Answer:
Step-by-step explanation:
A∪B = {1,2,3,4,5}
B∩C = {4}
I don't know what CD means.
A' = {5,6,7,8,9}
Find the zeros of the function. Enter the solutions from least to greatest. f(x) = (x - 2)(3x + 3)
The zeros of the given function are x = 2 and x = -1
Zeros of a functionFrom the question, we are to determine the zeros of the given function
The given function is
f(x) = (x - 2)(3x + 3)
To determine the zeros of a function, we will set the function equal to zero
That is,
(x - 2)(3x + 3) = 0
Then,
x - 2 = 0 OR 3x + 3 = 0
x = 2 OR 3x = -3
x = 2 OR x = -3/3
x = 2 OR x = -1
Hence, the zeros of the given function are x = 2 and x = -1
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Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwise indicated. Integrate c ln(x+y)dx-x^2 dy where C is the rectangle with vertices (1,1), (3,1), (1,4), and (3,4).
Using Green's Theorem to evaluate the given line integral with the given conditions and vertices gives us; -30
How to evaluate an Integral with Green's Theorem?
The line integral of a vector-valued function along the edges of a rectangle or any other closed curve can be found by converting the line integral into a double integral. We apply Green's theorem to do this. The resulting double integral is integrated over the two-dimensional region bounded by the same closed curve.
Green's Theorem can be applied as follows:
∮_c (P.dx + Q.dy) = ∫∫_R ((dQ/dx) - (dP/dy))dA
The vertices of the rectangle (1,1), (3,1), (1,4), and (3,4).
Applying Green's Theorem to the given function gives;
∮_c (ln x + y) dx - x² dy
= ∫14∫13 Dx(-x2) -Dy(ln(x) +y) dx dy
= ∫₁⁴∫₁³ (-2x - 1) dx dy
= -3·[x² +x]₁³
= -30
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What is the range of the function graphed below? A bidirectional arrow rises steeply through (negative 2, negative 8), (negative 1 point 5, negative 4), (negative 1, 0), (0, 2) and extends linearly through (2, 2), (3, 2), (4, 2), (5, 2), (6, 2) and (8, 2) on the x y coordinate plane. A. B. C. D.
Answer:
A. -∞ < y < 2
Step-by-step explanation:
The range is the vertical extent of the graph.
Lower limitThe arrow pointing down tells you the graph extends toward -∞.
Upper limitThe arrow pointing right suggests that y=2 is a horizontal asymptote. A graph will approach, but never cross, an asymptote. Thus, we can conclude y < 2.
RangeThe range is the set of values that lie between the limits:
-∞ < y < 2
Choose the two answers that are solutions to the equation. (X+7)^2=121
A. x=4
B. x=-18
C. x=18
D. x=-4
Answer: A. x = 4
Step-by-step explanation:
Substituting 4 for x..
(4+7)^2 = 121
(11)^2 = 121
11 * 11 = 121
Need help with this one
Answer: [tex]\frac{9g}{4y}[/tex]
Step-by-step explanation:
[tex]\frac{6g}{2} \times \frac{3}{4y}=\frac{18g}{8y}=\frac{9g}{4y}[/tex]
[tex] \sqrt{7} [/tex]
multiplicative inverse (reciprocal)
Answer: [tex]\frac{\sqrt{7}}{7}[/tex]
========================================================
Explanation:
The reciprocal of x is 1/x where x is nonzero. Multiplying x with 1/x leads to 1. For example, the numbers 9 and 1/9 are multiplicative inverses of each other.
We'll stick 1 over the given square root expression. Then follow these steps to rationalize the denominator.
