Answer:
The correct option is (A).
Step-by-step explanation:
The range of a data set is a measure of variability of that data set.
The range is the difference between the maximum and minimum value of the set.
[tex]\text{Range}=\text{Maximum}-\text{Minimum}[/tex]
Since the maximum value is used in the computation of range, changing the maximum value affects the range greatly.
The correct option is (A).
Need help with trig question
Answer:
0 +256i
Step-by-step explanation:
According to Euler's formula, ...
(4 cis π/8)^4 = (4^4) cis (4×π/8) = 256 cis π/2 = 0 +256i
_____
"cis" is an abbreviation sometimes used for "cosine + i×sine". It simplifies writing the expression. Engineers sometimes simplify it further, writing 4∠(π/8) for the expression in this problem statement.
Find an equation of the tangent line to the curve at the given point.
y = √ (x) , (16, 4)
Answer: y=1/8*x+2
Step-by-step explanation:
The equation of any tangent line is y=a*x+b (1)
To the equation of the tangent line we have to find the coefficients a and b and the to substitute them to equation (1).
As we know a=y'(x0) ( where x0=16)
So y'(x)= (√ (x) )' = 1/(2*√x)
a=y'(x0)= 1/(2*√16)=1/(2*4)=1/8
So lets substitute a in equation (1):
y=1/8 *x+b
Now we have to find b
We know that the point (16, 4) belongs to the tangent line.
That means
4=1/8*16+b => 4=2+b => b=2
SO the equation of the tangent line is y=1/8*x+2
. The monthly worldwide average number of airplane crashes of commercial airlines is 2.2. What is the probability that there will be a. more than 2 such accidents in the next month?
Answer:
Probability (N more than 2) = 0.3773
Step-by-step explanation:
Given:
Average number of crashes (N) = 2.2
Find:
Probability (N more than 2)
Computation:
Probability (N more than 2) = [1-P(N=0)-P(N=1)-P(N=2)]
Probability (N more than 2) = [1 - e⁻²°² - 2.2e⁻²°² - (2.2²e⁻²°²)/2]
Probability (N more than 2) = 0.3773
A math teacher asks Nico and Katya to solve the following word problem. A car travels 98 miles in 1.7 hours on a freeway where the speed limit is 55 mph. Was the car speeding? Nico and Katya both agree that they should use their calculators to divide the miles by the hours to find the speed of the car, and then compare the answer to 55 mph. However, Nico says it's okay to round what his calculator says to the nearest whole number. Katya says that because the calculator displays eight numbers after the decimal point, they shouldn't round. She says they should write down exactly what the calculator shows. Do you agree with Nico or with Katya? In a short paragraph, explain who you agree with and provide the reasons why.
Answer:
- Was the car speeding?
Yes, the car was speeding as its current speed of 57.65 mph was more than the speed limit of that freeway.
- Do you agree with Nico or with Katya?
I agree somewhat with both Nico and Katya, but, I agree more with Nico.
- Explain your reasoning.
Like I said, I agree more with Nico's method of rounding the speed to the nearest whole number. This is because in this question, the standard speed we want to compare the calculated speed with is given as a whole number. Hence, it is more proper to estimate the calculated speed to its nearest whole number too.
Step-by-step explanation:
Speed during a travel is given as distance travelled divided by time taken
Speed = (Distance/time)
Distance = 98 miles
Time = 1.7 hours
Speed = (98/1.7) = 57.6470588235 = 57.65 mph = 58 mph
- Was the car speeding?
The speed limit for the road is 55 mph and the current speed of the car = 57.65 mph
Since 57.65 > 55
The car was overspeeding.
- Nico says it's okay to round what his calculator says to the nearest whole number. Katya says that because the calculator displays eight numbers after the decimal point, they shouldn't round. She says they should write down exactly what the calculator shows. Do you agree with Nico or with Katya?
