This is a matched pairs design because both types of tread were randomly assigned to each vehicle.
What is matched pairs design?The term matched pairs design has to do with the situation in which participants are randomly assigned to an experiment or a control group. For each participant assigned to an experimental group, another is assigned to the control group.
Thus, this is a matched pairs design because both types of tread were randomly assigned to each vehicle.
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Given that ‘z’ is in set of complex number and ‘a’ is any real numbers. Solve the trigonometric equation sin(z) = a for all general solutions.
Recall that for all [tex]z\in\Bbb C[/tex],
[tex]\sin(z) = \dfrac{e^{iz} - e^{-iz}}{2i}[/tex]
so that
[tex]\sin(z) = a \iff e^{iz} - e^{-iz} = 2ia[/tex]
Multiply both sides by [tex]e^{iz}[/tex] to get a quadratic equation,
[tex]e^{2iz} - 2iae^{iz} - 1 = 0[/tex]
Solve for [tex]e^{iz}[/tex]. By completing the square,
[tex]e^{2iz} - 2ia e^{iz} + i^2a^2 = 1 + i^2a^2[/tex]
[tex]\left(e^{iz} - ia\right)^2 = 1 - a^2[/tex]
[tex]e^{iz} - ia = \pm \sqrt{1-a^2}[/tex]
[tex]e^{iz} = ia \pm \sqrt{1-a^2}[/tex]
[tex]iz = \log\left(ia \pm \sqrt{1-a^2}\right)[/tex]
[tex]iz = \ln\left|ia \pm \sqrt{1-a^2}\right| + i \left(\arg\left(ia \pm \sqrt{1-a^2}\right) + 2\pi n\right)[/tex]
[tex]\boxed{z = -i \ln\left|ia \pm \sqrt{1-a^2}\right| + \arg\left(ia \pm \sqrt{1-a^2}\right) + 2\pi n}[/tex]
where n is any integer.
We are given with:
[tex]{\quad \qquad \longrightarrow \sin (z)={\sf a}\:,\:z\in \mathbb{C}}[/tex]
Recall the identity what we have for the sine function of complex numbers
[tex]{\boxed{\bf{\sin (z)=\dfrac{e^{\iota z}-e^{-\iota z}}{2\iota}}}}[/tex]Put the values to thus obtain:
[tex]{:\implies \quad \sf \dfrac{e^{\iota z}-e^{-\iota z}}{2\iota}=a}[/tex]
[tex]{:\implies \quad \sf e^{\iota z}-e^{-\iota z}=2a\iota}[/tex]
Multiply both sides by [tex]{\sf e^{\iota z}}[/tex]
[tex]{:\implies \quad \sf e^{\iota z}\cdot e^{\iota z}-e^{-\iota z}\cdot e^{\iota z}=2a\iota e^{\iota z}}[/tex]
[tex]{:\implies \quad \sf (e^{\iota z})^{2}-2a\iota e^{\iota z}-1=0}[/tex]
Put x = [tex]{\sf e^{\iota z}}[/tex]:
[tex]{:\implies \quad \sf x^{2}-2a\iota x-1=0}[/tex]
Find the discriminant, here D will be, D = (-2ai)² - 4 × 1 × (-1) = 4 - 4a² = 4(1-a²)
Now, By quadratic formula:
[tex]{:\implies \quad \sf x=\dfrac{-(-2a\iota)\pm \sqrt{4(1-a^{2})}}{2}}[/tex]
[tex]{:\implies \quad \sf x=\dfrac{a\iota \pm \sqrt{1-a^{2}}}{2}}[/tex]
[tex]{:\implies \quad \sf e^{\iota z}=\dfrac{a\iota \pm \sqrt{1-a^{2}}}{2}}[/tex]
[tex]{:\implies \quad \sf \iota z=log\bigg(\dfrac{a\iota \pm \sqrt{1-a^{2}}}{2}\bigg)}[/tex]
Using the formula for logarithms, we have:
[tex]{:\implies \quad \sf \iota z=log(a\iota \pm \sqrt{1-a^{2}})-log(2)}[/tex]
[tex]{:\implies \quad \sf z=\dfrac{1}{\iota}log(a\iota \pm \sqrt{1-a^{2}})-\dfrac{1}{\iota}log(2)}[/tex]
The sine function is periodic on 2πn and zero on (π/2), and the logarithmic expression becomes undefined for all ia±√(1-a²) < 0, so we will take modulus of it
[tex]{:\implies \quad \boxed{\bf{z=\dfrac{1}{\iota}log\bigg|a\iota \pm \sqrt{1-a^{2}}\bigg|-\dfrac{1}{\iota}log(2)+\dfrac{\pi}{2}+2\pi n\:\:\forall \:n\in \mathbb{Z}}}}[/tex]
please solve this problem using the pythagorean theorem, and give me the right answer and I will give you brainliest. :)
Answer:
6.1 km
Step-by-step explanation:
The Pythagorean theorem tells you the relationship between the lengths of the sides of a right triangle.
