Answers
The graph of the quadratic function is given below.
What are Quadratic Functions?Quadratic functions are polynomial functions consisting of variables and exponents and the degree of the variable is 2.
The general form of a quadratic function is f(x) = ax² + b x + c.
Given is a quadratic function.
y = 3x² + 1
We know that graph of a quadratic function is a parabola.
Since the leading coefficient is +3, positive. So the graph opens upward.
Vertex = (-b/2a, f(-b/2a))
-b/2a = -0/(2 × 3) = 0
f(-b/2a) = (3 × 0) + 1 = 1
(0, 1) is the vertex.
x = 1, then y = 3 + 1 = 4
x = -1, then y = 3 + 1 = 4
x = 2, then y = 12 + 1 = 13
x = -2, then y = 12 + 1 = 13
x = 3, then y = 27 + 1 = 28
x = -3, then y = 27 + 1 = 28
Some of the points are (-3, 28), (-2, 13), (-1, 4). (0, 1), (1, 4), (2, 13) and (3, 28).
Hence the graph through the given points is given below.
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Related Questions
Tarzan loaded 14 trucks every 35 minutes. At that rate how long in minutes will it take to load 8 trucks
Answers
Patrick and Brooklyn are making decisions about their bank accounts. Patrick wants to deposit $300 as a principal amount with an interest of 3% compounded quarterly Brooklyn
wants to deposit $300 as the principal amount, with an interest of 5% compounded monthly Explain which method results in more money after 2 years Show all work
Answers
Answer:
To compare the amount of money that Patrick and Brooklyn would have after 2 years, we need to calculate the interest earned using each of their methods.
For Patrick, who deposited $300 with an interest rate of 3% compounded quarterly, the formula to calculate the amount after 2 years (8 quarters) is:
A = P(1 + r/n)^(nt)
Where:
P = principal amount ($300)
r = interest rate (3%)
n = number of times compounded per year (4)
t = time in years (2)
Substituting the values into the formula:
A = $300(1 + 0.03/4)^(4 * 2)
A = $300(1.0075)^8
A = $300 * 1.06173
A = $318.52
For Brooklyn, who deposited $300 with an interest rate of 5% compounded monthly, the formula to calculate the amount after 2 years (24 months) is:
A = P(1 + r/n)^(nt)
Where:
P = principal amount ($300)
r = interest rate (5%)
n = number of times compounded per year (12)
t = time in years (2)
Substituting the values into the formula:
A = $300(1 + 0.05/12)^(12 * 2)
A = $300(1.00417)^24
A = $300 * 1.09722
A = $328.17
Therefore, after 2 years, Brooklyn would have $328.17, which is more money than Patrick's $318.52.
Which two sets of values make the inequality 3(n – 2) ≤ 2n – 3 true?
A. {−2, −1, 3}
B. {−2, −1, 4}
C. {−1, 0, 3}
D. {−1, 1, 4}
E. {1, 0, 5}
Answers
A. {−2, −1, 3}
For n = −2, 3(n – 2) = 3(-2 – 2) = −12 and 2n – 3 = 2(-2) – 3 = −7, so −12 ≤ −7 is false.
For n = −1, 3(n – 2) = 3(-1 – 2) = −9 and 2n – 3 = 2(-1) – 3 = −5, so −9 ≤ −5 is false.
For n = 3, 3(n – 2) = 3(3 – 2) = 3 and 2n – 3 = 2(3) – 3 = 3, so 3 ≤ 3 is true.
B. {−2, −1, 4}
For n = −2, 3(n – 2) = 3(-2 – 2) = −12 and 2n – 3 = 2(-2) – 3 = −7, so −12 ≤ −7 is false.
For n = −1, 3(n – 2) = 3(-1 – 2) = −9 and 2n – 3 = 2(-1) – 3 = −5, so −9 ≤ −5 is false.
For n = 4, 3(n – 2) = 3(4 – 2) = 6 and 2n – 3 = 2(4) – 3 = 5, so 6 ≤ 5 is false.
C. {−1, 0, 3}
For n = −1, 3(n – 2) = 3(-1 – 2) = −9 and 2n – 3 = 2(-1) – 3 = −5, so −9 ≤ −5 is false.