[tex]\frac{1}{\sqrt{7}}\\\\\\\frac{1*\sqrt{7}}{\sqrt{7}*\sqrt{7}}\\\\\\\frac{\sqrt{7}}{(\sqrt{7})^2}\\\\\\\frac{\sqrt{7}}{7}\\\\[/tex]
In short, [tex]\frac{1}{\sqrt{7}}=\frac{\sqrt{7}}{7}[/tex]
Evaluate ( 75 − 3/17 + 1 ) 2
Answer:
2=1289/17
Step-by-step explanation:
use the given functions to set up and simplify 2
find RY if RV=8 and VW=12
Johnny is starting a zoo. His favorite animals are lions, tigers and snakes. These are the only animals in the zoo and he has them in the ratio of 5 : 3 : 2. If he has a total of 50 animals in the zoo, how many snakes does he have?
*
The total number of snakes in the zoo is 10.
How to use ratio to find the number of snake?The number of snake can be found using ratio as follows:
The animals in the zoo are lions, tigers and snakes and he has them in the ratio of 5 : 3 : 2. The total animal is 50 animals.
Therefore,
total snakes = 2 / 10 × 50
total snakes = 100 / 10
total snakes = 10
Therefore, the total number of snakes in the zoo is 10.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
1.The center of the circle lies on the x-axis
2.The radius of the circle is 3 units.
3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
1. Is the average change in population is the same now as it was 50 years ago? Explain your answer.
HURRY PLEASE NEED IT URGENTLY!!!!!!!!!!!!
No, the average change in population is not the same as it was 50 years ago.
Reason in Support of the Answer:
In many important ways, the demographic future of the United States and the rest of the world is substantially different from the recent past. The world's average population approximately tripled between 1950 and 2010, and the U.S. population nearly doubled.
However, it is anticipated that between 2010 and 2050, both globally and in the United States, average population growth will be substantially slower and will disproportionately favor the oldest age groups. Hence it is seen that the average change in population is never constant. It depends on the demographic trends and conditions, whether the average change in population will be larger or comparatively trivial in the future. And, similarly, it can be said that the average change in population is not the same as it was 50 years ago.
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What is the product?
Sr-203r-40
O 157-8
0157-8
O 15/+14-8
0152²-140-8
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are:
Suppose now that your portfolio must yield an expected return of 12% and be efficient, that is, on the best feasible CAL.
This problem is about pension fund management. It is to be noted that the best Feasible Capital Allocation Line (CAL) is: 0.3162.
What is Capital Allocation Line (CAL)?
A graph's capital allocation line depicts all conceivable combinations of risky and risk-free assets, allowing investors to estimate future returns depending on risk.
What is the calculation for the above solution?
It is to be noted that the optimal risky portfolio's stock percentage is determined by:
Weight of Stock = ((Return on Stock - Risk Free Rate) * Variance of bond) - ((Return on Bond - Risk Free Rate) * Co-Variance of bond & Stock)/ ((Return on Stock - Risk Free Rate) * Variance of bond + (Return on Bond - Risk Free Rate) * Variance of Stock - ((Return on Bond - Risk Free Rate + Return on Stock - Risk Free Rate + ) * Co-Variance of bond & Stock)
→ The weight of stock
= ((15% - 5.5%) * 529) - ((9% - 5.5%) * 110.40)/ ((15% - 5.5%) * 529) + (9% - 5.5%) * 1,024 - ((15% - 5.5% + 9% - 5.5%) * 110.40)
= [(50.255) * (3.864) /(50.255) + (46.08) - (14.352)]
Weight of Stock = 0.646628
Weight of Bonds = 1 - 0.646628
Weight of Bonds= 0.353372
Expected return of portfolio = 0.646628 * 15% + 0.353372 * 9%
= 12.88%
Standard Deviation of Portfolio (SDP)= (0.6466282² * 1,024 + 0.3533722² * 529 + 2 * 0.646628* 0.353372* 110.40)⁰·⁵
SDP = (544.67)⁰·⁵
SDP = 23.34%
Hence,
Best feasible CAL = (12.88% - 5.5%)/ 23.34%
Best feasible CAL = 0.3162
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Full Question
See the attached spread sheet for additional information related to the questions.
