Answer:
0.37
Step-by-step explanation:
we have given that emails arrives at the server at the rate of 10 per hour means [tex]\frac{10}{60}=0.166[/tex] per minute
we have to find the probability that the time difference between the two email is more than 2 minute
so probability [tex]P\left ( X> 2 \right )=e^{-2\lambda }=e^{-2\times 0.166}=0.7166[/tex]
The probability that the time between two consecutive emails arriving at the server is more than two minutes is 0.72 (or 72%).
Given:
- Average rate of email arrivals [tex](\( \lambda \))[/tex] = 10 per hour
1. Understanding the Poisson Process:
- In a Poisson process, the time between events (in this case, email arrivals) follows an exponential distribution.
- If [tex]\( \lambda \)[/tex] is the average rate of events per unit time (here, per hour), the time between events (interarrival time) T follows an exponential distribution with parameter [tex]\( \lambda \)[/tex].
2. Parameter Conversion:
- Since [tex]\( \lambda = 10 \)[/tex] emails per hour, we convert this to the rate per minute:
[tex]\[ \lambda_{\text{minute}} = \frac{10}{60} = \frac{1}{6} \text{ emails per minute} \][/tex]
3. Probability Calculation:
- We are interested in the probability that the time between two consecutive emails is more than two minutes.
- Let X denote the time between two consecutive emails. X follows an exponential distribution with rate [tex]\( \lambda_{\text{minute}} = \frac{1}{6} \)[/tex].
[tex]\[ P(X > 2) = e^{-\lambda_{\text{minute}} \cdot 2} \][/tex]
Substitute [tex]\( \lambda_{\text{minute}} = \frac{1}{6} \)[/tex]:
[tex]\[ P(X > 2) = e^{-\frac{1}{6} \cdot 2} \] \[ P(X > 2) = e^{-\frac{1}{3}} \][/tex]
4. Calculating the Probability:
- Use a calculator to find [tex]\( e^{-\frac{1}{3}} \)[/tex].
[tex]\[ e^{-\frac{1}{3}} \approx 0.7165 \][/tex]
Therefore, the probability that the time between two consecutive emails is more than two minutes is approximately 0.72 (rounded to two decimal places).
This result aligns with the characteristics of a Poisson process with an average arrival rate of 10 emails per hour.
one x-intercept for a parabola is at the point (3.22,0) find the other x-intercept for the parabola defined by this equation y=2x^2-8x+5 round to the nearest hundredth if necessary
Answer:
(0.78,0)
Step-by-step explanation:
I would use the quadratic formula.
[tex]a=3[/tex]
[tex]b=-8[/tex]
[tex]c=5[/tex]
[tex]\text{ The quadratic formula is } x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{ Let's find } b^2-4ac \text{ first}\\(-8)^2-4(2)(5)\\64-8(5)\\64-40\\24\\\\\text{ Now let's find } -b\\-b=8\\\text{ And } 2a\\2(2)=4\\\\\text{ Let's plug in this information }\\x=\frac{8 \pm \sqrt{24}}{4}\\\\\text{ We are now going to simplify }\\x=\frac{8}{4} \pm \frac{\sqrt{24}}{4} \\x=2 \pm \frac{\sqrt{4 \cdot 6}}{4}\\x=2 \pm \frac{\sqrt{4} \sqrt{6}}{4} \\x=2 \pm \frac{2 \sqrt{6}}{4}\\[/tex]
[tex] x=2 \pm \frac{\sqrt{6}}{2}[/tex]
So let's put both of these into out calculator
2 + sqrt(6)/2 and 2-sqrt(6)/2
One of them should be approximately 3.22 as the question suggests.
3.22 0.78
So the other x-intercept is approximately (0.78,0)
Please help me with this problem.
Answer:
b. 9/5
Step-by-step explanation:
Cotangent is the inverse of tangent.
tan θ = y/x
cot θ = x/y
cot θ = (-9)/(-5)
cot θ = 9/5
just to add to that great reply by @MathPhys above
[tex]\bf (\stackrel{adjacent}{-9},\stackrel{opposite}{-5})~\hfill cot(\theta )=\cfrac{\stackrel{adjacent}{-9}}{\stackrel{opposite}{-5}}\implies cot(\theta )=\cfrac{9}{5}[/tex]
bear in mind that, the value coordinate pairs we get is the (x,y) coordinates, and x = adjacent side of the triangle whilst y = opposite side of it.
Can someone please help me, I need to know the missing side length (x) using trigonometric ratios.
