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Mandarinka [93]
2 years ago
8

Mario and Bowser begin with a hat that has 5 balls in it: 3 are red, 2 are green. Bowser secretly picks a ball and tells Mario i

t is red, although he might be lying about the color. If there is an 80% chance Bowser is lying, what is the probability that Mario draws 2 red balls in a row after Bowser's initial draw?
Mathematics
1 answer:
dangina [55]2 years ago
5 0
20% probability. because 100-80=20 so therefore it would be 20%
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Suppose f and g are continuous functions such that g(2) = 6 and lim x → 2 [3f(x) + f(x)g(x)] = 36. find f(2).
True [87]

Answer: f(2) = 4

Step-by-step explanation:

F(x) and g(x) are said to be continuous functions

Lim x=2 [3f(x) + f(x)g(x)] = 36

g(x) = 2

Limit x=2

[3f(2) + f(2)g(2)] = 36

[3f(2) + f(2) . 6] = 36

[3f(2) + 6f(2)] = 36

9f(2) = 36

Divide both sides by 9

f(2) = 36/9

f(2) = 4

7 0
2 years ago
Tony and Manuel were trimming the branches of a tree. Tony was using an 18 ft ladder and Manuel was using a 24 ft ladder. Both l
REY [17]

Answer:

9.33 feet = 111.96 inches

Step-by-step explanation:

If we have similar triangles, the rate between matching sides is the same.

So the length of the smaller ladder (18 ft) over the length of the taller ladder (24 ft) is equal to the distance from the bottom of the smaller ladder to the tree (7 ft) over the distance from the bottom of the taller ladder to the tree (x ft):

18 / 7 = 24 / x

x = 7 * 24 / 18

x = 9.33 feet

To find this measure in inches, we just need to multiply by 12:

x = 9.33 * 12 =  111.96 inches

3 0
2 years ago
Henry is designing a model for a dome shaped glasshouse. He creates the model and records the horizontal distance from the edge
dolphi86 [110]

Answer:

Correct choice is B

Step-by-step explanation:

All given options represent quadratic function. Let the equation of this quadratic function be

f(x)=ax^2+bx+c.

Then

1. f(0)=2=a\cdot 0^2+b\cdot 0+c\Rightarrow c=2;

2. f(1)=7.5=a\cdot 1^2+b\cdot 1+c\Rightarrow 7.5=a+b+2;

3. f(2)=12=a\cdot 2^2+b\cdot 2+c\Rightarrow 12=4a+2b+2.

Solve the system of two equations:

\left\{\begin{array}{l}a+b+2=7.5\\4a+2b+2=12\end{array}\right.\Rightarrow\left\{\begin{array}{l}a=5.5-b\\4(5.5-b)+2b=10\end{array}\right.

Then

22-4b+2b=10,\\ \\-2b=-12,\\ \\b=6,\\ \\a=5.5-6=-0.5.

Thus, the equation of the function is

f(x)=-\dfrac{1}{2}x^2+6x+2.

Note that

f(3)=-\dfrac{1}{2}\cdot 3^2+6\cdot 3+2=-4.5+20=15.5;

f(4)=-\dfrac{1}{2}\cdot 4^2+6\cdot 4+2=18.

8 0
2 years ago
Read 2 more answers
The mean yearly rainfall in Sydney, Australia, is about 134 mm and the standard deviation is about 66 mm ("Annual maximums of,"
svetlana [45]

Answer:

At least 202.44 mm in the top 15%.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 134, \sigma = 66

How many yearly mm of rainfall would there be in the top 15%?

At least X mm.

X is the 100-15 = 85th percentile, which is X when Z has a pvalue of 0.85. So X when Z = 1.037.

Z = \frac{X - \mu}{\sigma}

1.037 = \frac{X - 134}{66}

X - 134 = 66*1.037

X = 202.44

At least 202.44 mm in the top 15%.

5 0
2 years ago
For the school's sports day, a group of students prepared 12 1/2 litres of lemonade. At the end of the day they had 2 5/8 litres
Hoochie [10]

Given :

For the school's sports day, a group of students prepared 12 1/2 litres of lemonade. At the end of the day they had 2 5/8 litres left over.

To Find :

How many litres of lemonade were sold.

Solution :

Initial amount of lemonade, I = 12 1/2 = 25/2 litres.

Final amount of lemonade, F = 2 5/8 = 21/8 litres.

Amount of lemonade sold, A = I - F

A = 25/2 - 21/8 litres

A = 9.875 litres

Therefore, 9.875 litres of lemonade were sold.

Hence, this is the required solution.

7 0
2 years ago
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