9514 1404 393
Answer:
1.3363
Step-by-step explanation:
The basic idea here is to find an expression for the direction vector between a point on L1 and a point on L2. Then, solve for the points on L1 and L2 that make that vector perpendicular to both lines L1 and L2. (The dot product of direction vectors is zero.) The distance between the points found is the shortest distance between the lines.
__
Let P be a point on L1. Then the parametric equation for P is ...
P = (6t, 0, -t) . . . . . . origin + t × direction vector
Let Q be a point on L2. The direction vector for L2 is given by the difference between the given points. It is (4-1, 1-(-1), 6-1) = (3, 2, 5). Then the parametric equation for Q is ...
Q = (3s+1, 2s-1, 5s+1) . . . . (1, -1, 1) + s × direction vector
The direction vector for PQ is ...
Q -P = (3s+1-6t, 2s-1, 5s+1+t)
The dot product of this and the two lines' direction vectors will be zero:
(3s+1-6t, 2s-1, 5s+1+t)·(6, 0, -1) = 0 = 13s -37t +5 . . . perpendicular to L1
(3s+1-6t, 2s-1, 5s+1+t)·(3, 2, 5) = 0 = 38s -13t +6 . . . perpendicular to L2
The solution to these equations is ...
s = -157/1237
t = 112/1237
Then (Q-P) becomes (94, -1551, 564)/1237, and its length is ...
|PQ| = √(94² +1551² +564²)/1237 ≈ 1.3363
The distance between the two lines is about 1.3363 units.
The Starlight movie theater charges $4.95 per box of popcom. Each box of popcorn costs the theater $0.87 to make. How much money does the theater eam on the sale of 94 boxes of popcorn after the costs are subtracted?
Answer:383.52
Step-by-step explanation: you subtract how much it costs them to make and then times the amount of boxes they’re making.
100 POINTS AND BRAINILY
Answer:
Step-by-step explanation:
In a right-angled triangle, by definition:
sinX = opposite side / hypothesis
= 5/13
tanX = opposity side / adjacent side
= 5/12
cosX = adjacent side / hypothesis
= 12/13
\(\\ \rm\hookrightarrow sinX=\dfrac{Perpendicular}{Hypotenuse}=\dfrac{5}{13}\)
\(\\ \rm\hookrightarrow cosX=\dfrac{Base}{Hypotenuse}=\dfrac{12}{13}\)
\(\\ \rm\hookrightarrow tanX=\dfrac{sinX}{cosX}=\dfrac{5}{12}\)
A, B and C are currencies of different countries. Three As are worth four Bs and five Bs are worth one C. How many As are two Cs worth?
When B and C are the currencies of different nations, two Cs are worth 7.5 As. Five Bs are equivalent to one C, while three As are worth four Bs.
what is equation ?Its precise nature is understood to be the figure is probably smallest equivalent fraction. How to determine the simplest form. Look for shared factors in the median and excess. A fractional number can always be checked to discover if it is a prime number. A statement having two equal sides and an equal sign in the intermediate is referred to as a linear expression. Every variable's classes are listed in lowest to highest in the general form of any formula. The formula for a linear function is x + b = 0. The simplified version of a two-variable mathematical expression is an x + b y + c = 0. (or something similar). Either conditioned equations or identities provide categories for equations. An identity holds true because of whatever value of the variables.
given
The aforesaid issue is easily resolved by doing the following:
Considering that,
Four Bs are worth three As.
It can be written as;
3A = 4B
determining B's value
B = 3A/4 (Equation 1) (Equation 1)
Now,
A B is worth five Cs.
So, 5B = C (Equation 2) (Equation 2)
Calculating B's value in equation 1
= 15A/4 = C
= 4C = 15A
2C = (15/2)A
2C = 7.5A
Therefore, the solution is 2C = 7.5A
When B and C are the currencies of different nations, two Cs are worth 7.5 As. Five Bs are equivalent to one C, while three As are worth four Bs.
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Easy Question / algebra 1
The quadratic function of the distance of the diver from sea level is: d(t) = -2(t - 3)^2 - 8
How to determine the quadratic functionA quadratic function can be represented in the form of d(t) = a(t - h)^2 + k where a is the leading coefficient, (t - h) is the horizontal shift, and k is the vertical shift.
To find this quadratic function, we need to find the values of a, h, and k.
