Do the 1. In a class of 60 students, a survey was conducted, 30 students had applied for Addis Ababa University, 25 students applied for Bahir Dar University and 24 students applied for Wachemo University. 11 students applied for both Addis Ababa and Bahir Dar Universities, 6 applied for both Addis Ababa and Wachemo Universities, 9 applied for both Wachemo and Bahir Dar Universities while 4 applied neither of the aforementioned universities. Find i. 11. 111. iv. number of students that applied for all the universities. number of students that applied for at least two of the universities. number of students that applied at most two universities. number of students that applied for Addis Ababa but not Bahir Dar University. 13Z 2. Solve the equation: = 11-3i, Z E C, where Z = x + iy, x&y E R. Z+1 3. Given that Z & W are complex numbers. 2 Prove that IZ + W1²-|Z - W² = 4Re(Z)Re(W). 4. Solve the equation: 2² + 4z +20 + iz(A + 1) = 0 where A is a constant, has complex conjugate root. If one of the roots of this quadratic is Z = B + 2i, where B is a real constant, find the possible values of A.
Answers
The number of students that applied for all universities is 3, the number of students that applied for at least two of the universities is 20, the number of students that applied for at most two of the universities is 53, and the number of students that applied for Addis Ababa but not Bahir Dar University is 5.
Given that there are 60 students out of which 30 students had applied for Addis Ababa University, 25 students applied for Bahir Dar University and 24 students applied for Wachemo University. 11 students applied for both Addis Ababa and Bahir Dar Universities, 6 applied for both Addis Ababa and Wachemo Universities, 9 applied for both Wachemo and Bahir Dar Universities while 4 applied neither of the aforementioned universities.
Let A, B, and W denote the sets of students apply to Addis Ababa Uni (A), Bahir Dar Uni (B), or Wachemo Uni (W). Let U denote the universal set of all students in the class.
We're given the cardinalities of several sets:
total number of students n(U)=60, A applicants is n(A)=30, B applicants n(B)=25, W applicants n(W)=24, A and B applicants n(A∩B)=11, A and W applicants n(A∩W)=6, B and W applicants n(B∩W)=9 non-applicants n(U\(A∪B∪W))=4
The last cardinality tells us n(A∪B∪W),60-4=56 students applied anywhere at all.
We want to find n(A∩B∩W), the number of students that applied to each of the three universities.
By the inclusion/exclusion principle,
n(A∪B∪W)=n(A)+n(B)+n(W)-n(A∩B)-n(A∩W)-n(B∩W)+n(A∩B∩W)
56=30+25+24-11-6-9+n(A∩B∩W)
n(A∩B∩W)=3
Now, we will find the number of students that applied for at least two of the universities.
n(A∩B)=n(A∩B∩W)+n(A∩B∩W')
11=3+n(A∩B∩W')
8=n(A∩B∩W')
Similarly, we will find
n(A∩B'∩W)=3
n(A'∩B∩W)=6
n(A∩B'∩W')=16
n(A'∩B∩W')=8
n(A'∩B'∩W)=12
then the total number of students applied for at least two students is
n(A∩B∩W')+n(A∩B'∩W)+n(A'∩B∩W)+n(A∩B∩W)=20
Now, we will find the number of students that applied for atmost two universities, we get
n(A∩B∩W')+n(A∩B'∩W)+n(A'∩B∩W)+n(A∩B'∩W')+n(A'∩B∩W')+n(A'∩B'∩W)=53
now, we will find the number of students that applied for Addis Ababa but not Bahir Dar University is
n(A∩B')=n(A)-n(B)
n(A∩B')=30-25
n(A∩B')=5
hence, the total students is 60 and the number of students that applied for all universities is 3, the number of students that applied for at least two of the universities is 20, the number of students that applied for at most two of the universities is 53, and the number of students that applied for Addis Ababa but not Bahir Dar University is 5.
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Related Questions
Which of the following inequalities represents the number line below?
Answers
Answer:
x ≤ 4
Step-by-step explanation:
the solid dot at 4 indicates that x can equal 4
the arrow points to the left indicating values less than 4 , then
x ≤ 4
Reagan has a part-time job walking dogs. She makes $12.20 per hour. If she earns $106.75 this week, how many hours does she work?
Answers
Step by step. $106.75 earned divided by $12.20 per hour = 8.75 hours worked.
Answer:
8.75
Step-by-step explanation:
106.75 divided by 12.20= 8.75
Consider an urn containing 8 white balls, 7 red balls and 5 black balls.
