From the definition of conditional probability:
[tex]P(R_1\mid Q)=\dfrac{P(R_1\cap Q)}{P(Q)}[/tex]
By the law of total probability,
[tex]P(Q)=P(Q\cap R_1)+P(Q\cap R_2)+P(Q\cap R_3)[/tex]
[tex]P(Q)=P(Q\mid R_1)P(R_1)+P(Q\mid R_2)P(R_2)+P(Q\mid R_3)P(R_3)[/tex]
[tex]P(Q)=0.42[/tex]
Since
[tex]P(R_1\cap Q)=P(Q\mid R_1)P(R_1)[/tex]
we end up with
[tex]P(R_1\mid Q)=\dfrac{0.03}{0.42}\approx0.0714[/tex]
27) A man on the third floor of a building shouts down to a person on the street. If the man is 25 feet up and the distance between the person on the street and the man in the building is 50 feet, what is the angle of elevation (in degrees) between the person on the street and the person in the building?
A) 15°
B) 30°
C) 45°
D) 60°
Answer:
Option B) 30°
Step-by-step explanation:
Given : A man on the third floor of a building shouts down to a person on the street. If the man is 25 feet up and the distance between the person on the street and the man in the building is 50 feet.
To find : What is the angle of elevation (in degrees) between the person on the street and the person in the building?
Solution :
According to question, a rough diagram is framed which shows the position of man on street and man on building.
Refer the attached figure below.
A man on the third floor of a building is 25 feet up i.e. AB=25 feet.
The distance between the person on the street and the man in the building is 50 feet i.e. BC=50 feet.
We have to find the angle of elevation i.e. ∠C.
It form a right angle triangle,
Applying sin property of trigonometric,
[tex]\sin \theta=\frac{\text{Perpendicular}}{\text{Hypotenuse}}[/tex]
[tex]\sin \theta=\frac{AB}{BC}[/tex]
[tex]\sin \theta=\frac{25}{50}[/tex]
[tex]\sin \theta=\frac{1}{2}[/tex]
[tex]\sin \theta=\sin 30^\circ[/tex]
[tex]\theta=30^\circ[/tex]
Therefore, Option B is correct.
The angle of elevation is 30°.
Answer:
Its B
Step-by-step explanation:
I just did the test.
Calculate the flux of the vector field f(x, y, z) = 3hx + y, x − y, x2 + y 2 − 2zi through the surface s parametrized by φ(u, v) = u + 2v, u − 2v, u2 + 2v 2 with 0 ≤ u, v ≤ 1, and oriented by φu × φv
I'm not sure what to make of the "h" and "i" in your question, so I'll just ignore them (and the 3). Looks like we have
[tex]\vec f(x,y,z)=(x+y,x-y,x^2+y^2-2z)[/tex]
and a surface parameterzied by
[tex]\varphi(u,v)=(u+2v,u-2v,u^2+2v^2)[/tex]
with [tex]0\le u\le1[/tex] and [tex]0\le v\le1[/tex]. Then
[tex]\varphi_u\times\varphi_v=(4u+4v,4u-4v,-4)[/tex]
so that the flux is given by the integral
[tex]\displaystyle\iint_S\vec f\cdot\mathrm d\vec S=\int_0^1\int_0^1(2u,4v,4v^2)\cdot(4u+4v,4u-4v,-4)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle8\int_0^1\int_0^1(u^2+3uv-4v^2)\,\mathrm du\,\mathrm dv=\boxed{-2}[/tex]
To calculate the flux of the given vector field through the surface S, you need to calculate the partial derivatives of the parametrization, then find the cross product of these partial derivatives, and finally evaluate the double integral over the surface using the flux formula.
