Answer:
The dice has 6 options:
if the outcome is 5, player wins 50
if the outcome is 6, player wins 200
if the outcome is another number, the player does not win anything.
Now, remember that the expected value can be written as:
E = ∑xₙpₙ
where xₙ is the event n, and pₙ is the probability of that event.
for a dice, the probabilty for each number is 1/6
The expected value is:
E = (1/6)*(0 + 0 + 0 + 0 + 50 + 200) = 41.66
The expected gain will be E - 100 (because the player pays 100 in order to play)
Then the expected gain is:
G = 41.66 - 100 = -58.33
The standard deviation can be written as:
s = √( ∑(x - x)^2/n)
where x is the mean, in this case the mean is:
(200 + 50 + 4*0)/6 = 41.66 and n = 6.
s = √( (1/6)*(4*(0 - 41.66)^2 + (50 - 41.66)^2 + (200 - 41.66)^2) ) = 73
So we have a lot of standard deviation on Y.
Emile is a long-distance trucker. In one week he drives miles from his home in Fort Lauderdale, FL, to Benson, NC. He then drives miles to Barstow, CA, and continues driving miles to Bakersfield, CA. From there, Emile drives miles to Seattle, WA. Estimate the total distance Emile travels by first rounding each distance to the nearest hundred. Do not put units in your answer.
Answer:
Estimated total distance is 1,900 miles.
Step-by-step explanation:
We begin by adding each distance traveled by Emile:
1. Fort Lauderdale, FL, to Benson, NC = 748 miles
2. Barstow, CA, to Bakersfield, CA = 130 miles
3. Bakersfield, CA. to Seattle, WA = 1030 miles
Total miles = 1,908.
Therefore, in one week Emile's total distance to the nearest hundred is 1,900.
Note: the distances where gotten via Google Map.
Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 8 sin(xy), (0, 9)
Answer:
The maximum rate of change of f at (0, 9) is 72 and the direction of the vector is [tex]\mathbf{\hat i}[/tex]
Step-by-step explanation:
Given that:
F(x,y) = 8 sin (xy) at (0,9)
The maximum rate of change f(x,y) occurs in the direction of gradient of f which can be estimated as follows;
[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (x,y) \hat i \ + \ \dfrac{\partial }{\partial y } (x,y) \hat j \end {bmatrix}[/tex]
[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (8 \ sin (xy) \hat i \ + \ \dfrac{\partial }{\partial y } (8 \ sin (xy) \hat j \end {bmatrix}[/tex]
[tex]\overline V f (x,y) = \begin {bmatrix} (8y \ cos (xy) \hat i \ + \ (8x \ cos (xy) \hat j \end {bmatrix}[/tex]
[tex]| \overline V f (0,9) |= \begin {vmatrix} 72 \hat i + 0 \end {vmatrix}[/tex]
[tex]\mathbf{| \overline V f (0,9) |= 72}[/tex]
We can conclude that the maximum rate of change of f at (0, 9) is 72 and the direction of the vector is [tex]\mathbf{\hat i}[/tex]
A line runs tangent to a circle at the point (4, 2). The line runs through the origin. Find the slope of the tangent line.
Answer:
Slope of the tangent line (m) = 1 / 2
Step-by-step explanation:
Given:
Point A = (4,2)
Origin point = (0,0)
Find:
Slope of the tangent line (m)
Computation:
Slope of the tangent line (m) = (y2-y1) / (x2-x1)
Slope of the tangent line (m) = (2-0) / (4-0)
Slope of the tangent line (m) = 2 / 4
Slope of the tangent line (m) = 1 / 2
The difference of two trinomials is x2 − 10x + 2. If one of the trinomials is 3x2 − 11x − 4, then which expression could be the other trinomial? 2x2 − x − 2 2x2 + x + 6 4x2 + 21x + 6 4x2 − 21x – 2
Answer: [tex]4x^2-21x-2[/tex] .
Step-by-step explanation:
Given: The difference of two trinomials is [tex]x^2 -10x + 2[/tex]. If one of the trinomials is [tex]3x^2 - 11x - 4[/tex].