Select the correct answer. In right triangle ABC, b^2+c^2=34 and bc=15. What is the approximate length of side a? Note: Use the law of cosines.
(the triangle is a right triangle with an angle of 53)
Using the law of cosines, it is found that the approximate length of side a is 3.99 units.
What is the law of cosines?The law of cosines states that we can find the side c of a triangle as follows:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
in which:
C is the angle opposite to side c.a and b are the lengths of the other sides.In the context of this problem, we have that side a is opposite to the angle of 53º, hence:
[tex]a^2 = b^2 + c^2 - 2bc\cos{53^\circ}[/tex]
We are given that:
b² + c² = 34.bc = 15.Then:
[tex]a^2 = 34 - 30\cos{53^\circ}[/tex]
a² = 15.95
[tex]a = \sqrt{15.95}[/tex]
a = 3.99.
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Suppose that, for a certain mathematics class, the scores are normally distributed with a mean of 75 and a standard deviation of 9. The teacher wishes to give A's to the top 7% of the students and F's to the bottom 7%. The next 17% in either direction will be given B's and D's, with the other students receiving C's. Find the bottom cutoff for receiving an A grade. (You may need to use the standard normal distribution table. Round your answer to the nearest whole number.)
The bottom cutoff for receiving an A grade is 88.
What is the bottom cutoff for receiving an A grade?The bottom cutoff for receiving an A grade is found as follows:
The mean of the distribution = 75
The standard deviation = 9
The z-score for the 93% = 1.476
The score for an A grade, x = mean + z-score * standard deviation
Score for an A grade, x = 75 + 1.476 * 9
Score for an A grade, x = 88
In conclusion, the minimum score for an A grade is obtained from the mean, the z-score and the standard deviation.
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Q, Fixed a system of coordinates in the plane, conficer the curve C having equation y = (x-2)^2. The line x + y - 2 = 0 intersects C in:
(A)1 poin
(B) no point
(C) 2 points
(D) infinitely many points
3 points
Answer:
C
Step-by-step explanation:
y = (x - 2)² = x² - 4x + 4 → (1)
x + y - 2 = 0 → (2)
substitute y = x² - 4x + 4 into (2)
x + x² - 4x + 4 - 2 = 0
x² - 3x + 2 = 0
(x - 1)(x - 2) = 0
equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 2 = 0 ⇒ x = 2
substitute these values into (2) and solve for y
x = 1 : 1 + y - 2 = 0 ⇒ y - 1 = 0 ⇒ y = 1 ⇒ (1, 1 )
x = 2 : 2 + y - 2 = 0 ⇒ y + 0 = 0 ⇒ y = 0 ⇒ (2, 0 )
the line intersects curve C at 2 points (1, 1 ) and (2, 0 )
Solve for x. Round your answer to the nearest tenth if necessary. Figures are
not necessarily drawn to scale.
T
63°
72°
18
19
45
630
37
72°
W
45°
X
X
Answer:
18/19= X/37 because 18 and x are both between 72 and 45 degrees
Multiply 18 and 37 then divide by 19 to get answer
Step-by-step explanation:
Find cos B, sinB,tanb
Using right triangle relations, we will get:
tan(B) = 1.05sin(B) = 0.735cos(B) = 0.7How to find the value of the trigonometric equations?
We assume that bot triangles are equivalent, then the angle B will be the same as the angle Z.