Explanation:To calculate the flux of the vector field f(x, y, z) = 3hx + y, x − y, x2 + y2 − 2zi through the surface S parametrized by φ(u, v) = u + 2v, u − 2v, u2 + 2v2 with 0 ≤ u, v ≤ 1 and oriented by φu × φv:
Calculate the partial derivatives of φ(u, v) with respect to u and v.Calculate the cross product φu × φv using the partial derivatives obtained in the previous step.Plug the vector field f(x, y, z), the parametrization φ(u, v), and the cross product φu × φv into the flux formula Φ = ∫∫S f • (φu × φv) dA.Evaluate the double integral over the surface S using the limits of integration 0 ≤ u, v ≤ 1.What does the number 160 represent in the rational function that models the situation?
a) distance, in miles, between the cities
b) amount of fuel, in gallons, used by the train
c) time, in minutes, needed to travel between the cities
Answer:
the answer is A.
Step-by-step explanation:
Answer:
A) distance, in miles, between the cities
Step-by-step explanation:
correct on edge
Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 121212 feet^3 3 start superscript, 3, end superscript of fluffy material. What is the length of the pillow?
Answer:
The question is incomplete, the complete question is Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 12 ft³ of fluffy material. The base is 3 ft, the height is 2 ft, what is the length of the pillow?
The length of the pillow is 4 feet
Step-by-step explanation:
The formula of the volume of the wedge is [tex]V=\frac{1}{2}bhl[/tex] , where
b is the base of ith is the height of itl is the length of it∵ The pillow in the shape of a wedge
∵ The pillow is filled with 12 ft³ of fluffy material
∴ The volume of the wedge = 12 ft³
∵ The base = 3 feet
∵ The height = 2 feet
- Use the formula of the volume above to find its length
∵ [tex]V=\frac{1}{2}(2)(3)l[/tex]
∴ V = 3 l
∵ V = 12 ft³
- Equate 3 l by 12
∴ 3 l = 12
- Divide both sides by 3
∴ l = 4 feet
∴ The length of the pillow is 4 feet
The radius of Earth is about 3960 miles. The radius of the moon is about 1080 miles. a. Find the surface area of Earth and the moon. Round your answer to the nearest tenth of a million. The surface area of the Earth is about million square miles and the surface area of the Moon is about million square miles. b. Compare the surface areas of Earth and the moon. Round your answer to the nearest tenth. The surface area of the Earth is about times greater than the surface area of the moon. c. About 70% of the surface of Earth is water. How many square miles of water are on Earth’s surface? Round your answer to the nearest tenth of a million. There are about million square miles of water on the Earth's surface.
A) The formula for surface area of a sphere is A = 4*PI*r^2
using 3.14 for PI:
Surface area for Earth = 4 * 3.14 x 3960^2 = 196,960,896 miles^2
Surface area of the moon: 4 * 3.14 * 1080^2 = 14,649,984 miles^2
B)Divide the Surface of the Earth by the moon:
196,960,896 / 14,649,984 = 13.44
The Earths surface is 13.4 times larger than the moon.
C) Multiply the surface of the Earth by 70%:
196,960,896 * 0.70 = 137,872,627.2 million square miles of water.
Calculating surface areas of Earth and the moon, comparing them, and determining the amount of water on Earth's surface.
a. Find the surface area of Earth and the moon:
Surface area of Earth = 4 x π x (3960 miles)2 ≈ 196.9 million square milesSurface area of Moon = 4 x π x (1080 miles)2 ≈ 14.6 million square milesb. Compare the surface areas of Earth and the moon: Earth's surface area is approximately 13.5 times greater than the Moon's surface area.
c. About 70% of Earth's surface is water: There are approximately 137.9 million square miles of water on Earth's surface.
When completely factored, 3x2−48 equals -
Final answer:
The quadratic expression 3x^2-48 can be completely factored as 3(x-4)(x+4) by first factoring out the common factor and then utilizing the difference of squares.
