The probability that the two candies selected by Laura from the box are taffy which has 14 candies in it: 3 are butterscotch, 7 are peppermint, and 4 are taffy is 0.230.
What is the conditional probability?The conditional probability is the happening of an event, when the probability of occurring of other event is given.
A box has 14 candies in it: 3 are butterscotch, 7 are peppermint, and 4 are taffy. (Each candy falls into only one of these categories.)
Let A is the event of selecting taffy in first attempt. Thus, the probability of it is,
[tex]P(A)=\dfrac{4}{14}[/tex]
Now 13 candies remain, in which 3 taffy candies are present. Let B is the event of selecting taffy in again. Thus, the probability of it is,
[tex]P(B)=\dfrac{3}{13}[/tex]
The probability of happening both event is,
[tex]P(A\cap B)=\dfrac{4}{14}\times\dfrac{3}{13}\\P(A\cap B)=\dfrac{12}{182}[/tex]
The probability that the two candies selected by Laura from the box are taffy is,
[tex]P(B| A)=\dfrac{\dfrac{12}{182}}{\dfrac{4}{14}}\\P(B| A)=0.230[/tex]
Thus, the probability that the two candies selected by Laura from the box are taffy which has 14 candies in it: 3 are butterscotch, 7 are peppermint, and 4 are taffy is 0.230.
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At noon, ship A is 170 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing north at 15 km/h. How fast (in km/hr) is the distance between the ships changing at 4:00 p.m.? (Round your answer to three decimal places.)
Distance is the product of speed and time. The rate at which the distance between the ships changes at 4:00 p.m is 27.293 km/h.
What is the distance?Distance is the product of speed and time. It is given by the function,
[tex]\rm Distance = Time \times speed[/tex]
Given at noon the distance between two ships is 170 km. Furter ship A is moving towards the east at a speed of 40 km/h, therefore, the distance covered by Ship A in 4 hours will be,
[tex]\rm \text{Distance covered by Ship A in 4 hours} = 4 \times 40 = 160\ km[/tex]
The distance covered by Ship B in 4 hours will be,
[tex]\rm \text{Distance covered by Ship B in 4 hours} = 4 \times 15= 60\ km[/tex]
At 4 pm the distance between the two ships is the hypotenuse of the red triangle as shown below,
[tex]\rm Hypotenuse = \sqrt{10^2 + 60^2} = \sqrt{100+3600 }= 60.827\ km[/tex]
The rate of change in the distance between the two ships can be written as,
[tex]\rm \text{Rate of change of distance} = \dfrac{170-60.827}{4} = 27.293\ km/h[/tex]
Hence, the rate at which the distance between the ships changes at 4:00 p.m is 27.293 km/h.
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help pretty please!
Cyrus lives 11 miles due south of Adriana, Adriana live 19 miles due west of Jane, Jane lives 12 miles due south of Madisyn.
The shortest distance between Cyrus' house and Jane's house is
•21.95
•481.802
•0.52
The shortest distance between Adriana's house and Madisyn's house is
•504.901
•22.47
•44.42
Answer:
A.) 21.95
B.)22.47
Step-by-step explanation:
A.) An easy way to solve this is to use the Pythagorean theorem. Since the only person between Cyrus and Jane is Adriana, we will use her as a measuring point. Adriana's distance to Jane is 19, we will set a = 19, Adriana also is 11 miles away from Cyrus, and we will set b = 11. Now we plug it into the Pythagorean theorem.
[tex]a^2+b^2=c^2\\19^2+11^2=c^2\\\sqrt{482} =\sqrt{c^2}\\ 21.95=c[/tex]
B.) Using the same principle but for Adriana and Madisyn, we will use Jane as she is between them. Adriana is 19 miles from Jane, so we will set a=19, Madisyn is also 12 miles from Jane, so we will set b=12. Plug it for the Pythagorean theorem.
[tex]a^2+b^2=c^2\\19^2+12^2=c^2\\505=c^2\\\sqrt{505}=\sqrt{c^2}\\ 22.47 = c[/tex]
Kristina house is 11 3/10 Luke house is 9 2/10
Answer:
they are 3 1/10 units away from each other
Step-by-step explanation:
11 3/10 - 9 2/10
3 1/10
please help and please leave a legit answer
Answer:
y= -12/x + 3
Step-by-step explanation:
Here's my answer
At midnight the temperature
was -12°C. Twelve hours
later the temperature had risen
19°C. What was the midday
temperature?
Answer:
7C
Step-by-step explanation:
Plss answer it, it is supposed to be done-
Use the shape to complete Questions 8, 9, and 10.
8. Draw a triangle around a point
9. Draw a box around a line segment.
10. Circle an angle.
The answers to the question are all attached given that they are all drawings. The subject here is shapes, lines, and angles.
What is a Triangle around a Point?A triangle around a point is a triangle that is constructed such that a point is equidistant from all the angles and all the sides that triangle. This point is thus referred to as the circumcenter of the triangle.
The triangle in the attached image is drawn around point D.
What is a Line Segment?A Line segment is the part of a line with two endpoints. The box in the diagram is drawn between points A and B.