Answer:
x = 5.34
Step-by-step explanation:
The reference angle is 24 degrees. I'm sure you are aware from the square at the other base angle that is a right triangle. Right triangles have ratios by which we can determine missing side and angle measures. The sin of a reference angle has a ratio that is side opposite/hypotenuse. The cos of a reference angle has a ratio that is side adjacent/hypotenyse. The tan of a reference angle has a ratio that is side opposite/side adjacent.
We need to decide which of these fits our needs according to the angle and sides we are given and need to find. We have the reference angle as 24 degrees, we have the side adjacent to this angle as 12. We are looking for x, which is the side opposite the reference angle. Looking to what our definitions are for each ratio, the sides opposite and adjacent are defining the tan of the reference angle. Setting up the ratio then looks like this:
[tex]tan(24)=\frac{x}{12}[/tex]
Multiply both sides by 12 to get
12 tan(24) = x
Do this on your calculator in DEGREE mode to get that
x = 5.342744224
Not sure what your teacher has you round to, but I usually have my students give me 2 decimal places
Find the y value at the point x = -2.
By looking at the graph, we can visually determine that the value of y when point x = -2 is -4.
Answer:
-4
Step-by-step explanation:
The y value at x=-2 is -4 because when you go to -2 on the x-axis the function is below there. You can only go straight up or straight down to determine the y-value that corresponds to x=-2 so we go down because the function is below the x-axis there.
We are going to go down until we get on the graph of the line. Scroll over with eyeballs to see that the y there is -4 (use the y-axis).
So the ordered pair (-2,-4) is on our line and when x=-2, y=-4.
Another example:
y=0 when x=2
Another example:
y=2 when x=4
Another example:
y=-3 when x=-1
Which products result in a perfect square trinomial? Check all that apply. (x + 9)(x 9) (xy + x)(xy + x) (2x 3)(3 + 2x) (16 x2)(x2 16) (4y2 + 25)(25 + 4y2)
Answer:
(xy + x)(xy + x)(16 x2)(x2 16) (4y2 + 25)(25 + 4y2)Step-by-step explanation:
The product of two identical binomial factors will be a perfect square trinomial. The appropriate answer choices are those having both factors the same.
Answer:
2nd 3rd5thStep-by-step explanation:
(xy + x)(xy + x)
(16 x2)(x2 16)
(4y2 + 25)(25 + 4y2)
Given h(x) = x-3 and f(x) = x3-x2-x-15 is h(x) a factor of f(x)?
Answer:
Yes.
Step-by-step explanation:
To see if h is a factor of f, we can use the factor theorem.
h(x)=x-3 has a zero at x=3 because h(3)=3-3=0.
So we want to see if the zero of h is a zero of f.
Is x=3 a zero of f?
You can check using synthetic division or just plug in 3.
Let's do both.
If you use synthetic you are trying to see if you get a remainder of 0.
If you plug it in you are trying to see if you get 0 as the output when plugging your input 3.
Let's do synthetic first:
Since we are checking to see if x=3 is a zero, that will go on the outside:
3 | 1 -1 -1 -15
| 3 6 15
- ------------------------
1 2 5 0
So yep the remainder is 0 so the answer is yes.
Let's plug it in:
f(3)=3^3-3^2-3-15
f(3)=27-9-3-15
f(3)=18-3-15
f(3)=15-15
f(3)=0
The result is 0 so the answer is yes.
You pick your favorite way here.
Find the length of "a", to
the nearest tenth, using
the Pythagorean Theorem.
Enter
Answer:
[tex]\sqrt{28} \approx 5.3[/tex]
Step-by-step explanation:
The Pythagorean Theorem says if you have a right triangle, then relationship between the three sides is the sum of the square of each leg is the hypotenuse squared.
So [tex]a^2+b^2=c^2[/tex]
where a and b are legs and c is the hypotenuse.
Plug in your a,b, and c. In this case it is a,6, and 8.
This means we have
[tex]a^2+6^2=8^2[/tex]
Simplify where you can before we begin the solving (the moving around of things to other sides).
[tex]a^2+36=64[/tex]
Now time for the solving. We are first going to get [tex]a^2[/tex] by itself.
To do this, we just need to subtract 36 on both sides giving us:
[tex]a^2=64-36[/tex]
[tex]a^2=28[/tex]
Now to get rid of the square on a, just square root both sides:
[tex]a=\sqrt{28}[/tex].
When a boy pulls his sled with a rope, the rope makes an angle of 35° with the horizontal. If a pull of 16 pounds on the rope is needed to move the sled, what is the horizontal component force?