Explanation:
To factor this expression completely, we first need to look for common factors and any patterns that might help simplify the expression. Both terms in the expression 3x2−48 have a common factor of 3. Factoring out this common factor gives us:
3(x2 − 16)Notice that the expression inside the parenthesis, x2 − 16, is a difference of squares, which can be factored further into (x − 4)(x + 4). Therefore, the fully factored form of the original expression is:
3(x − 4)(x + 4)This shows how identifying common factors and utilizing the difference of squares helps in completely factoring the given expression.
Which function f (x) , graphed below, or g (x) , whose equation is g (x) = 3 cos 1/4 (x + x/3) + 2, has the largest maximum and what is the value of this maximum?
f(x), and the maximum is 3.
g(x), and the maximum is 5.’
f(x), and the maximum is 2.
g(x), and the maximum is 2.
Answer:
g(x), and the maximum is 5
Step-by-step explanation:
for given function f(x), the maximum can be seen from the shown graph i.e. 2
But for the function g(x), maximum needs to be calculated.
Given function :
g (x) = 3 cos 1/4 (x + x/3) + 2
let x=0 (as cosine is a periodic function and has maximum value of 1 at 0 angle)
g(x)= 3 cos1/4(0 + 0) +2
= 3cos0 +2
= 3(1) +2
= 3 +2
= 5 !
The ratio of students who walk home from school to the students who ride the bus home is 2 : 7. The number of bus riders is how many times the number of students who walk home?
Answer:
3.5
Step-by-step explanation:
7/2=3.5
Answer:
3.5
Step-by-step explanation:
Ratio of
those who walk : those who ride = 2 : 7
This means that for every 2 students who walk, there are 7 students who ride
Therefore, for every 1 student that walks, (hypothetically) there are 3.5 (7/2) students who ride
Then the number of bus riders is 3.5 times the number of students that walk.
Rewrite the equation in polar form.
Answer:
C) √5(cos(117°) +i·sin(117°))
Step-by-step explanation:
The rectangular number a+bi can be written in polar form as ...
√(a^2+b^2)×(cos(arctan(b/a)) + i·sin(arctan(b/a)))
Here, we have a=-1, b=2, so the magnitude is ...
√((-1)^2 +2^2) = √(1+4) = √5
and the angle is ...
arctan(2/(-1)) = arctan(-2) ≈ 116.565° . . . . . a 2nd-quadrant angle
Then you have ...
-1 +2i = √5(cos(117°) +i·sin(117°)) . . . . . . customary "polar form"
_____
Comment on the answer
The "polar form" is generally written as ...
(magnitude)·(cos(angle) +i·sin(angle))
You may also see it as ...
(magnitude) cis (angle) . . . . . . . where "cis" is shorthand for "cos + i·sin"
In my engineering courses, we often used the form ...
(magnitude) ∠ (angle)
The form used by my calculator is ...
(magnitude)·e^(i·angle) . . . . . where angle is usually in radians
Victoria has a health care plan with a prescription benefit that offers four different options.
Option A: $55 monthly premium and $20 co-pay per prescription
Option B: $60 monthly premium and $15 co-pay per prescription
Option C: $65 monthly premium and $25 co-pay per prescription
Option D: $50 monthly premium and $30 co-pay per prescription
If Victoria fills an average of five prescriptions each month, which option is the least expensive? (4 points)
Option A
Option B
Option C
Option D
Answer:
OPTION B
Step-by-step explanation:
To solve, create a formula.
y= 5(copay)+premium
Using this you get:
Option A: 5(20)+55= $155
Option B: 5(15)+60= $135
Option C: 5(25)+65= $190
Option D: 5(30)+50= $200
Answer:
Option B
Step-by-step explanation:
Option A : 55 + 20(5) = 155
Option B : 60 + 15(5) = 135
Option C : 65 + 25(5) = 190
Option D : 50 + 30(5) = 200
The area of the circular base of a cylinder is 36π square units. The height of the cylinder is 2 units.