c² = a² +b² . . . . a, b are the short sides; c is the hypotenuse
__
The geometry of this problem can be modeled by a right triangle with legs 3.7 km and 4.9 km. The distance of interest is the hypotenuse of the triangle.
c² = 3.7² +4.9² = 13.69 +24.01 = 37.70
c = √37.70 ≈ 6.1
The straight-line distance is about 6.1 km.
the area is 72 square meters. the lenght is 9 meters. what is the width
Answer: 8 meters
Step-by-step explanation: 72/9 = 8
Answer:
8 meters
Step-by-step explanation:
Since there is so little information given, I'm assuming this is just the area of a rectangle. The formula you used to find the area of a rectangle is "area = length * width" or "A = l*w".
We are given the area and the length, so we can fill in those spaces in the formula-
72 = 9 * w
Now, in order to find the width. we have to undo in reverse order. We have to divide 72 by 9.
72 (/ 9) = 9 * w (/ 9)
8 = w
Therefore, the width is 8 meters. I hope this helps! Have a lovely day!! :)
What is the value of y?
2
5
7
8
20 cm
10 cm
Find the area of this figure.
[?] square centimeters
6 cm
Answer:
260 cm^2
Step-by-step explanation:
Area of rectangle = 20 x 10 = 200 cm^2
Area of triangle = 6 x 20 /2 = 60 cm ^2
Area of figure = 200 + 60 = 260 cm^2
A company that makes boxes finds that 7 out of 25 boxes are damaged. What percent of the boxes are damaged
Answer:
15%
Step-by-step explanation:
see the picture for explanation
Answer:
28%.
Step-by-step explanation:
That would be 100 * 7/25
= (100/25) * 7
= 4*7
= 28.
Is this true or false?
Answer:
true
Step-by-step explanation:
Question 1 (1 point)
Consider this right triangle. Determine whether each equation is correct. Select Yes or No fo
each equation
А
5
3
4
4
С
00
B
COS(A)
5
3
O Yes
ONO
Next Page
Yes
Step-by-step explanation:
[tex] \cos( \alpha ) = \frac{base}{hypoteneuse} [/tex]
Its just correct..
I know the answer but I would like to know how to solve it
Step-by-step explanation:
We can use long division to solve this
First place a 5 in the tens place, this means we are multiplying 5 by 50. This will subtract 250 from 280, leaving us with 30.
Next place a 6 in the ones place, this means we are multiplying 5 by 6. This will subtract 30 from 30, leaving us with 0.
This means we have found our answer of 56.
Answer:
See explanation
Step-by-step explanation:
Basically, division is just saying "how many numbers would go into this number this many times?" We can break this problem down into 200/5 and 80/5. 200/5 is 40, and 80/5 is 16. 40+16 is 56, so the answer is 56.
(I can elaborate further if needed)
Hope this helps!
2. The annual cost of science club membership is $ 95. The cost
increases by $20 every year. How much will it cost in 9 years?
