The probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
41% of adults say cashews are their favorite kind of nut.
P = 41% = 0.41
Q = 1 - P = 1 - 0.41 = 0.59
n = 2
From the binomial distribution:
[tex]\rm P(X = r) = C(n, r) P^r(1-P)^{n-r}[/tex]
a) Exactly three
[tex]P(X=3) = C(12, 3) (0.41)^3(0.59)^9[/tex]
P(X = 3) = 0.131
b) At least four:
P(X≥4) = P(X=4)+ P(X=5)+ P(X=6)+..............+ P(X=13)
[tex]\rm P(X\geq 4)=C(12, 4) (0.41)^4(0.59)^9+C(12, 5) (0.41)^5(0.59)^8+...............+C(12, 3)(0.41)^3(0.59)^9[/tex]
P(X ≥ 4) = 0.795
c) At most two:
P(X≤2) =P(X=0)+ P(X=1)+ P(X=2)
[tex]\rm =C(12, 0) (0.41)^0(0.59)^12+C(12, 1) (0.41)^1(0.59)^1^1+C(12, 2)(0.41)^2(0.59)^1^0[/tex]
P(X ≤ 2) = 0.0733
Thus, the probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.
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A snack bar offers chili and/or cheese on its hot dogs for an additional fee.
The owner kept track of the hot dog orders over the course of a week. His
data are shown in a relative frequency table.
Answer:
the answer is c. the row is chili, the column is no cheese
The graph of the function f(x) is shown below.
-a
If a = 9, then find the value of
3a
f(x) d
-a
f(x) dx =
a
3a
fr f(x) dx.
-a
ROUND YOUR FINAL ANSWER TO 4 DECIMAL PLACES.
2a
3a
The integral of [tex]f(x)[/tex] over the interval [tex][-a,a][/tex] corresponds to the area of a semicircle of radius [tex]a[/tex], so
[tex]\displaystyle \int_{-a}^a f(x) \, dx = \frac{\pi a^2}2[/tex]
The integral over [tex][a,3a][/tex] corresponds to the negative area of a trapezoid with height [tex]a[/tex] and base lengths [tex]2a[/tex] and [tex]a[/tex], so
[tex]\displaystyle \int_a^{3a} f(x) \, dx = -\frac{a(2a+a)}2 = -\frac{3a^2}2[/tex]
Then combining the integrals, we have
[tex]\displaystyle \int_{-a}^{3a} f(x) \, dx = \frac{\pi a^2}2 + \left(-\frac{3a^2}2\right) = \frac{(\pi-3)a^2}2[/tex]
When [tex]a=9[/tex], the integral evaluates to
[tex]\displaystyle \int_{-9}^{27} f(x) \, dx = \frac{(\pi-3)\times81}2 \approx \boxed{5.7345}[/tex][/tex]
How much will 1,000.00 amount to in 2 years at 13%2% simple interest
Huilan is years 15 younger than Thomas. The sum of their ages is 73 . What is Thomas's age?
thomas age:44
huilan age: 29
Step-by-step explanation:
h = t + 15
t + t + 15 = 73
2t = 73 - 15
2t = 58
t = 29
Which expression is equivalent to 2x² - x + ?
O A
O
B
C
D
²(x - 2)²
2
IN
2 X-
16
Answer: [tex]2\left(x-\frac{1}{4} \right)^{2}[/tex]
Step-by-step explanation:
[tex]2x^{2}-x+\frac{1}{8}\\\\=2\left(x^{2}-\frac{1}{2}x \right)+\frac{1}{8}\\\\=2\left(\left(x-\frac{1}{4} \right)^{2}-\frac{1}{16} \right)+\frac{1}{8}\\\\=2\left(x-\frac{1}{4} \right)^{2}-\frac{1}{8}+\frac{1}{8}\\\\=\boxed{2\left(x-\frac{1}{4} \right)^{2}}[/tex]
Evaluate the expression. 7^14/7^15 Evaluate the expression . 714 715
Answer:
1/7
Step-by-step explanation:
Alternative Form: 0.142857, 7^-1
How to find x and y
he value of x and y from the given figure are 49/5 and 49/15
Similarity theorem of trianglesFrom the given similar triangles, the following expression is true
21/30 = 7/15 = k
Also, x/21 = y/7 = 7/15
Equate
x/21 = 7/15
15x = 7 * 21
5x = 7 * 7
x = 49/5
Similarly
y/7 = 7/15
15y = 49
y = 49/15
Hence the value of x and y from the given figure are 49/5 and 49/15
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The repeating decimal z=0.142857142857142857 as fraction
Answer:
[tex] \frac{1}{7} [/tex]
Use the grouping method to factor this polynomial completely.