What is the lateral area of the cylinder? Express the answer in terms of π.
12π square units
24π square units
60π square units
72π square units
Answer: second option.
Step-by-step explanation:
The formula used for calculate the lateral area of a cylinder is this one:
[tex]LA=2\pi rh[/tex]
Where "r" is the radius and "h" is the height
The formula for calculate the area of a circle (which is the base of a cylinder) is:
[tex]A=\pi r^2[/tex]
Knowing the area of the base, you can solve for the radius:
[tex]36\pi=\pi r^2\\\\r=\sqrt{\frac{36\pi units^2}{\pi}} \\\\r=6units[/tex]
Substitute the radius and the height into the formula [tex]LA=2\pi rh[/tex]:
[tex]LA=2\pi (6units)(2units)[/tex]
[tex]LA=24\pi\ units^2[/tex]
Answer:
24π square units (edge)
Step-by-step explanation:
A train travels 480 miles at a constant speed (x), in miles per hour. Write an equation that can be used to find the speed of the train, if the time to travel 480 miles is 6 hours. you do not need to solve the equation
Answer:
480 = x(6)
Step-by-step explanation:
Given in the question that,
distance travelled by the train = 480 miles
time taken by the train to travel 480 miles = 6 hours
Suppose speed of train = x miles/hour
Formula to use to drive the equation
distance = speed x time480 = x(6)
x = 480/6
x = 80 miles/hour
Jamal is x years old. His mother is 28 years older than Jamal. Jamal's uncle is two times older than Jamal's mother. Write and simplify an expression that represents Jamal's uncle age in years
Answer:
From the information, we know that Jamal's mother is 28 years older than Jamal, so his mothers age should be:
x + 28 (years)
Also, we know that his uncle's age is twice as much as Jamal's mother age, so we have the following expression:
(x + 28) · 2 = 2x + 56
*Hope this help you
Jamal's uncle's age can be expressed as 2(x + 28), which simplifies to 2x + 56 years.
Jamal is x years old, and his mother is 28 years older than him. Therefore, his mother's age can be represented by x + 28. Jamal's uncle is two times older than Jamal's mother, which means we need to multiply his mother's age by 2 to get the uncle's age. So, the expression for Jamal's uncle's age is 2(x + 28). Simplifying this expression, we get:
2(x + 28)
2x + 2(28)
2x + 56
Thus, Jamal's uncle's age is represented by the expression 2x + 56 years.
SOMEONE PLEASE HELP!!! 45 POINTS!!
Inscribed angles homework sheet for geometry
Answer:
h
Step-by-step explanation:
A fruit stand has to decide what to charge for their produce. They need \$5.30$5.30dollar sign, 5, point, 30 for 111 apple and 111 orange. They also need \$7.30$7.30dollar sign, 7, point, 30 for 111 apple and 222 oranges. We put this information into a system of linear equations.
Answer:
3.30 for apple and 2.00 for an orange
Step-by-step explanation:
To solve this problem, we can set up a system of linear equations to represent the charges for apples and oranges at the fruit stand. We can then solve this system using the elimination method to find the cost of an apple and an orange.
Explanation:To solve this problem, we can set up a system of linear equations to represent the charges for apples and oranges at the fruit stand. Let's use x to represent the cost of an apple and y to represent the cost of an orange.
From the given information, we can set up the following equations:
111x + 111y = 5.30
111x + 222y = 7.30
Next, we can solve this system of equations by using substitution or elimination. Let's use the elimination method:
Multiply the first equation by 2, and multiply the second equation by 1:
222x + 222y = 10.60
111x + 222y = 7.30
Subtract the second equation from the first:
111x = 3.30
Divide both sides by 111:
x = 0.03
Substitute this value back into either equation to solve for y:
111(0.03) + 222y = 7.30
3.33 + 222y = 7.30
222y = 3.97
y = 0.01
Therefore, the cost of an apple is $0.03 and the cost of an orange is $0.01 at the fruit stand.