I agree somewhat with both Nico and Katya as the both methods of recording the speed ate right, depending on what the speed is required for.
Although, I agree more with Nico's method as it seems like a better fit for the situation described in the question.
- explain who you agree with and provide the reasons why.
Like I said earlier, I agree more with Nico's method of rounding the speed to the nearest whole number. This is because in this question, the standard speed we want to compare the calculated speed with is given as a whole number. Hence, it is more proper to estimate the calculated speed to its nearest whole number too.
Katya's method of writing the calculated speed as is will be correct in cases where extreme accuracy is required, not an estimate. For this question, the estimate will do.
Hope this Helps!!!
Answer:
Yes, the car was speeding as its current speed of 57.65 mph was more than the speed limit of that freeway.
Step-by-step explanation:
Nico and Katya i agree with.
A child is playing games with empty soda cups. There are three sizes: small, medium, and large. After some experimentation
she discovered she was able to measure out 160 ounces in the following ways:
1) 2 small, 2 medium, 4 large
2) 2 small, 6 medium, 1 large
3) 5 small, 1 medium, 3 large
Determine the size of the cups.
Answer:
S is the volume of the small cup, M the volume of the medium cup and L the volume of the large cup:
2*S + 2*M + 4*L = 160oz
2*S + 6*M + 1*L = 160oz
5*S + 1*M + 3*L = 160oz.
First, we must isolate one of the variables, for this we can use the first two equations and get:
2*S + 2*M + 4*L = 160oz = 2*S + 6*M + 1*L
We can cancel 2*S in both sides:
2*M + 4*L = 6*M + 1*L
now each side must have only one variable:
4*L - 1*L = 6*M - 2*M
3*L = 4*M
L = (4/3)*M.
now we can replace it in the equations and get :
2*S + 2*M + 4*(4/3)*M = 160oz
2*S + 6*M + (4/3)*M = 160oz
5*S + 1*M + 4M = 160oz.
simplifing them we have:
2*S + (22/3)*M + = 160oz
2*S + (22/3)*M = 160oz
5*S + 5*M = 160oz.
(the first and second equation are equal because we used those to get the relation of M and L, so we now have only two equations):
2*S + (22/3)*M = 160oz
5*S + 5*M = 160oz.
We can take the second equation and simplify it:
S + M = 160oz/5 = 32oz
S = 32oz - M
Now we can replace it in the first equation and solve it for M
2*S + (22/3)*M = 2*(32oz - M) + (22/3)*M = 160oz
62oz - 2*M + (22/3)*M = 160oz
-(6/3)*M + (22/3)*M = 98oz
(18/3)*M = 98oz
M = (3/18)*98oz = 16.33 oz
Then:
L = (4/3)*M =(4/3)*16.33oz = 21.78 oz
and:
S = 32oz - M = 32oz - 16.33oz = 15.67oz
Brainliest? Get this correct What is the difference of the rational expressions below?
Answer:
A. [tex]\frac{x^2-3x+6}{x^2 - 2x}[/tex]
Step-by-step explanation:
1. Move all of numerators above the corresponding common denominator
2. Multiply inside the parentheses then remove any remaining parenthesis to get your final answer to get your fraction.
Answer:
[tex] \dfrac{x^2 - 3x + 6}{x^2 - 2x} [/tex]
Step-by-step explanation:
[tex] \dfrac{x}{x - 2} - \dfrac{3}{x} = [/tex]
[tex] = \dfrac{(x)x}{(x)(x - 2)} - \dfrac{(x - 2)(3)}{(x - 2)(x)} [/tex]
[tex] = \dfrac{x^2}(x - 2)} - \dfrac{3x - 6}{(x - 2)(x)} [/tex]
[tex] = \dfrac{x^2 - (3x - 6)}{x^2 - 2x} [/tex]
[tex] = \dfrac{x^2 - 3x + 6}{x^2 - 2x} [/tex]
given that f(x) = x² + 6x and g(x) = x + 9 calculate
a) f•g (4) =
B) g•f (4) =
Answer:
247
49
Step-by-step explanation:
a) f•g (4) =
f•g (x) = f(g(x)) = (x + 9)^2 + 6(x + 9)
f•g (4) = (4 + 9)^2 + 6(4 + 9)
= 13^2 + 6(13)
= 247
B) g•f (4) =
g•f (x) = g(f(x)) = x^2 + 6x + 9
g•f (4) = 4^2 + 6(4) + 9
= 16 + 24 + 9
= 49
At noon, ship A is 120 km west of ship B. Ship A is sailing east at 20 km/h and ship B is sailing north at 15 km/h. How fast is the distance between the ships changing at 4:00 PM?
Answer:
1.39 km/h
Step-by-step explanation:
Let the initial position of ship B represent the origin of our coordinate system. Then the position of ship A as a function of time t is ...
A = -120 +20t . . . (east of the origin)
and the position of B is ...
B = 15t . . . (north of the origin)
Then the distance between them is ...
d = √(A² +B²) = √((-120 +20t)² +(15t)²) = √(625t² -4800t +1440)
And the rate of change is ...
d' = (625t -2400)/√(625t² -4800t +14400)
At t = 4, the rate of change is ...
d' = (625·4 -2400)/√(625·16 -4800·4 +14400) = 100/√5200 = 1.39 . . . km/h
The distance between the ships is increasing at about 1.39 km/h.
Simplify (20x^-3/10x^-1)^2
Answer: 4 / x^4
Step-by-step explanation:
(20x^-3 / 10x^-1)^2
Simplify,
(2 / x^2)^2
= 4 / x^4
What is the value of a?
Answer:
[tex]\huge\boxed{a=\dfrac{16}{3}=5\dfrac{1}{3}}[/tex]
Step-by-step explanation:
[tex]\triangle ZYW\sim\triangle WYX\ (AAA)\\\\\text{Therefore corresponding sides are in proportion}\\\\\dfrac{YX}{YW}=\dfrac{YW}{ZY}\\\\\text{substitute}\\\\YX=a;\ YW=4;\ ZY=3\\\\\dfrac{a}{4}=\dfrac{4}{3}\qquad\text{multiply both sides by 4}\\\\4\cdot\dfrac{a}{4}=4\cdot\dfrac{4}{3}\qquad\text{cancel 4}\\\\a=\dfrac{16}{3}[/tex]
Verify the continuity type C° and C1 between curve(l) and curve(2).
Curve 1: (0,0), (1,1), (4,1), and (6,0)
Curve 2: (6,0), (7,-1), (10,-1), and (12,0)
Step-by-step explanation:
to be honest I'm not sure how to do
Comment
Solve the algebraic expressio (0.4)(8)−2
Answer: -6.4
Step-by-step explanation:
(0.4)(8)(-2)
3.2*-2
-6.4
Which number is a solution of the inequality: B > 2.1
A: -8
B: -12
C:5
D: 1
Answer:
C. 5 is solution of the inequality: B>2.1
Select the correct answer from each drop down menu. AB is dilated by a scale factor of 3 to form A 1 B1. Point O, which lies on AB, is the center of dilation. The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O.
Answer:
the slope of A'B' = 3
A'B' passes through point O
Step-by-step explanation:
A dilation with scale factor 3 gives the effect of stretching the line AB three times longer. As dilation does not change the direction of the line, the slope will stay the same. If point O lies on AB and is the center of dilation, then the point O must also lie on A'B'
The required black space in the statement "The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O". is filled by 3 and passes.
Given that,
To Select the correct answer from each drop-down menu. AB is dilated by a scale factor of 3 to form A 1 B1. Point O, which lies on AB, is the center of dilation. The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O.
The scale factor is defined as the ratio of modified change in length to the original length.