Now remember the relations:
tan(θ) = (opposite cathetus)/(adjacent cathetus).sin(θ) = (opposite cathetus)/(hypotenuse)cos(θ) = (adjacent cathetus)/(hypotenuse).If we step on angle B, we have:
opposite cathetus = 29.4adjacent cathetus = 28hypotenuse = 40.6Replacing that, we get:
tan(B) = 29.4/28 = 1.05sin(B) = 29.4/40.6 = 0.735cos(B) = 28/40.6 = 0.7If you want to learn more about trigonometric functions:
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Solve the following equation for y to find the slope and the y-intercept: 2y - x = 6
Step-by-step explanation:
2y - x = 6
2y = x + 6
y = (x + 6) / 2
the slope is 1 and the y int is 3
The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Complete parts (a) through (d) below.
a. Find the probability of getting exactly 6 girls in 8 births.
b. Find the probability of getting 6 or more girls in 8 births.
c. Which probability is relevant for determining whether 6 is a significantly high number of girls in 8 births: the result from part (a) or part (b)?
d. Is 6 a significantly high number of girls in 8 births? Why or why not? Use 0.05 as the threshold for a significant event.
Number of Girls x P(x)
0 0.002
1 0.016
2 0.109
3 0.199
4 0.348
5 0.199
6 0.109
7 0.016
8 0.002
The answers to the questions are
0.1090.127b is a relevant factor6 is not highHow to solve for the probabilitya. From the table the probability of having 6 girls in 8 birth is given as
0.109.
b. The probability of 6 or more girls in 8 births
p(6) + p(7) + p(8)
= 0.109 + 0.016 + 0.002
= 0.127
c. The result from b is the relevant factor given that it includes the probability of getting 6, 7 and 8 girls.
D. No six is not a significantly high number of girls in 8 births. This conclusion is from the fact that 0.109 is greater than 0.05.
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What is S10 of the geometric sequence? Round to the nearest whole number.
8, 20, 50, 125, …
15,263
50,857
317,886
The sum of the ten terms to the nearest whole number is 50857.
How to find the sum of a geometric sequence?Using geometric sequence formula,
nth term = arⁿ⁻¹
where
a = first termr = common ration = number of termsr = 20 / 8 = 5 / 2
a = 8
Hence,
s₁₀ = a(rⁿ - 1) / r - 1
s₁₀ = 8((5 / 2)¹⁰ - 1) / 5 / 2 - 1
s₁₀ = 8(9535.74316406) / 1.5
s₁₀ = 50857.296875
s₁₀ = 50857
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Using the slope and the y-intercept, graph the line represented by the following equation. Then select the correct graph. x - y - 3 = 0
The graph that represents the given line with slope and y-intercept is as attached below.
How to interpret Linear Graphs?
We are given the equation;
x - y - 3 = 0
Now, the standard way we should put the equation would be in slope intercept form which is; y = mx + c
where;
m is slope
c is y-intercept
Thus, our equation can be rearranged to get;
y = x - 3
Thus, y-intercept is c = -3
The graph that represents the given line is as attached below.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the expressions with their resultant terms in exponential form.
137
1319
131
13-22
13-14
1315
13-7
Resultant Terms in Exponential Form
Expressions
13-11 × 1316 × 13-3 × 134 × 13-5
arrowBoth
13-21 × 13-4 × 13-5 × 1314 × 13-6
arrowBoth
1333 × 13-2 × 135 × 13-13 × 13-8
arrowBoth
130 × 1310 × 13-12 × 135 × 134
arrowBoth
The correct matching of the exponential form is given.
How to illustrate the information?1: 13^-11 × 13^16 × 13^-3 × 13^-4 × 13^-5
= 13
2. 13^-21 × 13^-4 × 13^-5 × 13^14 × 13^-6
= 13^-22
3. 13^0 × 13^10 × 13^-12 × 13^5 × 13^4
= 13^7
This illustrates the exponential form.
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Which inequality can be used to explain why these three segments cannot be used to construct a triangle?
AC + AB > CB
AC + CB < AB
AC + CB > AB
AC + AB < CB
The answer choice which explains that the three segments cannot be used to construct a triangle is; AC + CB < AB.
Which inequality explains why the three segments cannot be used to construct a triangle?Since, It follows from the triangle inequalities theorem that sum of the side lengths of any two sides of a triangle is greater than the length of the third side.
Hence, since the sum of sides AC + CB is less than AB, it follows that the required inequality is; AC + CB < AB.