9 lb
13 lb
19 lb
22 lb
Answer:
13 lb
Step-by-step explanation:
The horizontal component of the force is the magnitude of the force multiplied by the cosine of the angle with the horizontal.
(16 lb)·cos(35°) ≈ 13.1 lb ≈ 13 lb
Answer:
b.13 lb
Step-by-step explanation:
We are given that a boy pulls his sled with a rope .
The rope makes an angle with horizontal =[tex]35^{\circ}[/tex]
If a pull on the rope is needed to move the sled=16 pounds
We have to find the horizontal component of force
We know that horizontal component force=[tex]fcos\alpha[/tex]
Therefore, we have f=16 pound
Then, horizontal component of force=[tex]16cos 35^{\circ}[/tex]
Horizontal component of force=[tex]16\times 0.819=13.1lb[/tex]
Hence, horizontal component of force=13 lb
Answer:b.13 lb
Use the discriminant to determine how many and what kind of solutions the quadratic equation x^2−x=−1/4 has
Select one:
a. two real solutions
b. no real or complex solutions
c. one real solution
d. two complex (nonreal) solutions
its c
Using the discriminant to know about the nature of the solution of the quadratic equation x² -x = -1/4 tells us the fact as given by: Option c. one real solution
How to use discriminant to find the property of solutions of given quadratic equation?Let the quadratic equation given be of the form [tex]ax^2 + bx + c = 0[/tex], then
The quantity [tex]b^2 - 4ac[/tex] is called its discriminant.
The solution contains the term [tex]\sqrt{b^2 - 4ac}[/tex] which will be:
Real and distinct if the discriminant is positiveReal and equal if the discriminant is 0Non-real and distinct roots if the discriminant is negativeThere are two roots of a quadratic equations always(assuming existence of complex numbers). We say that the considered quadratic equation has 2 solution if roots are distinct, and have 1 solutions when both roots are same.
For this case, the given equation is:
[tex]x^2 - x = -1/4[/tex]
Converting this to the form [tex]ax^2 + bx + c = 0[/tex], we get:
[tex]x^2 - x + 1/4= 0\\or\\4x^2 -4x + 1 = 0[/tex]
Thus, we get:
a = 4, b = -4, c = 1
Putting these values in the expression for discriminant, we get:
[tex]D = b^2 - 4ac =(-4)^2 - 4(4)(1) = 16 - 16 = 0[/tex]
The discriminant is 0, so the considered quadratic equation is going to have both roots real and equal. Or in terms of distinct solutions, it is going to have one real solution (distinct).
Thus, using the discriminant to know about the nature of the solution of the quadratic equation x² -x = -1/4 tells us the fact as given by: Option c. one real solution
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Can u guys PLEASE do this question 31
Answer:
see below
Step-by-step explanation:
The attached printable graph paper is a scale drawing. The 1 : 100 scale means each meter will be represented by 1 cm.
Can someone help me with this math question
Answer:
2/3
Step-by-step explanation:
These two figures are similar since they have the same shape but not the same size
Yellow figure is larger than the orange figure therefore, the yellow figure is a larger or a dilated version of the orange figure.
Scale factor = Small side
Large side
Scale factor = 10/15
Scale factor = 2/3
The scale factor of this dilation is 2/3. The orange figure is dilated 2/3 times to form the yellow figure.
!!
Answer:
It's 2/3
Step-by-step explanation:
Trust me
Solve, then check algebraically and graphically. 9x-3=78
Answer:
x=9
Step-by-step explanation:
I have answered ur question
Which statement is true?
All rectangles are squares.
All squares are rectangles.
All quadrilaterals are rectangles.
All parallelograms are rectangles.
Answer:
B. All squares are rectangles.
Step-by-step explanation:
B is the correct answer, because all the squares are rectangles have 4 sides.
The accurate statement is that all squares are rectangles.
The statement that is true among the options provided is All squares are rectangles. This is because squares have all the properties of a rectangle, which is a quadrilateral with four right angles, but with the additional property of having all four sides of equal length. Therefore, because a square fulfills all the criteria of a rectangle, we can conclude that all squares are indeed rectangles. On the other hand, not all rectangles are squares since rectangles do not require all sides to be equal, only that the opposite sides are equal. Similarly, not all quadrilaterals are rectangles because other quadrilaterals, like rhombuses or kites, do not have the necessary four right angles. Finally, while all rectangles are parallelograms (a quadrilateral with opposite sides that are equal and parallel), not all parallelograms have right angles and thus are not all rectangles.