1)Randomly select 2 balls without replacement. The probability of getting 2 white balls is equal to:
2)Randomly select 5 balls without replacement. the probability of getting 2 white balls is equal to:
3) randomly select 150 balls with replacement. The probability of getting at least 72 white balls is:
Answers
Answer + Step-by-step explanation:
1) The probability of getting 2 white balls is equal to:
[tex]=\frac{8}{20} \times \frac{7}{19}\\\\= 0.147368421053[/tex]
2) the probability of getting 2 white balls is equal to:
[tex]=C^{2}_{5}\times (\frac{8}{20} \times \frac{7}{19}) \times (\frac{12}{18} \times \frac{11}{17} \times \frac{10}{16})\\=0.397316821465[/tex]
3) The probability of getting at least 72 white balls is:
[tex]=C^{72}_{150}\times \left( \frac{8}{20} \right)^{72} \times \left( \frac{7}{20} \right)^{78} +C^{73}_{150}\times \left( \frac{8}{20} \right)^{73} \times \left( \frac{7}{20} \right)^{77} + \cdots +C^{149}_{150}\times \left( \frac{8}{20} \right)^{149} \times \left( \frac{7}{20} \right)^{1} +\left( \frac{8}{20} \right)^{150}[/tex]
[tex]=\sum^{150}_{k=72} [C^{k}_{150}\times \left( \frac{8}{15} \right)^{k} \times \left( \frac{7}{15} \right)^{150-k}][/tex]
First of all, we would determine the total number of balls in the urn as follows:
Total number of balls = 8 + 7 + 5
Total number of balls = 20 balls.
Next, we would determine the probability of getting two (2) white balls without replacement:
P(2 white balls) = 8/20 × 7/19
P(2 white balls) = 2/5 × 7/19
P(2 white balls) = 0.1474.
Part 2.When 5 balls are selected without replacement, the probability of getting two (2) white balls would be calculated as follows:
P = [⁵C₂ × (8/20 × 7/19) × (12/18 × 11/17 × 10/16)]
P = [5!/(2! × (5 - 2)!) × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]
P = [5!/(2! × 3!) × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]
P = [20/2 × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]
P = [10 × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]
P = 0.3456.
Part 3.When 150 balls are randomly selected with replacement, the probability of getting at least seventy two (72) white balls would be calculated by applying binomial probability equation. Mathematically, binomial probability is given by this equation:
[tex]P =\; ^nC_r (p)^r (q)^{(n-r)}[/tex]
Substituting the given parameters into the formula, we have;
P = [¹⁵⁰C₇₂ × (8/20)⁷² × (8/20)⁽¹⁵⁰ ⁻ ⁷²⁾]
P = [150!/(72! × (150 - 72)!) × (8/20)⁷² × (8/20)⁽¹⁵⁰ ⁻ ⁷²⁾]
P = [150!/(72! × (78)!) × (4/5)⁷² × (4/5)⁽⁷⁸⁾]
P = 0.7948.
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The angle bisectors of a triangle intersect at a point called the
Answers
Answer:
incenter
Step-by-step explanation:
Prove: In an equilateral triangle the three medians are equal
Answers
Step-by-step explanation:
Let ABC be the equilateral triangle. Let AE, BD and CF be the medians. A meridian divides a side into two equal parts. Hence, proved that medians of an equilateral triangle are equal .
AN ARTICLE IN USA TODAY STATED THAT “INTERNAL SURVEYS PAID FOR BY DIRECTORY ASSISTANCE PROVIDERS SHOW THAT EVEN THE MOST ACCURATE COMPANIES GIVE OUT WRONG NUMBERS 15% OF THE TIME.” ASSUME THAT YOU ARE TESTING SUCH A PROVIDER BY MAKING 10 REQUESTS AND
ALSO ASSUME THAT THE PROVIDER GIVES THE WRONG TELEPHONE NUMBER 15%
OF THE TIME. FIND THE PROBABILITY OF GETTING ONE WRONG NUMBER.
Answers
Step-by-step explanation:
I assume this means exactly one wrong number in the 10 attempts.
the probability to get a wrong number is 0.15 (15%).
therefore, the probability to get a correct number is
1 - 0.15 = 0.85
in 10 tries to get 1 wrong number (and 9 correct numbers) looks like this :
0.15×0.85⁹ = 0.034742542...
this would be the probability to e.g. get a wrong number at the first attempt, and all other attempts are correct.
how many different constellations can we have that way ?