Answer:
275
Step-by-step explanation:
20 x 9 = 180
180 + 95 = 275
HOWW DO I DO THIS????
WEIRD EXACT TRIG QUESTION (cannot use a calculator)
Answer:
[tex]\huge{\red{\angle ABC = \boxed{30}\degree}}[/tex]
Step-by-step explanation:
[tex]\sin \angle ABC =\frac{p}{30}......(1)[/tex] (Given)In [tex] \triangle ABC,[/tex] sin ratio of [tex] \angle ABC[/tex] can be given as:[tex]\sin \angle ABC =\frac{AC}{AB}[/tex][tex]\implies \sin \angle ABC =\frac{2p+10}{80}......(2)[/tex]From equations (1) and (2), we find:[tex] \frac{p}{30}=\frac{2p+10}{80}[/tex][tex]\implies 80(p)=30(2p+10)[/tex][tex]\implies 80p=60p+300[/tex][tex]\implies 80p-60p=300[/tex][tex]\implies 20p=300[/tex][tex]\implies p=\frac{300}{20}[/tex][tex]\implies p=15[/tex][tex]\implies \sin \angle ABC =\frac{15}{30}[/tex][tex]\implies \sin \angle ABC =\frac{1}{2}[/tex][tex]\implies \sin \angle ABC =\sin 30\degree\:\:\:\:(\because \sin 30\degree=\frac{1}{2})[/tex][tex]\implies \huge{\red{\angle ABC = \boxed{30}\degree}}[/tex]Use the table below to answer this question:
x y
−1
7
3
3
5
1
Find the average rate of change for the given function from x = −1 to x = 5. (5 points)
−6
−1
1
6
Using it's concept, it is found that the average rate of change of the function from x = -1 to x = 5 is of -1.
What is the average rate of change of a function?It is given by the change in the output divided by the change in the input.
In this problem, the output changes by -6(from 7 to 1) when the input changes by 6(from -1 to 5), hence the average rate is given by:
r = -6/6 = -1.
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Use the distributive property to write an equivalent expression.
10(y-7z+1)
Answer:
10y - 70z + 10.
Step-by-step explanation:
10(y-7z+1) Multiply each term in the brackets by 10:
= 10y - 70z + 10
Boris wants to sort his crayons and give out the
yellow ones. He has 360 crayons altogether.
of the crayons are blue.
18
60% of the crayons are red.
The rest are yellow.
Work out the number of crayon he gives out
Answer:
126 yellow crayons
Step-by-step explanation:
Finding the number of each of the crayons :
Blue = 18Red = 60% of total = 60% x 360 = 0.6 x 360 = 216Number of yellow crayons :
Total - [Blue + Red]360 - [18 + 216]360 - 234126 yellow crayonsexponential function question
Answer: [tex]y = 850(0.943)^t[/tex]
Reason:
The exponential of the form [tex]y = a*b^x[/tex] has 'a' as the initial term and b as the growth or decay factor.
a = 850 is the starting amount
b = 1 + r = 1 + (-0.057) = 0.943 is the decay factor
If the sample loses 5.7% of its mass each year, then it keeps the remaining 94.3% of it.
A box of chocolates contains 10 milk chocolates, 8 dark chocolates and 6 white chocolates. Sung randomly chooses a chocolate, eats it, then randomly chooses another. What is the probability Sung chose a milk chololate then a white chocolate
Using it's concept, it is found that there is a 0.1087 = 10.87% probability Sung chose a milk chocolate then a white chocolate.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
Initially, there are 10 + 8 + 6 = 24 chocolates, out of which 10 are milk, hence the probability of eating a milk chocolate first is given by: [tex]\frac{10}{24} = \frac{5}{12}[/tex].Then, there will be 23 chocolates, out of which 6 will be white, hence the probability of eating a white chocolate first is given by: [tex]\frac{6}{23}[/tex].Thus, the probability of milk then white is given by:
[tex]p = \frac{5}{12} \times \frac{6}{23} = \frac{30}{12 \times 23} = 0.1087[/tex]
0.1087 = 10.87% probability Sung chose a milk chocolate then a white chocolate.