For n = 0, 3(n – 2) = 3(0 – 2) = −6 and 2n – 3 = 2(0) – 3 = −3, so −6 ≤ −3 is false.
For n = 3, 3(n – 2) = 3(3 – 2) = 3 and 2n – 3 = 2(3) – 3 = 3, so 3 ≤ 3 is true.
D. {−1, 1, 4}
For n = −1, 3(n – 2) = 3(-1 – 2) = −9 and 2n – 3 = 2(-1) – 3 = −5, so −9 ≤ −5 is false.
For n = 1, 3(n – 2) = 3(1 – 2) = −3 and 2n – 3 = 2(1) – 3 = −1, so −3 ≤ −1 is false.
For n = 4, 3(n – 2) = 3(4 – 2) = 6 and 2n – 3 = 2(4) – 3 = 5, so 6 ≤ 5 is false.
E. {1, 0, 5}
For n = 1, 3(n – 2) = 3(1 – 2) = −3 and 2n – 3 = 2(1) – 3 = −1, so −3 ≤ −1 is false.
For n = 0, 3(n – 2) = 3(0 – 2) = −6 and 2n – 3 = 2(0) – 3 = −3, so −6 ≤ −3 is false.
For n = 5, 3(n – 2) = 3(5 – 2) = 9 and 2n – 3 = 2(5) – 3 = 7, so 9 ≤ 7 is false.
So, only for n = 3, the inequality 3(n – 2) ≤ 2n – 3 is true. Hence, the only set of values that makes the inequality true is C. {−1, 0, 3}.
emma has 0.5 lb of sugar. How much water would she add to make the following concenstractions? Tell Emma how much syrup she would have each case. 50% syrup
Answers
To make the concentration of 50% syrup,
she needs to add 0.5 lb of sugar.
What is a percentage?A percentage is a ratio or number that may be expressed as a fraction of 100. Moreover, it is denoted by the sign "%."
Given:
Emma has half a pound of sugar.
To make the concentration of 50% syrup:
Let n be the required amount.
In decimals, 50% is 0.5.
Applying the percentage formula;
we get,
[tex]\frac{0.5}{n + 0.5} \cdot 100 = 50[/tex]
Applying cross multiplication,
we get,
[tex]\frac{0.5}{n + 0.5} = 0.5[/tex]
0.5 = 0.5(n + 0.5)
1 = n + 0.5
n = 1 - 0.5
n = 0.5 lb.
Therefore, she would have 0.5 + 0.5 = 1 pound of sugar.
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Find side RT
10 m
13m
14 m
16 m
Answers
The side RT of the triangle is 13 m.
How to find the side RT of the triangle?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
The sine law is a mathematical formula used in trigonometry to relate the sides and angles of a triangle. The sine law states that:
a/sin(A) = b/sin(B) = c/sin(C)
where:
a, b, and c are the lengths of the sides of the triangle
A, B, and C are the angles opposite those sides
Using sine law:
RT/sin 34° = ST/sin 109°
RT/sin 34° = 22/sin 109°
RT = (22 * sin 34°)/(sin 109°)
RT = 13 m
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Find the number of solutions for the given equation for 0° ≤ θ ≤ 360°.
sin2x - 2sinx - 3 = 0
1
2
3
4
0
Answers
The number of solutions to the trigonometric equation is; 1 solution which is x = 270°
How to find the trigonometric solution?The trigonometric equation is given as;
sin²x - 2sin x - 3 = 0
Now, factorizing this gives us;
(sin x - 3)(sin x + 1) = 0
Thus, we now have;
sin x - 3 = 0
sin x = 3
At this point, x has no real solution
For the second factor, we have;
sin x + 1 = 0
sin x = -1
x = sin⁻¹ -1
x = 270°
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3. Find the volume of a cone with radius 6 m and height 20 m
Answers
Answer: 753.98m³
Formula:V=πr2h3=π·62·203≈753.98224m³
Solve for x with the given measures
Answers
Triangle adb, point c lies on segment ab and forms segment cd, angle acd measures 90 degrees. Point a is labeled jungle gym and point b is labeled monkey bars. Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. If beth places the swings at point d, how could she prove that point d is equidistant from the jungle gym and monkey bars?.
