
2x + 0 = 12
x=12/2=6
y-intercept:
0 + 3y =12
y= 12/3 = 4
Therefore, you can graph the equation line by plotting the intercepts (6,0) and (0,4) and connecting them together. The graph is shown in the left side of the picture.
The next step would be testing the inequalities. Let's choose a point that does not coincide with the lines. That point could be (-5,-1).
x + y ≥ 4
-5 + -1 ≥4
-6 ≥ 4 --> this is not true. Thus, the solution of the graph must not include the area of this point. It includes everything to the right of the line denoted by the blue-shaded region.
2x + 3y < 12
2(-5) + 3(-1) <12
-13 < 12 ---> this is true. Thus, the solution would include this point. That includes all points to the left of the orange line denoted by the orange-shaded the region.
The region where blue and orange overlap is the solution of the system of equations, denoted by the green-shaded region.
To answer that question
Answers
Find all solutions in the interval [0, 2π).
sin^2 x + sin x = 0
Answers
sin x( sin x + 1) = 0
sin x = 0 , or sinx + 1 = 0 giving sin x = -1
when sin x = 0 x = 0 , pi
when sin x = -1, x = pi + pi/2 = 3pi/2
solutions in given interval are 0,pi and 3pi/2
Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 13 in. by 8 in.
Answers
2) Call x the length of the sides of the squares cut off.
3) The base of the box will have dimensions: (13 - 2x) and (8 - 2x)
4) The height of the box will be x
5) The volume of the box will be the area of the base times the height:
Volume = (13 - 2x)(8 -2x)x = (4x^2 - 42x + 104)x = 4x^3 - 42x^2 + 104x
6) The maximum volume is calculated by finding the point where the derivative of the volume is zero =>
d (volume) / dx = 12x^2 - 84x + 104 = 0
7) Solve the quadratic equation 12x^2 - 84x + 104 = 0
=> 4(3x^2 - 21x + 26) = 0
=> 3x^2 - 21x + 26 = 0
=> 3 (x^2 - 7x) + 26 = 0
=> 3 [(x - 7/2)^2 - (7/2)^2] + 26 = 0
=> 3 (x - 7/2)^2 - 3* 49/4 + 26 = 0
=> 3 (x - 7/2)^2 = 3*49/4 - 26
=> (x -7/2)^2 = (49/4 - 26/3)
=> x = 7/2 +/- √(49/4 - 26/3)
x = 7/2 + √3.583 and x = 7/2 - √3.583
x = 5.393 and x = 1.607
=> Volume =
1) 4(5.393)^3 - 42(5.393)^2 + 104(5.393) = -33.26 ---> it does not have physical meaning
2) 4(1.607)^3 - 42(1.607)^2 + 104(1.607) = 75.27 ---> this is the answer
Answer: 75.27 in^3
9log9(4) =
A. 3
B. 4
C. 9
D. 81
Answers
Kenji buys 3 yards of fabric for 7.47$. Then he realizes that he needs 2 more yards. How much will the extra fabric cost?
Answers
7.47 / 3 = 2.49
Now that we know that each yard costs $2.49, we can multiply it by the number of yards you need to buy (two).
2 • 2.49 = 4.98
Your total for two yards of fabric is $4.98
A rectangular picture frame measures 4.0 inches by 5.5 inches. To cover
the picture inside the frame with glass costs $0.99 per square inch.
What will be the cost of the glass to cover the picture?
Answers
area = 4 x 5.5 = 22 square inches
cost is 0.99 per sq. inch
22 * 0.99 = 21.78
cost is $21.98
To find the cost of the glass for a 4.0 inch by 5.5 inch picture frame, calculate the frame's area and multiply it by the cost per square inch. The glass would cost $21.78.
To calculate the cost of the glass needed to cover the picture, you first need to determine the area of the glass required. The frame measures 4.0 inches by 5.5 inches, so the area can be found using the formula for the area of a rectangle, which is length multiplied by width.
The area is therefore 4.0 inches × 5.5 inches = 22.0 square inches. With the cost of glass being $0.99 per square inch, the total cost can be calculated by multiplying the area of the glass by the cost per square inch:
Total cost = 22.0 square inches × $0.99/square inch = $21.78.
Therefore, the cost of the glass to cover the picture would be $21.78.
Find the slope in line perpendicular x-y=16
Answers
X - y = 16
-y = -x + 16
So slope = - 1 / 1
determine which of the following logarithms is condensed correctly
Answers
alogb = log b^a
log a + log b = log (ab)
log a - log b = log (a/b)
for letter A,
xlogb r + logb s - logb t = logb [(rs)^x]/t
is wrong because the s part from logb s has no x before the logb
for letter B,
xlogb r + xlogb s - logb t = logb (rs/t)^x
is wrong because the t part from logb t has no x before logb
for letter C,
logbr - xlogb s + xlogb t = logb (r)/(st)^x
is correct because after the minus sign, condensing it would form a fraction, the plus sign will form a multiplication and both s and t are raised to the power of x.
So the answer is letter C.