10.
because the wrong number could be given at any of the 10 attempts.
so, the probability to get exactly 1 wrong answer is
10×0.15×0.85⁹ = 0.34742542... ≈ 35%
now, if the question is about the probability to get at least one number wrong, then we can say this is the opposite of the probability to get all 10 numbers correctly.
the probability to get all 10 numbers correctly is
0.85¹⁰ = 0.196874404... ≈ 20%
and therefore, the probability to get at least 1 number wrong is
1 - 0.196874404... = 0.803125596... ≈ 80%
FYI :
this would be, of course, also the result of we did it the complex way :
the sum of the probabilities of
exactly 1 number wrong
exactly 2 numbers wrong
...
exactly 9 numbers wrong
all 10 numbers wrong
and for each of the cases of n wrong numbers the probability is
(10! / (n! × (10-n)!)) × 0.15^n × 0.85^(10-n)
this represents the constellation of n numbers wrong (and 10-n numbers right) multiplied by the number of possible combinations of picking n numbers out of 10.
and again, all this summed up (1 <= n <= 10) is the same as
0.803125596...
The probability of at most one wrong number i got P(x ≤ 1) = 6.76 % ≠ 15 % the original probability of at most one are not equal, it thus appears that the original probability of 15 % is wrong.
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Now, Let q = probability of giving out wrong number = 15 % = 0.15
And, p = probability of not giving out wrong number = 1 - q
= 1 - 0.15 = 0.75
Hence, For a binomial probability,
P(x) = ⁿCₓ qˣ pⁿ⁻ˣ.
With n = 10 and x = 1, the probability of getting a number wrong
P(x = 1) = ¹⁰C₁q¹p¹⁰⁻¹
= 10(0.15)(0.75)⁹
= 1.5(0.0751)
= 0.1126
= 11.26 %
b. At most one wrong is P(x ≤ 1) = P(0) + P(1)
= ¹⁰C₀q⁰p¹⁰⁻⁰ + ¹⁰C₁q¹p¹⁰⁻¹
= 1 × 1 × (0.75)¹⁰ + 10(0.15)(0.75)⁹
= 0.0563 + 0.01126
= 0.06756
= 6.756 %
≅ 6.76 %
Since the probability of at most one wrong number i got P(x ≤ 1) = 6.76 % ≠ 15 % the original probability of at most one are not equal, it thus appears that the original probability of 15 % is wrong.
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The scouts packed 9 boxes of different kinds of chips for their trip. Each box had 10 bags of chips. These clues show what they had left at the end of the trip. They ate all the rest.
Clues:
2 full boxes of potato chips and 3 bags left over
1 fewer box of nacho chips than potato chips, with no bags left over
twice as many loose bags of barbecue chips than loose bags of potato chips, with no full boxes left over
How many bags of chips did the scouts eat on their trip?
Answers
The scouts eat 51 bags of chips on their trip
How to determine the number of bags of chips?The given parameters are:
Boxes = 9
Bag = 10 chips
2 full boxes of potato chips and 3 bags left over.
This represents:
Potato chips = 2 * 10 + 3
Potato chips = 23 i.e. 23 bags potato chips are left over
1 fewer box of nacho chips than potato chips, with no bags left over
This represents
Nacho chips = (2 - 1) * 10
Nacho chips = 10 i.e. 10 bags of nacho chips are left over
The loose bags of potato chips is 3.
So, we have:
Barbecue chips = 2 * 3 bags
Barbecue chips = 6 bags
At this point, we have:
Potato chips = 23 bagsNacho chips = 10 bags Barbecue chips = 6 bagsThe total number of bags left over is
Total = 23 + 10 + 6
Total = 39
The number of bags eaten is:
Eaten = 9 * 10 - 39
Evaluate
Eaten = 51
Hence, the scouts eat 51 bags of chips on their trip
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An unknown radioactive element decays into non-radioactive substances. In 340
days the radioactivity of a sample decreases by 61 percent.
(a) What is the half-life of the element?
half-life: ? (days)
(b) How long will it take for a sample of 100 mg to decay to 81 mg?
time needed: ? (days)
Answers
(a) The half-life of the unknown radioactive element is 250.28 days.
(b) The time taken for a sample of 100 mg to decay to 81 mg is 76.1 days.
Half life of the unknown radioactive elementN(t) = N₀(0.5)^t/h
where;
t is time of decayh is half lifeN₀ is initial massN(t) remaining mass at time, tin 340 days; N(340) = N₀(0.39);
1 - 0.61 = 0.39
N(340) = N₀(0.5)^340/h
N(340)/N₀ = 0.5^340/h
0.39 = 0.5^340/h
log(0.39) = 340/h x log(0.5)
log(0.39) /log(0.5) = 340/h
1.358 = 340/h
h = 340/1.358
h = 250.28 days
Time taken for the sample to decay 81 mg81 = 100(0.5)^t/250.28
81/100 = (0.5)^t/250.28
0.81 = (0.5)^t/250.28
log(0.81) = t/250.28 x log(0.5)
log(0.81) / log(0.5) = t/250.28
0.304 = t/250.28
0.304(250.28) = t
76.1 days = t
Thus, the half-life of the unknown radioactive element is 250.28 days and the time taken for a sample of 100 mg to decay to 81 mg is 76.1 days.
