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2 years ago

8

Sharon is decreasing the size of a diagram of a leaf that is 30 centimeters long by 10 centimeters wide if the reduced diagram i

s 4 cm wide how long will it be

1 answer:

Lyrx [107]2 years ago

4 0

Do it in ratio form, 30/10=x/4, 30*4=120/10=12. it will be 12 centimeters long

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A certain type of thread is manufactured with a mean tensile strength of 78.3 kilograms and a standard deviation of 5.6 kilogram

azamat

Answer:

(a) The variance decreases.

(b) The variance increases.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we take appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Then, the mean of the sample mean is given by,

$\mu_{\bar x}=\mu$

And the standard deviation of the sample mean is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

The standard deviation of sample mean is inversely proportional to the sample size, <em>n</em>.

So, if <em>n</em> increases then the standard deviation will decrease and vice-versa.

(a)

The sample size is increased from 64 to 196.

As mentioned above, if the sample size is increased then the standard deviation will decrease.

So, on increasing the value of <em>n</em> from 64 to 196, the standard deviation of the sample mean will decrease.

The standard deviation of the sample mean for <em>n</em> = 64 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{64}}=0.7$

The standard deviation of the sample mean for <em>n</em> = 196 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{196}}=0.4$

The standard deviation of the sample mean decreased from 0.7 to 0.4 when <em>n</em> is increased from 64 to 196.

Hence, the variance also decreases.

(b)

If the sample size is decreased then the standard deviation will increase.

So, on decreasing the value of <em>n</em> from 784 to 49, the standard deviation of the sample mean will increase.

The standard deviation of the sample mean for <em>n</em> = 784 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{784}}=0.2$

The standard deviation of the sample mean for <em>n</em> = 49 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{49}}=0.8$

The standard deviation of the sample mean increased from 0.2 to 0.8 when <em>n</em> is decreased from 784 to 49.

Hence, the variance also increases.

6 0

2 years ago

The curvature of the Tacoma Narrows Bridge in

8_murik_8 [283]

Answer:

Width of the arch = 105 m

Step-by-step explanation:

Function representing the width of the arch,

f(x) = -0.016(x - 52.5)² + 45

where x = width of the base of the arch or horizontal distance from arch's left end

f(x) = vertical distance of the arch

From the given quadratic function, vertex of the parabola is (52.5, 45).

Coordinates of the vertex represents,

Height of the arch = 45 m

Half of the horizontal distance from the left end = 52.5 m

Therefore, width of the bridge = 2(Half the width of the bridge from left end) = 2×52.5

= 105 m

Therefore, given bridge is 105 m wide.

4 0

2 years ago

After triangle ace is dilated by a factor of 5, it has an area of 100 square inches. What was its area before dilation?

NISA [10]

Answer:

20in^2

Step-by-step explanation:

Since you multiply the original area of the triangle by the scale factor to get the new area, you can find the original area (before dilation) by dividing the dilated triangle's area by the scale factor. Since 100 is the area of the dilated triangle, and 5 is your scale factor, you do 100/5 to get the area of the triangle before it was dilated.

5 0

2 years ago

The sum of 6 consecutive even numbers is <br> 270.<br> What is the second number in this sequence?

KonstantinChe [14]

Lets find all the numbers..

x (1st number)
x + 2 ( 2nd number)
x + 4 (3rd number)
x + 6 (4th number)
x + 8 (5th number)
x + 10 (6th number)

Now add all those expressions and set them equal to 270 because that is the total.

x + x + 2 + x + 4 + x + 6 + x + 8 + x + 10 = 270
6x + 30 = 270
6x = 240
x = 40

Now we will substitute 40 for x in the expression of the second number.

x + 2
40 + 2
42

So the second number is 42

Hope this helps :)

4 0

2 years ago

A boat is traveling east across a river that is 112 meters wide at 8 meters per second. If the river has a northward current of

andreyandreev [35.5K]

This is the concept of application of the Pythagorean theorem. The resultant speed of the motorboat which is crossing the river that has a northward current of 5 m/s at a speed of 8 m/s will be given by:
c^2=a^2+b^2
c^2=8^2+5^2
c^2=64+25
c^2=89
c=sqrt89
c=9.4 m/s

6 0

2 years ago

Read 2 more answers