Here, is o is the center of the line AB and slope of line AB is 3 than the line dilated with scale factor 3 A1B1 has also a scale factor of 3 because Position of dilation is center 0 thus dilation did not get any orientation.
And the center of dilation is O so line A1B1 passes through O.
Thus, the required black space in the statement "The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O". is filled by 3 and passes.
Learn more about line Scale factors here:
https://brainly.com/question/22312172
#SPJ2
Triangle ABC has vertices A(-5, -2), B(7, -5), and C(3, 1). Find the coordinates of the intersection of the three altitudes
Answer:
The coordinates of the intersection of the three altitudes = (-3.5, -1)
Step-by-step explanation:
The altitude of a triangle is a line which passes through a vertex of the triangle and is perpendicular to the opposite side.
There are therefore three altitudes possible in a triangle, one from each vertex. All three altitudes always intersect at the same point called the orthocenter of the triangle.
Let the triangle ABC have altitudes AD, BE and CF as shown in the attached image to this solution. Let the orthocentre be O.
The point O is the point where all the coordinates AD, BE and CF meet.
Hence, to obtain the coordinates of O, we just need to equate the equations of two of the lines that serve as the altitude.
Before that, we need to c9mpute the equations of the two altitudes that we will use.
Noting that the altitudes are perpendicular to the sides of the triangle, we can compute the slopes of the altitudes from caldilating the slopes of the sides.
Slope of AB
= (y₂-y₁)/(x₂−x₁)
= (-5 - (-2))/(7 - (-5))
= (-3/12)
= (-1/4)
Slope of its altitude, CF
= -1 ÷ (Slope of AB)
= -1 × (-1/4)
= 4
The equation of CF is given using point C as,
y – y₁ = m(x – x₁)
y - 1 = 4 (x – 3)
y - 1 = 4x - 12
y = 4x + 13
Slope of BC
= (y₂-y₁)/(x₂−x₁)
= (1 - (-5))/(3 - 7)
= (6/-4)
= (-3/2)
Slope of AD
= −1 ÷ (Slope of BC)
= -1 ÷ (-3/2)
= (2/3)
The equation of AD using point A given as,
y – y₁ = m(x – x₁)
y – (-2)) = (2/3) (x – (-5))
y + 2 = (2x/3) + (10/3)
y = (2x/3) + (4/3)
Now equation the equations of the altitudes CF and AD
y = 4x + 13
y = (2x/3) + (4/3)
4x + 13 = (2x/3) + (4/3)
4x - (2x/3) = (4/3) - 13
(10x/3) = (-35/3)
10x = -35
x = -3.5
y = 4x + 13
y = (4×-3.5) + 13 = -14 + 13 = -1
coordinates of the orthocentre of the triangle = (-3.5, -1)
Hope this Helps!!!
A graph is given to the right. a. Explain why the graph has at least one Euler path. b. Use trial and error or Fleury's Algorithm to find one such path starting at Upper A, with Upper D as the fourth and seventh vertex, and with Upper B as the fifth vertex. A C B D E A graph has 5 vertices labeled A through E and 7 edges. The edges are as follows: Upper A Upper C, Upper A Upper B, Upper A Upper D, Upper C Upper D, Upper C Upper E, Upper B Upper D, Upper D Upper E. a. Choose the correct explanation below. A. It has exactly two odd vertices. Your answer is correct.B. It has exactly two even vertices. C. It has more than two odd vertices. D. All graphs have at least one Euler path. b. Drag the letters representing the vertices given above to form the Euler path.
Answer:
a. It has exactly two odd vertices
b. A C E D B A D C
Step-by-step explanation:
(a) There will not be an Euler path if the number of odd vertices is not 0 or 2. Here, the graph has exactly two odd vertices: A and C.
__
(b) We are required to produce a path of the form {A, _, _, D, B, _, D, _}.
Starting at A, there is only one way to get to node D as the 4th node on the path: via C and E. Node B must follow. From B, there is exactly one way to cover the remaining three edges that have not been traversed so far.
