The distance between you and your friend is changing at a rate of 20 miles per hour.
What is the Pythagorean theorem?
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Here, we
Let the east direction is denoted by x and
the north direction is denoted by y.
dx / dt = 16 miles per hour
dy / dt = 12 miles per hour
x = 4 miles
Let the distance between both the friends be s.
Time is taken by you to travel 4 miles,
time = distance / speed = 4 / 12 = 1/4 hour
Distance traveled by your friend in time t,
y = speed x time = 12 x 1/4 = 3 miles
By Using the Pythagorean theorem,
x² + y² = s² ..... (1)
Substitute, x = 4 mile, y = 3 mile
s² = 16 + 9 = 25
s = 5 miles
Now, Differentiate equation (1) with respect to t, we get
2x dx/dt + 2y dy/dt = 2s ds/dt
4 (16) + 3 (12) = 5 ds/dt
ds/dt = 20 miles per hour
Hence, the distance between you and your friend is changing at a rate of 20 miles per hour.
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Use Descartes' Rule of Signs to determine how many positive and how many negative real zeros the polynomial can have. Then determine the possible total number of real zeros. (Enter your answers as comma-separated lists.)P(x) = x^3 − x^2 − x − 5number of positive zeros possible number of negative zeros possible number of real zeros possible
The number of positive and negative real roots of the function
x³ - x² - x - 5 are 1 and 2 respectively.
What is Descartes' Rule?
Descartes' rule of sign is used to determine the number of real zeros of a polynomial function. It tells us that the number of positive real zeros in a polynomial function f(x) is the same or less than by an even numbers as the number of changes in the sign of the coefficients.
Number of positive real roots of f(x) ≤ Number of sign changes f(x)
Number of negative roots of f(x) ≤ Number of sign changes of f(-x)
According to the given questions:
The given polynomial function f(x) = x³ - x² - x - 5
We can observe the number of sign changes in the coefficients
The sign changes only once
hence there is one positive real root
Now, f(-x) = -x³ + x² - x + 5
Clearly sign changes 2 times evenly
Therefore the function has 2 negative real roots
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Which graph represents the step function f(x)=⌊x+1⌋ ?
The graph which represents the equation f ( x ) = [ x + 1 ] is Option 4.
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = [ x + 1 ]
The function f ( x ) can be written as
y = [ x + 1 ] , where the equation f ( x ) = y
Substituting the value for x , we get
a)
when x = 0
The value of equation is
y = [ x + 1 ]
y = [ 0 + 1 ]
y = 1
So , the coordinates are ( 0 , 1 )
b)
when x = 1
The value of equation is
y = [ x + 1 ]
y = [ 1 + 1 ]
y = 2
So , the coordinates are ( 1 , 2 )
c)
when x = 2
The value of equation is
y = [ x + 1 ]
y = [ 2 + 1 ]
y = 3
So , the coordinates are ( 2 , 3 )
d)
when x = -1
The value of equation is
y = [ x + 1 ]
y = [ -1 + 1 ]
y = 0
So , the coordinates are ( -1 , 0 )
Hence ,
On plotting the points in the graph , we get the equation as y = x + 1
And the solution is Option D.
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the time is 11:06 in 2 hours it will be
Answer:
Step-by-step explanation:
01:06
Answer:
1:06
Step-by-step explanation:
11:06 + 2:00 = 13:06
13:06-12:00= 1:6
from a group of 7 men and 6 women a committee consisting of 4 men and 3 women is to be formed. how many different committees are possible if (a) 2 of the men refuse to serve together?
500 Different number of committees are possible.
Initially we have 7 men and 6 women.
We have to select 4 men and 3 women to form a committee
Number of men are possible 7C4 = 35
Number of women are possible 6C3 = 20
2 of the men are refusing to server together
so we have to subtract the possibilities when these 2 men are sitting together.
we are considering 2 men are already sitting together.
now, we have only need of 2 men from remaining 5 men.
number of ways to select 2 men from 5 men is 5C2 = 10
We have to subtract 10 from number of men possible.
Number of men possible when 2 of the men refuse to serve together =
35 - 10 = 25.
Number of possible committees are 25*20 = 500.
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y+8>10 solve the following inequality
Answer:
y>2
Step-by-step explanation:
subtract 8 on both sides
Answer:
y > 2
Step-by-step explanation:
y + 8 > 10
Subtract 8 from both sides.
y > 10 - 8
y > 2
consider slotted aloha with nodes retrying with probability p a. recall that when there are n active nodes, the probability that any node has successful transmission is np(1 − p)n−1. find the value of p that maximizes this expression. show your work. b. using the value of p found in (a), find the efficiency of slotted aloha by letting n approach infinity.