Factor the expression
4b^2+28b+49
Answers
find the point on the terminal side of θ = negative three pi divided by four that has an x coordinate of negative 1
Answers
[tex]\bf tan(\theta)=\cfrac{opposite}{adjacent}\qquad tan\left( -\frac{3\pi }{4} \right)=\cfrac{y}{x}\implies tan\left( -\frac{3\pi }{4} \right)=\cfrac{y}{-1} \\\\\\ -1\cdot tan\left( -\frac{3\pi }{4} \right)=y\implies -1\cdot \cfrac{sin\left( -\frac{3\pi }{4} \right)}{cos\left( -\frac{3\pi }{4} \right)}=y \\\\\\ -1\cdot \cfrac{-1}{-1}=y\implies -1[/tex]
The point on the terminal side is (1,-1) and this can be determined by using the trigonometric functions.
Given :
The point on the terminal side of θ = negative three [tex]\pi[/tex] divided by four that has an x coordinate of negative 1.
The following steps can be used in order to determine the point on the terminal side:
Step 1 - Write the given expression.
[tex]\theta = -\dfrac{3\pi}{4}[/tex]
Step 2 - The value of the trigonometric function is given by:
[tex]\rm tan \dfrac{3\pi}{4} =-1[/tex]
Step 3 - The trigonometric function can also be written as:
[tex]\rm tan \theta=\dfrac{y}{x}=-1[/tex]
Step 4 - Substitute the value of 'x' in the above expression.
y = -1
So, the point on the terminal side is (1,-1).
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Probability theory predicts that there is a 44% chance of a water polo team winning any particular match. If the water polo team playing 2 matches is simulated 10,000 times, in about how many of the simulations would you expect them to win exactly one match?
Answers
water polo team wins none, wins 1 or wins both games.
chance that they win both matches are:
0.44*0.44 = 0.1936 in relative value
Chance that they lose both matches are:
(1-0.44)*(1-0.44) = 0.3136 in relative value
If we multiply these relative values by number of matches and subtract that from number played double games (10000) we will get number of times they won only once.
10000 - 10000* (0.3136+ 0.1936) = 4928
Tim bought a soft drink for 2 dollars and 5 candy bars. He spent a total of 22 dollars. How much did the candy bar costs?
Answers
Subtract 2 from both sides
5x=20
Divide both sides by 5
x=4
Final answer: $4.00
What is the value of X that makes the given equation true? 4x-16=6(3+x)
Answers
The figures in each pair are similar. Find the value of each variable. Show your work.
Answers
Next question is basically like the first one, but you have to divide instead. 12÷4=3, and so 8×3=24, so y=24. 18÷3=6, so x=6. Last one, 6÷4= 1.5. 8÷1.5=5.3 and 7÷1.5=4.6, so x=4.6 and y=5.3
The rectangle:
[tex]\frac{16}{8}=\frac{x}{2}[/tex]
[tex]2=\frac{x}{2}\quad |\cdot 2[/tex]
[tex]4=x[/tex]
The triangle I:
[tex]\frac{y}{12}=\frac{8}{4}[/tex]
[tex]\frac{y}{12}=2\quad |\cdot 12[/tex]
[tex]y=24[/tex]
[tex]\frac{12}{4}=\frac{18}{x}[/tex]
[tex]3=\frac{18}{x}\quad |\cdot x[/tex]
[tex]3x=18\quad |:3[/tex]
[tex]x=6[/tex]
The triangle II:
[tex]\frac{8}{6}=\frac{y}{4}[/tex]
[tex]32=6y\quad |:6[/tex]
[tex]y=5\frac{1}{3}[/tex]
[tex]\frac{6}{4}=\frac{7}{x}[/tex]
[tex]\frac{3}{2}=\frac{7}{x}[/tex]
[tex]3x=14[/tex]
[tex]x=4\frac{2}{3}[/tex]
:)
Determine the value of a so that the line whose equation is ax+y-4=0 is perpendicular to the line containing the points (2,-5) and (-3,2)
Answers
We can use 2 point form, or point-slope form.
Let's use point-slope form.
the slope m is [tex] \frac{-5-2}{2-(-3)}= \frac{-7}{5} [/tex], then use any of the points to write the equation. (ex, pick (2, -5))
y-(-5)=(-7/5)(x-2)
y+5=(-7/5)x+14/5
y= (-7/5)x+14/5 - 5 =(-7/5)x+14/5 - 25/5 =(-7/5)x-11/5
Thus, the lines are
i) y=-ax+4 and ii) y=(-7/5)x-11/5
the slopes are the coefficients of x: -a and (-7/5),
the product of the slopes of 2 perpendicular lines is -1,
so
(-a)(-7/5)=-1
7/5a=-1
a=-1/(7/5)=-5/7
Answer: -5/7
please help me idk how to do this at all I've been stuck on it for awhile.
Answers
(x,y)
we are given x=2
find what y is when x=2
subsitute 2 for x
y=2x+5
y=2(2)+5
y=4+5
y=9
so the blank is 9
when numbers are in parenthesis the first number is x the second is y
(x,y)
sine they give you (2, blank)
2 = x so replace x in the equation with 2
so y=2x+5 becomes y=2(2)+5
so y = 2*2+5 = 9
y=9
so it should be (2,9)