Answers
To prove that point d is equidistant from the jungle gym and monkey bars, we need to show that the distances from d to both points are equal.
Let's call the distance from d to the jungle gym "x" and the distance from d to the monkey bars "y". We need to show that x = y.
Since angle acd is a right angle, we can use the Pythagorean theorem to relate the distances:
ad^2 + cd^2 = ac^2
We know that ad = bd (since the jungle gym and monkey bars are the same distance from d), so we can write:
bd^2 + cd^2 = ac^2
We also know that c lies on ab, so we can write:
ac = ab - bc
Substituting this into our equation, we get:
bd^2 + cd^2 = ab^2 - 2abbc + bc^2
Since d is on cd, we can write cd = y, and since c is on ab, we can write ab = x + y. Substituting these into our equation, we get:
bd^2 + y^2 = (x + y)^2 - 2xy + x^2
Simplifying, we get:
bd^2 - x^2 = 2xy - y^2
Now, if we can show that bd = x, then we will have proven that y = x and therefore that point d is equidistant from the jungle gym and monkey bars.
To do this, we can use the fact that triangle adb is isosceles (since ad = bd). This means that angle adb is equal to angle bad. We also know that angle acd is a right angle. Therefore, angle adb + angle acd = 90 degrees.
Since angle adb = angle bad, we can write:
2 angle adb + angle acd = 180 degrees
Substituting in the values of our angles, we get:
2 angle adb + 90 degrees = 180 degrees
Solving for angle adb, we get:
angle adb = 45 degrees
Now, we can use the fact that triangle adb is isosceles to write:
angle bad = (180 - 45)/2 = 67.5 degrees
Finally, we can use the law of sines to relate bd and x:
bd/sin(67.5) = x/sin(45)
Simplifying, we get:
bd = x
Therefore, we have shown that point d is equidistant from the jungle gym and monkey bars.
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PLS HELP
Matt released his new game app, Serpent of the Sphinx, and it received 548 downloads the first week. He expects the number of weekly downloads to increase by about 4% each week. You can use a function to approximate the number of weekly downloads x weeks after the release date.
Write an equation for the function. If it is linear, write it in the form h(x)=mx+b. If it is exponential, write it in the form h(x)=a(b)x.
Answers
The number of weekly downloads can be modeled using an exponential function h(x) = 548 × 1.04ˣ.
What is exponential function?
An exponential function is a mathematical function in which the value of the output is proportional to the value of a fixed number (known as the base) raised to the power of the input value. The general form of an exponential function is:
y = abˣ
where a and b are constants, x is the input value, and y is the output value. The constant a controls the vertical scaling of the function, while the constant b controls the rate of growth or decay. If b is greater than 1, the function grows rapidly as x increases. If 0 < b < 1, the function decays as x increases. If b is equal to 1, the function is a linear function.
Exponential functions are widely used in many fields, including finance, biology, physics, and engineering, to model growth and decay processes.
The number of weekly downloads can be modeled using an exponential function.
h(x) = 548 * 1.04ˣ
where x is the number of weeks after the release date, h(x) is the estimated number of weekly downloads, and 1.04 is the growth factor (1 + the expected weekly increase of 4%).
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what decimal is equivalent to 29 11
Answers
Answer:
2.64
Step-by-step explanation:
Find the slope of a line parallel to 25x-5y=-10
.
Answers
The slope of a line parallel to another line will have the same slope as the original line. To find the slope of the line 25x - 5y = -10, we need to rearrange the equation into the slope-intercept form y = mx + b, where m is the slope.
First, we'll isolate y:
25x - 5y = -10
5y = 25x + 10
y = (25/5)x + 2
So the slope of the line 25x - 5y = -10 is m = 25/5 = 5.
Therefore, a line parallel to 25x - 5y = -10 will have a slope of m = 5.
decimal of 3\4 and percent
Answers
Equivalence means to be same, whether it be value, temperature, size, etc.
First, let's convert [tex]\frac{3}{4}[/tex] into a different fraction.
[tex]\frac{3}{4}[/tex] = [tex]\frac{75}{100}[/tex]We know this because each side of the fraction [tex]\frac{3}{4}[/tex] can be multiplied by 25 to get [tex]\frac{75}{100}[/tex].
