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1 year ago

Gavyn rolls a fair dice 540 times. How many times would Gavyn expect to roll a four?

Mathematics

2 answers:

Kisachek [45]1 year ago

5 0

Answer:

135

We need to divide 540/4 which gives us 135

Flura [38]1 year ago

3 0

540 / 4 = 135 times.

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Traffic speed: The mean speed for a sample of cars at a certain intersection was kilometers per hour with a standard deviation o

aliina [53]

Answer:

Step-by-step explanation:

Hello!

X₁: speed of a motorcycle at a certain intersection.

n₁= 135

X[bar]₁= 33.99 km/h

S₁= 4.02 km/h

X₂: speed of a car at a certain intersection.

n₂= 42 cars

X[bar]₂= 26.56 km/h

S₂= 2.45 km/h

Assuming

X₁~N(μ₁; σ₁²)

X₂~N(μ₂; σ₂²)

and σ₁² = σ₂²

<em>A 90% confidence interval for the difference between the mean speeds, in kilometers per hour, of motorcycles and cars at this intersection is ________.</em>

The parameter of interest is μ₁-μ₂

(X[bar]₁-X[bar]₂)± $t_{n_1+n_2-2}$ * $Sa\sqrt{\frac{1}{n_1} +\frac{1}{n_2} }$

$t_{n_1+n_2-2;1-\alpha /2}= t_{175; 0.95}= 1.654$

$Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{134*16.1604+41*6.0025}{135+42-2} } = 3.71$

[(33.99-26.56) ± 1.654 *( $3.71*\sqrt{\frac{1}{135} +\frac{1}{42} }$ )]

[6.345; 8.514]= [6.35; 8.51]km/h

<em>Construct the 98% confidence interval for the difference μ₁-μ₂ when X[bar]₁= 475.12, S₁= 43.48, X[bar]₂= 321.34, S₂= 21.60, n₁= 12, n₂= 15</em>

$t_{n_1+n_2-2;1-\alpha /2}= t_{25; 0.99}= 2.485$

$Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{11*(43.48)^2+14*(21.60)^2}{12+15-2} } = 33.06$

[(475.12-321.34) ± 2.485 *( $33.06*\sqrt{\frac{1}{12} +\frac{1}{15} }$ )]

[121.96; 185.60]

I hope this helps!

3 0

2 years ago

The Venn diagram shows the results of two events resulting from rolling a number cube.

tankabanditka [31]

Answer:

$P(A|B)=\frac{2}{3}$

$P(A)*P(B)=\frac{1}{3}$

$P(A) =\frac{2}{3}$

$P(B) =\frac{1}{2}$ .

Step-by-step explanation:

We use the Venn diagram to calculate the desired probabilities.

Note that there are 6 possible results in the sample space

S = {1, 2, 3, 4, 5, 6}

Then note that in the region representing the intercept of A and B there are two possible values.

$P (A\ and\ B) = \frac{2}{6} = \frac{1}{3}$

In the region that represents event A there are 4 possible outcomes {4, 5, 1, 2}

$P(A) = \frac{4}{6} = \frac{2}{3}$

In the region that represents event B there are 3 possible outcomes {1, 2, 6}

$P(B) = \frac{3}{6} = \frac{1}{2}$ .

Now

$P(A | B)=\frac{P(A \ and\ B)}{P(B)}\\\\P(A | B)=\frac{\frac{1}{3}}{\frac{1}{2}}\\\\P(A|B)=\frac{2}{3}$

$P(A)*P(B)=\frac{2}{3}*\frac{1}{2}=\frac{1}{3}$

6 0

2 years ago

A certain shade of green paint is made from 5 parts yellow mixed with three parts blue if 2 cans of yellow are used how many can

wariber [46]

Because the ratio of yellow to blue can be expressed as 5/3, you would solve the equation 5/3= 2/x. To solve, you would get x alone by cross multiplying and getting 5x=6. Divide both sides by 5 and get 6/5 or 1 and 1/5 cans of blue paint

5 0

2 years ago

Two identical decks of 52 cards are mixed together, yielding a stack of 104 cards. How many different ways are there to order th

kumpel [21]

Answer:

here the order will be 104! = $1.029e^{166}$

Step-by-step explanation:

since the cards are to arranged in no particular order that is why we used combination to find the result.

Combination can simply be explained as the method of selecting items from a collection of items where the order of the selections does not matter.

7 0

2 years ago

M<2=34 find m<4 and explain how you know

Naily [24]

Angle 4 equals 34 degrees since angle 2 and 4 are opposite angles and opposite angles are congruent

6 0

2 years ago