To find the vertex, we can use the point where the diver reaches the maximum depth, which is 8 meters at 3 minutes,
So the vertex is at (h, k) = (3, -8).
When the time are converted to minutes:
To find the value of a, we can use the point (2,-10) and the vertex form equation:
d(t) = a(t - h)^2 + k
Substitute the coordinates of the point and the vertex form equation:
-10 = a(2-3)^2 -8
Solving the system of equation, we find a = -2
Therefore, the quadratic function is: d(t) = -2(t - 3)^2 - 8
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Please help asap!!!!!!
By SAS congruence triangle MLN and triangle OLN are congruent.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Given that, LM≅LO, ∠MLN≅∠OLN.
LM≅LO (Given)
∠MLN≅∠OLN (Given)
LN≅LN (Reflexive property of congruence)
ΔMLN≅ΔOLN (SAS congruence)
∠M≅∠O (CPTC)
MN≅ON (CPTC)
Therefore, by SAS congruence triangle MLN and triangle OLN are congruent.
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hi if anyone is good with extraneous solutions pleaseeeeeee help meeee tessa solves the equation below by first squaring both sides of the equation√x^2-3x-6=x-1 what extraneous solution does tessa obtain x=
Answer:
x = -7/5
Step-by-step explanation:
If we square both sides of the equation, we get:
\(\sqrt{x^2-3x-6}=x-1\\ (\sqrt{x^2-3x-6})^2=(x-1)^2\\x^2-3x-6=x^2-2x+1\\\)
Then, solving for x, we get:
\(x^2-3x-6=x^2-2x+1\\-3x-6=2x+1\\-6-1=2x+3x\\-7=5x\\\frac{-7}{5}=x\)
So, x is equal to -7/5
Answer:
its -7
Step-by-step explanation:
gots it right!
In a lab experiment, 610 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 23 hours. How long would it be, to the nearest tenth of an hour, until there are 1040 bacteria present?
Answer:
It would take 19 hours and 36 minutes until there are 1040 bacteria present.
Step-by-step explanation:
Given that in a lab experiment, 610 bacteria are placed in a petri dish, and the conditions are such that the number of bacteria is able to double every 23 hours, to determine how long would it be, to the nearest tenth of an hour, until there are 1040 bacteria present, the following calculation must be performed:
610X = 1040
X = 1040/610
X = 1.7049
2 = 23
1.7049 = X
1.7049 x 23/2 = X
39.2131 / 2 = X
19.6 = X
100 = 60
60 = X
60 x 60/100 = X
36 = X
Therefore, it would take 19 hours and 36 minutes until there are 1040 bacteria present.
HELP PLEASE 8TH GRADE MATH
The measures of the angles are 33°, 105° and 42°
We can call the top angle P, the bottom left angle Q, and the bottom right angle R. We are also given that angle P is (x - 9) degrees, angle Q is (x + 63) degrees, and angle R is x degrees.
Now, we can use the fact that the sum of the angles in a triangle is 180 degrees to set up an equation:
Angle P + Angle Q + Angle R = 180
To find Angle, we can use the fact that the sum of the angles in a straight line is 180 degrees. We can see that Angle and Angle A are on a straight line, so we have:
(x – 9) + ( x + 63) + x = 180
=> 3x + 54 = 180
=> 3x = 126
=> x = 42
We can now use this value to find the measures of the angles.
Angle P is (x -9) degrees, so Angle P = 42 - 9 = 33 degrees.
Angle Q is (x + 63) degrees, so Angle Q = 42 + 63 = 105 degrees.
Angle R is x degrees, so Angle R = 42 degrees.
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ax+ay/xy^2*x^2y/3x+3y
The simplified form of the expression \((\frac{ax + ay}{xy^2}) (\frac{x^2y}{3x + 3y} )\) is \(\frac{3ax^2 + 6axy + 3ay^2 + xy}{3xy + 3y^2}\).
What is LCM?Least Common Multiple is the meaning of the abbreviation LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It can also be computed using two or more numbers. Finding the LCM of a given collection of numbers can be done in a variety of ways. Using the prime factorization of each number and then calculating the product of the greatest powers of the shared prime factors is one of the quickest techniques to determine the LCM of two numbers.