3 × 25 = 754 × 25 = 100Now that we know this, we can convert the fraction [tex]\frac{75}{100}[/tex] into a percentage.
What is a percentage?A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.
if we know that percentages are expressed as a fraction of 100, we know that [tex]\frac{75}{100}[/tex] is equal to %75.
To convert percentages into decimals, we can just take the percentage (%75) and fit it into 0.00, making it 0.75.
Therefore, the fraction [tex]\frac{3}{4}[/tex] as a percentage is %75, and as a decimal it is 0.75.
A school newspaper reporter decides to randomly survey 13 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 23% of students attend Tet festivities. We are interested in the number of students who will attend the festivities. Part (a) Part (b) List the values that X may take on. O X =0, 1, 2..... 23 x = 1, 2, 3....23 x = 1, 2, 3....13 OX0.1.2..... 13 OO Part (c) Give the distribution of X. X-OX (0:0) Part (d) How many of the 13 students do we expect to attend the festivities? (Round your answer to the nearest whole number.) student(s) O Part (e) Find the probability that at most 3 students will attend. (Round your answer to four decimal places.) Part (0) Find the probability that more than 2 students will attend. (Round your answer to four decimal places.)
Answers
The probability that more than 2 students will attend is 0.9179.
Part (a) List the values that X may take on.
X may take on the values 0, 1, 2, 3, ..., 13.
Part (b) Give the distribution of X.
The distribution of X can be represented as follows: X-0:0, 1:0.23, 2:0.23, 3:0.23, 4:0.23, 5:0.23, 6:0.23, 7:0.23, 8:0.23, 9:0.23, 10:0.23, 11:0.23, 12:0.23, 13:0.23
Part (c) How many of the 13 students do we expect to attend the festivities? (Round your answer to the nearest whole number.)
We can expect 3 students to attend the festivities.
Part (d) Find the probability that at most 3 students will attend. (Round your answer to four decimal places.)
The probability that at most 3 students will attend is 0.6923.
Part (e) Find the probability that more than 2 students will attend. (Round your answer to four decimal places.)
The probability that more than 2 students will attend is 0.9179.
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Miguel was selling apples, plums, and peaches at the local farmer’s marker. He sold 18 more
pounds of apples than pounds of plums. He sold 9 pounds less of peaches than pounds of
plums. He sold a total of 69 pounds of fruit. How many pounds of each fruit did he sell?
Answers
Answer:
He sold 32 pounds of apples, 14 pounds of plums and 23 pounds of peaches.
Step-by-step explanation:
Let:
x = Mass of Apples (pounds)
y = Mass of plums (pounds)
z = Mass of peaches (pounds)
He sold 18 more pounds of apple than pounds of plums: [tex]x = 18 + y[/tex]
He sold 9 less pounds of peaches than pounds of plums: [tex]z - 9 = y[/tex]
He sold a total of 69 pounds of fruit: [tex]x + y + z = 69[/tex]
We have 3 unknown variables, therefore a system of 3 linear simultaneous equations:
[tex]x = 18 + y[/tex] ——- (equation i)
[tex]z - 9 = y[/tex]
∴ [tex]z = 9 + y[/tex] ——— (equation ii)
[tex]x + y + z = 69[/tex] ——- (equation iii)
The above linear simultaneous equations can be solved by Substitution Method:
Substitute (equation i) and (equation ii) into (equation iii) to solve for y. Expand the parenthesis and bring all the like terms together. y has to be made the subject of the equation:
[tex](18 + y) + y + (y + 9) = 69[/tex]
= [tex]18 + y + y + y + 9 = 69[/tex]
= [tex]y + y + y = 69 - 18 - 9[/tex]
= [tex]3y = 42[/tex]
= [tex]y = \frac{42}{3}[/tex]
∴ y = Mass of plums = 14 pounds
Substitute the calculated value of y into the other two equations to solve for x and for z:
[tex]x = 18 + (14)[/tex]
∴ x = Mass of apples = 32 pounds
[tex]z = 9 + (14)[/tex]
∴z = Mass of peaches = 23 pounds
Convert the complex number 2√2(cos 135° + i sin 135°) into rectangular
(standard) form. Express your answer in simplest radical form.