4x³ + 8x²+3x+6
O A. (4x2 + 2)(x+3)
OB. (4x2+2)(x+2)
O C. (4x²+3)(x+3)
D. (4x² + 3)(x + 2)
Answer:
D. [tex](4x^2 + 3)(x + 2)[/tex]
Step-by-step explanation:
Hello!
We can group the first two terms and the last two terms and factor each group.
Factor by Grouping[tex]4x^3 + 8x^2 + 3x + 6[/tex][tex](4x^3 + 8x^2) + (3x + 6)[/tex][tex]4x^2(x + 2) + 3(x + 2)[/tex]Now we can combine the like factors:
[tex](4x^2 + 3)(x + 2)[/tex]The answer is Option D.
a) Write VW as a column vector.
b) Write WV as a column vector.
c) Write a sentence to explain what you notice about
your answers.
W
V
Answer:
vector VW= w - v
vector WV= v - w
Step-by-step explanation:
there are no figures to solve the question so i'll just write the formula..
vector VW= w - v
vector WV= v - w
NEED HELP ASAP !!
Which equations are equivalent to 2 + 2 12-x1=1? Check all that apply.
Answer:
[tex]\frac{2}{3}|2-x|=\frac{1}{15}[/tex]
Step-by-step explanation:
[tex]\frac{1}{5} + \frac{2}{3} |2-x| = \frac{4}{15} \\\\\frac{1}{5}*(\frac{3}{3}) = \frac{3}{15}\\\\\frac{3}{15}-\frac{3}{15} + \frac{2}{3}|2-x| =\frac{4}{15}-\frac{3}{15}\\\\\frac{2}{3}|2-x|=\frac{1}{15}[/tex]
Which of these could be the graph of F(x) = log₂ x?
A
A. Graph A
B. Graph B
C. Graph C
D. Graph D
The graph of the function is shown in the attached image.
Another day, another math problem 3
If f(x)=x²+2 and g(x)=x²+5 then the domain of the (fog) (x) is (-∞,∞).
Given the f(x)=x²+2 and g(x)=x²+5
We have to find the domain of the (fog) (x)
The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.
then,(fog) (x)= (x²+5)²+ 2
=x⁴+25+10x²+2
= x⁴+27+10x²
Now on any real value of x the value of (fog) (x) exists therefore (fog) (x) can take all the values of the real number.
So domain (fog) (x)= (-∞,∞).
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Jakub wants to build a new shed.
The area of the shed is 37 m².
The width of the shed is 5 m.
What is the length of the shed?
3
Answer:
74 mStep-by-step explanation:
Jakub wants to build a new shed.
The area of the shed is 37 m².
The width of the shed is 5 m.
What is the length of the shed?
to find the side, having the area, you need to use the inverse formula Area = W * L
so
L = A: W
L = 37 : 5 = 7.4 m
If the area of the shed is 37 m²,width of the shed is 5 m as a result the length of the shed will be 7.4 m.
What is a rectangle?It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral. The area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is given that, the area of the shed is 37 m². The width of the shed is 5 m.
Since the shed is rectangular. The length of width is found as,
Area = length × width
A = l × w
l=A/w
l=37/5
l=7.4 m
Thus, if the area of the shed is 37 m², the width of the shed is 5 m as a result the length of the shed will be 7.4 m.
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How do I solve this problem?
Answer:
y≤x²+4x-1.
Step-by-step explanation:
1) to define the equation of the given graph; it is y=x²+4x-1 (its vertex is (-2;-5));
2) to define inequation accorging to the given graph (the area outside of the parabola means ≤).
Given 2 (x+3) - 4x = x
Prove = 2
Complete the proof. Provide reasons for 1-6 below.
step-by-step explanation:
#1: simplify both sides of the equation.
2(x+3)−4x=x
(2)(x)+(2)(3)+−4x=x
2x+6+−4x=x
(2x+−4x)+(6)=x
−2x+6=x
−2x+6=x
***
#2: subtract x from both sides.
−2x+6−x=x−x
−3x+6=0
***
#3: subtract 6 from both sides.
−3x+6−6=0−6
−3x=−6
***
step 4: divide both sides by -3.
−3x/-3 = -6/-3
solution x = 2
How does understanding of 5 x 12 = 60 help to solve for the product of 5
x 120? Explain in words
Answer:
c6
Step-by-step explanation:
justjustcancacanjustadda0totheproduct of5cxwewtogetthesameresultasx1totoandtimes
3) Number: 640,700
the value of 4 in this number is 40,000
Number: 64,070
the value of 4 in this number is 4,000
So, times greater: 40,000 ÷ 4,000 = 10 times greater.
4)
The multiplication, 5 × 12 = 60. So, 5 × 120 = 600.
There is an extra zero at the very last of the result as '120' was multiplied with 5 instead of '12' which does not have zero at last which changes the result.
Similar cases with: 5 × 10 = 50. So, 5 × 100 = 500.
Review the graph.