The efficiency of slotted aloha by letting n approach infinity is 1/e and the maximum value of probability is 1/n.
Given that:
No. of nodes = (n)
The efficiency of slotted aloha by letting n approach infinity is E (p)= np(1-p)^(n-1).
By derivation,
E' (p) = n(1-p)^(n-1) - np(n-1)(1-p)^(n-2)
E' (p) = n(1-p)^(n-2) x [(1- p) - p(n-1)]
E' (p) = n(1-p)^(n-2) x [1-np]
Let E'(p) =0
i.e. Either, n(1-p)^(n-2) = 0
=> p = 1 (minima)
Or [1-np] = 0
=> p = 1/n (maxima)
So, for the value of p* = 1/n, we can maximize this expression.
When p = 1/n, the efficiency of slotted aloha is
E(p*) = n.1/n (1-1/n)^(n-1)
E(p*) = (1-1/n)^(n-1)
E(p*) = (1-1/n)^n/(1-1/n)
Since, [tex]\lim_{n \to \infty} (1-1/n) = 1\\[/tex]
[tex]\lim_{n \to \infty} (1-1/n)^n = 1/e[/tex]
So, when n approaches infinite,
Efficiency => [tex]\lim_{n \to \infty} E(p*) = 1/e[/tex]
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A problem solving method that involves trying all possible solutions until one works is using ___________. a. an algorithm b. trial-and-error c. deductive reasoning d. a heuristic please select the best answer from the choices provided a b c d
The correct option b. trial-and-error, is employed in the approach to issue solving that entails testing each potential solution until one is successful.
Explain the term trial-and-error?Trial and error is attempting a way, seeing if it succeeds, and trying a different method if the first one doesn't.
Up till a solution or achievement is achieved, this procedure is repeated.A process of trying out several methods and recognizing and removing mistakes or reasons for a failure to determine the best strategy to achieve a goal or the best answer. also: attempting various things till something works. Finding the optimal approach to get the intended result through trial and error involves identifying and eradicating faults or failures using a variety of experimental methodologies.Thus, trial-and-error, is employed in the approach to issue solving that entails testing each potential solution until one is successful.
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jessica has a die with 10 sides, another with 13 sides, and a third one with 5 sides. she rolls the three dice once. let z be the number of ones showing. find the expectation of z using the indicator method.
Jessica has three dice with 10 sides, 13 sides and 5 sides respectively and she rolls all dice once and if Z is number of ones occur then
The expectation value i.e, E(Z) is 0.376 and variance V[Z] = 0.321..
Indicator method :
This is a powerful way to find expected counts. This follows from the observation that the number of "good" outcomes in a trial can be counted by first coding each "good" outcome as one, coding each other outcome as zero, and then adding 1 and 0.
let X₁ be the outcome of a 10 sided die
X₂ be the outcome of 13 sided die
X₃ be the outcome of 5 sided die
let l₁ ,I₂ ,I₃ be three indicator functions such that
I₁ =1 if X₁ = 1
=0 otherwise
I₂ = 1 if X₂ = 1
=0 otherwise
I₃ = 1 if X₃ = 1
=0 otherwise
so Z denotes the number of ones showing when the three dice are rolled once.
so Z=I₁ +I₂ +I₃
so E[Z]=E[I₁]+E[I₂]+E[I₃]
so E[I₁]=1×P[X₁=1] = 1/10
E[I₂]=1×P[X₂=1] = 1/13
E[I₃]=1×P[X₃=1] = 1/5
so, E[Z]=1/10+1/13+1/5=49/130 = 0.3769
the variance = V[Z] = V[I₁]+V[I₂]+V[I₃] since the outcomes of the 3 different die are independent to each other hence no covariance term.
V[I₁]= 1²P[X₁=1]- E²[I₁]=1/10 -(1/10)²= 0.09
V[I₂]= 1²P[X₂=1]- E²[I₂]=1/13-(1/13)²= 12/169 = 0.071
V[I₃]= 1²P[X₃=1]- E²[I₃]=1/5 -(1/5)²= 4/25 = 0.16
so V[Z]= 0.09 + 0.071 + 0.16 = 0.321
Hence, the expectation value i.e, E(Z) is 0.3769..