Answers
The solution to the complex number in rectangular form is; -2 + 2i
How to express complex number in rectangular form?The complex number is given as;
2√2(cos 135° + i sin 135°)
The standard form is a + bi.
The value of cos 135° is; -(√2)/2
The value of sin 135° is; (√2)/2
Plugging these values into the given equation is;
2√2(-(√2)/2 + ((√2)/2)i)
Expanding the bracket gives;
-2 + 2i
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What might the composer do to write a piece with a carefree and ecstatic mood?
A. A lively accompaniment
B. Dissonant chords
C. A slow tempo
D. A minor key
Answers
Answer:
A. A lively accompaniment
Step-by-step explanation:
B. Dissonant - would most likely result in a eerie mood
C. A slow tempo - could result in melancholy or calm emotions
D. A minor key - could also result in melancholy emotions
If sec 0 = √2, find 0 and identify all angles 0° < 0 < 360° that are co-terminal with the
given angle.
Answers
In the trigonometry relation the value of θ is 45 degrees and the coterminal angle between 0° < θ < 360° is 315 degrees
How to find conterminal of the angleCoterminal angles are angles that have the same terminal side in a given circle. They are angles that differ by a multiple of 360 degrees.
In other words, if two angles are coterminal, they have the same trigonometric functions, despite having different degrees.
If sec θ = √2
θ = arc sec (√2)
θ = arc cos (1/√2))
θ = 45 degrees
coterminal of angle 45 degrees between 0° < θ < 360°
360 - 45 = 315.
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I need help solving part b)
Answers
The answers to the questions are:
a) P(A|B) = 1/3
b) P(B|A) = 1.15
c) A. A student given a $1 bill is more likely to have kept the money.
What is the probability?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Because the probability of 0.659 is almost two times greater than 0.341
Assuming the following table:
Purchased Gum Kept the Money Total
Students Given 4 Quarters 25 19 44
Students Given $1 Bill 13 26 39
Total 38 45 83
a. find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill.
For this case let's define the following events
B= "student was given $1 Bill"
A="The student spent the money"
For this case we want this conditional probability:
P(A|B) = P(A And B) / P(B)
We have that
P(A) = 38/83, P(B) = 39/83
P(A And B) = 13/83
And if we replace we got:
P(A|B) = (13/83)/(45/83) = 13/39 = 1/3
b. find the probability of randomly selecting a student who kept the money, given that the student was given a $1 bill.
For this case let's define the following events
B= "student was given a $1 Bill"
A="The student kept the money"
P(A|B) = P(A And B) / P(B)
We have that
P(A) = 45/83, P(B) = 39/83
P(A And B) = 26/83
And if we replace we got:
P(B|A) = (45/83)/(39/83) = 45/39 = 1.15
c. what do the preceding results suggest?
For this case the best solution is:
A. A student given a $1 bill is more likely to have kept the money.
Because the probability of 0.659 is almost two times greater than 0.341
Hence, The answers to the questions are:
a) P(A|B) = 1/3
b) P(B|A) = 1.15
c) A. A student given a $1 bill is more likely to have kept the money.
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Find the sample variance and standard deviation.
23, 16, 5, 7, 11 q
OA. s² =
2
S
OB. 0²=
Answers
The sample variance and the standard deviation are 52.8 and 7.26
How to determine the sample variance and standard deviationFrom the question, we have the following parameters that can be used in our computation:
23, 16, 5, 7, 11
Calculate the mean
Mean = (23 + 16 + 5 + 7 + 11)/5
Mean = 12.4
The standard deviation is
SD = √[Sum of (1 - Mean)²]/[N - 1]
So, we have
SD = √[(23 - 12.4)² + (16 - 12.4)² + (5 - 12.4)² + (7 - 12.4)² + (11 - 12.4)²]/[5 - 1]
This gives
SD = √211.2/4
So, we have
SD = √52.8
SD = 7.26
Hence, the standard deviation is 7.26
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The vet says that raise puppy will grow to be at most 28 inches tall raise. Puppy is currently 1 foot tall how much more will the puppy grow?
Write an inequality to solve the problem
Answers
Answer:
16 inches
Step-by-step explanation:
28 - 12 = 16 inches
1 foot = 12 inches
The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
Answers
Box plot, because the median can easily be determined from the large set of data.
