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3 years ago

A major baseball diamond is a square with side lengths of 90 feet.

Mathematics

1 answer:

iren2701 [21]3 years ago

7 0

Answer: $\bold{a)\quad 90\sqrt2\qquad \qquad b)\quad 45\sqrt2}$

<u>Step-by-step explanation:</u>

Since you are looking for the distance from home plate to second base, you are actually looking for the length of the diagonal of the square. Use the Pythagorean Theorem: a² + b² = c² where a and b are the side lengths and c is the length of the diagonal.

$90^2+90^2=c^2\\8100+8100=c^2\\16200=c^2\\\sqrt{16200}=c\\\boxed{90\sqrt2}=c\qquad \qquad \text{which is approximately 127.28}\\\\\\\\\text{Halfway between home plate and 2nd base means divide that length by 2:}\\\\\dfrac{90\sqrt2}{2}=\boxed{45\sqrt2}$

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A researcher reports a 98% confidence interval for the proportion of Drosophila in a population with mutation Adh-F to be [0.34,

Fantom [35]

Answer:

$0.34 \leq p \leq 0.38$

For this case we can conclude that with 98% of confidence the true proportion of Drosophila in a population would be between 0.34 and 0.38.

But that doesn't means that we have 98% of PROBABILITY that the true proportion would be between 0.34 and 0.38, because we are constructing a confidence interval with sample data and we can't analyze this using probability.

Then the best answer is:

2. False

Step-by-step explanation:

For this case we have a confidence interval for the proportion of Drosophila in a population with mutation Adh-F to be given by:

$0.34 \leq p \leq 0.38$

For this case we can conclude that with 98% of confidence the true proportion of Drosophila in a population would be between 0.34 and 0.38.

Then the best answer is:

2. False

3 0

3 years ago

Simplify the expression.<br> -2 + 2/5b - 1/4b +6=

OleMash [197]

Answer:

3b/20+4

Step-by-step explanation:

-2 + 2/5b - 1/4b + 6

Combine 2/5b and 1/4b to get 3/20b

-2 + 3/20b + 6

Add −2 and 6 to get 4.

4+3/20b

8 0

3 years ago

Find −315÷134. Write your answer as a mixed number in simplest form.

kipiarov [429]

Answer:

$-2\frac{47}{134}$

Step-by-step explanation:

$-2\frac{47}{134} = -\frac{315}{134}$

$134$ can go into $-315$ twice at the most, so doubling $134$ will give us $268$ , which leaves us with $47$ left over to reach 315, which is why $47$ is the numerator. The remainder is ALWAYS the numerator.

I am joyous to assist you anytime.

3 0

3 years ago

For a normal distribution,

Anni [7]

Answer:

1.282, -0.5244,...

Step-by-step explanation:

We know that Z is a standard normal variate with mean =0, and std dev =1

a) z-score separates the highest 10% from the rest of the scores

= 90th percentile = 1.282

b) z-score separates the lowest 30% from the rest of the scores

= 30th percentile = -0.5244

c) z-score separates the lowest 40% from the rest of the scores

= 40th percentile = -0.2533

d) z-score separates the lowest 20% from the rest of the score

=20th percentile = -0.8416

7 0

3 years ago

Find the equation of a circle with a center at (–7, –1) where a point on the circle is (–4, 3).

gogolik [260]

Answer:

(x + 7)^2 + (y + 1)^2 = 25.

Step-by-step explanation:

The center of a circle is easy to set up. According to the formula below, the formula for the circle will be (x - a)^2 + (y - b)^2 = r^2.

In this case, a = -7 and b = -1, so we have...

(x - (-7))^2 + (y - (-1))^2 = r^2

(x + 7)^2 + (y + 1)^2 = r^2

To get the radius, we need to find the distance between the center and the point on the circle. The distance formula is d = sqrt((x2 - x1)^2 + (y2 - y1)^2).

In this case, x2 = -4, x1 = -7, y2 = 3, and y1 = -1.

sqrt((-4 - -7)^2 + (3 - -1)^2) = sqrt((-4 + 7)^2 + (3 + 1)^2) = sqrt((3)^2 + (4)^2) = sqrt(9 + 16) = sqrt(25) = plus or minus 5.

Since distance can only be positive, the distance is 5 units, meaning that the radius is 5 units.

5^2 = 25

So, your equation should be (x + 7)^2 + (y + 1)^2 = 25.

Hope this helps!

8 0

3 years ago