Answer:
2 days
Step-by-step explanation:
Expected number of days until prisoner reaches freedom=E(x)=?
E(x)=x*p(x)
Where x is the number of days and p(x) is the probability associated with them.
X 1 2 3
P(x) 0.5 0.3 0.2
E(x)=1*0.5+2*0.3+3*0.2
E(x)=0.5+0.6+0.6
E(x)=1.7.
Thus, the expected number of days until prisoner reaches freedom are 2 days.
Find the surface area of a
sphere with a diameter of
15 in.
Can someone please explain how?
Answer:
About 706.5 square inches.
Step-by-step explanation:
Surface area of a sphere is: [tex]SA=4\pi r^2[/tex]
The radius is half the diameter. So, the radius of the given sphere is 7.5 in.
15/2 = 7.5
Find the surface area:
I use 3.14 for pi.
[tex]SA=4*3.14*7.5^2\\\\SA=4*3.14*56.25\\\\SA=12.56*56.25\\\\\boxed{SA=706.5}[/tex]
The surface area is about 706.5 square inches.
Hope this helps.
Answer:
SA=706.86 in²
Step-by-step explanation:
surface area of a sphere = 4πr²
radius r=d/2=15/2=7.5
SA=4(π)(7.5)²
SA=706.86 in²
Suppose that Frida selects a ball by first picking one of two boxes at random and then selecting a ball from this box at random. The first box contains three white balls and two blue balls, and the second box contains four white balls and one blue ball. What is the probability that Frida picked a ball from the first box if she has selected a blue ball
Answer:
3/4
Step-by-step explanation:
Given the following :
Number of boxes = 2
First box :
White balls = 3
Blue balls = 2
Second box:
White balls = 4
Blue balls = 1
What is the probability that Frida picked a ball from the first box if she has selected a blue ball?
Probability (P) = (required outcome / Total possible outcomes)
Probability of picking first box : P(F) = 1/2
Probability of not picking second box :P(S) 1/2
Probability of picking blue from first box : P(B | F) = 3/5
Probability of picking blue, but not from first box : P(Blue not from second box) P(B|S) = 1/5
probability that Frida picked a ball from the first box if she has selected a blue ball?
P(F) * P(B|F) ÷ (P(F) * P(B|F)) + (P(S) * P(B|S))
(1/2 * 3/5) ÷ ((1/2 *3/5) + (1/2 * 1/5)
3/10 ÷ (3/10 + 1/10)
3/10 ÷ 4/10
3/10 * 10/4
= 3/4
Write 70cents to $1.80 as a fully simplified ratio by first converting to the same units, and then simplifying.
Answer:
7 : 18
Step-by-step explanation:
1. Convert to the same units (cents)
70 cents = 70 cents
$1.80 = 180 cents
2. Simplify
70 : 180 (divide both by ten)
7 : 18
7 and 18 cannot be simplified any further.
PLEASE HELP!! It’s for a math class and I can’t figure it out been trying every website nothing has helped!
Answer:
11.6%
I hope this helps!
i need to know the area
Answer:
I got option 1.
Step-by-step explanation:
See pictures
Use the quadratic formula to solve x - 5x+3 = 0.
Answer:
(D) [tex]\begin{array}{*{20}c} {x=\frac{{ 5 \pm \sqrt {13} }}{{2}}} \end{array}[/tex]
Step-by-step explanation:
The quadratic formula is:
[tex]\begin{array}{*{20}c} {\frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} \end{array}[/tex]
Assuming that a is our x² term, b is our x term, and c is the constant, we can substitute inside the equation.
[tex]\begin{array}{*{20}c} {\frac{{ - (-5) \pm \sqrt {5^2 - 4\cdot1\cdot3} }}{{2\cdot1}}} \end{array}[/tex]
[tex]\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {25 - 12} }}{{2}}} \end{array}[/tex]
[tex]\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {13} }}{{2}}} \end{array}[/tex]
So the answer is D, [tex]\begin{array}{*{20}c} {x=\frac{{ 5 \pm \sqrt {13} }}{{2}}} \end{array}[/tex].
Hope this helped!
. Use the quadratic formula to solve each quadratic real equation. Round
your answers to two decimal places. If there is no real solution, say so.
a) x^2 - 5x + 11 = 0
b) -2x^2 - 7x + 15 = 0
c) 4x^2 - 44x + 121 = 0
Answer:
A. No real solution
B. 5 and -1.5
C. 5.5
Step-by-step explanation:
The quadratic formula is:
[tex]\begin{array}{*{20}c} {\frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} \end{array}[/tex], with a being the x² term, b being the x term, and c being the constant.