Then, the other trinomial will be ([tex]3x^2 - 11x - 4[/tex] ) + ([tex]x^2 -10x + 2[/tex])
[tex]=3x^2-11x-4+x^2-10x+2\\\\=3x^2+x^2-11x-10x-4+2\\\\=4x^2-21x-2[/tex]
Hence, the other trinomial could be : [tex]4x^2-21x-2[/tex] .
Solve 45 - [4 - 2y - 4(y + 7)] = -4(1 + 3y) - [4 - 3(y + 2) - 2(2y -5)] (make sure to type the number only - rounded to the tenth)
Answer:
Rounded: -5.5
Step-by-step explanation:
Work above :)
A. f(x) = -x^2 - x - 4
B. f(x) = -x^2 + 4
C. f(x) = x^2 + 3x + 4
D. f(x) = x^2 + 4
Answer:
B: -x^2 + 4
Step-by-step explanation:
If the equation was [tex]f(x)=x^2[/tex], then the vertex would be at 0, and the "U" would be facing straight up. Here, the "U" is upside down, so that means the "x^2" would have to be a negative number ([tex]-x^2[/tex]) to get the upside-down "U". Then, we could see that the vertex is at positive 4, so that means that the parabola moved up 4 units, so the equation should end in +4.
Our answer is:
B: -x^2 + 4
To paint his apartment, Alex but 6 gallons of paint to cover 1440 ft.². What is the ratio of square feet to gallons of paint?
Answer & Step-by-step explanation:
The ratio of square feet to gallons of paint:
[tex]1440:6[/tex]
This can also be written as:
[tex]\frac{1440}{6}[/tex]
This fraction can be simplified by dividing the numerator and denominator by 6:
[tex]\frac{1440}{6}=\frac{240}{1}[/tex]
So, the ratio of square feet to gallons of paint is:
1 gallon for every 240 ft².
:Done
(-2×3)+(3×2) how do we solve it
Answer:
0
Step-by-step explanation:
- 2×3= - 6
2×3=6
-6+6=0
Answer:
0
Step-by-step explanation:
first
(-2x3)+(3x2)
-6+6=0
1. What is the difference between an exponential growth and exponential decay? 2. What is an example equation for expoential growth and an example equation for exponential decay?
Answer: see below
Step-by-step explanation:
The standard form of an exponential equation is: y = a(b)ˣ where
a is the initial valueb is the rateGrowth:
Exponential growth is where the final value (y) is greater than the initial value (a).
An example would be the spreading of a rumor:
You tell 1 person (a = 1) who then tells 2 people each minute (b = 2). How many people will they have spread the rumor to after 5 minutes (x = 5)?
y = 1(2)⁵
= 32
Decay:
Exponential decay is where the final value (y) is less than the initial value (a).
An example would be the decrease of bacteria in a person:
A person has 100 bacteria (a = 1) who takes a pill that is supposed to cut in half the number of bacteria each hour (b = 1/2). How many bacteria will the person have after 2 hours (x = 2)?
[tex]y=100\bigg(\dfrac{1}{2}\bigg)^2\\\\\\.\quad =100\bigg(\dfrac{1}{4}\bigg)\\\\\\.\quad = 25[/tex]
A project has an initial cost of $40,000, expected net cash inflows of $10,000 per year for 8 years, and a cost of capital of 14%. What is the project's NPV? (Hint: Begin by constructing a time line.) Do not round intermediate calculations. Round your answer to the nearest cent.
Answer:
50k
Step-by-step explanation:
What is the area of the house (including the drawing room, TV room, balcony, hallway, kitchen, and bedroom)?
Answer:
1256 i think
Step-by-step explanation:
Which cross-sectional shapes do you find the most surprising? Which shapes do you find the least surprising? Explain why.
Answer:
I was surprised that a plane parallel to the vertical axis creates a rectangular cross-section. I guess I was expecting to always see a circle or a circular shape in the cross-section, not purely straight edges as seen in a rectangle.
Step-by-step explanation:
edmentum answer
Answer:
The circles were the least surprising because the base of the cone is a circle. The curves that look like bent rods were the most surprising because I have not seen geometric figures like those before.