Given that the expression is:
\((\frac{ax + ay}{xy^2}) (\frac{x^2y}{3x + 3y} )\)
Cancelling the like terms:
\((\frac{ax + ay}{y}) (\frac{x}{3x + 3y} )\)
Taking the LCM:
\(\frac{3ax^2 + 6axy + 3ay^2 + xy}{3xy + 3y^2}\)
Hence, the simplified form of the expression \((\frac{ax + ay}{xy^2}) (\frac{x^2y}{3x + 3y} )\) is \(\frac{3ax^2 + 6axy + 3ay^2 + xy}{3xy + 3y^2}\).
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What the meaning of "f is order-preserving if x < y implies f(x) < f(y)"?
An order-preserving function is a function that preserves the order of its inputs. In other words, if x is less than y, then f(x) will be less than f(y).
The statement "f is order-preserving if x < y implies f(x) < f(y)" means that if x is less than y, then f(x) must be less than f(y). This is a necessary condition for a function to be order-preserving. However, it is not a sufficient condition. For example, the function f(x) = x^2 is not order-preserving, because 2 < 3, but f(2) = 4 > f(3) = 9.
In summary, order-preserving functions are useful in situations where we need to preserve the order of a set of data.
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The graph below represents results of a survey in which students stated the numberof minutes they'd spent watching TV the previous day.
Explanation:
First, we need to find what is the total number of values in the data. So, taking into account the height of the bars, we can calculate the size of the data as follows:
6 + 2 + 3 + 5 + 4 + 4 = 24
Where each number in the sum is the height of each bar.
Then, the position of the median can be calculated using the following equation:
\(\frac{n+1}{2}=\frac{24+1}{2}=\frac{25}{2}=12.5\)Where n is the size of the data.
Finally, the value in position 12.5 is in the interval 90 - 119
Because, there are 6 values in 0- 29, there are
please help asap thanks . i’ll mark brainliest !!
Answer: 3
Step-by-step explanation: Whenever we have midsegment, the length of it is half of the base which is 30 so 5x =15.
if f={(1,3),(4,9),(5,2),(6,8)} and f(a)=8, what are all of the possible values for a?
The mean value theorem is used to link the average rate of change and the derivative of a function.
The value of V is 8.
The givenparameters are:
Mean value theorem states that:
If [a,b] and
(a,b),
Then there is a point c in (a,b), such that:
From the question, we understand that: f is differentiable
This means that:
avethat:
The equation becomes
Cross mltiply
o both side
From the question, we have:
By comparisons;
Hence, the value of V is 8.
Get it right please.
A zoologist recorded the speed of two cheetahs. Cheetah A ran 17 miles in 8 minutes. Cheetah B ran 56 miles in 20 minutes. Which statement is correct?
Cheetah A has a higher ratio of miles per minute than Cheetah B because 17 over 8 is less than 56 over 20.
Cheetah B has a higher ratio of miles per minute than Cheetah A because 17 over 8 is greater than 56 over 20.
Cheetah B has a higher ratio of miles per minute than Cheetah A because 17 over 8 is less than 56 over 20.
Both cheetahs have the same ratio of miles per minute.
The answer would be C - "Cheetah B has a higher ratio of miles per minute than Cheetah A because 17 over 8 is less than 56 over 20."
also "get it right please" ?! how rude
Give the mean of the following probability distribution?
x
P(x)
1
0.20
2
0.10
3
0.35
4
0.05
5
0.30
A) 1.20 B) 1.46 C) 3.15 D)
2.13
QUESTION 8
Answer:
C
Step-by-step explanation:
Solve algebraically for x 3600 + 1.02x < 2000 + 1.04 x
Answer:
x>80000
Step-by-step explanation:
3600+1.02x<2000+1.04x=x>80000
(b) 25% of what number is 17?
Answer:
68
Step-by-step explanation:
derive that 25 percent of 68 equals 17.
Answer:
25 percent of 68 equals 17.
Step-by-step explanation:
code: M74 E allowed Second chance! Review your workings and see if you can correct your mistake. A parallelogram is shown below. Work out the size of the angle marked c. 46° C Not drawn accurately
Angle a + Angle d = 180 degreesAngle b + Angle c = 180 degrees.
In a parallelogram, adjacent angles are supplementary. As a result, we can express c in terms of the angles adjacent to it as follows: Angle a + Angle c = 180 degreesAngle c + 46 degrees = 180 degreesAngle c = 180 degrees - 46 degrees = 134 degreesTherefore, the size of angle c is 134 degrees.