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Consider the curve C in the Cartesian plane described in polar coordinates by given:
See picture:
a. Determine a Cartesian equation that describes curve C. Hint: first multiply (c) by r.
b Describe this curve and use this description to obtain the area inside C.
c Use (c) to set up an integral that computes the area inside C that is also within the rst quadrant.
d Evaluate this integral to determine the area.
Answers
a. Recall that in polar coordinates, we can parameterize [tex]x=r\cos(\theta)[/tex] and [tex]y=r\sin(\theta)[/tex]. So, doing as the hint suggests, we have
[tex]r = 6\cos(\theta) + 8 \sin(\theta)[/tex]
[tex]\implies r^2 = 6r\cos(\theta) + 8r\sin(\theta)[/tex]
[tex]\implies \boxed{x^2 + y^2 = 6x + 8y}[/tex]
b. By completing the square, we get
[tex]x^2 + y^2 = 6x + 8y[/tex]
[tex]x^2 - 6x + y^2 - 8y = 0[/tex]
[tex]x^2 - 6x + 9 + y^2 - 8y + 16 = 25[/tex]
[tex](x-3)^2 + (y-4)^2 = 5^2[/tex]
which is the equation of the circle centered at (3, 4) with radius 5. Thus the area bounded by [tex]C[/tex] is [tex]\pi\cdot5^2 = \boxed{25\pi}[/tex].
c. This is made easier if you can consult a plot (attached). In the first quadrant, we have [tex]0\le\theta\le\frac\pi2[/tex], while the radial coordinate [tex]r[/tex] runs uninterrupted from the origin [tex]r=0[/tex] to the circle [tex]r=6\cos(\theta)+8\sin(\theta)[/tex]. So the area is
[tex]\displaystyle \int_0^{\pi/2} \int_0^{6\cos(\theta) + 8\sin(\theta)} r\,dr\,d\theta = \boxed{\frac12 \int_0^{\pi/2} \left(6\cos(\theta) + 8\sin(\theta)\right)^2 \, d\theta}[/tex]
d. Evaluate the integral.
[tex]\displaystyle \frac12 \int_0^{\pi/2} \left(36\cos^2(\theta) + 96\sin(\theta)\cos(\theta) + 64 \sin^2(\theta)\right) \, d\theta[/tex]
Simplify the integrand with the help of the identities
[tex]\cos^2(x) + \sin^2(x) = 1[/tex]
[tex]\sin(x)\cos(x) = \dfrac12 \sin(2x)[/tex]
[tex]\sin^2(x) = \dfrac{1 - \cos(2x)}2[/tex]
[tex]\displaystyle \frac12 \int_0^{\pi/2} \left(50 + 48\sin(2\theta) - 14 \cos(2\theta)\right) \, d\theta[/tex]
The rest is easy. You should end up with
[tex]\displaystyle \frac12 \int_0^{\pi/2} \left(6\cos(\theta) + 8\sin(\theta)\right)^2 \, d\theta = \boxed{24 + \frac{25\pi}2}[/tex]
a) The Cartesian equation that described curve C is x² + y² = 6 · x + 8 · y.
b) The area inside C is A = π · 5² = 25π square units.
c) The integral that computed the area inside curve C within the first quadrant is A = (1 / 2)∫ (6 · cos θ + 8 · sin θ)² dθ, for θ ∈ [0, 0.5π].
d) The integral evaluated at the given limits is equal to an area of 20.139π square units.
How to analyze a polar equation and find its area by geometric and calculus means
In this question we find a polar equation in explicit form. a) To find the equivalent form in rectangular coordinates, we must apply the following substitutions x = r · cos θ, y = r · sin θ:
r = 6 · cos θ + 8 · sin θ
r² = 6 · r · cos θ + 8 · r · sin θ
x² + y² = 6 · x + 8 · y (1)
The Cartesian equation that described curve C is x² + y² = 6 · x + 8 · y.
b) Perhaps the equation represents a conic section, possibly a circunference. To prove this assumption, we must apply algebraic handling until standard form is obtained:
x² - 6 · x + y² - 8 · y = 0
x² - 6 · x + 9 + y² - 8 · y + 16 = 25
(x - 3)² + (y - 4)² = 5² (1b)
Which indicates a circumference centered at point (h, k) = (3, 4) and with a radius of 5 units. By the area formula for a circle we find that the area inside C is A = π · 5² = 25π square units.