Let's solve for a.
[tex]\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {5^2 - 4\cdot1\cdot11} }}{{2\cdot1}}} \end{array}[/tex]
[tex]\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {25 - 44} }}{{2}}} \end{array}[/tex]
[tex]\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {-19} }}{{2}}} \end{array}[/tex]
We can't take the square root of a negative number, so A has no real solution.
Let's do B now.
[tex]\begin{array}{*{20}c} {\frac{{ 7 \pm \sqrt {7^2 - 4\cdot-2\cdot15} }}{{2\cdot-2}}} \end{array}[/tex]
[tex]\begin{array}{*{20}c} {\frac{{ 7 \pm \sqrt {49 + 120} }}{{-4}}} \end{array}[/tex]
[tex]\begin{array}{*{20}c} {\frac{{ 7 \pm \sqrt {169} }}{{-4}}} \end{array}[/tex]
[tex]\begin{array}{*{20}c} {\frac{{ 7 \pm 13 }}{{-4}}} \end{array}[/tex]
[tex]\frac{7+13}{4} = 5\\\frac{7-13}{4}=-1.5[/tex]
So B has two solutions of 5 and -1.5.
Now to C!
[tex]\begin{array}{*{20}c} {\frac{{ -(-44) \pm \sqrt {-44^2 - 4\cdot4\cdot121} }}{{2\cdot4}}} \end{array}[/tex]
[tex]\begin{array}{*{20}c} {\frac{{ 44 \pm \sqrt {1936 - 1936} }}{{8}}} \end{array}[/tex]
[tex]\begin{array}{*{20}c} {\frac{{ 44 \pm 0}}{{8}}} \end{array}[/tex]
[tex]\frac{44}{8} = 5.5[/tex]
So c has one solution: 5.5
Hope this helped (and I'm sorry I'm late!)
The equation of line AB is y = 2x + 4. Write an equation of a line parallel to line AB in slope-intercept form that contains point (3, −2). A. y = 2x + 4 B. y = negative 1 over 2 , x − 1 over 2 C. y = − 1 over 2 , x − 7 over 2 D. y = 2x − 8
Answer:
The answer is option DStep-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
y = 2x + 4
comparing with the above equation for a line
The slope / m = 2
Since the lines are parallel their slope are also the same
Slope of parallel line = 2
So we have
The equation of the line using point
( 3 , -2) and slope 2 is
y + 2 = 2( x - 3)
y + 2 = 2x - 6
y = 2x - 6 - 2
We have the final answer as
y = 2x - 8Hope this helps you
Answer:
y=2x-8
Step-by-step explanation:
Given triangle ABC is similar to triangle DEF , calculate the value of BC. Picture is below
Hello! :)
Answer:
[tex]\huge\boxed{BC = 6.4 }[/tex]
Given ΔABC ~ ΔDEF, we can set up a proportion to solve for BC, where:
[tex]\frac{AC}{DF} = \frac{BC}{EF}[/tex]
Let BC = x:
[tex]\frac{8}{15} = \frac{x}{12}[/tex]
Cross multiply:
[tex]8 * 12 = 15 * x[/tex]
[tex]96 = 15x[/tex]
[tex]x = 6.4[/tex]
Therefore, BC = 6.4 units.
Hope this helped you!
Help I don’t know the answer
Answer:
(D) 6
Step-by-step explanation:
We can substitute the values of a (7) and b (-4) into the equation to find it's result.
[tex]\frac{|2a| -b}{3} \\\\\\\frac{|2\cdot7|-(-4)}{3}\\\\\frac{|14|+4}{3}\\\\\frac{14+4}{3}\\\\\frac{18}{3}\\\\ 6[/tex]
So 6 is the value of this expression when a is 7 and b is -4.
Hope this helped!
I NEED THIS ANSWER IN THE NEXT 10 MIN PLS. WILL GIVE BRAINLEST!!! Find the center, vertices, and foci of the ellipse with equation x squared divided by 9 plus y squared divided by 25 = 1.
Answer:
center=0,0 vertices=(0,5)(0,-5) foci=(0,4)(0,-4)
Step-by-step explanation:
used calculator
Solve this quadratic equation.
[tex]2x {}^{2} - 5x + 2 = 0[/tex]
Answer:
x = 1/2 or 2
Step-by-step explanation:
You can factor this as ...
2x^2 -4x -x +2 = 0 . . . rewrite the middle term to enable factoring
2x(x -2) -1(x -2) = 0 . . . . factor by grouping
(2x -1)(x -2) = 0 . . . . factor out (x -2)
x = 1/2, 2 . . . . . . values of x that make the factors zero
Yael used to have a square garage with 254 ft2 of floor space. She recently built an addition to it. The garage is still a square, but now it has 50% more floor space. What was the length of one side of the garage originally? What is the length of one side of the garage now? What was the percent increase in the length of one side?