A parallelogram is a four-sided quadrilateral that has opposite sides parallel and equal in length. Each of the opposite angles is also equal in size.In general, if we label the angles of a parallelogram as follows: Angle a, Angle b, Angle c, and Angle d,.
we have the following:Angle a = Angle c (opposite angles are equal)Angle b = Angle d (opposite angles are equal)Adjacent angles in a parallelogram are supplementary, which means they add up to 180 degrees.
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If bcd~gef find value of x
Answer:
\(x = 13\)
Step-by-step explanation:
Given
See attachment
Required
Find x
From the attachment, we have:
\(BC = x + 4\)
\(BD = 2x - 7\)
\(GE = 51\)
\(GF = 57\)
Because both triangles are similar, we use the following equivalent ratios:
\(BC : BD = GE : GF\)
Substitute values for each parameter
\(x + 4 : 2x- 7 = 51 : 57\)
Convert to fractions
\(\frac{x + 4}{2x- 7} = \frac{51 }{ 57}\)
Simplify the right-hand side
\(\frac{x + 4}{2x- 7} = \frac{17}{19}\)
Cross Multiply
\(19(x + 4) = 17(2x - 7)\)
\(19x + 76 = 34x - 119\)
Collect Like Terms
\(19x - 34x = -76 - 119\)
\(-15x = -195\)
Solve for x
\(x = \frac{-195}{-15}\)
\(x = 13\)
Answer: x=13
Step-by-step explanation:
:(x+4) 57 = (2x-7) 5157x + 228 = 102x - 357357+228 = 102x - 57x585 = 45x13 =
if 3*2=12,3*5=24and 15-6=3then 16/2=?
a.4
b.6
c.8
d.12
Answer:
16 divided by 2 equals C which is 8.
Step-by-step explanation:
If α=.10 and β=.33, then the probability of rejecting the null when the alternative is true is ___.a. 0.10b. 0.90c. 0.33d. 0.67
The probability of rejecting the null when the alternative is true is d. 0.67
Given :
If α=.10 and β=.33, then the probability of rejecting the null when the alternative is true is .
Probability :
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
Null hypothesis :
A null hypothesis is a type of statistical hypothesis that proposes that no statistical significance exists in a set of given observations.
we know that ,
probability = 2 * 0.33 + 0.01
= 0.66 + 0.01
= 0.67
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Consider a tech company that wants to offer free breakfast to its employees if their confidence interval shows it will decrease the
proportion of employees who skip breakfast.
Each interval shows the difference in proportion of p₁ - P2 where p₁ represents the employees who skip breakfast when free
breakfast is offered and p2 represents the employees who skip breakfast when free breakfast is not offered. Determine if there is
enough evidence to suggest that offering free breakfast results in an increase in the proportion of employees who don't skip
breakfast.
(-0.44,-0.16)
Yes, we can be confident that employees will skip breakfast less when free breakfast is offered than when it's not.
Or
No, our confidence interval shows that there could be no difference in the proportion of employees who skip breakfast.
(-0.25, 0.05)
Yes, we can be confident that employees will skip breakfast less when free breakfast is offered than when it's not.
Or
No, our confidence interval shows that there could be no difference in the proportion of employees who skip breakfast.
(-0.23, 0.15)
Yes, we can be confident that employees will skip breakfast less when free breakfast is offered than when it's not.
Or
No, our confidence interval shows that there could be no difference in the proportion of employees who skip breakfast.
Answer:
Step-by-step explanation:
In this scenario, the confidence interval represents the possible range of differences in the proportion of employees who skip breakfast when free breakfast is offered and when it's not. A confidence interval that does not include zero indicates that there is statistically significant evidence to suggest a difference in proportions between these two groups.
Therefore, for the first interval (-0.44,-0.16), since it does not include zero, we can be confident that offering free breakfast results in a decrease in the proportion of employees who skip breakfast.
For the second interval (-0.25, 0.05), since it contains zero, we cannot be confident that there is a difference in the proportion of employees who skip breakfast between the two groups.
Similarly, for the third interval (-0.23, 0.15), since it contains zero, we cannot be confident that there is a difference in the proportion of employees who skip breakfast between the two groups.
So, the correct answer is:
For the interval (-0.44,-0.16), we can be confident that employees will skip breakfast less when free breakfast is offered than when it's not.