c) The polar form of the area integral is presented herein:
A = ∫ ∫ r dr dθ, for r ∈ [0, r(θ)] and θ ∈ [0, 0.5π]
A = (1 / 2)∫ [r(θ)]² dθ, for θ ∈ [0, 0.5π]
A = (1 / 2)∫ (6 · cos θ + 8 · sin θ)² dθ, for θ ∈ [0, 0.5π]
The integral that computed the area inside curve C within the first quadrant is A = (1 / 2)∫ (6 · cos θ + 8 · sin θ)² dθ, for θ ∈ [0, 0.5π].
d) By algebraic handling, trigonometric formulas and integral properties:
A = 25 ∫ dθ + 24 ∫ sin 2θ dθ - 14 ∫ cos 2θ dθ, for θ ∈ [0, 0.5π]
A = 25 · θ - 12 · cos 2θ - 7 · sin 2θ, for θ ∈ [0, 0.5π]
A = 20.139π
The integral evaluated at the given limits is equal to an area of 20.139π square units.
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The volume of a sphere is 4500π m3. What is the surface area of the sphere to the nearest square meter?
Answers
Answer:
2827 m²
Step-by-step explanation:
The equation for volume of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Using this equation and the given volume of the sphere, we can find the radius of the sphere.
Finding the Radius[tex]V=\frac{4}{3}\pi r^3[/tex]
[tex]4500\pi = \frac{4}{3}\pi r^3[/tex]
Divide both sides by π
[tex]4500=\frac{4}{3}(r^3)[/tex]
Multiply both sides by 3
[tex]13500=4( r^3)[/tex]
Divide both sides by 4
[tex]3375=r^3[/tex]
Take the cube root of both sides
[tex]r=15[/tex]
Thus the radius of the sphere is 15m. We can use this information to find the surface area of the sphere.
Finding the Surface AreaThe equation for surface area of a sphere is [tex]4\pi r^2[/tex]. Substituting the value we found for the radius into the equation, we find:
[tex]SA=4\pi r^2\\SA=4\pi 15^2\\SA=4\pi 225\\SA=900\pi\\SA\approx2827$ m^2[/tex]
The surface area of the sphere, rounded to the nearest square meter, is 2827 m².
The world price of umbrellas is $20 each. The pre-trade price of baskets in England is S15 each. What would happen if England allows trade in baskets?
Answers
Answer: Ans. Option c As the price of basket in England is $15, which is less than the world
please help with the first one
Answers
Answer:
y = x +5
Step-by-step explanation:
The equation of a parallel line will have the same x- and y-coefficients, but a different constant. You need to find the constant that makes the line go through the given point.
ApplicationThe given line is y = x +1. The equation you're looking for is
y = x +c . . . . . . for some new constant c
We want this equation to be true for (x, y) = (-2, 3). Putting these values into the equation, we can solve for c.
3 = -2 +c
5 = c . . . . . . add 2
The desired equation is y = x +5.
61% of owned dogs in the United States are spayed or neutered. Round your answers to four decimal places. If 46 owned dogs are randomly selected, find the probability that
a. Exactly 29 of them are spayed or neutered.
b. At most 29 of them are spayed or neutered.
c. At least 28 of them are spayed or neutered.
d. Between 28 and 32 (including 28 and 32) of them are spayed or neutered.
A good calculator is found at: Stattrek Binomial Calculator Round answers to at least 4 decimal places.
Answers
Using the binomial distribution, the probability that:
(a) Exactly 29 of them are spayed or neutered, that is, P(X = 29) = 0.1163.
(b) At most 29 of them are spayed or neutered, that is, P(X ≤ 29) = 0.6648.
(c) At least 28 of them are spayed or neutered, that is, P(X ≥ 28) = 0.5714.
(d) Between 28 and 32 (including 28 and 32) of them are spayed or neutered, that is, P(28 ≤ X ≤ 32) = 0.48345.
A binomial distribution, with a success rate of p on each trial, gives us the probability of x number of success in n number of trials, using the formula:
P(X = x) nCx.pˣ.qⁿ⁻ˣ, where q = 1 - p.
In the question, we are informed that 61% of owned dogs in the United States are spayed or neutered, and are given that 46 owned dogs are randomly selected.
This can be seen as a binomial probability distribution, with n = 46, and p = 61% = 0.61, q = 1 - p = 1 - 0.61 = 0.39.
(a) We are asked for the probability of exactly 29 of them being spayed or neutered.
Thus, x = 29, and we need to find P(X = 29).
Using the given calculator, P(X = 29) = 0.1163.