Please select the best answer from the choices provided
Answer:
[tex]x=\frac{5\pi}{4}[/tex]
Step-by-step explanation:
We want to solve;
[tex]\cscx=-\sqrt{2}[/tex] in the 3rd quadrant
Recall that;
[tex]\sin x=\frac{1}{\csc x}[/tex]
We use the reciprocal ratio to get;
[tex]\sin x=-\frac{\sqrt{2}}{2}[/tex]
In the third quadrant the solution is
[tex]x=\pi+\sin^{-1}(\frac{\sqrt{2} }{2} )[/tex]
[tex]x=\pi+\frac{\pi}{4}[/tex]
[tex]x=\frac{5\pi}{4}[/tex]
Find the product 12, -5
12• (-5)= - 120/2 = -60
ANSWER
The product is
[tex] - 60[/tex]
EXPLANATION
We want to find the product of 12 and -5.
This means that we should find the result of multiplying 12 and -5
Recall that:
[tex]12 \times 5 = 5 \times 12 = 60[/tex]
Therefore,
[tex]12 \times ( - 5) = - 5 \times 12 = 60[/tex]
The product is -60
The beginners field hockey kit costs $150 it is $15 more than three times the cost of the basic kit. What is the cost of the basic kit
Answer:
45
it is what it is
The cost of basic hokey kit is $45.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, the beginners field hockey kit costs $150 it is $15 more than three times the cost of the basic kit.
Let the cost of the basic kit be x.
Now, 3x+15=150
3x=135
x=$45
Therefore, the cost of basic kit is $45.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ5
Megan has 25 phone numbers stored in her cell phone. Abby has some phone numbers stored in her cell phone. Together they have a total of 61 phone numbers stored. If n= the number of phone numbers Abby has stored in her cell phone, which mathematical sentence expresses the information above?
Answer:
61-25=n
Step-by-step explanation:
Four loan balances are $6,500, $3,600, $5,400, and $7,500, respectively. The current interest rates for the loans are 7%, 5%, 6%, and 9%, respectively. If the four are to be consolidated into one loan, what is the WEIGHTED AVERAGE interest rate on that loan?
A) 6.75%
B) 7.01%
C) 7.04%
D) 7.10%
[(455 + 180 + 324 + 675)/(65 + 36 + 54 + 75)] = 7.10
Answer is D.
Answer:
7.10% is the answer.
A rectangle with an area of 4/7 m2 is dilated by a factor of 7. What is the area of the dilated rectangle
according to the picture we have:
x.y=4.7
(7)x(7)y=49xy=(49)(4.7)=230.3
Triangle DEF is a scale drawing of triangle ABC. Triangle DEF has side lengths of 12 inches.Triangle ABC has side lengths of 84 inches. What is the scale.
Answer:
The scale is 7
Step-by-step explanation:
Divide 12 from 84 to get the answer.
Hope this helps! :)
Answer:
Step-by-step explanation:
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Vanessa has two bags that contain slips of paper. One bag has 4 slips of paper that are numbered 2, 3, 4, and 5. The other bag has 4 slips of paper that are numbered 3, 4, 5, and 6.
Vanessa chooses one slip of paper from each bag without looking.
The random variable X is the product of the numbers on the slips of paper.
What is P(12 ≤ X ≤ 15)?
Enter your answer, in simplest fraction form, in the box.
Answer: 5/16
Step-by-step explanation:
First, let's calculate the total number of possible outcomes:
4 options in the first bag and 4 options in the second bag = 16
Here is the list:
23 24 25 26
33 34 35 36
43 44 45 46
53 54 55 56
Next, calculate the total number of outcomes which result in the product of 12, 13, 14, or 15.
Here are their products:
6 8 10 12
9 12 15 18
12 16 20 24
15 20 25 30
There are 5 outcomes that include a product of 12, 13, 14, & 15.