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point A is (1, negative 2), B is (1, negative 6), C is (9, negative 2), D is (9, negative 6), z 1 is (3, negative 4), and z 2 is (negative 4, 1).
Which expression is the result of subtracting (z2 – 3i) from (z1 + 2)?
A
B
C
D
[tex]z_{2}-3i=(-4+i)-3i=-4-2i\\\\z_{1}+2=(3-4i)+2=5-4i\\\\(z_{1}+2)-(z_{2}-3i)=(5-4i)-(-4-2i)=9-4i+4+2i=9-2i[/tex]
which corresponds with point C
The expression which is the result of subtracting (z2-3i) from (z1+2) is 9-2i.
Given On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point A is (1, -2), B is (1, -6), C is (9,- 2), D is (9, - 6), z 1 is (3, - 4), and z 2 is (- 4, 1).
Coordinate plane is a two dimensional plane formed by the intersection of two number lines. One is horizontal line and one is vertical. On horizontal line x values are denoted and on vertical line y values are written. There can be three dimensional plane also.
z2-3i=(-4+i)-3i=-4-2i
z1+2=(3-4i)+2=5-4i
(z1+2)-(z2-3i)=(5-4i)-(-4-2i)
=9-4i+4+2i
=9-2i
Hence for the expression (z1+2)-(z2-3i)=9-2i
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ments
nts
ns
Mai says, "I know how to find the area of a sector or the length of an arc for central angles like 180
degrees or 90 degrees. But I don't know how to do it for central angles that make up more complicated
fractions of the circle."
1. In the diagram, the sector's central angle measures 8 degrees and the circle's radius is r units. Use
the diagram to tell Mai how to find the area of a sector and the length of an arc for any angle and
radius measure.
2. This image shows a circle with radius and central angle measurements. Find the area of the shaded
sector, and the length of the arc defined by the sector.
160%
5 in
The sector area and the arc length are 34.92 square inches and 13.97 inches, respectively
How to find a sector area, and arc length?For a sector that has a central angle of θ, and a radius of r;
The sector area, and the arc length are:
[tex]A = \frac{\theta}{360} * \pi r^2[/tex] --- sector area
[tex]L = \frac{\theta}{360} * 2\pi r[/tex] ---- arc length
How to find the given sector area, and arc length?Here, the given parameters are:
Central angle, θ = 160
Radius, r = 5 inches
The sector area is
[tex]A = \frac{\theta}{360} * \pi r^2[/tex]
So, we have:
[tex]A = \frac{160}{360} * \frac{22}{7} * 5^2[/tex]
Evaluate
A = 34.92
The arc length is:
[tex]L = \frac{\theta}{360} * 2\pi r[/tex]
So, we have:
[tex]L = \frac{160}{360} * 2 * \frac{22}{7} * 5[/tex]
L = 13.97
Hence, the sector area and the arc length are 34.92 square inches and 13.97 inches, respectively
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Choose the letter of the equation for
the graph.
The graphed trigonometric function is the one in option a.
Which is the equation of the graph?The key parts that we can see on the graph are:
The midline is y = 1.From this we know that the correct option is either a or b.
at x = 0, f(x) = 0.Now we can evaluate options a and b in x = 0 and see which one is equal to zero.
for a:
y = sin(0 - pi/2) + 1 = sin(-pi/2) + 1 = -1 + 1 = 0
for b:
y = cos(0 + pi/2) + 1 = 0 + 1 = 1
Then we can see that option a is the correct option.
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Which of the following is the balance for a single $2.520 deposit in an account with an APR of 1.16% that compounds interest monthly and is invested for 37 years? Which of the following is the balance for a single $ 2.520 deposit in an account with an APR of 1.16 % that compounds interest monthly and is invested for 37 years ?
Answer:
The balance after 37 years is $3869.99
Step-by-step explanation:
Given:
Principal (P) = $2,520Rate of Interest (R) = 1.16%Time (t) = 37 yearsCompounds Interest Monthly (n) = 12The Amount (A),
A = P (1 + [tex]\frac{R}{100n}[/tex][tex])^{nt}[/tex] if compound n times per year
Amount (A) at 37 years,
A = ($2,520) (1 + [tex]\frac{1.16}{100(12)}[/tex][tex])^{12 x 37}[/tex]
A = ($2,520) (1 + [tex]\frac{1.16}{1,200}[/tex][tex])^{444}[/tex]
A = ($2,520) (1.00096667 [tex])^{444}[/tex]
A = ($2,520) (1.5357)
A = $3869.9944
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Find the domain and range of the function graphed below. Write your answers in interval notation.
Answer:
Domain: [tex](-\infty, \infty)[/tex]Range: [tex](-\infty, -1][/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Find the principal needed now (the present value) in order to get $10,000 after 15 years, compounded
semiannually at a rate of 5%.