What exactly is a median?
The median is defined as the value in the centre of a given set of numbers or statistics. There are three main measures in mathematics that are used to calculate the average value for a given group of integers. They are the mean, the median, and the mode. These three indicators are known as central tendency measures. Mean computes the average value of the provided data. A median defines the midway value of the provided data. Mode defines the repeating value of the input data.
Now,
As, A box plot is a very visual means of displaying a concise overview of one or more sets of data. It is especially handy for quickly summarising and comparing several sets of findings from various trials. A box plot, at a glance, gives a graphical representation of the distribution of findings as well as indicators of symmetry within the data.
and it can handle a large set of data.
Hence,
Box plot, because the median can easily be determined from the large set of data.
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Answer:box plots
Step-by-step explanation:
i did it
10p - 3p/4- 2 +5 when p= 10
Answers
The value of 10p - 3p/4- 2 +5 for p=10 is 95.5.
What is Solution of Equation?An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.
Given:
We have 10p - 3p/4- 2 +5.
Now put the value of p =10 we get
= 10p - 3p/4- 2 +5
= 10(10) - 3(10)/4- 2 +5
= 100 - 30/4 -2 + 5
= 100 -7.5 -2 +5
= 95.5
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Isaac made all these rectangles with 24cm lengths of string. This implies that the perimeter of all these rectangles are equal. What do you observe about the sun of the length and the width, give a reason for your answer?
Answers
Answer: Since the perimeter of all the rectangles is equal (24 cm), the sum of the length and width of each rectangle must be equal for each rectangle. This is because the perimeter of a rectangle is equal to the sum of its lengths plus the sum of its widths, multiplied by 2.
For example, if the length of one rectangle is "l" cm and its width is "w" cm, then its perimeter would be 2l + 2w = 24 cm.
So, in general, we can write the equation: l + w = P/2, where P is the perimeter of the rectangle (in this case, P = 24 cm).
Therefore, the sum of the length and width of each rectangle is equal and constant, regardless of the individual values of the length and width. This means that as the length of a rectangle increases, its width must decrease by an equal amount to keep the sum constant. And vice versa.
In conclusion, the sum of the length and width of each rectangle is equal, and it is equal to half of the perimeter of the rectangle.
Step-by-step explanation:
Figure ABCD is a kite.
Find the value of x.
A
X =
= [?]
14x - 22
H
B
C
Answers
The value of x is equal to 8, in the equation 14x -22.
What is equation?An equation is a mathematical statement consisting of two expressions joined by an equal sign.
Solution:
The diagonals of the dragon intersect at right angles. This gives a solvable relationship for x.
setting the displayed dimensions correspond to 90° angular dimensions.
14x -22 = 90
You can solve this two-level linear equation in the usual way.
14x = 112. . . . . . Step 1, add the reciprocal of the constant to get just x
x = 112/14 = 8 . . . Step 2, divide by the factor of x
Hence, the value of x is 8.
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Graph the following points on the coordinate plane. Find the measure of ∠ACB
to the nearest tenth.
A (-3, 2), B (0, 0), C (2, 3)
Answers
The measure of angle ∠ACB is 45 degrees
How to find the measure of ∠ACBFrom the question, we have the following parameters that can be used in our computation:
A (-3, 2), B (0, 0), C (2, 3)
The graph is attached
The lines AB and BC are perpendicular lines
This means that
∠B = 90 degrees
Calculate the length AB and BC using
distance = √[(x2 - x1)² + (y2 - y1)²]
So, we have
AB = √[(-3 - 0)² + (2 - 0)²] = √13
BC = √[(0 - 2)² + (0 - 3)²] = √13
The angle C is then calculated as
tan(C) = AB/BC
tan(C) = √13/√13
tan(C) = 1
Take the arctan of both sides
C = 45
Hence, the measure of ∠ACB is 45 degrees
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How many cups will you get if you mix 2 gallons, 4 quarts, and 1 pint?
You will get
cups.
Answers
Answer: 50 Cups
Step-by-step explanation:
16 cups in a gallon. so times that by 2, which equals 32. There are four cups in one quart so times 4 by 4 which is 16 and add to 32. 16 + 32 = 48
Two cups in a pint so add 2 to 48 which is 50
Answer:
You will get 25 cups if you mix 2 gallons, 4 quarts, and 1 pint.