What does it mean to circle an angle?When you put a circle around an angle, you have circled that angle. This most case is used to highlight an angle.
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The area of the circle
Answer:
A=1
4πd2=1
4·π·122≈113.09734
Step-by-step explanation:
Answer:
113.04 feet :)
Step-by-step explanation:
First we divide 12 by 2 to find the radius!
12/2 = 6
Now we can solve!!
3.14(6^2)
3.14(36)
113.04
Have an amazing day!!
Please rate and mark brainliest!!
Please help!
Olivia's mom decided to wallpaper the living room. At the store, the wallpaper was selling for $11.68 for a roll with 100 linear feet. What is the price per linear foot of the wallpaper?
I need help figuring out the answers
Answer:
The answer would be The answer would be 26 meters squared.
Step-by-step explanation:
1. Identify three rectangles
(The ones I identified were 5 by 2 [twice!] and 3 by 2)
2. Do 5x2 (10)
3. Do 5x2 again (10)
4. Do 3x2 (6)
5. Add 10, 10, and 6, to get 26
6. Label to get 26 meters squared. I hope this helps! :)
Liz wants to hang a painting on her
wall so that it is centered. The wall is
110 inches wide, and the painting is
28 inches wide.
3
Determine how far the edges of the
painting need to be from the ends of
the wall, expressed as a mixed number.
Answer:
[tex]41\frac{1}{8}[/tex]
Shortly after their arrival, Europeans began introducing pigs to the Americas as a source of food. Some escaped, and others were intentionally released into the wild,
where they thrived. Assume that the wild pig population is modeled by the
formula P = P0•(1.2)^t .If there were five million wild pigs in 2010 (no one really knows the exact number), what was the population of wild pigs in 2000?
Answer: About 800 thousand
The more accurate value is 807,528 but this is also an approximation.
=======================================================
Work Shown:
[tex]t = \text{number of years since the year 2000}[/tex]
[tex]P_0 = \text{population (in millions) in the year 2000}[/tex]
[tex]P = P_0(1.2)^t\\\\5 = P_0(1.2)^{10}\\\\5 \approx P_0*6.1917364224\\\\P_0 \approx \frac{5}{6.1917364224}\\\\P_0 \approx 0.80752791444922\\\\P_0 \approx 0.807528\\\\[/tex]
That's the rough population of wild pigs (in millions) for the year 2000.
Multiply by [tex]10^6[/tex] to get it in terms of units instead.
[tex]0.807528\times10^6 = 807,528[/tex]
There were roughly 800 thousand wild pigs in the year 2000.
help me find Find m< G .
Answer:
∠G=110°
Step-by-step explanation:
The 4 interior angles of a kite add up to 360. 100+40=140. 360-140=220. E and G are the only angles left so we know together they must equal 220. And ∠E and ∠G are congruent angles beceause of kite rules. So, we divide by 2 to get how much angle E and G are individually.
How can you use mental math to find 195 × 6?
HELP, i need help!!!!!!!!!!!!!!
Answer:
t = 7.46, 0.42
Explanation:
h = 126t - 16t² [ "h" is height, "t" is time ]
when height is 50 feet
126t - 16t² = 50-16t² +126t -50 = 016t² -126t +50 = 0==================
[tex]\sf use \ quadratic \ formula : x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ ax^2 + bx + c = 0[/tex]
==================
[tex]\Longrightarrow \sf t = \dfrac{-126\pm \sqrt{126^2-4\left(-16\right)\left(-50\right)}}{2\left(-16\right)}[/tex]
[tex]\Longrightarrow \sf t = \dfrac{63\pm\sqrt{3169}}{16}[/tex]
[tex]\Longrightarrow \sf t = 7.46, \ 0.42[/tex]
Let's find
h=126t-16t²Put h=50
-16t²+126t=50-16t²+126t-50=0Use quadratic formula
[tex]\\ \rm\Rrightarrow t=\dfrac{-126\pm\sqrt{126²-4(-16)(-50)}}{-32}[/tex]
[tex]\\ \rm\Rrightarrow t=7.5s,0.4s[/tex]
Find the area of the figure.
A) 114 cm2
B) 350 cm2
C) 418 cm2
D) 447 cm2
Answer:
418 cm2
Step-by-step explanation:
Divide the figure into a square and a triangle. Find the area of each and add. Make sure you do not combine them, and do one at a time.
s2 = area of square
192 = 361 cm
BH= area of triangle
(6)(19) = 57 cm2
361 + 57 = 418 cm
Answer:
c= 418cm2
Step-by-step explanation:
good bye now human
Alyssa is enrolled in a public-speaking class. Each week she is required to give a speech of
greater length tharr the speech she gave the week before. The table below shows the
lengths of several of her speeches.
Alyssa's Speeches
Answer: this question search it up because i don't think and know if anyone knows this even i don't know so sorry
Step-by-step explanation:
A triangle has sides with lengths of 6 yards, 10 yards, and 12 yards. Is it a right triangle?
yes
no
Submit
F(x)=2x^2+7x-5 and g(x)=-8x^2-3x+5
What is g(x) +f(x)
What is the area of the figure?
