The distribution of X is X ~ N (20 , 6) and the probability that this American will receive no more than 24 Christmas cards this year is 0.7486.
Probabilitya. Distribution
X ~ N (20 , 6)
b. P(x ≤24)
= P[(x - μ ) / σ (24 - 20) / 6]
= P(z ≤0.67)
= 0.74857
=0.7486
Hence:
Probability = 0.7486
c. P(21 < x < 26)
= P[(21 - 26)/ 6) < (x - μ ) / σ < (24 - 20) / 6) ]
= P(-0.83 < z < 0.67)
= P(z < 0.67) - P(z < -0.)
= 0.74857- 0.2033
= 0.54527
Hence:
Probability =0.54527
d. Using standard normal table ,
P(Z < z) = 66%
P(Z < 0.50) = 0.66
z = 0.50
Using z-score formula,
x = z× σ + μ
x = 0.50 × 6 + 20 = 23
23 Christmas cards
Therefore the distribution of X is X ~ N (20 , 6) and the probability that this American will receive no more than 24 Christmas cards this year is 0.7486.
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You are choosing between two different cell phone plans. The first plan charges a rate of
24 cents per minute. The second plan charges a monthly fee of $49.95 plus 11 cents per
minute.
Lett be the number of minutes you talk and C₁ and C₂ be the costs (in dollars) of the first
and second plans. Give an equation for each in terms of t, and then find the number of
talk minutes that would produce the same cost for both plans (Round your answer to one
decimal place).
C₁ =____
C₂ =____
If you talk for
_____ minutes the two plans will have the same cost.
If you talk for 384.23 minutes the two plans will have the same cost.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
x is the number of minutes that will be used during a month:
C₁ = 0.24x
C₂ = 49.95 + 0.11x
So, when 1st = 2nd
0.24x = 49.95 + 0.11x
0.24x - 0.11x = 49.95
0.13x = 49.95
x = 49.95/0.13
x = 384.23 minutes
Hence, If you talk for 384.23 minutes the two plans will have the same cost.
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if f(x)=5^2x-2 and g(x)=x+1, find (f-g) (x)
The function (f-g) (x) is represented as 5^2x - 3 - x .
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
Given;
f(x)=5^2x-2
g(x)=x+1
Then, the function
(f-g) (x) = 5^2x-2 - (x+1)
Distribute the negative;
(f-g) (x) = 5^2x-2 - x - 1
(f-g) (x) = 5^2x - 3 - x
Hence, the function (f-g) (x) is represented as 5^2x - 3 - x .
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(x^4-13x^2+36)/(2x^2+10+12)
Answer:
Step-by-step explanation:
Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(5, 5),A(5,5),A, left parenthesis, 5, comma, 5, right parenthesis, comma B(7,5)B(7,5)B, left parenthesis, 7, comma, 5, right parenthesis, C(7,-1)C(7,−1)C, left parenthesis, 7, comma, minus, 1, right parenthesis, and D(5,-1)D(5,−1)D, left parenthesis, 5, comma, minus, 1, right parenthesis.
Given these coordinates, what is the length of side BCBCB, C of this rectangle?
Answer:
The length of the side BC is 6 units.
Step-by-step explanation:
Distance formula: This works for any two points in 2D space with coordinates (x₁, y₁) for the first point and (x₂, y₂) for the second pointIt is the length of the line segment joining two pointsd = [tex]\sqrt{(x_{2} {-} x_{1})^{2} +(y_{2} {-} y_{1})^{2}}[/tex]For the given question:Rectangle ABCD
Coordinates of Point A,B,C,D
[tex]A = ( 5 , 5)B = (7, 5)C = (7 , -1)D = (5 , -1)[/tex]
As we are asked to find the length of side BC, we'll apply the Distance formula on side BC
BC = [tex]\sqrt{(7_ {-} 7)^{2} +(-1 {-} 5)^{2}}[/tex]
= [tex]\sqrt{(0)^{2} +(-6)^{2}}[/tex]
= [tex]\sqrt{ 36}[/tex]
= [tex]6[/tex]
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For the following function y = f(x) = 4x^3 - 5
I worked out this Calculus problem, but I keep getting 1/-432 for part c. Can anyone work out the problem step-by-step so I can understand what I’m doing wrong? It would be greatly appreciated.