(b) We are asked for the probability of at most 29 of them being spayed or neutered.
Thus, we need to find P(X ≤ 29).
Using the given calculator, P(X ≤ 29) = 0.6648.
(c) We are asked for the probability of at least 28 of them being spayed or neutered.
Thus, we need to find P(X ≥ 28).
Using the given calculator, P(X ≥ 28) = 0.5714.
(d) We are asked for the probability between 28 and 32 of them are spayed or neutered.
Thus, we need to find P(28 ≤ X ≤ 32), which can be shown as;
P(28 ≤ X ≤ 32) = P(X ≤ 32) - P(X < 28).
Using the given calculator, P(X ≤ 32) = 0.91209.
Using the given calculator, P(X < 28) = 0.42864.
Thus, P(28 ≤ X ≤ 32) = P(X ≤ 32) - P(X < 28) = 0.91209 - 0.42864 = 0.48345.
Thus, using the binomial distribution, the probability that:
(a) Exactly 29 of them are spayed or neutered, that is, P(X = 29) = 0.1163.
(b) At most 29 of them are spayed or neutered, that is, P(X ≤ 29) = 0.6648.
(c) At least 28 of them are spayed or neutered, that is, P(X ≥ 28) = 0.5714.
(d) Between 28 and 32 (including 28 and 32) of them are spayed or neutered, that is, P(28 ≤ X ≤ 32) = 0.48345.
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Help me with this question asap please !
Answers
Answer:
BA
CB
CA
Step-by-step explanation:
this simply means that such a letter combination stands for a line that goes through the points with these letters.
and a "ray" means a straight line (not one that goes around a corner). "from this figure" means lines (or connections between points) that are drawn in this graphic.
BA yes
B is just a point, no line. therefore, no.
DBA guys around a corner (from D to B, and then from there to A). therefore, no.
AD would be a straight line, but it is not drawn in the graphic. therefore, no.
ADB is partly not drawn, and it goes around a corner. therefore, no.
CB, CA are both straight lines in the graphic. yes.
Describe the translation.
y=(x−5)2+5 → y=(x−0)2+0
A. T<−5,5>
B. T<5,−5>
C. T<−5,−5>
D. T<5,5>
Answers
Answer:
C
Step-by-step explanation:
This is a translation 5 units left and 5 units dowh.
Here, the translation is [tex]T < 5,-5 >[/tex].
What is translation?The translation is a coordinate transformation operation in which a point or a figure moves left/right/up or down in a coordinate system or a set of axes. After applying translation, the size of the figure remains unchanged, just the position changes. For example, consider a function [tex]y=f(x)[/tex]. If we translate it to the new function [tex]y'=f(x+a)+b[/tex], then the graph of [tex]y[/tex] moves [tex]a[/tex] units to the right and [tex]b[/tex] units to the up and in this case the translation is denoted by [tex]T < a,b >[/tex]Here, the translation is given as: [tex]y=2(x-5)+5\longrightarrow y=2(x-0)+0[/tex].
i.e. [tex]y=2(x-5)+5\longrightarrow y=2(x-5+5)+(5-5)[/tex].
So, the graph of [tex]y[/tex] moves 5 units to the right and (-5) units to the up i.e., 5 units to the down.
Therefore, here, the translation is [tex]T < 5,-5 >[/tex].
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look at the screenshot and explain your answer pls
Answers
Answer:
f(x) = g(x) + 9 because it is shifted 9 to the right
What is 3/2+ t = 1/2
Answers
Answer:
t=-1Step-by-step explanation:
To find the value of t, isolate it on one side of the equation.
[tex]\sf{\dfrac{3}{2}+t=\dfrac{1}{2}}[/tex]
First, you subtract by 3/2 from both sides.
[tex]\Longrightarrow: \sf{\dfrac{3}{2}+t-\dfrac{3}{2}=\dfrac{1}{2}-\dfrac{3}{2}}[/tex]
Solve.
1/2-3/2
1-3/2
1-3=-2
-2/2
Divide.
-2/2=-1
[tex]\Longrightarrow: \boxed{\sf{t=-1}}[/tex]
Therefore, the solution is t=-1, which is our answer.
I hope this helps, let me know if you have any questions.
STEP BY STEP EXPLANATION;
1.To solve the equation,the least common multiple of the denominators must be found.
LCM=2
Therefore,
3/2 +t =1/2
2.Each term must be multiplied by the LCM.
i.e
2(3/2)+2(t)=2(1/2)
3+2t=1
2t=1-3 ( subtracting 3 from each side of the equation)
2t=1-3
2t/2=-2/2 (dividing both sides of the equation by the co-efficient of t)
t=-1
Question: 1 An analysis of an unknown compound found it contained 40 g potassium, 52 g chromium and 56 g of oxygen. a) What is the empirical formula for this compound? b) What type of compound is it, ionic, covalent or a combination of both? Explain your choice.