The Euler path meeting the requirements is ...
A C E D B A D C
It is shown by the arrows on the edges in the graph of the attachment.
Please answer this correctly
Answer:
Question 1
Step-by-step explanation:
1) Let the outside temperature = x ° F
Now, the inside temperature = (x + 3)° F
Outside temperature has increased by 3,
So, outside temperature at lunch time = (x + 3)°F
So, at lunch time the outside & inside temperature are same.
So, the difference in temperature at lunch time is 0
if every 500 points is 00.5 how many points will it take to get 5.00?
Answer:
5000
Step-by-step explanation:
500×2=1000
1000=1.00
1000×5=5.00
Answer:
The writer worries about being left out.
Step-by-step explanation:
The completion times for a job task range from 11.1 minutes to 19.2 minutes and are thought to be uniformly distributed. What is the probability that it will require between 14.8 and 16.5 minutes to perform the task?
Answer:
[tex] P(14.8< X<16.5)= \frac{16.5-11.1}{19.2-11.1} -\frac{14.8-11.1}{19.2-11.1}= 0.667-0.457= 0.210[/tex]
The probability that it will require between 14.8 and 16.5 minutes to perform the task is 0.210
Step-by-step explanation:
Let X the random variable "completion times for a job task" , and we know that the distribution for X is given by:
[tex] X \sim Unif (a= 11.1, b= 19.2)[/tex]
And for this case we wantto find the following probability:
[tex] P(14.8< X<16.5)[/tex]
And for this case we can use the cumulative distribution given by:
[tex] F(x) =\frac{x-a}{b-a} , a\leq X \leq b[/tex]
And using this formula we got:
[tex] P(14.8< X<16.5)= \frac{16.5-11.1}{19.2-11.1} -\frac{14.8-11.1}{19.2-11.1}= 0.667-0.457= 0.210[/tex]
The probability that it will require between 14.8 and 16.5 minutes to perform the task is 0.210
Mary won £5000 in a competition.
She used the money to pay for herself and 8 friends
to go on a holiday.
Flights cost £279 for each of them.
Accommodation cost £184 for each of them.
How much of the £5000 did she have left after paying for
flights and accommodation for herself and the 8 friends?
Answer:
$833
Step-by-step explanation:
Since there are 9 people, we need to determine the cost of accommodation and flights for all 9 people:
9(273) + 9(184) = 2457 + 1656 = 4167 for 9 people
We then subtract that amount from the amount of money she won:
5000 - 4167 = 833
It was reported that 23% of U.S. adult cellphone owners called a friend for advice about a purchase while in a store. If a sample of 15 U.S adult cellphone owners is selected, what is the probability that 7 called a friend for advice about a purchase while in a store
Answer:
[tex] P(X=7)[/tex]
And using the probability mass function we got:
[tex]P(X=7)=(15C7)(0.23)^7 (1-0.23)^{15-7}=0.0271[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=15, p=0.23)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find the following probability:
[tex] P(X=7)[/tex]
And using the probability mass function we got:
[tex]P(X=7)=(15C7)(0.23)^7 (1-0.23)^{15-7}=0.0271[/tex]
BEST GETS BRAINLIEST Proof for Pythagoras Theorem (I’ll take multiple different approaches) Please make it logical/satisfying.
Answer:
Proofs for Pythagoras Theorem usually use visual/geometry approaches. I don't post pictures in my answers, so I will present a linear algebra approach. You can see it in the blog posted by Professor Terence Tao.
Note that there are several elegant proofs using animations and drawings, but this is just personal.
I've seen this some time ago, it is really interesting proof.
It states that [tex]a^2+b^2=c^2[/tex] is equivalent to the statement that the matrices
[tex]%\begin{pmatrix}a & b \\ -b & a%\end{pmatrix}%[/tex] [tex]\begin{pmatrix}a& b \\-b & a\\\end{pmatrix}[/tex] and [tex]\begin{pmatrix}c & 0\\0 & c \\\end{pmatrix}[/tex] have the same determinant.