Step-by-step explanation:
Find the area of the shaded regions.
Answer:
7 pi cm^2 or approximately 21.98 cm^2
Step-by-step explanation:
First find the area of the large circle
A = pi r^2
A = pi 3^2
A = 9 pi
Then find the area of the small unshaded circle
A = pi r^2
A = pi (1)^2
A = pi
There are two of these circles
pi+ pi = 2 pi
Subtract the unshaded circles from the large circle
9pi - 2 pi
7 pi
If we approximate pi as 3.14
7(3.14) =21.98 cm^2
Answer:
[tex]\boxed{\sf 7\pi \ cm^2 \ or \ 21.99 \ cm^2 }[/tex]
Step-by-step explanation:
[tex]\sf Find \ the \ area \ of \ the \ two \ smaller \ circles.[/tex]
[tex]\sf{Area \ of \ a \ circle:} \: \pi r^2[/tex]
[tex]\sf r=radius \ of \ circle[/tex]
[tex]\sf There \ are \ two \ circles, \ so \ multiply \ the \ value \ by \ 2.[/tex]
[tex](2) \pi (1)^2[/tex]
[tex]2\pi[/tex]
[tex]\sf Find \ the \ area \ of \ the \ larger \ circle.[/tex]
[tex]\sf{Area \ of \ a \ circle:} \: \pi r^2[/tex]
[tex]\sf r=radius \ of \ circle[/tex]
[tex]\pi (3)^2[/tex]
[tex]9\pi[/tex]
[tex]\sf Subtract \ the \ areas \ of \ the \ two \ circles \ from \ the \ area \ of \ the \ larger \ circle.[/tex]
[tex]9\pi -2\pi[/tex]
[tex]7\pi[/tex]
Circle O has a circumference of approximately 28.3 cm. Circle O with radius r is shown. What is the approximate length of the radius, r? 4.5 cm 9.0 cm 14.2 cm 28.3 cm
Answer:
4.5cm
Step-by-step explanation:
Circumference = 2[tex]\pi[/tex]r
28.3=2[tex]\pi[/tex]r
28.3/2[tex]\pi[/tex]=r
4.456
The radius of the circle O is 4.5 cm.
What is radius?A radius is a measure of distance from the center of any circular object to its outermost edge or boundary.
Given that, a circle having a circumference of approximately 28.3 cm, we need to find its radius,
So, Circumference = 2 π × radius
2 π × radius = 28.3
Radius = 28.3 / 2π
Radius = 28.3 / 6.28
Radius = 4.5
Hence, the radius of the circle O is 4.5 cm.
Learn more about radius, click;
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An aluminum bar 4 feet long weighs 24 pounds. What is the weight of a similar bar that is 3 feet 3 inches long? WILL MARK BL
Answer:
19.5 pounds
Step-by-step explanation:
1 foot = 12 inches
3 inches = 3/12 = 0.25 feet
3 feet 3 inches = 3.25 feet
then:
24 pounds is 4 feet
A pounds is 3.25 feet
A = 24*3.25/4
A = 19.5 pounds
Answer:
19.50 pounds
Step-by-step explanation:
1 foot = 12 inches
3 inches = 3/12 = 0.25 feet
3 feet 3 inches = 3.25 feet
then:
24 pounds is 4 feet
A pounds is 3.25 feet
A = 24*3.25/4
A = 19.50 pounds
Find the solution of the system of equations.
2x – 10y = -28
-10x + 10y = -20
GbA
Answer:
(6, 4 )
Step-by-step explanation:
Given the 2 equations
2x - 10y = - 28 → (1)
- 10x + 10y = - 20 → (2)
Adding (1) and (2) term by term eliminates the term in y, that is
- 8x = - 48 ( divide both sides by - 8 )
x = 6
Substitute x = 6 into either of the 2 equations and evaluate for y
Substituting into (1)
2(6) - 10y = - 28
12 - 10y = - 28 ( subtract 12 from both sides )
- 10y = - 40 ( divide both sides by - 10 )
y = 4
Solution is (6, 4 )
Best Buy is currently selling the latest model of the iPad
Pro for $549.99. Since you are an employee there, you
receive a 5% discount. How much will the iPad Pro cost
you if you use your employee discount (before taxes).