The answer for each of the differentiation are; f'(-6) = 432; f⁻¹(y) = ∛((y + 5)/4); df⁻¹/dy = 1/432
How to differentiate functions?
1) f(x) = 4x³ - 5
We will differentiate it to get;
f'(x) = df/dx = 12x²
f'(-6) = 12(-6)²
f'(-6) = 432
2) We are given the formula;
x = f⁻¹(y)
Thus;
y = 4x³ - 5
4x³ = y + 5
x³ = (y + 5)/4
x = ∛((y + 5)/4)
f⁻¹(y) = ∛((y + 5)/4)
c) f⁻¹(y) = ∛((y + 5)/4)
df⁻¹/dy = -1/12y²
At f(-6), we have;
df⁻¹/dy = 1/432
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An economy package of cups has 690 green cups. If the green cups are 30% of the total package, how many cups are in the package?
The total number of cups in the package is 2300.
What is Percentage?Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
Here,
Let the total number of cups in the package be x.
Number of green cup = 690
Weightage of green cup in total = 30%
Now,
30% of x = 690
30/100 X x = 690
x = 690 X 100/30
x = 23 X 100
x = 2300
Thus, the total number of cups in the package is 2300.
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The two triangles are similar What is the value of x? Enter your answer in the box x =
Answ x=59
Step-by-step explanation:
The polynomial f(x) has degree 3. Choose each statement that could describe all zeros of f.
The true statements are
(a) -one zero with multiplicity 3(d) -one zero with multiplicity 1 and one zero with multiplicity 2(l) -Three zeros with multiplicity 1Missing information in the question-one zero with multiplicity 3
-one zero with multiplicity 4
-one zero with multiplicity 5
-one zero with multiplicity 1 and one zero with multiplicity 2
-one zero with multiplicity 1 and one zero with multiplicity 3
-one zero with multiplicity 2 and two zeros with multiplicity 1
-one zero with multiplicity 2 and three zeros with multiplicity 1
-Two zeros with multiplicity 2
-Two zero with multiplicity 2 and two zeros with multiplicity 1
-Two zero with multiplicity 2 and three zeros with multiplicity 1
-Two zero with multiplicity 1
-Three zeros with multiplicity 1
-Four zeros with multiplicity 1
-Five zeros with multiplicity 1
How to determine the true statements?The function is given as:
f(x)
And it has a degree of 3
This means that
The total multiplicity of the zeros of the function is 3 It cannot have more than three zeros i.e. it can have 1, 2 or 3 zerosUsing the above highlight as a guide, the true statements are (a), (d),and (l)
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The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1. On a coordinate plane, a parabola, labeled f of x, opens up. It goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). Which graph represents g(x)? On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10). On a coordinate plane, a parabola opens up. It goes through (2, 8), has a vertex at (5, negative 11), and goes through (8, 8). On a coordinate plane, a parabola opens up. It goes through (negative 8, 10), has a vertex at (negative 5, 1), and goes through (negative 2, 10). On a coordinate plane, a parabola opens up. It goes through (negative 8, 8), has a vertex at (negative 5, negative 11), and goes through (negative 2, 8).
The transformation of a function may involve any change. When the graph of f(x) is transformed into 5 units to the right and one unit up, then the function g(x) is obtained.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k \times f(x)Horizontal stretch by a factor k: y = f(x/k)Given the function f(x)=x², which is transformed to g(x)=(x-5)²+1, therefore, the graph of both the functions are given below.
When the graph of f(x) is transformed into 5 units to the right and one unit up, then the function g(x) is obtained.
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10% of an amount is 6.2 . Wirk out the original account
Answer:
the original amount was 62
Step-by-step explanation:
You can use the part over whole formula like this:
[tex]\frac{part}{whole} = ( \frac{6.2}{?} * \frac{10}{100})\\ ? = 62[/tex]
why?
because we know that 10% = 10/100, we can easily find out the answer by cross multiplying
? * 10 (let's use x, instead of ?)
=10x
6.2 * 100
= 620
Now we have an equation that looks like this: 10x = 620
By using the inverse operation tool (dividing each side by 10 to isolate x) we have:
x (or ?) = 62
GUYS PLEASE HELP WITH THIS PLEASE
Examine how sounds of music are related to trigonometric functions.
