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ycow [4]
3 years ago
9

There are only red counters and blue counters in a bag. The ratio of red counters to blue counters is 5:4. There are 27 blue cou

nters. How many red counters are there?
Mathematics
1 answer:
Anastaziya [24]3 years ago
7 0

Answer:

<em>33.75 red counters</em>

Step-by-step explanation:

Given the ratio of the  red counters to  blue counters as 5:4. The total ratio will be 5 + 4 = 9

If there are 27 blue counters in the bag, the total amount of counters there will be gotten using the expression;

4/9 * x = 27

x is the total counter in the bag.

4x/9 = 27

4x = 9*27

x = (9*27)/4

x = 60.75

The amount of red counters there will be

red counters = Total - blue counter

red counter = 60.75 - 27

<em>red counter = 33.75 red counters</em>

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Step-by-step explanation:

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3 years ago
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal dist
Tcecarenko [31]

Answer:

a. 0.7291

b. 0.9968

c. 0.7259

Step-by-step explanation:

a. np and n(1-p) can be calculated as:

np=23\times 0.48\\\\=11.04\\\\n(1-p)=23(1-0.52)\\\\=11.96

#Both np and np(1-p) are greater than 5, hence, normal approximation is most appropriate:

\mu_x=11.04\\\\\sigma^2=np(1-p)=0.48\times 0.52\times 23=5.7408

#Define Y:

Y~(11.04,5.7408)

P(X\leq 12)\approx P(Y\leq 12.5)\\\\P(Z\leq \frac{(12.5-11.04)}{\sqrt{5.7408}})=\\\\=1-0.2709\\\\=0.7291

Hence, the probability of 12 or fewer is 0.8291

b. The  probability that 5 or more fish were caught.

#Using normal approximation:

P(X \geq 5) \approx P(Y \geq 4.5) = P(Z \geq\frac{ (4.5-11.04)}{\sqrt{(5.7408)}})\\\\=1-0.0032\\\\=0.9968

Hence, the probability of catching 5+ is 0.9968

c. The probability of between 5 and 12 is calculated as;

-From b above P(X\geq 5)=0.9968 and a ,P(X\leq 12)=0.7291

P(5\leq X\leq 120\approx P(4.5\leq Y\leq  12.5)\\\\=0.7291-(1-0.9968)\\\\=0.7259

Hence, the probability of between 5 and 12 is 0.7259

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3 years ago
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3 years ago
Find the missing side length XI. round your answer to the nearest tenth.​
lianna [129]

Answer: XI = 10.35 mm

Step-by-step explanation:

Considering the given triangle XIF, to determine XI, we would apply the sine rule. It is expressed as

a/SinA = b/SinB = c/SinC

Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Likening it to the given triangle, the expression becomes

XI/SinF = XF/SinI = FI/SinX

The sum of the angles in a triangle is 180°. It means that

F + 63 + 52 = 180

F = 180 - (63 + 52)

F = 65°

Therefore

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Cross multiplying, it becomes

XISin52 = 9Sin65

0.788XI = 9 × 0.906

0.788XI = 8.154

XI = 8.154/0.788

XI = 10.35

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3 years ago
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