For the intervals (-0.25, 0.05) and (-0.23, 0.15), our confidence interval shows that there could be no difference in the proportion of employees who skip breakfast.
I don’t know how to do this problem help me!!
\(x-9z^5+4z+11+2z^5+14=-5z^5-3z+25\\x=2z^5-7z\)
Therefore, it's \(2z^5-7z\).
10-10=69.420!!!!!!!!!!
mr. Webster cut a triangle with a height of 4 inches and a base of 6 inches out of a sheet of paper measuring 10 inches by 12 inches she recycled the unused paper what was the area of the cheaper shipping recycled
Answer:
108 in²
Explanation:
The area of the recycled part can be calculated as the difference between the area of the sheet of paper and the area of the triangle.
So, the area of the sheet of paper can be calculated as:
Ar = Base x Height
Ar = 10 in x 12 in
Ar = 120 in²
Then, the area of the triangle can be calculated as:
At = (1/2) x Base x Height
At = (1/2) x 6 in x 4 in
At = 12 in²
Therefore, the area of the recycled part is equal to:
A = Ar - At
A = 120 in² - 12 in²
A = 108 in²
So, the answer is 108 in²
Can someone help me with this? I can't figure it out
In linear equation, 9 is the constant of variation k.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.
given x varies inversely with y then
xy = k ← k is the constant of variation
to find k use the condition x = - 4 when y = - 9, hence
k = -4 × -9 = 36
x = 36/y
when x = 4 , then y = 36/4
x = 9
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The true statements are
The value of f(–10) = 82
The graph of the function is a parabola.
The graph contains the point (20, –8).
What is a Parabola:A parabola is a type of conic section that is formed when a plane intersects a cone in such a way that the angle between the plane and the vertical axis of the cone is equal to the angle between the plane and a generator (a straight line passing through the vertex and the base of the cone).
The resulting shape is a symmetrical, U-shaped curve. The standard form of the parabola is a quadratic function.
Here we have
The quadratic function f(x) = x²/5 – 5x + 12
Now check each option as follows
1. The value of f(–10) = 82
To check this find f(-10) as follows
f(-10) =1/5 (-10)²– 5(-10) + 12 = 20 + 50 + 12 = 82
Hence, The value of f(–10) is equal to 82
2. The graph of the function is a parabola.
As we know the standard equation of a parabola is a quadratic function that is in the form of ax² + bx + c
Hence, the quadratic function represents a parabola
3. The graph of the function opens down.
In the given function f(x) = x²– 5x + 12, the coefficient of the x² term is 1. Since the coefficient of x² is positive, the parabola opens upwards.
Hence, The graph of the function opens down is false
4. The graph contains the point (20, –8).
To check this substitute the point in f(x)
=> –8 = 1/5(20)²– 5(20) + 12
=> –8 = 80 – 100 + 12
=> –8 = –8 [ Which is true ]
Hence, The graph contains the point (20, –8).
5. The graph contains the point (0, 0).
=> 0 = (0)²– 5(0) + 12
=> 0 = 12 [ which is not true ]
Hence, The graph doesn't contain the point (0, 0).
Therefore,
The true statements are
The value of f(–10) = 82
The graph of the function is a parabola.
The graph contains the point (20, –8).
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Three watches and five lamps cost $176 in all. Five watches and three lamps cost $208 in all. What is the cost of one lamp?
$200/5 lamps= $40 per lamp
Final answer: $40
Using the elimination principle, the cost of one lamp is $16
Let :
watches = a Lamps = b3a + 5b = 176 - - - - (1)
5a + 3b = 208 - - - (2)
Multiply (1) by 5 and (2) by 3
15a + 25b = 880 - - - - (3)
15a + 9b = 624 - - - - - (4)
Subtract (3) and (4)
16b = 256
b = (256 ÷ 16)
b = $16
Therefore, the cost of one lamp is $16
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Select the outlier in the data set.
72
82
86
88
89
92
96
98
306
Answer:
306
Step-by-step explanation:
An outlier is a number that is not near the other numbers
306 is not near the other numbers
During an unusual storm, the temperature fell 8° C, rose 5° C, fell 4° C,
and then rose 6° C. If the temperature was 32° C at the outset of the storm,
what was it after the storm was over?
(X^3)^2 without exponents
\((x^3)^2 \)
\((x^{3×2})\)
\(x^6 \)