Kevin read the number''two hundred seven thousand,forty-eight'' in the book.What is this number in standard form?

The probability that Jane will go to a ballgame (event A) on a Monday is 0.73, and the probability that Kate will go to a ballga

cricket20 [7]

Events A and B are called independent, when

$Pr(A\cap B)=Pr(A)\cdot Pr(B),$

otherwise events A and B are dependent.

The events A, B and A∩B are:

A - Jane will go to a ballgame on Monday;
B - Kate will go to a ballgame on Monday;
A∩B - Kate and Jane both go to the ballgame on Monday.

$Pr(A)=0.73,\ Pr(B)=0.61,\ Pr(A\cap B)=0.52.\\ \\ Pr(A)\cdot Pr(B)=0.73\cdot 0.61=0.4453\neq 0.52=Pr(A\cap B).$

Answer: events A and B are dependent

4 0

3 years ago

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The hypotenuse of a 45°-45°-90° triangle measures 10 StartRoot 5 EndRoot in. A right triangle is shown. The hypotenuse has a len

suter [353]

Answer:

$5\sqrt{10}\ units$

5 StartRoot 10 EndRoot

Step-by-step explanation:

we know that

The legs of a 45°-45°-90° triangle are congruent

Let

x ----> the length of one leg of the triangle

Applying the Pythagorean Theorem

$c^2=a^2+b^2$

where

c is the hypotenuse

a and b are the legs

we have

$c=10\sqrt{5}\ units$

$a=b=x\ units$

substitute

$(10\sqrt{5})^2=x^2+x^2$

$500=2x^2\\x^2=250\\x=\sqrt{250}\ units$

Simplify

$x=5\sqrt{10}\ units$

5 StartRoot 10 EndRoot

4 0

2 years ago

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Carlos is using the distributive property to evaluate the expression 14 (49) by using friendlier numbers. His work is shown belo

Mrac [35]

Answer:

The 1st error that Carlos made was in Step 2...

In step 2 , Carlos multiplied 14 only with 40. If he would have multiplied 14 with both 40 & 9 , then it could have been alright.....

3 0

2 years ago

Which pair of expressions has equivalent values? 1 Superscript 13 and 1 Superscript 15 6 Superscript 1 and 9 Superscript 1 7 Sup

lora16 [44]

Answer:

1 Superscript 13 and 1 Superscript 15

Step-by-step explanation:

The process of exponentiation can be mathematically written as:

a^b

where a is called the base, and b is called the exponent.

Basically it means that we have to multiply the base with itself as many times as the value of the exponent.

For example 2^4 is 2•2•2•2

Having this in mind, 1^13 and 1^15 have equivalent values, because no matter how many times we multiply 1 with itself it will always be equal to 1.

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2 years ago

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Without properly working spark plugs, a vehicle will not run. For a specific vehicle, the spark plugs are supposed to have a gap

Salsk061 [2.6K]

Answer:

The probability that the spark plugs are supposed to have a gap between 3.9mm and 4.3mm.

P(3.9≤X≤4.3) = 0.9922

Step-by-step explanation:

Step(i):-

Given that the mean of the Normal distribution = 4.1mm

Given that the standard deviation of the Normal distribution = 0.0075mm

Let 'X' be the random variable in a normal distribution

Given that X₁ = 3.9mm

$Z_{1} = \frac{X_{1} -mean}{S.D}$

$Z_{1} = \frac{3.9 -4.1}{0.075} = -2.666$

Given that X₂ = 4.3mm

$Z_{2} = \frac{X_{2} -mean}{S.D}$

$Z_{1} = \frac{4.3 -4.1}{0.075} = 2.666$

Step(ii):-

The probability that the spark plugs are supposed to have a gap between 3.9mm and 4.3mm.

P(3.9≤X≤4.3) = P(-2.666≤Z≤2.666)

= P(Z≤2.666)-P(Z≤-2.666)

= 0.5 +A(2.666) - (0.5-A(2.666)

= 2 × A(2.666)

= 2×0.4961

= 0.9922

Final answer:-

The probability that the spark plugs are supposed to have a gap between 3.9mm and 4.3mm.

P(3.9≤X≤4.3) = 0.9922

3 0

1 year ago