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Which conclusion is appropriate at the 5% level of significance? check all that apply. Group of answer choices the differences observed in sample means do not provide strong evidence of a difference in mean course load for freshmen, sophomores, juniors and seniors at this university. There are statistically significant differences in mean course loads for freshmen, sophomores, juniors and seniors at this university. This study provides strong evidence that the mean course loads differ for freshmen, sophomores, juniors and seniors at this university. This study provides strong evidence that the mean course loads for freshmen are larger than the mean for sophomores. This study suggests that the mean course loads are the same for freshmen, sophomores, juniors and seniors at this university. We cannot draw a conclusion because conditions for the anova f-test are not met
A 5% chance exists of concluding there is a difference when there isn't at a significance level of 0.05. Lower levels of significance suggest that you need more proof before you can rule out the null hypothesis.
What is Anova test?In statistics, the analysis of variance (ANOVA) method is used to compare the means of two groups.
In an experiment with a completely randomized design, samples are at random assigned to either a treatment group or a placebo group.
For instance, if 40 persons are chosen to evaluate the effects of an analgesic,
four groups—Groups A, B, C, and D—could be created. Different dosages of the medication can be administered to Groups A, B, and C, while Group D receives a placebo. Due to the random grouping of the participants
, this is an illustration of a randomized design.
We assume that the sample populations are normally distributed and have the same variances in order for an ANOVA test to display completely randomized design.
Hence, A 5% chance exists of concluding there is a difference when there isn't at a significance level of 0.05. Lower levels of significance suggest that you need more proof before you can rule out the null hypothesis.
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a survey of patients at a hospital classified the patients by gender and blood type, as seen in the two-way table. gender blood type male female total a 105 93 198 b 99 84 183 o 160 140 300 ab 15 18 33 total 379 335 714 based on the data, what percent is the probability that a female patient will have type-o blood? round your answer to the nearest tenth of a percent.
The percent of the probability that a female patient will have type-o blood is 46.7%
To know the percent of female patients who will be having type 0 blood, all you have to do is divide the number of female patients with O-blood type by the total number of patients with O-blood type. Then finally you will have to multiply the quotient by 100 to get the percent as follows:
number of females with o-blood type = 140 Females
total number of patients with o-blood type = 300 patients
Percentage of Females with o-blood type = (140/300) * 100 = 46.7%
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what is an equation of the line that passes through the point (4,-3)(4,−3) and is perpendicular to the line 4x y
The equation of the line is [tex]y = -\frac{3}{4}x[/tex].
What is the equation of a line?
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.
We have,
the line passes through the point (4,-3),
the points perpendicular to the line 4x - 3y = 3
The equation of a line in slope-intercept form is y = mx + c ( m is the slope and c is the y-intercept).
rearrange 4x - 3y = 3 into this form
subtract 4x from both sides
- 3y = - 4x + 3 ( divide all terms by - 3 )
[tex]y = \frac{4}{3}x - 1[/tex] ← in slope-intercept form
with slope m = 4/3,
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular} = \frac{1}{-m} = \frac{1}{-\frac{4}{3} } = \frac{3}{-4}[/tex]
[tex]y = -\frac{3}{4}x + c[/tex] ← is the partial equation
To find c substitute (4, -3) into the partial equation,
-3 = -3 + c
c = -3 + 3
c = 0,
[tex]y = -\frac{3}{4}x[/tex]
Hence, the equation of the line is [tex]y = -\frac{3}{4}x[/tex] .
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at what rate is the angle between a clock's minute and hour hands changing at 10 o'clock in the morning?
The angle between a clock's minute and hour hands changing at 10 o'clock in the morning is 5.5 degrees/minute.
what is the rate of change in calculus?
The rate of change defines the relationship between two changing variables. Consider a moving object that moves twice as much in the vertical direction (y) as it does in the horizontal direction (x). This can be expressed mathematically as y = 2x.
Let 'θ' represent the angle between the minute and hour hand.
Let θ1 be the angle between the minute hand and 12.
[tex]\frac{d\theta_2}{dt}=\frac{1}{60*12}\times2\pi\\\\\frac{d\theta_2}{dt}=\frac{\pi}{360}[/tex](Between hour hand and 12)
[tex]\theta=\pm(\theta_1-\theta_2)\\\\\frac{d\theta}{dt}=\pm(\frac{d\theta_1}{dt}-\frac{d\theta_2}{dt})\\\\\frac{d\theta}{dt}=\pm(\frac{\pi}{30}-\frac{\pi}{360})\\\\\frac{d\theta}{dt}=\pm5.5$ degree$[/tex]
Hence the angle between a clock's minute and hour hands changing at 10 o'clock in the morning is 5.5 degrees/minute.
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in comparing the galilean transformations with the lorentz transformations, what multiplicative factor appears in the lorentz transformations that is not in the galilean ones?