Answer:
$522.49
Step-by-step explanation: 549.99*.05=27.50 (discount)
549.99-27.50=$522.49
Answer:
$522.49
Step-by-step explanation:
First, find the discount amount. You can do this by multiplying the original cost by the discount amount. A little trick for remembering to multiply instead of divide is to think "five percent of the original amount"
5% = 0.05
549.99 ⋅ 0.05 = 27.4995
That means the discount amount is $27.50
Subtract the discount amount from the original price
$549.99 - $27.50 = $522.49
2
Select the correct answer.
which number is the additive Inverse of -10 ?
O A 10 1
Ос. о
OD. -41
Reset
Next
Answer:
[tex]\boxed{\sf 10}[/tex]
Step-by-step explanation:
The additive number of any number is the number when added to the number gives a result of zero.
So, if we add 10 to -10 we get a result of zero.
=> -10+10
=> Zero
Help with a problem again please
Answer:
9x³ + 27x²
Step-by-step explanation:
What the question is asking is to multiply f(x) and g(x) together:
Step 1: Write out expression
(fg)(x) = 3x²(3x + 9)
Step 2: Distribute
(fg)(x) = 9x³ + 27x²
Answer:
[tex]\huge\boxed{Option \ 3 : (fg)(x) = 9x^3+27x^2}[/tex]
Step-by-step explanation:
[tex]f(x) = 3x+9\\g(x) = 3x^2[/tex]
Multiplying both
[tex](fg)(x) = (3x+9)(3x^2)\\(fg)(x) = 9x^3+27x^2[/tex]
PLEASE ANSWER ASAP!!!
Answer options given in picture
Michael can skateboard 100 feet in 5.4 seconds. Which choice below shows how fast Micheal is going miles per 1 hour? Remember that since you are using multiplication to make conversions, you need to set up the units diagonal from each other in order to cancel.
any unrelated answer will be reported
Answer:
A
Step-by-step explanation:
The algebraic expression for the product of five and the cube of a number decreased by 40
Answer:
5a³ - 40
Step-by-step:
The algebraic expression is:
5a³ - 40
Starting at point A, a ship sails 18.9 km on a bearing of 190 degrees and then turns and sails 47.2km on a bearing of 318 degrees. Find the distance of the ship from point A. (Use trigonometry)
Answer:
Approximately 38.56 kilometers
Step-by-step explanation:
So, from the picture, we want to find x.
To do this, we can use the Law of Cosines. We simply need to find the angle between the two sides and then plug them into the Law of Cosines. First, the Law of Cosines is:
[tex]c^2=a^2+b^2-2ab\cos(C)\\[/tex]
The c in this equation is our x, and the C is the angle we need to find.
From the picture, you can see that angle C is the sum of the red and blue angles.
From a bearing of 190 degrees, we can determine that the red angle measures 10 degrees. Then by alternate interior angles, the other red angle must also measure 10 degrees.
From a bearing of 318 degrees, the remaining 48 degrees is outside the triangle. However, we have a complementary angle, so we can find the angle inside the triangle by subtracting in into 90. Therefore, the blue angle inside is 90-48=42 degrees.
Therefore, angle C is 42+10 which equals 52 degrees. Now we can plug this into our formula:
[tex]x^2=a^2+b^2-2ab\cos(C)\\\\x^2=(18.9)^2+(47.2)^2-2(18.9)(47.2)\cos(52)\\x=\sqrt{(18.9)^2+(47.2)^2-2(18.9)(47.2)\cos(52)}\\\text{Use a Calculator}\\x\approx38.5566 \text{ km}[/tex]
find the value of X?
Answer:
x = 58
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
90 = 32+x
Subtract 32 from each side
90-32 = x
58 =x
In the expression 3x2 + y − 5, which of the following choices is the exponent in the term 3x2?
Answer:
2
Step-by-step explanation:
The term 3x² has 2 as an exponent, the correct option is C.
What are Exponents?Exponents are the base raised by power, it is written in the superscript of a number.
The expression is 3x² +y-5
The term 3x² has 2 as an exponent.