To elaborate, a rectangle is defined as a parallelogram with right angles. When it comes to comparing areas, the area of a rectangle is calculated by multiplying its base by its height. And in the case of squares, since all sides are equal, it's just the side length squared. However, when you have two shapes with equal area -- for instance, a square and a rectangle -- the one with the longer perimeter would be the one with the less compact shape, which in most cases would be the rectangle unless it is also a square.
(QUICK!!!!!!!!!!!!) Write an equation of the line below.
Answer:
[tex]\large\boxed{y=\dfrac{3}{5}x-2}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of aline:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfraxc{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have the points:
(-5, -5)
y-intercept (0, -2) → b = -2
Calculate the slope:
[tex]m=\dfrac{-2-(-5)}{0-(-5)}=\dfrac{3}{5}[/tex]
Put the value of the slope and the y-intercept to the equation of a line:
[tex]y=\dfrac{3}{5}x-2[/tex]
A mouse traveled a total distance of 3/24 of a mile in a maze over the past three hours the mouse travel the same distance each hour to determine the distance that the mouse traveled age our map reformed the calculations below he concluded that the mouse travel 3/8 of a mile each hour what is Matt's error
i was a
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Identify each line or segment that intersects ⊙ S.
Answer:
AC, CE, AB, and AS
I belive those are your answers
Answer:
chords: CE and AB; secant: CE; tangent:t; diameter AB; radii: AS and SB
Step-by-step explanation:
Write an equation in point-slope form of the line having the given slope that contains the given point.
m = 5/6, (30, 12)
A) y = 5/6 x - 37
B) y - 30 = 5/6 (x - 12)
C) y + 12 = 5/6 (x - 30)
D) y - 12 = 5/6 (x - 30)
Answer:
c
Step-by-step explanation:
It would be c because you would add subtract 30 - x which equals 30x then you would divided 5 / 6 which equals 0.12 then you would add y plus some number which equals 12y then you would add 12y+12=24y=24y / 2=12 thenyou have 30x,12y.
Answer:
D
Step-by-step explanation:
A might be right for the wrong linear equation type. It could be describing a y intercept slope line. So even if it is right, it is not the answer. Actually the answer to A should be y = (5/6)x - 13
The general formula for the answer you want is
Givens
y -y1 = m(x - x1)
x1 = 30
y1 = 12
m = 5/6
Solution
y - 12 = (5/6)(x - 30)
That makes the answer D
A nontoxic furniture polish can be made by combining vinegar and olive oil. The amount of oil should be five times the amount of vinegar. How much of each ingredient is needed in order to make 57 oz of furniture polish?
To make 57 oz of furniture polish, ____ oz of vinegar and
________ oz of olive oil are needed.
(Simplify your answers. Type mixed numerals, if possible. Otherwise, type integers or fractions.)
Answer:
See below in bold.
Step-by-step explanation:
The ratio of oil to vinegar is 5 : 1. That means that 5/6 of the mixture is oil and 1/6 is vinegar.
So to make 57 oz of the polish, 57/ 6 = 9 1/2 oz is vinegar and 5/6 * 57 =
47 1/2 oz is olive oil.
For 20 Points.
=============
Answer:
B
Step-by-step explanation:
Answer:
Its B) 60°
Step-by-step explanation:
135°=75°+CAD
135°-75°=CAD
60°=CAD
If events A and B are independent, what must be true?
P(AB) = P(B)
P(AB) = P(A)
P(A) = P(B)
P(AB) = P(BA)
Answer:
The last option is correct for two independent events.
P(A and B) = P(A) P (B)
And P(B and A) = P(B) P(A) which is equal. And other three cases are false.
P(AB) = P(BA) is true.
What are independent events ?
If outcomes of an event doesn't affect the outcomes of other event, the the events are called independent events, i.e. they are independent to each other.
Which option is true ?For two independent events,
P(AB) = P(A)P(B)
Also, P(BA) = P(B)P(A)
And, P(A)P(B) = P(B)P(A)
Hence, we can say that P(AB) = P(BA)
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Jose is the water maintenance supervisor for his city. He knows the rate rainwater flows through a pipe is modeled by the equation R(x)= -0.1x^3+1.4x^2-1.5x, where R is the amount of water, in cubic feet, and X is time, in hours. Jose a developer of a new neighborhood that if she decreases the size of the pipe, the water flow will decrease. The function that models the decrease is D(x)-0.04x^3+0.5x^2+x, where D is the amount of water in cubic feet, and X is time, in hours.