Answer:
10000×(1+5%)^(15×2)=43219.4238
What are the zeros of the quadratic function f(x)=6x^2+12x-7?
The zeroes of the quadratic function f(x) = 6x² + 12x – 7 will be given below. Then the correct option is A.
What is a quadratic function ?The quadratic function is given as ax² + bx + c = f(x).
For finding the zeroes of the polynomial we have to find the roots of the polynomial , The value of f(x) = 0
The given function is f(x) = 6x² + 12x – 7
Then the zeroes of the quadratic function will be
[tex]roots = \dfrac {-b \pm \sqrt{b^2 -4ac}}{2a}\\\\[/tex]
Here a =6 , b = 12 ,c = -7
Therefore the zeroes are
[tex]\rm roots = \dfrac {-12 \pm \sqrt{12^2 -4 * 6 * (-7)}}{2 *6}\\\\[/tex]
[tex]\rm root_1 = -1 + \sqrt{\dfrac {13}{6}}\\\\\rm root_2 = -1 - \sqrt{\dfrac {13}{6}}[/tex]
Therefore the correct option is A.
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(correct answers only)
A sailfish is swimming after a herring in a straight line at 11.8 m/s and begins to accelerate at 6.39 m/s². How long does it take for the sailfish to reach the herring if it is 55.0 m away?
(unit=s)
According to second equation of kinematics
s=ut+1/2at²55=11.8t+1/2(6.39)t²110=23.6t+6.39t²6.39t²+23.6t-110=0Take positive value
t=2.7sAnswer:
2.7 s (1 d.p.)
Step-by-step explanation:
Use the Constant Acceleration Equations where:
s = displacement in metersu = initial speed in m/sv = final speed in m/sa = acceleration in m/s²t = time in s (seconds)Given:
s = 55 mu = 11.8 m/sa = 6.39 m/s²[tex]\begin{aligned}\text{Using }s & =ut+\dfrac{1}{2}at^2\\\implies 55 & =11.8t+\dfrac{1}{2}(6.39)t^2\end{aligned}[/tex]
Rearrange the equation to equal zero:
[tex]\implies 3.195t^2+11.8t-55=0[/tex]
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Use the quadratic equation to solve for t:
[tex]\implies a=3.195, \quad b=11.8, \quad c=-55[/tex]
[tex]\implies t=\dfrac{-11.8 \pm \sqrt{11.8^2-4(3.195)(-55)} }{2(3.195)}[/tex]
[tex]\implies t=2.694780675, -6.388051411[/tex]
As time is positive:
[tex]\implies t=2.694780675... \:\text{s}[/tex]
[tex]\implies t=2.7 \: \text{s (1 d.p.)}[/tex]
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Pls ,see the attachment
(a) Solve the following formula for b.
1
A = Zab
6
(b) Evaluate b when A= 18 and a = 5
1
(a) The formula A = ab solved for b is b =
6
(b) Evaluate b when A= 18 and a =
5
b = (Type an integer or a simplified fraction.)
Answer:
J Trump has to be a great day of school and I have a great
Step-by-step explanation:
you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you for your loss of school and I have a great day of school ii
On January 1, 2021, Princess Corporation leased equipment to King Company. The lease term is 12 years. The first payment of $716,000 was made on January 1, 2021. The equipment cost Princess Corporation $5,188,466. The present value of the lease payments is $5,588,516. The lease is appropriately classified as a sales-type lease. Assuming the interest rate for this lease is 9%, how much interest revenue will Princess record in 2022 on this lease? (Round your answer to the nearest whole dollar amount.)
The amount of the interest revenue that Princess will record in 2022 on this lease is:$413,553.82.
Interest revenue
First step
Lease value payments after first payment:
Lease value payments= $5,588,516- $716,000
Lease value payments= $4,872,516
Second step
Lease value payments after second payment:
Lease value payments=$4,872,516+ ($4,872,516×9%) - $716,000
Lease value payments=$4,872,516+$438,526.44-$716,000
Lease value payments=$4,595,042.44
Third step
2022 Interest revenue=$4,643,787.6×9%
2022 Interest revenue=$413,553.8196
2022 Interest revenue=$413,553.82 (Approximately)
Therefore the amount of the interest revenue that Princess will record in 2022 on this lease is:$413,553.82.
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A photographer needs a frame for a 16 x 20 inch picture, such that the total area is 340 in^2. Calculate the width of the frame. Which of the following quadratic equations would be used when solving this?
2x^2 + 36x = 20
2x^2 + 72 = 20
4x^2 + 36x = 20
4x^2 + 72x = 20
A woman bought some large frames for $10 each and some small frames for $4 each at a closeout sale. If she bought 22 frames for $106, find how many of each type she bought.
Answer:
19 small frames and 3 large frames
Step-by-step explanation:
follows the steps in the attached