What does change of amplitude do? How about frequency?
Using graphs and equations, represent multiple transformations explaining their relevancy to the sound wave
Trigonometry functions is often employed in taking the measurement of the level or the pitch of a sound wave or musical note.
The change of amplitude of a sound wave's amplitude is linked to the change in pressure that occurs due to the wave measured at a given location.
Frequency tells the number of waves that pass a fixed location in a specific time frame.
How does sound waves relate to trigonometric functions?Sound engineers uses the basic laws of trigonometry via sine and cosine graphs.
Note that all sounds can be broken down into a lot of sine waves, as sine waves comes together to form sounds.
Therefore, Trigonometry functions is often employed in taking the measurement of the level or the pitch of a sound wave or musical note.
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Each salesperson at an insurance agency is rated either below average, average, or above
average with respect to sales ability. Each salesperson is also rated with respect to his or her
potential for advancement either fair, good, or excellent. These traits for the 500 sales people
were cross-classified into the following table.
Potential for Advancement
Sales Ability Fair Good Excellent Total
Below Average 16 12 22 50
Average 45 60 45 150
Above Average 93 72 135 300
Total 154 144 202 500
If a salesperson is selected at random what is the probability:
A. The salesperson has “Fair” potential for advancement.
B. The salesperson has “Fair” potential or has Above Average Sales ability
C. The salesperson has “Fair” potential given they have Above Average Sales ability.
D. Of selecting 2 salespersons and finding they both have Fair potential for advancement.
Probability that the salesperson has “Fair” potential or has Above Average Sales ability is; 90.8%
How to find the probability?A) Probability that the salesperson has “Fair” potential for advancement = (16 + 45 + 93)/500 = 154/500 = 30.8%
B) Probability that the salesperson has “Fair” potential or has Above Average Sales ability = 30.8% + (300/500)% = 90.8%
C) Probability that the salesperson has “Fair” potential given they have Above Average Sales ability = P(A|B) = P(A ∩ B)/P(B) = (93/500)/0.6 = 0.31 = 31%
D) P(selecting 2 salespersons and finding they both have Fair potential for advancement) = (154/500) * (153/499) = 9.44%
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Evaluate: √121m²n6 if m = 3, n = 2
Answer:
1188
Step-by-step explanation:
√121 (3^2)(2(6)) = 1188
Answer:
264
Step-by-step explanation:
√(121m^2 n^6) = 11 m n^3
sub in the values given for m and n
11 (3)(2^3) = 11 * 3 * 8 = 264
A dragon flew 300 miles from his castle to visit a friend. Flying with the wind, his trip took 2 hours. His return trip against the wind took 3 hours. What was the speed of the wind and the speed of the dragon in still air?
The speed of the wind and the speed of the dragon in still air are respectively; 142.5 mph and 7.5 mph
How to calculate the speed?The dragon flew 300 miles with the wind in two hours.
After flying against the wind for two hours, he had made 270 miles of the return trip.
Let s be the speed in still air
Let w be the speed of the wind
Thus;
(s - w) = effective speed against the wind
and
(s + w) = effective speed with the wind
We know that;
distance = time * effective speed
Thus;
2(s + w) = 300
2(s - w) = 270
This can be simplified to get;
s + w = 150 -----(1)
s - w = 135 -----(2)
Add both equations to get;
2s = 285
s = 285/2
s = 142.5 mph.
Then, plane speed in still air is;
142.5 + w = 150
w = 150 - 142.5
w = 7.5 mph is the speed of the wind
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Question 4tiple Choice Worth 5 points)
(07.03 MC)
Circle A has center of (6, 7) and a radius of 4, and circle B has a center of (2, 4) and a radius of 16. What steps will help show that circle A is similar to circle B?
O Translate circle A using the rule (x+4y+3)
O Rotate circle A 45" about the center
O Dilate circle A by a scale factor of 4
O Reflect circle A about the origin
Answer:
Dilate circle A by a scale factor of 4.
Step-by-step explanation:
To show that two circles are similar, use transformations to map one to the other.
Step 1
Translate circle A so that its center is the same as circle B.
Center of circle A = (6, 7)Center of circle B = (2, 4)Translate circle A using the rule (x - 4, y - 3)
Step 2
Find the scale factor needed to dilate circle A to the size of circle B using the radii of the circles.