Write a function, H(x), for the rate at which rainwater flows in the smaller pipe.
Please Help
so the rainwater flows as R(x), and the decrease of the flow will be D(x), the new smaller pipe after the decrease will have water flowing at R(x) - D(x)
[tex]\bf \begin{cases} R(x)=-0.1x^3+1.4x^2-1.5x\\ D(x)=-0.04x^3+0.5x^2+x \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{R(x)}{(-0.1x^3+1.4x^2-1.5x)}-\stackrel{D(x)}{(-0.04x^3+0.5x^2+x)} \\\\\\ (-0.1x^3+1.4x^2-1.5x)+0.04x^3-0.5x^2-x \\\\\\ -0.1x^3+1.4x^2-1.5x+0.04x^3-0.5x^2-x \\\\\\ -0.10x^3+0.04x^3+1.4x^2-0.5x^2-1.5x-x\implies \stackrel{H(x)}{-0.6x^3+0.9x^2-1.6x}[/tex]
To find the rate of water flow through the smaller pipe, subtract the decrease function from the original rate function.
Explanation:To find the rate at which rainwater flows through the smaller pipe, we need to subtract the decrease function from the original rate function. Let's call this new function H(x). So, H(x) = R(x) - D(x).
Substituting the given values, H(x) = (-0.1x^3 + 1.4x^2 - 1.5x) - (-0.04x^3 + 0.5x^2 + x). Simplifying, H(x) = -0.1x^3 + 1.4x^2 - 1.5x + 0.04x^3 - 0.5x^2 - x.
Combining like terms, H(x) = -0.06x^3 + 0.9x^2 - 2.5x.
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Find the total area of the solid figure.
Answers:
90 sq. ft.
126 sq. ft.
150 sq. ft.
Answer:
90 sq. ft.
Step-by-step explanation:
To find the "volume," you will need to multiply every the LxWxH.
Length = L
Width = W
Height = H
Then the answer is 90 sq. ft.
Answer:
Surface area = 126 square ft .
Step-by-step explanation:
Given : Rectangular cuboid .
To find : Find the total area of the solid figure.
Solution : We have given Rectangular cuboid .
Length = 3 ft .
Width = 5 ft .
Height = 6 ft .
Surface area = 2 ( l*w + w*h + l *h).
Plug the values
Surface area = 2 ( 3*5 + 5*6 + 3 *6).
Surface area = 2 (15 + 30 + 18).
Surface area = 2 ( 63).
Surface area = 126 square ft .
Therefore, Surface area = 126 square ft .
You put the names of all the students in your class in a paper bag. There are 16 boys and 18 girls. If you draw a name at random, what is P(boy’s name)?
Answer:
Step-by-step explanation:
The probability of drawing a boy's name is found in:
number of boys/total number of students
Our ratio then is
16/16+18 which is
16/34 which reduces to
8/17
As a percentage, it would be about 47%
Total students = 16 + 18 = 34
16 boys
Probability of picking boy = 16/34
Which reduces to 8/17
I need your help with this problem
Answer:
12.9 m
Step-by-step explanation:
Let d represent the length of the diagonal. Then d-2 is the length and d-6 is the width. The Pythagorean theorem can be used to relate these measures, which are the legs and hypotenuse of a right triangle.
d² = (d-2)² + (d-6)²
d² = d² -4d +4 + d² -12d +36 . . . . eliminate parentheses
0 = d² -16d +40 . . . . . . . . . . . . . . . subtract d², collect terms
0 = d² -16d +64 -24 . . . . . . . . . . . rearrange the constant to make a square
0 = (d -8)² -24 . . . . . . write in vertex form
d -8 = √24 . . . . . . . . . add 24 and take the square root
d = 8 + √24 . . . . . . . . the negative square root is extraneous in this problem
d ≈ 12.9 . . . meters
The length of the diagonal is about 12.9 meters.
If (x-2)^2=49 then x could be
-9
-7
2
5
9
Answer:
9
Step-by-step explanation:
Plug the numbers in
The result for each number when plugged in order is:
121
81
0
9
49
So 9 would be the answer
Answer:
9
Step-by-step explanation:
If (x-2)^2=49 then x could be 9.
(x-2)^2 = 49
x or 9 - 2 = 7
7^2 = 49
Find the mean and standard deviation of the probability distribution. Round answer to the nearest hundredth. Would it be unusual to have 3 defective computers in the batch? The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.4096 , 0.4096 , 0.1536 , 0.0256 , and 0.0016 , respectively.