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Answer: Option 2 or B. AC + CB < AB
Step-by-step explanation: Trust Me! It is correct on Edge!
Q: Which inequality can be used to explain why these three segments cannot be used to construct a triangle?
A: AC + CB < AB
please help....title of the work assignment...WHERE DOES THE DECIMAL GO USING ESTIMATION WHEN DIVIDING DECIMALS.....
146÷0.7. SOLUTION AND REASONING...
The correct equation of 146 ÷ 7 = 20857 is 146.0 ÷ 7.0 = 20.857
How to divide the decimals?The equation is given as:
146 ÷ 7 = 20857
The above equation is wrong.
The equation can be rewritten as:
146.0 ÷ 7.0 = 20857
The significant digits in 146.0 and 7.0 are 3 and 1, respectively.
3 - 1 = 2
This means that
So, the decimal place in the result must be after the second digit.
So, we have:
146.0 ÷ 7.0 = 20.857
Using the above highlights, we have:
146 ÷ 0.7 = 208.57
1.46 ÷ 7 = 0.20857
14.6 ÷ 0.7 = 20.857
1460 ÷ 70 = 20.857
The reasoning behind the above equations is that the decimal position in the results is dependent on the decimal positions in the dividend and divisor
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which linear inequality is represented by the graph
Answer:
The correct awnser is A : )
Step-by-step explanation:
Split [tex](4ax-a^2)/(x^2+ax-2a^2)[/tex] into partial fractions.
The decomposition of the partial fraction is [tex]\frac{4ax-a^2}{(x+ 2a)(x-a)} = \frac{A}{x + 2a} + \frac{B}{x - a}[/tex]
How to split the fraction?The expression is given as:
[tex]\frac{4ax-a^2}{x^2+ax-2a^2}[/tex]
Expand the denominator
[tex]\frac{4ax-a^2}{x^2- ax+2ax-2a^2}[/tex]
Factorize
[tex]\frac{4ax-a^2}{x(x- a)+2a(x-a)}[/tex]
Factor out x - a
[tex]\frac{4ax-a^2}{(x+ 2a)(x-a)}[/tex]
The denominator of the partial fraction is a product of two linear factors.
So, the decomposition can be represented as:
[tex]\frac{4ax-a^2}{(x+ 2a)(x-a)} = \frac{A}{x + 2a} + \frac{B}{x - a}[/tex]
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a In a concert band, the probability that a member is in the brass section is
0.50. The probability that a member plays trombone, given that he or she is in
the brass section, is 0.24.
What is the probability that a randomly selected band member is in the brass
section and plays trombone?
A. 0.26
B. 0.74
C. 0.12
D. 0.48
Answer:
C. 0.12
Step-by-step explanation:
Let's use a sample number of 100
Out of 100 members, 50 are in the brass section
Out of those 50, 24% play the trombone. This means that 12 people total play the trombone.
12/100 is .12.. That is the final answer
On Monday, Cinthia studied for 3 1/2 hours. On Tuesday, she studies 2/3 of her study time on Monday. How many hours did Cinthia study on Tuesday?
Answer:
Cinthia studied 2/3 of her time on Tuesday
a car's velocity is modeled by
[tex] v(t) = 0.5t {}^{2} - 10.5t + 45 \: for\leqslant t \leqslant 10.5[/tex]
Where velocity is in feet per second and time is in seconds. When does the car come to a complete stop?
In accordance with the function velocity, the car will have a complete stop after 6 seconds.
When does the car stop?
Herein we have a function of the velocity of a car (v), in feet per second, in terms of time (t), in seconds. The car stops for t > 0 and v = 0, then we have the following expression:
0.5 · t² - 10.5 · t + 45 = 0
t² - 21 · t + 90 = 0
By the quadratic formula we get the following two roots: t₁ = 15, t₂ = 6. The stopping time is the least root of the quadratic equation, that is, the car will have a complete stop after 6 seconds.
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