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If anyone can help me with this, please feel free to answer
Pam has 15 candies in a jar, her sister threw in some more ( the ones she doesn’t like) and now Pam has 27. Write an equation to determine how many candies ( x) her sister put in the jar. Solve using both inverse operations and balance scale.
Answer:
Step-by-step explanation:
Number of candies that her sister gave = x
Total candies that Pam has now = 27
x + 15 = 27
Inverse operation:
x + 15 = 27
x + 15 - 15 = 27 - 15
x = 12
Answer:
Equations :
27 - 15 = x
15 + x = 27
Step-by-step explanation:
So, we know that 1. Pam starts with 15 candies. and 2. Pam ends up having 27 candies. This means, that she gained candy.
To figure out how many candies her sister gave, her, we have to find the difference between 27 and 15 becuase she goes from having 15 to having 27 after her sister had given some.
x will represent how many cadies Pams' sister had given her :
27 - 15 = x
12 = x
This means Pams' sister gave 12 candies to Pam. To make sure we are correct, we can simply start with how many candies Pam started with (15). And add how many we think her sister added (12)
15 + 12
15 + 12 = 27
Therefore proving, and meaning, that Pams' sister gave her 12 candies.
Possible Equations :
27 - 15 = x
End total (27) minus starting total (15).
15 + x = 27
Starting total (15) plus how many she gained (x) equal to end total (27).
determine if the shape is a polyhedron using eulers formula
Answer:
Yes
Step-by-step explanation:
Euler's Formula for Polyhedrons :
Faces + Vertices = Edges + 2
Given :
Vertices = 12Edges = 18Faces = 8Verifying using Euler's Formula :
F + V = E + 2(8) + (12) = (18) + 220 = 20It is a polyhedronThe given shape is a polyhedron using the Euler's formula.
What is Polyhedron?Polyhedron is defined as the three dimensional shape which consists of flat shapes which are polygons.
Cubes, pyramids are all polyhedrons.
Euler's formula for polyhedron states that,
V - E + F = 2
where V, E and F are the number of vertices, number of edges and the number of faces respectively.
For the given polyhedron,
Number of vertices, V = 6 + 6 = 12
Number of edges, E = 6 + 6 + 6 = 18
Number of faces, F = 1 + 6 + 1 = 8
So, V - E + F = 12 - 18 + 8 = -6 + 8 = 2
Hence the given shape is a polyhedron.
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Select either relation (if the set is a relation but not a function), function (if the set is both a relation and a function), or
nelther (If the set is not a relation).
A={(1, 2) (2, 2) (3, 2) (4, 2)
A. Function
B. Relation
C. Neither
Answer:
C neither
the coordinates shows that only the x intercepts are moving not y the line of the graph will be horizontal and straight . it is not a function
3. The FFA had a fundraiser by selling hot dogs for $1.50 and drinks for $2.00. Their total sales were $400.
a) Write an equation to calculate the total of $400 based on the hot dog and drink sales.
b) Graph the relationship between hot dog sales.
The equation that represents the total of $400 based on the hot dog and drink sales is $400= $1.50H + $2.00D
Using equation for expressionsThe amount sold for each hot dog = $1.50
The total number of hot dogs sold = H × $1.50
The amount sold for each drink = $2.00
The total number of drinks sold = D× $2.00
The total sales made was = $400
Therefore the equation that represents the total of $400 based on the hot dog and drink sales is;
$400= $1.50H + $2.00D
The relationship that exists between the hot dog sales is that the cost is the drinks is higher than the cost of the hot dog.
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PLS HELP ITS WORTH 20 points
Answer:
x=3, Aly is correct.