Answer:
Mean = 0.8
Standard Deviation = 0.8
P(x = 3) is unusual event
Step-by-step explanation:
Part A)
The probability distribution with correct formatting is shown in the table attached with:
We have to find the mean and standard deviation of this distribution. The mean of the probability distribution is calculated as summation of the products of "the variable with its respective probability".
[tex]u = \sum x P(x)[/tex]
So, for the given distribution:
Mean = 0(0.4096) + 1(0.4096)+2(0.1536)+3(0.0256)+4(0.0016)
Mean = 0.8
Standard deviation is calculated by the following formula:
[tex]\sigma=\sqrt{\sum x^{2}P(x) - u^{2}}[/tex]
[tex]x^{2}P(x)=1.28[/tex]
Substituting the values, we get:
[tex]\sigma=\sqrt{1.28-(0.8)^{2}}\\\\ \sigma=0.8[/tex]
Part B)
Since the probability of 3 defective computers is less than 0.05, this is an unusual event.
So it would be unusual to have 3 defective computers in the batch.
Research suggests that the pressure of being timed may interfere with performance on tests that involve mathematical problems. A fictional study was conducted with 30 sixth graders. First, the sixth graders were given a math test that contained 50 problems and were told that they had only one hour to complete it (timed condition). The same sixth graders were later given a math test that contained 50 problems and were told that they could have as much time, as needed, to complete the test (unlimited time condition). The total number of correct answers for each sixth grader was then calculated for each condition. Then, for each student, the difference between the two scores (timed − untimed) was calculated. The researchers hypothesized that the sixth graders would get fewer correct answers when they took the test with a time limit than when they had unlimited time. If μ1and μ2 represent the number of correct answers during the timed condition and the unlimited time condition, respectively, and let μd be the mean of the differences in the number of correct answers (timed − untimed) of all sixth graders. Which of the following are the appropriate null and alternative hypotheses? H0: μd = 0 Ha: μd > 0 B. H0: μd = 0 Ha: μd < 0 C. H0: μd < 0 Ha: μd = 0 D. H0: μ1 − μ2 = 0 Ha: μ1 − μ2 < 0
Answer:
B. H0: μd = 0 Ha: μd < 0
Step-by-step explanation:
Let μ1 and μ2 represent the number of correct answers during the timed condition and the unlimited time condition, respectively.
Let μd be the mean of the differences in the number of correct answers (timed − un timed) of all sixth graders.
The answer is B. H0: μd = 0 Ha: μd < 0
Here we have to check that the students will get few correct answers in the timed condition as compared to the unlimited time condition.
To know this, difference was calculated so we get the correct hypotheses as : H0: μd = 0 and Ha: μd < 0 .
Answer:
Also "H0: μ1 − μ2 = 0 Ha: μ1 − μ2 < 0" is correct
Step-by-step explanation:
When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?
Answer:
[tex]\frac{2}{3}\text{ feet}[/tex]
Step-by-step explanation:
Let the equation that models the height of the tree after x years,
y = mx + c
Where, m is constant amount of increasing and c is any constant,
Given,
When x = 0, y = 4,
⇒ 4 = m(0) + c ⇒ c = 4,
Now, the height of plant after 4th year = m(4) + c = 4m + c
Also, the height of plant after 6th year = m(6) + c = 6m + c
According to the question,
6m + c is [tex]\frac{1}{5}[/tex] more than 4m + c,
[tex]6m+c=4m+c + \frac{1}{5}(4m+c)[/tex]
[tex]6m+c = \frac{6}{5}(4m+c)[/tex]
[tex]30m+5c=24m+6c[/tex]
[tex]6m=c[/tex]
By substituting the value of c
6m = 4
⇒ [tex]m=\frac{4}{6}=\frac{2}{3}[/tex]
Hence, 2/3 feet of height is increased each year.
Determine the scale factor for Δ ABC to Δ A¹B¹C¹.
Answer:
Answer B
Step-by-step explanation:
The triangle has side lengths that are dilated by 2x in the second triangle
Answer:
2
Step-by-step explanation:
A P E X
Please solve the following complex number system ASAP, show work and please simplify fully.
[tex]x^{2}[/tex]-16x+80=0
Answer:
x= 16±√-64 over 2
Step-by-step explanation:
x= -(-16)±√(-16)²-4×1×80 over 2×1
x= 16±√256-320 over 2
x= 16±√-64 over 2
can also be represented with all real numbers.