Radius of circle A = 4Radius of circle B = 16⇒ scale factor = 16 ÷ 4 = 4
Dilate circle A by a scale factor of 4.
Therefore, the only answer option that is correct is:
Dilate circle A by a scale factor of 4.
what is the difference between a relation and function? Classify each of the following as a function, or not a function. State the domain and range
{(1,7),(1,14),(1,21)}
The relation is/isn't a function
Domain _ _ _
Range _ _ _
Leave Unused Fields Blank
Answer:
A relation is a subset of cartesian product of two non empty sets whereas A function is a type of relation in which every element of first set has one and only image in the second set.
In a relation an element of the first set can have many images in the second set whereas in a function the first element can have only one image in the second set.
The given relation is not a function as the element 1 is related to 3 different elements in the second set.
Domain={1}
Range={7,14,21}
what is the equation
Answer:
[tex]y = \sin( \frac{2\pi}{3} x) [/tex]
Step-by-step explanation:
The equation of a sine function is y = a sin(bx), where a = amplitude (aka height) and b equals period (aka time). I'm assuming there isn't any information other than the graph shown, so let's assume that our amplitude is 1 and our period is 2pi/3. Plugging these values into the equation, we get:
[tex]y = (1) \sin(( \frac{2\pi}{3})x ) = \sin(\frac{2{\pi} }{3}x )[/tex]
Find f(g(3)) and g(f(-2)).
f(x)=x²-1 and g(x)=2x-3
Answer:
1. 8
2. 3
Step-by-step explanation:
[tex]f(g(3)) \\= f(2(3)-3))\\=f(3)\\=3^2-1\\= 9-1\\=8\\\\g(f(-2))\\= g((-2)^2-1)\\=g(4-1)\\=g(3)\\=2*3-3\\=3[/tex]
need help with this question im stuck
Answer:
answer is B. 100°
Step-by-step explanation:
if correct please I need brainlist
Answer:
100°
Step-by-step explanation:
Opposite angles of a quadrilateral inscribed in a circle are supplementary, i.e., they add up to 180°.
The 80° angle and angle x are opposite each other, so:
x + 80° = 180°
x = 180° - 80°
x = 100°
Angles A and B are complementary. If sin A = 4x + 10 and cos B = 2x + 16, what is the value of x? (1 point) 3 4 13 22
Answer: 3
Step-by-step explanation:
The sine of an angle is equal to the cosine of its complement, so
[tex]4x+10=2x+16\\\\2x+10=16\\\\2x=6\\ \\ x=3[/tex]
Outside of the United States, many countries use ____ for their accounting standard.
A. the Common Market accounting methods
B. the international agreement on taxes and tariffs
C. the International Financial Reporting Standards
D. generally accepted accounting practices
Which graph represents y = RootIndex 3 StartRoot x + 6 EndRoot minus 3?
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = negative 3 and it crosses the x-axis at x = negative 1.
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = negative 3 and it crosses the x-axis at x = negative 5.
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = 6 and it crosses the x-axis at x = 7.
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = 6 and it crosses the x-axis at x = 5.
The graph is: On a coordinate plane, a cubic function has a point of inflection at x = 5 and crosses the x-axis at x = 5
A cubic function in mathematics is one with the formula f(x)=ax3+bx2+cx+d, where aneq 0 and the coefficients a, b, c, and d are complex numbers, and the variable x has real values. In other words, it is a real function as well as a polynomial function of degree three.
The function we have is:
y = ∛(x - 5)
So cubic root is given
Here we notice that when x = 0, we have:
y = ∛-5, this is the y-intercept
And when x = 5 we have:
y = ∛0 = 0 which is the x-intercept, and also the inflection point because here we have the change of sign.
Hence option which describes graph best is On a coordinate plane, a cubic function has a point of inflection at x = 5 and crosses the x-axis at x = 5
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Answer:A
Step-by-step explanation: Edge 2022
What is the equation of the graph below
Answer:
y = csc(x)+2
Step-by-step explanation:
This is the graph of y = csc(x), shown in the attached image, shifted up 2 units.
what is the sign of f on the interval -5/9 < X < 2/3
Note that the sign of f on the interval -5/9 < x < 2/3 is negative. (Option B)
What is the explanation for the above?To determine the sign of f(x) on the interval -5/9 < x < 2/3, we need to evaluate f(x) at a test point within this interval and determine if it is positive or negative.