Probability is: (# of satisfactory outcomes)/(total outcomes) = 5/16
Identify 2 objects you could find in a grocery store that holds less than 100 millimeters.
Answer:
a food container and a bowl
How do you find the center and the radius for [tex]x^{2} +y^{2} =25[/tex]?
Answer:
The center is (0,0) and the radius is 5
Step-by-step explanation:
To find the center of a circle, you need to look at the equation
In this case this equation could be written as
[tex](x-0)^2+(y-0)^2=5^2[/tex]
The x value is x=0 for the center and the y values is y=0
The radius can be found by looking at the constant that is squared, so r=5
In the case of an equation like this
[tex](x-1)^2+(y+1)^2=3^2[/tex]
The center point would be (1,-1) and r=3
A person purchased 5k + 2 items for a total cost of 35k 2 + 29k + 6. Find the average cost per item of this purchase.
Answer:
[tex]\boxed{7k + 3}[/tex]
Step-by-step explanation:
Average cost = total cost/number of items = (35k² + 29k + 6)/(5k + 2)
Perhaps the best way to solve this problem is to use long division.
7k + 3
5k + 2)35k² + 29k + 6
35k² + 14k
15k + 6
15k + 6
0
Thus,
[tex]\frac{35k^{2}+29k+ 6}{5k + 2} = 7k+3[/tex]
The average cost per item is [tex]\boxed{7k+3}[/tex].
Answer:7k+3
Step-by-step explanation:
Please help me!!!!!!!!!!!
90 degrees
3 ( square root sign) 10
10√2
Then b = ------------ = 5√2
Answer:
5√2
Step-by-step explanation:
Notice that the sine function links side b, the hypotenuse (10) and the 45° angle:
1
sin 45° = ------ = b/10
√2
Then b = 10√2 / 2 = 5√2
a right triangle has one side that measures 4 in. the angle opposite that side measures 80° what is the length og the hypotenuse if the triangle? round to the nearest tenth.
Answer:
4.06 in.
Step-by-step explanation:
4
sin(80)= ---------- multiply by X
x
x* sin(80)= 4 divide by sin(80)
4
X=------------- simplify
sin(80)
X= 4.06 in.
Answer:
The length of the hypotenuse is 4.1 in
Step-by-step explanation:
By definition, the sine of an angle is:
[tex]sin(x) = \frac{opposite\ side}{hypotenuse}[/tex]
In this case they tell us that the opposite side measures 4 inches and the angle x measures 80 °.
With this information we can find the length of the hypotenuse h
[tex]sin(80\°) =\frac{4}{h}\\\\h = \frac{4}{sin(80\°)}\\\\h = 4.062\ in[/tex]
Finally the length of the hypotenuse is 4.1 in
There are two numbers, one is 7 more than twice the other. The sum of the numbers is 43. Make the equation to find the smaller number. Find the two numbers. Answer: If the smaller number is x, the equation will be . The numbers in ascending order are and .
Answer:
the numbers are 12, 31
Step-by-step explanation:
Factor the following equation to find its zeros.
y = x^2 - 15x +36
A| 12,3
B| Cannot be factored
C| 12, -3
D| -12, -3
Answer:
A| 12, 3
Step-by-step explanation:
The polynomial can be factored by looking for factors of 36 that sum to -15. The sum being negative while the product is positive means both factors will be negative. The answer choices suggest ...
y = (x -12)(x -3)
A quick check shows this product is ...
y = x^2 -12x -3x +36 = x^2 -15x +36 . . . . as required
The factors are zero when x is either 12 or 3.
The zeros of the equation are 12 and 3.
____
Once you realize the constants in the binomial factors both have a negative sign, you can immediately choose the correct answer (A).
Or, you can use Descartes' rule of signs, which tells you that the two sign changes in the coefficients (+-+) mean there are 2 positive real roots.