The determinant of the first matrix is [tex]a^2+b^2[/tex]
The determinant of the second matrix is [tex]c^2[/tex]
Once the linear transformations associated with these matrices differ by rotation, we claim that
[tex]a^2+b^2=c^2[/tex]
Express it in slope-intercept form.
could you please answer quickly?????!! thank you!
Answer:
31,5
Step-by-step explanation:
=7*3+(7*3)/2
Answer:
length x width = area
7 x 3 = 21 so the area of the rectangle is 21
divide 7 by 2 so we can find the length of each triangle. 7 / 2 = 3.5
length (or base) x height / 2 = area of triangle
3.5 x 3 = 10.5
You do not have to divide by two because there are two triangles
10.5 + 21 = 31.5 so the area is 31.5
Hope this helps
Step-by-step explanation:
Find the area of a triangle whose two sides are 12 inches and 14 inches long, and has a perimeter of 34 inches.
Answer:
[tex]\huge\boxed{A=3\sqrt{255}\ in^2\approx47.91\ in^2}[/tex]
Step-by-step explanation:
We have two sides
[tex]a=12in;\ b=14in[/tex]
and the preimeter
[tex]P=34in[/tex]
We can calculate the length of the third side:
[tex]c=P-a-b[/tex]
substitute
[tex]c=34-12-14=8\ (in)[/tex]
Use the Heron's formula:
[tex]A=\sqrt{p(p-a)(p-b)(p-c)[/tex]
where
[tex]p=\dfrac{P}{2}[/tex]
substitute:
[tex]p=\dfrac{34}{2}=17\ (in)\\\\A=\sqrt{17(17-12)(17-14)(17-8)}=\sqrt{(17)(5)(3)(9)}\\\\=\sqrt{9}\cdot\sqrt{(17)(5)(3)}=3\sqrt{255}\ (in^2)\approx47.91\ (in^2)[/tex]
Please Assist With This Equation
*Please Show Work*
Answer:
240 hours
Step-by-step explanation:
One person hour is a unit indicating the rate at which one person is working on the project .
The company estimates that it will take 2880 person- hours to complete the job
So let's determine how many hours it will take 12 workers to complete same job
The rate = 2880 person/hour
12 persons or workers =( 2880 person/hour)/12 persons
12 persons or workers = 2880/12
12 persons or workers=240 hours
It will take 12 workers 240 person hour to finish the project.
Thank you
What is the %_ee of a sample of carvone that exhibits an observed rotation of -20, given that the specific rotation of (R)-carvone is -61
Answer: 44
Step-by-step explanation:
44
volume of a cube size 7cm
Answer:
343 cm3
Step-by-step explanation:
Answer:
side(s) =7cm
volume (v)=l^3
or, v = 7^3
therefore the volume is 343cm^3.
hope its what you are searching for..
A map's scale is 1 inch : 3.5 miles.
If the distance on the map is
8 inches, then the actual distance
in real life is __miles.
Answer:
28 miles
Step-by-step explanation:
to fin the actual distance you must multiply the didtance on the map by the map scale
3.5*8=28
If a 1/5 of a gallon of paint is needed to cover 1/4 of a wall, how much paint is needed to cover the entire wall
Answer:
4/5 gallon per wall
Step-by-step explanation:
We can find the unit rate
1/5 gallon
------------------
1/4 wall
1/5 ÷ 1/4
Copy dot flip
1/5 * 4/1
4/5 gallon per wall
Answer:
4/5 gallon of paint
Step-by-step explanation:
1/5 gallon of paint is needed to cover 1/4 of the wall.
To cover the whole wall:
1/4 × 4 = 1 (whole)
1/5 × 4 = 4/5