All categories

2 years ago

A special 8-sided die is marked with the numbers 1 to 8. It is rolled 20 times with these outcomes:

Mathematics

2 answers:

Advocard [28]2 years ago

8 0

Answer:

One: C

Two: 60% and 10%

Step-by-step explanation:

horsena [70]2 years ago

4 0

Answer:

One: B

Two: 60% and 10%

Step-by-step explanation:

Problem One

There are only two numbers in the sample of 40 that are under 26. Both are 25. If you find more, make the adjustment. There are 2 more that are exactly 26 but they are not counted because the directions say "less than 26."

So set up your proportion

x/2000 = 2/40 Multiply both sides by 2000

x = 2/40 * 2000

x = 4000/40

x = 100

I don't know where 5 comes from. But it is not correct.

B should be the correct answer.

Exactly 100 pieces should be defective. That is the theoretical result. C is incorrect.

D is not correct. The sample size would not be 40. It would have to be 2000 for D to be correct. So D is wrong.

We have enough data to get an answer. E is incorrect.

Problem 2

The think you must NOT do is count 1 as being prime. The prime numbers are 2 3 5 7 between 1 and 8. They break down as follows.

Prime Number of them
2 3
3 4
5 2
7 3

The total number of primes = 12

There are 20 numbers in the sample

The experimental probability of tossing a prime is 12/20 * 100% = 60%

The non primes are 2 3 5 7 which is 4 out of 8

4/8 * 100 = 50%

The experimental value is 10% more than the theoretical value.

Discussion

Note: the problem may be one. This all depends on what you have been told about 1. I am using the exact wording of prime here. 1 is not a prime. It is also not a composite. So it has to be counted as part of the non primes.

You might be interested in

The diagram shows some land in the shape of a quadrilateral ABCD. AB = 6 km, AD = 5 km and CD = 12 km Angle BAC = 30 The land is

Goshia [24]

Answer:

£495 million

Step-by-step explanation:

To find out the total cost of the land, we need to first calculate the area of the land.

Step 1: Find area of right angled triangle ADC

AD = 5 km,

DC = 12 km

Area of the right triangle = ½*a*b

a = 5km

b = 12km

Area = ½*5*12

= 5*6

Area of ADC = 30 km²

Step 2: Find the area of triangle ABC

First, let's find the length of AC using Pythagorean theorem

AC² = AD² + DC²

AC² = 5² + 12² = 25 + 144

AC = √169

AC = 13km

Area of ∆ABC = ½*AB*AC*sin(30°)

= ½*6*13*0.5

= 3*13*0.5

Area of ∆ABC = 19.5 km²

Total area of the land = area of ∆ADC + ∆ABC = 30 + 19.5 = 49.5 km²

Step 3: calculate how much the land costs

If the land costs £10 million per km²,

Cost of 49.5 km² = 49.5 × 10 = £495 million

4 0

2 years ago

Anu bought an air cooler as shown below. Its water tank is in the shape of a cuboid and can take 40 litres of water. Its dimensi

Ksivusya [100]

Answer:

40 cm

Step-by-step explanation:

Using the conversion

1 litre = 1000 cm³, then

40 litres = 40 × 1000 = 40000 cm³

The volume ( V) of a cuboid is

V = lbh ( divide both sides by bh )

l = $\frac{V}{bh}$ = $\frac{40000}{50(20)}$ = $\frac{40000}{1000}$ = 40 cm

8 0

2 years ago

Evaluate the series shown. Then write an equivalent series using summation notation such that the lower index starts at 0.

Vitek1552 [10]

The summation indicates the sum from n = 1 to n = 3 of the expression 2(n+5).

2 (n+5) = 2n + 10

2n + 10 denotes an Arithmetic Series, with a common difference of two and first term as 12.

For n =1, it equals 12
For n = 2, it equals 14
For n = 3, it equals 16

So the sum from n=1 to n=3 will be 12 + 14 + 16 = 42

Sum of an Arithmetic Series can also be written as:

$S_{n} = \frac{n}{2}(2a_{1} +(n-1)d)$

Using the value of a₁ and d, we can simplify the expression as:

$S_{n} = \frac{n}{2} (24+2(n-1)) \\ \\ 
 S_{n} =n (12+(n-1))\\ \\ 
 S_{n} =n (11+n)$

This expression is equivalent to the given expression and will yield the same result.

For n=3, we get the sum as:

S₃ = 3(11+3) = 42

8 0

2 years ago

Read 2 more answers

Malachi took cans to the recycling plant and put them into the can-crusher one at a time. after he had already crushed some of t

ioda

2/3
it is 2/3 or not I don't know

3 0

2 years ago

Read 2 more answers

Information reference tables what is the solution set of the equation log4 (x2 + 3x) − log4 (x + 5) = 1?

faust18 [17]

Use this property of logarithms:

$\log_b\left(\dfrac{x}{y}\right)=\log_b x-\log_b y$

Your equation transforms into:

$log_4\left(\dfrac{x^2+3x}{x+5}\right)=1$

Now, you have to apply the definition of a logarithm to express the equation in exponential form:

$\dfrac{x^2+3x}{x+5} = 4^1$

In case you don't remember, this is the definition of a logarithm:

$\log_b x = y \iff b^y = x$

The log is the exponent (y) you have to raise the base (b) to in order to get the power (x).

Finally, solve the rational equation:

$\dfrac{x^2+3x}{x+5} =4 \iff x^2+3x=4(x+5)$
$\iff x^2-x-20=0$
$\iff x=\dfrac{1\pm\sqrt{(-1)^2-4\cdot(-20)}}{2}= \left \{ {{5} \atop {-4}} \right.$

The correct answer is d.

5 0

2 years ago