Answer:
120
Step-by-step explanation:
Tickets for the front section to a rock concert cost $25 each. The back section tickets sold for $15 each. If 400 tickets were sold for a total revenue of $7,500, how many of each each type of ticket were sold? 1. Front – 145, Back – 255 2. Front – 140, Back – 260 3. Front – 155, Back – 245 4. Front – 150, Back – 250
Answer:
150 front tickets and 250 back tickets
Step-by-step explanation:
make 2 equations 25x + 15y = 7500 and x + y = 400 and do substitution on a graphing calculator or by your self.
let me know if this helps
Type the expression that results from the following series of steps:
Start with
y
, times by 4, then subtract 9.
Answer:
4y - 9
Step-by-step explanation:
y×4= 4y
4y-9
In right triangle ΔABC (m∠C = 90°), point P is the intersection of the angle bisectors of the acute angles. The distance from P to the hypotenuse is equal to 4 in. Find the perimeter of △ABC if AB = 12 in.
Answer:
the perimeter of ΔABC is 32in
Step-by-step explanation:
We know that intersection point of the angle bisectors refers to the incenter of the triangle,.
Given tmthe radius of 4inch for the centre of the incircle.
One of the properties of the incircle is that the distances (d) from vertex C to the nearest touchpoints are equal and have the value
In an incircle , the distances (d) along vertex C and touchpoints have equal value and can be expressed as
d = 1/2(a +b -c)
And a, b, c represent lengths of the sides
We were given the hypotenuse (c) as 12 in, with the radius of 4inch for the
distance from the right-angle vertex C to the incircle touchpoints .
We can determine the sum a+b as
4 = (1/2)(a+b -12) .
4/(1/2)= (a+b -12)
8= (a+b -12)
20=a+b
Which is the addition of length of the two legs of the triangle.
We can determine the perimeter which is the addition of the leg lengths as well as the hypotenuse length.
perimeter = 20 in + 12 in = 32 in
Therefore, the perimeter of ΔABC is 32in
Solve for f.
-f + 2 + 4f = 8 - 3
f=
Answer:
1
Step-by-step explanation:
-f + 2 + 4f = 8 - 3
3f = 6 - 3
3f = 3
f = 1
Answer:
f=1
Step-by-step explanation:
-f+2+4f=8-3
First what you want to do i that you want to simplify as best as you can.
-f+2+4f=8-3 becomes 3f+2=8-3 because you add the 4f to the -1f.
Then, just subtract 2 from both sides to get 3f=8-5
Now, simplify even more
3f=8-5 becomes 3f=3
It should be easy now, but if you still need help, divide
f=1
LCM of x<sup>2</sup>+5x+6 and x<sup>2</sup>-x-6 is ………………………
Answer:
[tex] (x^2 - 9)(x + 2) [/tex]
Step-by-step explanation:
Given:
[tex] x^2 + 5x + 6 [/tex]
[tex] x^2 - x - 6 [/tex]
Required:
LCM of the polynomials
SOLUTION:
Step 1: Factorise each polynomial
[tex] x^2 + 5x + 6 [/tex]
[tex] x^2 + 3x + 2x + 6 [/tex]
[tex] (x^2 + 3x) + (2x + 6) [/tex]
[tex] x(x + 3) + 2(x + 3) [/tex]
[tex] (x + 2)(x + 3) [/tex]
[tex] x^2 - x - 6 [/tex]
[tex] x^2 - 3x +2x - 6 [/tex]
[tex] x(x - 3) + 2(x - 3) [/tex]
[tex] (x + 2)(x - 3) [/tex]
Step 2: find the product of each factor that is common in both polynomials.
We have the following,
[tex] x^2 + 5x + 6 = (x + 2)(x + 3) [/tex]
[tex] x^2 - x - 6 = (x + 2)(x - 3) [/tex]
The common factors would be: =>
[tex] (x + 2) [/tex] (this is common in both polynomials, so we would take just one of them as a factor.