Answers
1) The empirical formula for this compound is; K₂Cr₂O₇
2) It is an Ionic compound because it has two potassium ions (K+) and a negatively charged dichromate ion (Cr2O7-).
How to find the Empirical Formula?
1) Elements of the unknown compound are;
Potassium = 40 g
Chromium = 52 g
Oxygen = 56 g
Let us find the number of moles of each element;
Number of moles of Potassium = 40/39 = 1.026 mol K
Number of moles of Chromium = 52/52 = 1 mol Cr
Number of moles of oxygen = 56/16 = 3.5 mol O
Multiply through the number of moles by 2 and round up to the nearest whole number to get the empirical formula at; K₂Cr₂O₇
2) The compound K₂Cr₂O₇ is called Potassium dichromate. It is classified as an ionic compound because it has two potassium ions (K+) and a negatively charged dichromate ion (Cr2O7-).
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According to a recent poll at a university,70.7 % of high school seniors in a certain region had a driver's license. A sociologist thinks this rate has declined. The sociologist surveys randomly selected high school seniors and finds that have a driver's license. a. Pick the correct null hypothesis. b. Pick the correct alternative hypothesis. c. In this context, what does the symbol p represent?
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your mother i swear
Step-by-step explanation:
ask yo mom
The length of line segment AG is 17 m and the line segment AD is 25 m. What is the length of line segment GD?
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Answer:
AG = 17 m
AD = 25 m
GD = ?
AD = AG + GD
GD = AD - AG
= 25 - 17
= 8 m
the answer to your question is 8m
A positive integer is 10 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is frac(2,3), then find the two integers.
Answers
The two integers are are mathematically given as
x=3.70
y=13.7
What is the two integers?Generally, the equation for the two integers is mathematically given as
x + 10 = y
1/x + 2/y = 2/3
Substitute
1/x + 2/x+10 = 2/3
Multiply by 3
3/x + 6/x + 10 = 2
Multiply by x
2 + 6x/x + 10 = 2x
Multiply by x + 3
2(x + 10) + 6x = 2x(x + 3)
2x+20+6x=2x^2+6x
-2x^2+2x+20=0
x=3.70
hence y
x + 10 = y
3.70+ 10 = y
y=13.7
In conclusion, the two integers are
x=3.70
y=13.7
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PLEASEEEEEEEEEE HELPPPP. which of the following system of inequalities would produce the region indicated on the graph below?
Answers
Answer: C
Step-by-step explanation:
The line [tex]y=x+2[/tex] is shaded below and is solid.
This eliminates all the options except for C.
To reduce their expected estate tax liability prior to either spouse's death, the Hansens could?
Answers
If the Hansens want to reduce their expected estate tax liability prior to the death of either of the spouses, they could initiate a Marital Transfer.
What is a marital transfer?A Marital transfer simply means that the Hansens should bequest their assets to each each other in case either of them die.
If this happens, the surviving spouse will not be charged any estate taxes because bequests to spouses are not subject to taxation.
To do this, the Hansens should put it into both of their wills that they plan to gift/ bequest their assets to their spouse if they die.
The big disadvantage of using a marital transfer however, is that the estate will still be subject to taxes when the surviving spouse dies. All the estate taxes that had been avoided would then be incurred by the estate but only after the death of both spouses.
In conclusion, they should use a marital transfer.
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simplify 12x^6-4x^4+6x^2 over 2x^2
Answers
Answer:
6x⁴ - 2x² +3
Step-by-step explanation:
[tex]\frac{12x^6-4x^4+6x^2}{2x^2}=6x^4 - 2x^2 + 3[/tex]
please help.
A report by the NCAA states that 57.5% of football injuries occur during practices. A head trainer claims that this is too high for this conference, so he randomly selects 36 injuries and founds that 17 occurred during practices. Is his claims correct at a=0.05?
Answers
Answer:
he is more likely incorrect.
Step-by-step explanation:
Z = (ps - p0)/sqrt(p0(1-p0)/n)
ps = proportion sample
p0 = proportion null hypothesis (NCAA)
n = sample size
ps = 17 / 36/100 = 17/1 / 36/100 = 1700/36 =
= 47.22222222...%
Z = (0.47222... - 0.575)/sqrt(0.575(1 - 0.575)/36) =
= -0.10277777... /sqrt(0.244375 / 36) =
= -0.10277777... / 0.0823905... =
= -1.247446952... ≈ -1.25
p(-1.25) = 0.10565
0.10565 > 0.05
the null hypothesis is therefore likely, or at least cannot be rejected.
so, his claims are not supported, as surprising as this might feel given that the sample result itself is 10 points off the NCCA result, which feels to be a solid difference.