Step-by-step explanation:
To convert between gallons, quarts, and pints, we need to use the following conversions:
1 gallon = 4 quarts
1 quart = 2 pints
Here's the step-by-step process to convert the given volume to cups:
Convert gallons to quarts: 2 gallons * 4 quarts/gallon = 8 quarts
Add the number of quarts from step 1 to the number of quarts given: 8 quarts + 4 quarts = 12 quarts
Convert pints to quarts: 1 pint * 1 quart/2 pints = 0.5 quarts
Add the number of quarts from step 3 to the number of quarts from step 2: 12 quarts + 0.5 quarts = 12.5 quarts
Convert quarts to cups: 12.5 quarts * 2 cups/quart = 25 cups
Therefore, you will get 25 cups if you mix 2 gallons, 4 quarts, and 1 pint.
If X and Y are independent and identically distributed uniform random variables on (0, 1), compute the joint density of
(a) U = X + Y, V = X/Y
(b) U = X, V = X/Y
(c) U = X + Y, V = X/(X+Y)
Answers
If X and Y are independent and identically distributed uniform random variables on (0, 1), then the joint density of
(a) U = X + Y, V = X/Y is u/v² for v > 1 and 0 ≤ u ≤ 1.
(b) U = X, V = X/Y is 1/v for v > 1 and 0 ≤ u ≤ 1.
(c) U = X + Y, V = X/(X+Y) is v/(1+v)² for v > 0 and v/(1+v) ≤ u ≤ 1.
In probability theory, joint density is a mathematical function that describes the probability distribution of two or more random variables. It represents the probability of occurrence of different values of those variables in a particular region of space. In this problem, we have to calculate the joint density of U and V, where U and V are functions of X and Y.
(a) For U = X + Y and V = X/Y, we can find the joint density as follows:
First, we need to find the distribution of U and V separately. Since X and Y are independent and identically distributed uniform random variables on (0, 1), their individual probability density functions are f(x) = 1 for 0 ≤ x ≤ 1.
To find the density of U, we can use the convolution formula, which states that the density of the sum of two independent random variables is the convolution of their individual densities. Thus,
fU(u) = ∫ fX(u - y)fY(y) dy
= ∫ 1 dy
= u for 0 ≤ u ≤ 1.
Next, to find the density of V, we need to transform X and Y using the change of variables formula. Let Z = X/Y, then
fV(v) = fZ(z)|dz/dv|
= fX(vz)/(z²) |z|
= 1/(v²) for v > 1.
Therefore, the joint density of U and V is given by the product of their individual densities:
fUV(u,v) = fU(u) fV(v)
= u/v² for v > 1 and 0 ≤ u ≤ 1.
(b) For U = X and V = X/Y, we can similarly find the joint density as:
fUV(u,v) = fX(u) fV(v)
= 1/v for v > 1 and 0 ≤ u ≤ 1.
(c) For U = X + Y and V = X/(X+Y), we can use the same method as in (a) to find the individual densities of U and V:
fU(u) = u for 0 ≤ u ≤ 1,
fV(v) = v/(1+v)² for v > 0.
Then, the joint density of U and V is given by:
fUV(u,v) = fU(u) fV(v) |du/dx|
= v/(1+v)² for v > 0 and v/(1+v) ≤ u ≤ 1.
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A sign in the shape of a circle has a radius of 15 cm. What is the area of the sign? Use 3.14 for pi.
Answers
Answer:
The area of the sign is 706.5 cm^2.
Step-by-step explanation:
We know,
The formula of area of a circle,
A = πr^26
Here A is area and r is radius.
Here we have radius is 15 cm, so we can put the values in the above equation and find the area,
A = π * 15^2
A = 3.14 * 225
A = 706.5
The area of the sign is 706.5 cm^2.
is 5.2481 a ratinal number
Answers
Answer:
Step-by-step explanation:
Rational numbers are numbers that can be written in the form pq, where p and q are integers and q≠0. The difference between rational numbers and fractions lies in the fact that fractions cannot have negative numerator or denominator.
so, yes.