In Lorentz transformations we have velocity based factors that is not present in Galilean ones.
What is lorentz transformations?The relationship between two distinct coordinate frames that are moving relative to one another at a constant speed is known as a Lorentz transformation. Dutch physicist Hendrik Lorentz is credited with coining the name of the transformation. There are two frames of reference: Inertial Frames, which refer to motion that has a constant speed.
What are Galilean transformations?The relationship between two distinct coordinate frames that are moving relative to one another at a constant speed is known as a Lorentz transformation. Dutch scientist Hendrik Lorentz is credited with coining the term transformation. There are two frames of reference: Inertial Frames, which relate to motion that has a constant speed.
Any and all rulers and other self-contained length standards, such as those you might use to set up a measurement frame, can be contracted in length based on velocity. This results in the Lorentz factor at the place in the LT.
Any and all clocks and other physically independent systems, such as those used to record events in a measurement frame, are subject to velocity time dilation. As a result, the LF is temporarily in the LT.
The fact that applying Einstein synchronisation individually for each measurement frame turns out to be natural. Consequently, the position-dependent synchronisation offset between the clocks of one measurement frame and those of the other is represented by the enigmatic second term in the LT for the time.
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the population of a town increased from 3050 in 2006 to 5500 in 2009. find the absolute and relative (percent) increase. absolute increase: relative increase: % give answers accurate to at least 1 decimal place.
In the given question, the absolute percentage increase is 1050 and the relative percentage increase is 32.3076%.
What is the percentage increase?When you want to analyze how a value has evolved over time, a percentage increase is helpful.
Although percentage increase and absolute increase are fairly comparable, the former is more helpful when contrasting different data sets.
For instance, a change from 1 to 51 and a change from 50 to 100 both have an absolute change of 50, but the first change grew significantly more due to the higher percentage growth of 5000% compared to the second change of 100%.
The most popular method of assessing growth is percentage increase because of this.
So, the absolute and relative percentage increase is:
The town's population grew from 3,250 in 2008 to 4,300 in 2010.
2008: P1 = 3250
2010: P2 = 4330
Absolute variation:
Absolute difference = P2 - P1
Absolute difference = 4330 - 3250
Absolute difference = 1050
Relative increase:
Relative percentage = P2 - P1/P1 * 100
Relative percentage = 1050/3250 * 100
Relative percentage = 32.3076
Therefore, in the given question, the absolute percentage increase is 1050 and the relative percentage increase is 32.3076%.
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Correct question:
The population of the town increased from 3,250 in 2008 to 4,300 in 2010. Find the absolute and relative(percent) increase.
Help how do i answer this problem
Answer:
1. EF ≈ 22.00
2. m∠E ≈ 36.20°
3. m∠F ≈ 53.81°
Step-by-step explanation:
1. Use the trigonometric function sine.
sin(60°) = EF / 25.4
EF = 25.4 sin(60°)
EF ≈ 22.00
2. Use the inverse of the trigonometric function sine (denoted arcsin).
sin(m∠E) = 15/25.4
m∠E = arcsin(15/25.4)
m∠E ≈ 36.20°
3. Use the inverse of the trigonometric function cosine (denoted arccos).
cos(m∠F) = 15/25.4
m∠F = arccos(15/25.4)
m∠F ≈ 53.81°
A recipe for fruit salad includes 1/4 cup of grapes for 4 servings. How many cups of grapes are needed for 40 servings of this fruit salad
Answer: 2.5
Step-by-step explanation: 40 divided by 4 = 10 1.4 x 10 = 2.5
Answer:
2.5
Step-by-step explanation:
1/4 is equal to 0.25, So if it's 0.25 for 4 servings, the ratio is 0.25:4. You can the divide 40 by 4 and get 10. You can now take that ten and multiply it by 0.25 to get 2.5 or 2 and 1/2
Alexis wants to pave a square landing pad out of concrete for her model helicopter.
She has enough concrete to pave 140 square feet. Find the length of each side of the
square landing pad in feet using the formula s = √A where s is the side length and A
is the total area. Round your answer to one decimal place, if needed.
A Square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is given as side²
The formula to find the side length.
s = √A
The length of the side is 11.8 feet.
What is a square?A Square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is given as side²
We have,
The total area of the square landing path:
A = 140 square feet.
The formula to use is given,
s = √A
Now,
s = √140
s = √4 x 35
s = 2√35
[ √35 = 5.92 ]
s = 2 x 5.92
s = 11.8 feet
Thus,
The length of the side is 11.8 feet.
