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2 years ago

2. How much extra snow would a child need to make a snowball with a diameter of 8

Mathematics

1 answer:

BlackZzzverrR [31]2 years ago

7 0

Answer:

62.8 cm²

Step-by-step explanation:

First, you figure out the areas of both snowballs:

πr² = π4² = 3.14 × 16 = 50.24

πr² = π6² = 3.14 × 36 = 113.04

Then you subtract the two measurements:

113.04 - 50.24 = 62.8

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Find all the zeros of the equation 12x^2-64=-x^4

Natalija [7]

Answer: all the zeroes of the above equation will be

(x-4)(x+4)(x-2)(x+2)

Step-by-step explanation:

Since we have given that

$12x^2-64=-x^4\\\\x^4+12x^2-64=0$

We need to find the zeroes of the above equation.

So, we will use "Split the middle terms" :

$x^4+12x^2-64=0\\\\x^4+16x^2-4x^2-64=0\\\\x^2(x^2-16)-4(x^2-16)=0\\\\(x^2-4)(x^2-16)=0\\\\x^2-4=0\ or\ x^2-16=0\\\\\text{ "Using }a^2-b^2=(a+b)(a-b)"\\\\x^2-4=x^2-2^2=(x-2)(x+2)\\\\x^2-16=x^2-4^2=(x+4)(x-4)$

So, all the zeroes of the above equation will be

(x-4)(x+4)(x-2)(x+2)

7 0

2 years ago

The heights of students at a college are normally distributed with a mean of 175 cm and a standard deviation of 6 cm. One might

frosja888 [35]

Answer:

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 175cm

Standard deviation = 6 cm

Percentage of students below 163 cm

163 = 175 - 2*6

So 163 is two standard deviations below the mean.

By the Empirical rule, 95% of the heights are within 2 standard deviations of the mean. The other 100-95 = 5% are more than 2 standard deviations of the mean. Since the normal distribution is symmetric, 2.5% of them are more than 2 standard deviations below the mean(so below 163cm) and 2.5% are more than two standard deviations above the mean.

2.5% of the students have heights less than 163cm.

Out of 1000

0.025*1000 = 25

25 is the answer

8 0

2 years ago

Read 2 more answers

What is the value of x in simplest radical form?

Ostrovityanka [42]

In this case, we will use our Pythagorean Theorem.

a = 84
b = 13
c = x

$\sqrt{84^2 + 13^2} = 85$

Thus, x = 85.

8 0

2 years ago

Read 2 more answers

A guy wire is used to support flagpoles in windy areas. These wires are anchored in the ground to provide constant stability. Yo

r-ruslan [8.4K]

Answer: a) Length of wire to replace old one=9ft

b) Length of wire=3.09ft

Leftover wire=0.91ft

Step-by-step explanation: from the right angle triangle, Tan&=20/15

&=53.13°

Length of wire,x=cos 31.13=x/15

15cos31.13

X=9

b) Tan&=10/6

Tan^-110/6

&=59.05

Length= 6cos59.04

X=3.09

4-3.09=.91= leftover wire

8 0

2 years ago

Below are boxplots that summarize the weights (in pounds) of large samples from two breeds of dog: the Anatolian Shepherd and th

koban [17]

Answer:

(a) The median of both plots is same, 120 pounds is the median weight of Anatolian Shepherd and the Black Russian Terrier breed.

The range of both plots is also same that is 75 pounds.

The box plot of Anatolian Shepherd is skewed towards left therefore, it is considered to be positively distributed.

The box plot of Black Russian Terrier is skewed towards right therefore, it is considered to be negatively

(b) Any data point which is greater than 155 or smaller than 80 will be considered an outlier.

Step-by-step explanation:

A box plot is a graph which shows five statistical characteristics of a data set.

1. Maximum value

2. Minimum value

3. Median

4. Upper Interquartile

5. Lower interquartile

(a) Compare the distributions of weights for the two dog breeds

Please refer to the attached diagram of the question.

The median of both plots is same, 120 pounds is the median weight of Anatolian Shepherd and the Black Russian Terrier breed.

The range of Anatolian Shepherd is,

Range = Maximum value - Minimum value

Range = 175 - 100 = 75 pounds

The range of Black Russian Terrier is,

Range = Maximum value - Minimum value

Range = 155 - 80 = 75 pounds

Therefore, the range of both plots is also same that is 75 pounds.

A box-plot is considered to be normally distributed when the median is at the center of upper quartile and lower quartile.

The box plot of Anatolian Shepherd is skewed towards left therefore, it is considered to be positively distributed.

The box plot of Black Russian Terrier is skewed towards right therefore, it is considered to be negatively distributed.

(b) What weights would a Black Russian Terrier have to be to be considered an outlier?

An outlier is a data point in the data set that is very different from the other data points.

In this case, the maximum and minimum values in the Black Russian Terrier box-plot are

Maximum = 155

Minimum = 80

Therefore, any data point which is greater than 155 or smaller than 80 will be considered an outlier.

5 0

2 years ago