Since we know that f(x) has zeros at x = -4, x = -5/9, and x = 2/3, we can use these points as our reference to choose test points.
Specifically, since the zeros at x = -5/9 and x = 2/3 are not included in the interval -5/9 < x < 2/3, we can choose any test point within this interval, such as x = 0.
Evaluating f(x) at x = 0, we get:
f(0) = (3(0) - 2)(0 + 4)(9(0) + 5)
= (-2)(4)(5)
= -40
Since f(0) is negative, we can conclude that f(x) is negative on the interval -5/9 < x < 2/3.
Therefore, the sign of f on the interval -5/9 < x < 2/3 is negative
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Full Question:
f(x) = (3x - 2) (x+4) (9x +5) has zeros at x = -4, x = -5/9, and x = 2/3, that is the sign of f on the interval -5/9 < x < 2/3?
B is the set of odd numbers greater than 5 and less than 21
Answer:
List method: {7,9,11,13,15,17,19}
Set method: {X:N where N is odd, N>5 and N<21}
The odd numbers greater than 5 and less than 21 are {7, 9,11,13,15,17,19}.
What are odd numbers?Odd numbers are the numbers that cannot be divided by 2 evenly. It cannot be divided into two separate integers evenly.
Odd numbers are opposite to even numbers this means that even numbers are numbers that can be divided by 2.
When we say numbers greater than 5 and less than 21 this means 5< x < 21
The odd numbers greater than 5 and less than 21 are ;
{7, 9,11,13,15,17,19}. These odd numbers are greater than 5 and less than 21.
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find the perimeter of the triangle
Answer:
x²+14x+11
Step-by-step explanation:
Find the perimeter of the triangle.
The perimeter is:
add them
-x²+9x
2x²+6
5x+5
x²+14x+11
quizlet
Assuming that Hamid’s revenue is found by multiplying the book price by the number of copies sold, create an equation (in standard form) to model his revenue.
An equation of Hamid’s revenue by multiplying the book price by the number of copies sold is x = ny.
What is an equation?The process of equating one thing with another.
Let Hamid’s revenue is $x and the price of book is $y.
If he sold n number of copies.
Then, the general equation will be x = n * y.
Therefore, an equation of Hamid's revenue will be x = ny.
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What is the area of a rectangle with vertices at (6, −3), (3, −6) , (−1, −2), and (2, 1)? Enter your answer in the box. units²
The area of triangle is 24 sq. units
What is Area of rectangle?Area of rectangle is product of its length to its breadth.
i.e., Area of rectangle = length* breadth
let A(6, -3), B(3, -6), C( -1, -2) and D( 2, 1)
Using distance formula
AB = √(3-6)²+ (-6 +3)²
AB= √9 + 9
AB= √18
AB= 3√2
now,
BC= √(-1-3)²+ (-2 +6)²
BC = √16 +16
BC = √32
BC =4 √2
Now, Area of rectangle
= AB* BC
= 3√2 *4 √2
= 12*2
= 24 square units
Hence, area of rectangle is 24 sq. units
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The graphs below have the same shapes. What is the equation for the red graph?
The equation of the red graphed function is: g(x) = 1 - x².
How to Find the Equation of a Graphed Function?Given the graph shown in the attachment below, the graphed function heads downwards, and the x - axis is intercepted at ( 1, 0 ) and (-1,0).
Thus, the x-intercepts, which is the zeros of the function, are: 1 and -1.
So, g(x) = (x + 1)(x -1)
Expand:
g(x) = 1 - x²
The equation of the red graph is: g(x) = 1 - x².
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what is the least common multiple of the numbers 8 and 12?
A. 24
B. 8
C. 4
D.96
Answer:
A. 24
Step-by-step explanation:
Least common multiple of 8 and 12 = 24
8× 1 = 8 12×1 = 12
8×2 = 16 12×2=24
8×3 = 24
L.C.M (8,12) = 24
The greatest multiple that occurs in both the multiples of 8 and 12, is 24.
Hence, the least common multiple here is 24.