I need the answers to this question
Answers
Answer: Madison can travel 2.2 miles less than Anthony on one gallon of gas.
Step-by-step explanation:
The equation y = 39.1[tex]x[/tex] represents the number of miles, [tex]y[/tex], that madison can drive her car for every x gallons of gas.
Question: Madison can travel _ miles _ than Anthony on one gallon of gas.
Lets find how much Madison travels on 1 gallon of gas.
39.1(1) = 39.1
Therefore, Madison travels 39.1 miles on one gallon of gas.
Now lets solve for Anthony
Anthony travels 380.7 miles on 9 gallons of gas.
Therefore we can set up the equation:
9x = 380.7 to show that 9 gallons equates to 380.7 miles
to solve divide 9 from both sides
[tex]\frac{9x}{9} =\frac{380.7}{9}[/tex]
x = 41.3
So, Anthony travels 41.3 miles on one gallon of gas
Now find whether Madison travels more or less than Anthony on one gallon.
39.1 - 41.3 = -2.2
This means that Anthony can travel 2.2 miles more than Madison.
For your answer, this means that:
Madison can travel 2.2 miles less than Anthony on one gallon of gas
Hope this helped and have a nice day :)
If an event has a 55% chance of happening in one trial, how do I determine the chances of it happening more than once in 4 trials?
Answers
The chances of it happening more than once in 4 trials is 13%
How to determine the numberFrom the information given, we have can deduce that;
Probability of 1 trial = 55%
= 55/ 100
Find the ratio
= 0. 55
We are to find the probability of it happening more than once in 4 different trials
If the probability of it happening in one trial is 555 which equals 0. 55
Then the probability of it happening in 1 in 4 trials is given as;
P(1/4 trials) = 1/ 4 × 55%
P(1/4 trials) = 1/ 4 × 0. 55
Put in decimal form
P(1/4 trials) = 0. 25 × 0. 55
P(1/4 trials) = 0. 138
But we have to know the percentage
= 0. 138 × 100
Multiply the values, we have
= 13. 8 %
Thus, the chances of it happening more than once in 4 trials is 13%
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PLEASE HELP ASAPP PLEASE
Answers
Answer: Interior Angle
Step-by-step explanation:
The angle BAD is fully enclosed, it is on the inside
Select the correct answer. The graph of function f is shown. An exponential function passes through (minus 4, 9), (0, 1), (1, 0), and (5, minus 2). Function g is represented by the table. x -1 0 1 2 3 4 g(x) 24 6 0 -2 Which statement correctly compares the two functions? A. They have different end behavior as x approaches -∞ and different end behavior as x approaches ∞. B. They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞. C. They have the same end behavior as x approaches -∞ and the same end behavior as x approaches ∞. D. They have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.
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The answer choice which correctly draws a comparison between the end behaviours of the functions is; Choice C; They have the same end behavior as x approaches -∞ and same end behavior as x approaches ∞.
Which answer choice correctly compares the end behaviour of the functions?As given in the task content; the graph of the exponential function passes through (-4, 9), (0, 1), (1, 0), and (5, -2).
It therefore follows that as; x reduces (approaches -∞), the y value increases.
And, as x -increases (approaches +∞), the y-value decreases.
For the table, the values can be written as coordinates as follows; (-1,2), (0,4), (1,6), (2, 0), (3,-2).
Consequently, as x reduces (approaches -∞), the y- values decrease.
And, as x increases (approaches +∞), the y-values decrease.
Ultimately, the two functions in discuss can be concluded to have; Choice C.
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Talia noticed that she does not have a common factor. What should she do?
Talia needs to leave the polynomial as is because it is prime and cannot be factored.
Talia needs to factor out a 3x from the first group and a 4x from the second group.
Talia needs to factor out a negative from one of the groups so the binomials will be the same.
Talia needs to apply the distributive property to get the expression (3x + 4)(5x – 1).
Answers
The correct option regarding Talia factoring is given by:
Talia needs to factor out a negative from one of the groups so the binomials will be the same.
Which expression is Talia tying to factor?The expression is given by:
(15x² - 3x) + (-20x + 4).
Her first step was:
3x(5x - 1) + 4(-5x + 1)
After that, she did not factor out anything more out of the expression. However, looking at the two terms of the addition, we can realize that:
(-5x + 1) = -(5x - 1), hence she should factor out the negative.
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