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garik1379 [7]
3 years ago
11

A coin and a pentagonal spinner with edges marked A, B, C, D and E are tossed and twirled simultaneously. Find the probability o

f getting A head and a D A tail and either an A or a D.
Mathematics
1 answer:
Andre45 [30]3 years ago
5 0

Answer:

(Head and D) = 1/10

(Tails and A or D) = 1/5

Step-by-step explanation:

A coin has two sides so that a 50% chance that it will land on heads or tails

A pentagonal spinner has a 40% chance that it will land on D or A.

P (Heads) = 1/2

P (D)= 1/5

1/2 · 1/5 = 1/10

P (Heads and D) = 1/10

____________________________________________________________

P (Tails) = 1/2

P(A or D) = 2/5

1/2 · 2/5 = 1/5

P (Tails and A or D) = 1/5

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A standard weight known to weigh 10 grams. Some suspect bias in weights due to manufacturing process. To assess the accuracy of
notsponge [240]

Answer:

a) The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams

b) 49 measurements are needed.

Step-by-step explanation:

Question a:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.98}{2} = 0.01

Now, we have to find z in the Ztable as such z has a pvalue of 1 - \alpha.

That is z with a pvalue of 1 - 0.01 = 0.99, so Z = 2.327.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 2.327\frac{0.0003}{\sqrt{5}} = 0.00031

The lower end of the interval is the sample mean subtracted by M. So it is 10.0044 - 0.00031 = 10.00409 grams

The upper end of the interval is the sample mean added to M. So it is 10 + 0.00031 = 10.00471 grams

The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams.

(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence?

We have to find n for which M = 0.0001. So

M = z\frac{\sigma}{\sqrt{n}}

0.0001 = 2.327\frac{0.0003}{\sqrt{n}}

0.0001\sqrt{n} = 2.327*0.0003

\sqrt{n} = \frac{2.327*0.0003}{0.0001}

(\sqrt{n})^2 = (\frac{2.327*0.0003}{0.0001})^2

n = 48.73

Rounding up

49 measurements are needed.

7 0
2 years ago
2. Simplify. 7 + 8a – 2 + 9a
Alik [6]
5 + 17a is the answer you are looking for
8 0
3 years ago
Read 2 more answers
F(x)=2x^2-x+1 find the vertex
Galina-37 [17]

The Answer fam is (1/4,7/8)

5 0
3 years ago
What is the equation of a line that is perpendicular to −x+2y=4 and passes through the point (−2, 1) ? Enter your equation in th
ANTONII [103]
Perpendicular lines have slopes that multiply to get -1
y=mx+b is the slope intercept equation
m=slope

so get into y=mx+b form
-x+2y=4
solve for y
add x both sides
2y=x+4
divide by 2 both sides
y=(1/2)x+2
the slope is 1/2

perppendicular line slope multiplies to -1
1/2 times what=-1
times 2/1 both sides
what=-2/1=-2

y=-2x+b
find b
we are given a point is (-2,1)
when x=-2, y=1
1=-2(-2)+b
1=4+b
minus 3 both sides
-3=b

so the equation is
y=-2x-3

your teacher might want it in standard form (ax+by=c) so
add 2x both sides
2x+y=-3 is an equation


so y=-2x-3 is correct (slope intercept form)
2x+y=-3 is also correct (standard form)
6 0
2 years ago
"If the probability of an event is observed repeatedly during independent repetitions than the ratio of the observed to the tota
PIT_PIT [208]

Answer:

This is the Law of <u>large</u> Numbers.

Step-by-step explanation:

The Law of Large numbers states that as the sample size is increased the sample mean value gets closer to the population mean.

That is, as <em>n</em> → ∞ the value of \bar x → μ.

For instance, the theoretical probability of getting a Heads in a toss of a coin is, 0.50.

To check this perform an experiment whether the coin is tossed 20 times.

The probability of heads will be somewhere near 0.50.

Now toss the coins 50 times.

The probability of heads will be now closer to 0.50.

Now toss the coins 100 times.

The probability of heads will be approximately equal to 0.50.

Thus, as the number of tosses was increased the probability of getting a head is closer tot he theoretical probability.

Thus, the complete statement is:

This is the Law of <u>large</u> Numbers.

3 0
2 years ago
Read 2 more answers
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