[tex] (x + 3) [/tex] and,
[tex] (x - 3) [/tex]
Their product = [tex] (x - 3)(x + 3)(x +2) = (x^2 - 9)(x + 2) [/tex]
A car leaves Orlando, FL and travels east toward West Palm Beach. The
equation D = 280-59t can be used to represent the distance, D, from
Orlando after t hours. In this equation, the 59 represents
A.the car's distance from Orlando
B.the speed of the car
C.the distance between Orlando and West Palm Beach D.the number of hours driving
Answer:
Step-by-step explanation:
A) 280 Km
B) When D = 0: speed, S = 280/59 = 4,9 Km/hour
C) 280 Km
D) 59 hours
What is the area of a circle with a radius of 40 cm?
cm2
(Use 3.14 for Pi.)
hey i suck at math can someone help me with this question
we can subtract the trapezium (white part) formed after from the trapezium (including white and grey) to get area of striped part
area of trapezium is [tex]\frac H2(a+b)[/tex] where $a$ and $b$ are parallel sides.
for bigger trapezium, $h=4$ parallel sides are $5$ and $5$
hence area is $\frac{4(5+5)}{2}=20$
similarily area of white trapezium, $\frac{4(3+3)}{2}=12$
and area of striped part is $20-12=8$
Solve x∕4 + y∕3 = 1 for x.
Answer:
x = [tex]\frac{12-4y}{3}[/tex]
Step-by-step explanation:
Given
[tex]\frac{x}{4}[/tex] + [tex]\frac{y}{3}[/tex] = 1
Multiply through by 12 to clear the fractions
3x + 4y = 12 ( subtract 4y from both sides )
3x = 12 - 4y ( divide both sides by 3 )
x = [tex]\frac{12-4y}{3}[/tex]
The formula for the area of a triangle is A = 12bh, where b is the base of the triangle and h is the height of the triangle. What is the length of the base if the area is 32 cm2 and the height is 4 cm? A. 4 cm B. 8 cm C. 16 cm D. 18 cm
Answer:
guys its 8cm its the most logic answer because 8x 4 is 32, correct me if im wrong
Step-by-step explanation:
Find the area of the following shape. Please show work.
Answer:
Step-by-step explanation:
The area of a triangle is given by the formula:
● A = (b×h)/2
b is the base and h is the heigth.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Draw the heigth. This gives you two small right triangles.
Let's focus on the right one containing 45°.
● sin 45° = h/8
● h = sin 45° × 8 = 4√(2)
■■■■■■■■■■■■■■■■■■■■■■■■■■
Replace h by its value in the area formula. The base is 17
● A = (17× 4√(2))/ 2
● A = 34√(2)
● A = 48.08
Round to the nearest unit
● A = 48
Answer:
Area = 48 sq. units
Step-by-step explanation:
will make it short and simple.
area of a triangle = 1/2 * a * b * sinФ
area = 1/2 * 17 * 8 * sin(45°) = 48 sq. units
3. One rule of thumb for estimating crowds is that each person Occupies 2.5 square feet.
Use this rule to estimate the size of the crowd watching a parade along the 1-mile
section of the route in Question 2.
mile
Answer:
5.83142789
Step-by-step explanation:
did it on a graphing calculator, hope this helps
Microsoft Excel might be useful when establishing relationships involving vertex-edge graphs.
O True
False
Answer:
True
Step-by-step explanation:
Microsoft Excel is a great tool and has saved me on countless occasions in graphs and tables. I agree with the earlier answer by Hedland.
An 8-pack of beaded necklaces costs $7.60. What is the unit price?
Answer:
The unit price is $0.95 per pack.
Step-by-step explanation:
To find the unit price, we must find the price per pack of beaded necklaces. To do this, we should divide the total price ($7.60) by the number of items in the package (8).
$7.60/8 = $0.95
Therefore, the answer is that the unit price is $0.95.
Hope this helps!
someone help me really quick
Answer:
u^18
Step-by-step explanation:
(u^3)^6
=
u^(3*6)
=
u^18
Hope this helps!
The length of the major axis of the ellipse below is 10 What is the sum of the lengths of the red and blue line segments? A. 10 B. 5 C. 15 D. 20
Answer:
A. 10
Step-by-step explanation:
As we know that
The length of the major axis of the ellipse is 10
i.e
2 a = 10
Also, the ellipse is the curve that consists of 2 focal points in order that the total of the distance to the 2 focal points would remain constant for each and every point displayed in the curve
Now we assume that P is the curve point
So,
PF1 + PF2
i.e
2 a (blue line) + (red line)
2 a = 10
Therefore the sum of the length is 10
Answer:
10
Step-by-step explanation:
The number of polynomials having zeros as -2 and 5 is a)1 b)2 c)3 d)more than 3
Answer:
d) More than 3.
Step-by-step explanation:
The polynomial (x - 5)(x + 2) ( = x^2 - 3x + 10) has zeros of -2 and 5 but so have the polynomials formed by multiplying this by any integer:
- for example 2(x - 5)(x + 2) , 4(x - 5)(x + 2) and so on.