A. 18 yd
B. 54 yd
C. 72 yd
D. 90 yd
What is the answer to 3/4 times 6?
Answer:
4.5 or 4 1/2
Step-by-step explanation:
An easy way to do this problem is to divide 6 by 4, the denominator (1.5) then multiply it by the numerator, 3, which will now be 4.5.
Mikes parents bought him new gaming console he gets 72612312 games n puts in 5312 how much does he have left
Answer:
Seventy-two million, six hundred and seven thousand games remaining
please mark brainliest
Answer:
72607000
Step-by-step explanation:
just subtract 5312 from 72612312
39 28. If y = (1 - 3x), find the value of dy! dx at x = -1.
Answer:
the answer to this question is 52.18
i need help with this one
The value of x from the given figure is 8
How to calculate the interior angle of a triangleA triangle is a 2-dimensional shape with 3 sides an interior angle
Since the sum of the interior angles of a triangle is 180 degrees, hence;
8x - 4 + 76 + 44 = 180
8x + 116 = 180
8x = 180 - 116
8x = 64
x = 64/8
x = 8
Hence the value of x from the given figure is 8
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Worth 100 points IF answered correctly:
Answer:
8/6
Step-by-step explanation:
Sam has 8 times the number of eggs Kyle has can be expressed as:
[tex]\displaystyle \large{8\cdot \dfrac{1}{6}}[/tex]
As given, the number of eggs Kyle has is 1/6 so out of 6 eggs, Kyle only had 1.
Therefore, 8 multiplies/times the number of eggs is:
8/6
Amelia needs to buy some dog food. At the nearest store ,5 bags of dog food cost 12.50 how much would Amelia spend on three bags
Answer:
$7.50
Step-by-step explanation:
the question can be represented with:
12.5/5 and x/3
12.5/5 is 2.5, so that means each bag of dog food is $2.5
So then you multiply 2.5 by 3, = 1.20, so 3 bags of dog food is $7.50.
Answer:
Step-by-step explanation:
Remark
I take it you mean 5 and not 0.5.
If that is the case, this is a proportion question. A proportion consists of 4 parts. If you know 3 of the parts, you can solve for the 4th one.
Formula
Number of bags/Cost = new number of bags/Cost of the new number
Givens
original Number of bags = 5
Cost = 12.50
New number of bags = 3 bags
Cost = x
Solution
5/12.50 = 3/x Cross Multiply
5x = 12.50 * 3 Combine the right
5x = 37.5 Divide by 5
5x/5 = 37.5/5
x = 7.5
Answer: 3 bags cost 7.50 dollars.
Convert 85 miles per hour to meters per second. (Use 1.61 km = 1 mile)
show the steps
Answer:
38.0 m/s
Step-by-step explanation:
Units conversion can be done by multiplying by appropriate conversion factors. Each conversion factor has a value of 1: the numerator is equal to the denominator, but the units are different. The units are chosen so that cancelling unwanted units gives the set of units you want.
__
[tex]\dfrac{85\text{ mi}}{1\text{ h}}\times\dfrac{1.61\text{ km}}{1\text{ mi}}\times\dfrac{1000\text{ m}}{1\text{ km}}\times\dfrac{1\text{ h}}{3600\text{ s}}=\dfrac{85\cdot1.61\cdot1000\text{ m}}{3600\text{ s}}\\\\\approx\boxed{38.0\text{ m/s}}[/tex]
Approximate square root of 35 using an appropriate linear approximation.
Answer:
5.91
Step-by-step explanation:
35 is between the perfect squares 25 and 36.
√25 = 5
√36 = 6
/ 5 25 \
| d 10 |
1 < x 35 > 11
| 1 |
\ 6 36 /
11/1 = 10/d
11d = 10
d = 0.909
√35 = 5 + d = 5.909
√35 = 5.91
how many gallons each of 25% alcohol and 5% alcohol should be mixed to obtain 20 gal of 8% alcohol?
[tex]\begin{array}{lcccl} &\stackrel{solution}{gallons}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{gallons of }}{pure~alcohol}\\ \cline{2-4}&\\ \textit{25\% solution}&x&0.25&0.25x\\ \textit{5\% solution}&y&0.05&0.05y\\ \cline{2-4}&\\ mixture&20&0.08&1.6 \end{array}~\hfill \begin{cases} ~\hfill x + y &= 20\\\\ 0.25x+0.05y&=1.6 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=20\implies \underline{y = 20-x}} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.25x~~ + ~~0.05(\underline{20-x})~~ = ~~1.6}\implies 0.25x+1-0.05x=1.6 \\\\\\ 0.20x+1=1.6\implies 0.2x=0.6\implies x=\cfrac{0.6}{0.2}\implies \boxed{x=3}[/tex]
Help pls! pls explain too
Help again please 33 points
Answer:
the answer is 56in2
Step-by-step explanation:
[tex]b = 14in \\ h = 8in \\ area \: of \: triangle = \frac{1}{2} b \times h \\ = \frac{1}{2} \times 14 \times 8 \\ = 56inches[/tex]