Therefore, the correct option is C.
The missing options are
A.3x2
B. y
A 2
C. -5
D. None of these choices are correct.
To know more about Exponents
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Please Help me with this Click to select the following graphic figure. A square circumscribed about a circle:
The answer would be the first image.
Step-by-step explanation:
From context, it appears that to be circumscribed is to be drawn about; thus the square circumscribed about the circle is the first graph.
Answer:
The first image which is a circle in a square
Use the quadratic function to predict f(x) if x equals 2. f(x) = −3x2 + 180x − 285
Answer:
if x = 2
f(x) = -3x^2 + 180x -285
f(x) = -3*2*2 + 180*2 -285
f(x) = -12 + 360 -285
f (x) = 63
Step-by-step explanation:
12. 12 ounces is roughly the same as
O A. 340 grams.
B. 356 grams.
O C. 400 grams.
O D. 120 grams.
Mark for review (Will be highlighted on the movin
Answer:
A. 340 grams
Step-by-step explanation:
My brain
If h(x)=-2x-10 ,find h(-4)
Answer:
h(-4) = -2
Step-by-step explanation:
h(x)=-2x-10
Let x = -4
h(-4)=-2*-4-10
=8-10
= -2
Answer:
[tex]\huge \boxed{{-2}}[/tex]
Step-by-step explanation:
[tex]\sf The \ function \ is \ given:[/tex]
[tex]h(x)=-2x-10[/tex]
[tex]\sf To \ find \ h(-4), \ put \ x=-4.[/tex]
[tex]h(-4)=-2(-4)-10[/tex]
[tex]h(-4)=8-10[/tex]
[tex]h(-4)=-2[/tex]
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 4x2 − 3x + 2, [0, 2]
Answer:
Yes , it satisfies the hypothesis and we can conclude that c = 1 is an element of [0,2]
c = 1 ∈ [0,2]
Step-by-step explanation:
Given that:
[tex]f(x) = 4x^2 -3x + 2, [0, 2][/tex]
which is read as the function of x = 4x² - 3x + 2 along the interval [0,2]
Differentiating the function with respect to x is;
f(x) = 8x - 3
Using the Mean value theorem to see if the function satisfies it, we have:
[tex]f'c = \dfrac{f(b)-f(a)}{b-a}[/tex]
[tex]8c -3 = \dfrac{f(2)-f(0)}{2-0}[/tex]
since the polynomial function is differentiated in [0,2]
[tex]8c -3 = \dfrac{(4(2)^2-3(2)+2)-(4(0)^2-3(0)+2)}{2-0}[/tex]
[tex]8c -3 = \dfrac{(4(4)-3(2)+2)-(4(0)-3(0)+2)}{2-0}[/tex]
[tex]8c -3 = \dfrac{(16-6+2)-(0-0+2)}{2-0}[/tex]
[tex]8c -3 = \dfrac{(12)-(2)}{2}[/tex]
[tex]8c -3 = \dfrac{10}{2}[/tex]
8c -3 = 5
8c = 5+3
8c = 8
c = 8/8
c = 1
Therefore, we can conclude that c = 1 is an element of [0,2]
c = 1 ∈ [0,2]
For the given data value, find the standard score and the percentile. A data value 0.6 standard deviations above the mean.
Answer:
The z-score is [tex]z = 0.6[/tex]
The percentile is [tex]p(Z < 0.6) = 72.57\%[/tex]
Step-by-step explanation:
From the question we are told that
The data value is 0.6 standard deviations above the mean i.e [tex]x = \mu + 0.6 \sigma[/tex]
Where [tex]\mu[/tex] is the population mean and [tex]\sigma[/tex] is the standard deviation
Generally the z-score is mathematically represented as
[tex]z = \frac{x - \mu }{\sigma }[/tex]
=> [tex]z = \frac{(\mu + 0.6\sigma ) - \mu }{\sigma }[/tex]
=> [tex]z = 0.6[/tex]
The percentile is obtained from the z-table and the value is
[tex]p(Z < 0.6) = 0.7257[/tex]
=> [tex]p(Z < 0.6) = 72.57\%[/tex]