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Complete the statement Round to the nearest hundredth if necessary
14 m ≈ ? ft
Answer: 45.93 ft
Step-by-step explanation:
a rectangular crate has length 15 in, width 4 in, and height 10 in. find its volume as surface area.
Answer:
volume: 600 cubic inchesarea: 500 square inchesStep-by-step explanation:
You want the volume and surface area of a rectangular crate that is 15 in long, 4 in wide, and 10 in high.
VolumeThe volume is given by the formula ...
V = LWH
For the given crate, the volume is ...
V = (15 in)(4 in)(10 in) = 600 in³
AreaThe area is given by the formula ...
A = 2(LW +H(L +W))
For the given dimensions, the crate has an area of ...
A = 2((15 in)(4 in) +(10 in)(15 in +4 in)) = 2(60 in² +(10 in)(19 in))
= 2(60 in² +190 in²) = 500 in²
The crate's volume is 600 cubic inches; its area is 500 square inches.
Hey!, can you pls help me? I've been stuck on this for a long time...
PLEASE HELP ASAP!!!!!! WITH EXPLANATION >:(
Answer:
D. 7.00 < 210.00; h < 30; 30 hours
Step-by-step explanation:
He needs to do 30 hours because:
7.00 < 210$; representing h < = 30; and then you would equal 30 hours
Definitely not A or B because that would represent a fraction which we don’t want
C, also would not work because it would be the opposite.
( I am not stealing points. )
an izod impact test was performed on 20 specimens of pvc pipe. the sample mean is 1.25 and the sample standard deviation is 0.25. test the hypothesis that H0: ????
There is sufficient evidence to conclude that the population standard deviation is different from 0.1.
What is test statistic?
A test statistic is a figure obtained from a statistical analysis. It explains how far your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.
Given,
[tex]H_0:\sigma =0.1\\H_a:\sigma \neq 0.1[/tex]
Test statistic:
Chi square=(20-1)*0.25^2/0.1^2=118.75
df=20-1=19
p-value=CHIDIST(118.75,19)=0.0000
Reject the null hypothesis.
Hence, there is sufficient evidence to conclude that the population standard deviation is different from 0.1.
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What is 48,570 in scientific notation?
Answer: 4.857 x 10^4
Step-by-step explanation:
3(4x2) 5x = 6-7(-x-2)
Answer:
24
Step-by-step explanation:
I do not understand what I am supposed to do
Check the picture below.
A punch recipe calls for 1 1/2 quarts of sparkling water and 3/4 of a quart of grape juice. How much of each ingredient would you need to make 75 quarts of punch?
The number of each ingredient of water and grape juice you can use for 75 quarts of punch would be = 112.5 of sparkling water and 56.25 of grape juice.
What is recipe?Recipe is defined as the comprehensive list of items that includes various measurements which is used for making different food meals.
The quantity of sparkling water used for each punch quarts = 1½ = 1.5
1.5 = 1
X = 75
make X the subject of formula;
X = 75×1.5
X = 112.5
The quantity of grape juice used for each punch quarts= ¾ = 0.75
0.75 = 1
y = 75
make y the subject of formula;
y = 0.75×75
y = 56.25
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Find the slope of points passing through -2, 2 and -8, 5
Answer:
-1/2
Step-by-step explanation:
Slope= [tex]\frac{y_{2}-y_{1} }{x_{2}- x_{1} }[/tex].
(5-2)/(-8+2)
Simplify:
3/-6
-1/2
PLEASE MARK AS BRAINLIESThelp plsssssssssssssssss
Answer: A 121/324
Step-by-step explanation:
1.0489343455493443 is the result so it is irrational
A persons resting heart rate is typically between 60 and 100 beats per minute. Rushing looks at the watch and counts 8 heartbeats in 10 seconds. Is his heart rate typical?
Answer: No its not normal
Step-by-step explanation: The question says 60 and 100 beats per minute is normal. Rushing looks at his watch and counts 8 beats in 10 seconds
We can solve by:
[tex]\frac{8}{10}[/tex] = [tex]\frac{x}{60}[/tex] then from that answer we can check if x, the heartbeats falls between 60 and 100.
So to get 60, we have to multiply 10 by 6. We are using proportionality, so we do the same to the numerator to get 8 x 6= 48
We get [tex]\frac{8}{10}[/tex] = [tex]\frac{48}{60}[/tex]. 48 beats do not fall between 60 and 100, thus the answer is it is not normal.
Write a rule for g(x)=f(x+2) when f(x)=x+1.
Answer:
g(x) = x+3
Step-by-step explanation:
f(x) = x+1
g(x) = f(x+2)
so g(x) = (x+2)+1
g(x)=x+3