Step-by-step explanation:
a. angle YWZ
b. ZY = 9
c. the triangles are congruent so 7x-20=2x-5, 5x=15, and x=3
What is the probability that the spinner will land on a number greater than 4 or on a shaded section? two-ninths one-half two-thirds five-sixths
The probability that the spinner will land on a number greater than 4 or on a shaded section is 2/3
How to determine the probability?The given parameters are:
Sections = 6Numbers greater than 4 = 2Shaded section = 3Shaded section and greater than 4 = 1Using the above parameters, we have the following probabilities
P(Greater than 4) = 2/6
P(Shaded) = 3/6
P(Shaded section and greater than 4) = 1/6
The required probability is then calculated using:
P = 2/6 + 3/6 - 1/6
Evaluate
P = 4/6
Simplify
P = 2/3
Hence, the probability that the spinner will land on a number greater than 4 or on a shaded section is 2/3
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Beg someone helps me w this question
Answer:
[tex](x+1)^{2} +4[/tex]
a = 1
b = 4
Step-by-step explanation:
hope this helps!! p.s. i really need brainliest :)
When Tariq goes bowling, his scores are normally distributed with a mean of 110 and a standard deviation of 10. Using the empirical rule, what percentage of the games that Tariq bowls does he score between 80 and 140
Using the Empirical Rule, it is found that Tariq scores between 80 and 140 in 99.7% of the games that he bowls.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, considering the mean of 110 and the standard deviation of 10, scores between 80 and 140 are within 3 standard deviations of the mean, hence Tariq scores between 80 and 140 in 99.7% of the games that he bowls.
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Please help me I don’t how to do this
Answer:
C. 5f +25
Step-by-step explanation:
Find the surface area of the prism. Enter your answer in the box.
Answer:
Area of the prism = 2(lw + lh + wh)
l = length = 6 m
w = width = 3 m
h = height = 12 m
—
Area of the prism = 2(6*3 + 6*12 + 3*12) = 2(18 + 72 + 36) = 2(126) = 252 m²
—
Have a nice day!!
What is the area of a square with sides that each have a length of 1 meter?
Answer:
1 m^2
Step-by-step explanation:
A = W * L
1 * 1 = 1
Write the equality in the given diagram below
Answer:
The inequality for this diagram is x≥-1
Please the explanation... it always helpsssss....
Step-by-step explanation:
The first step is to look at the circle... is it filled in or not... in this case it is...
meaning the symbol is greater than or equal to OR less than or equal to
next the arrow is pointing to the right meaning the symbol must be greater than or equal to
then look at the value at the filled in circle (which in this case is -1)
meaning the inequality must be x≥-1
i really hope this helps!!!!
9. Draw a right triangle that has the 90° angle
between 6 cm and 8 cm sides. What is the
length of the third side? How do you know
without measuring?
!!!40 POINTS AND BRAINLIEST!!! PLEASE SHOW WORK!!!
How much ribbon would be needed to go around a package that had a length [tex]2x^2+3x-5/x^2+x-3[/tex] centimeters and width [tex]x^2-x-5/x^2+x-3[/tex] centimeters?
(SHOW YOUR WORK IF YOU CAN)
Answer:
(6x² +4x -20)/(x² +x -3) cm
Step-by-step explanation:
The perimeter of a rectangle is twice the sum of its length and width. Here, length and width are rational functions. The same relation to perimeter applies.
__
[tex]P = 2(L+W)\\\\P=2\left(\dfrac{2x^2 +3x-5}{x^2+x-3}+\dfrac{x^2-x-5}{x^2+x-3}\right)\qquad\text{use given values for $L$ and $W$}\\\\P=2\left(\dfrac{2x^2+3x-5+x^2-x-5}{x^2+x-3}\right)=\dfrac{2(3x^2 +2x-10)}{x^2+x-3}\\\\P=\dfrac{6x^2+4x-20}{x^2+x-3}\\\\\underline{\ \qquad}\\\\\textsf{It would take $\dfrac{6x^2+4x-20}{x^2+x-3}$ cm of ribbon to go around the package.}[/tex]
