A conical container, with vertex down, has a height of 6 cm and a diameter of 2 cm. It is leaking water at
the rate of 1 cubic centimeter per minute. Find the rate at which the water level h is dropping when h = 3 cm.

Traveling from Earth to Mars is approximately 9.249626 x 10^7 km farther than traveling from Earth to the moon.

Earth to Mars is compared to traveling from Earth to the moon, we need to calculate the difference between the distances.

The distance from Earth to the moon is approximately 3.74 x 10^5 km.

The distance from Earth to Mars is approximately 9.25 x 10^7 km.

To find the difference, we subtract the distance to the moon from the distance to Mars:

9.25 x 10^7 km - 3.74 x 10^5 km

To subtract these numbers, we need to make sure the exponents are the same. We can rewrite the distance to the moon in scientific notation with the same exponent as the distance to Mars:

3.74 x 10^5 km = 0.374 x 10^6 km (since 0.374 = 3.74 x 10^5 / 10^6)

Now we can perform the subtraction:

9.25 x 10^7 km - 0.374 x 10^6 km = 9.25 x 10^7 km - 0.374 x 10^6 km

To subtract, we subtract the coefficients and keep the same exponent:

9.25 x 10^7 km - 0.374 x 10^6 km = 9.25 x 10^7 - 0.374 x 10^6 km

Simplifying the subtraction:

9.25 x 10^7 - 0.374 x 10^6 km = 9.249626 x 10^7 km

Therefore, traveling from Earth to Mars is approximately 9.249626 x 10^7 km farther than traveling from Earth to the moon.

Scientific notation is a convenient way to express very large or very small numbers. It consists of a coefficient (a number between 1 and 10) multiplied by a power of 10 (exponent). It allows us to write and manipulate such numbers in a compact and standardized form.

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Answer:

119 ft ^2

Step-by-step explanation:

area of a triangle = 1/2 x base x height

=1/2 x 17 x 14

=119

There is no whole number by which you can multiply or divide 16087 to make it a perfect square.

To determine by which number you should multiply or divide 16087 to make it a perfect square, we can analyze its prime factorization. The prime factorization of 16087 is 13 × 1237.

In order to make 16087 a perfect square, we need each prime factor to have an even exponent. However, when we examine the prime factors of 16087, we find that both 13 and 1237 have an exponent of 1.

To make the exponents even, we need to multiply or divide 16087 by additional prime factors and their respective exponents. However, since 16087 is a product of two prime numbers (13 and 1237), we cannot introduce any additional prime factors to make the exponents even.

A perfect square is a number that can be expressed as the product of two equal factors. In the case of 16087, it cannot be transformed into a perfect square by multiplying or dividing by any whole number. The prime factors 13 and 1237 remain with an exponent of 1 each, indicating that there is no integer that can be applied to make them equal and convert 16087 into a perfect square.

Therefore, there is no whole number by which you can multiply or divide 16087 to make it a perfect square.

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The toast will land with buttered side 50% of the time.

First,

H₀:p=0.5, H₁: p₀ ≠0.5

P(butttered side down)= 19/51

π₀= 0.5

n= 51

Now, z = (p- π₀)/ √π₀(1-π₀)/n

z= (19/51 -0.5)/√0.5(1-0.5)/51

z= -1.82

as, α= 0.01 and \(z_{\alpha/2\)=  2.58

So, |z| < | \(z_{\alpha/2\)|

Thus, it reject H₀.

Thus, the toast will land with buttered side 50% of the time.

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Answer:

1) \(0.0826052-2.776\frac{0.000013424}{\sqrt{5}}=0.082588\)    

\(0.0826052+2.776\frac{0.000013424}{\sqrt{5}}=0.0826219\)    

b) \( ME= 2.776\frac{0.000013424}{\sqrt{5}}=0.0000166653\)

And we want 2/3 of the margin of error so then would be: \( 2/3 ME = 0.00001111\)

The margin of error is given by this formula:

\( ME=z_{\alpha/2}\frac{s}{\sqrt{n}}\)    (1)

And on this case we have that ME =0.00001111016 and we are interested in order to find the value of n, if we solve n from equation (1) we got:

\(n=(\frac{z_{\alpha/2} s}{ME})^2\)   (2)

Replacing we got:

\(n=(\frac{2.776(0.000013424)}{0.00001111})^2 =11.25 \approx 12\)

So the answer for this case would be n=12 rounded up to the nearest integer

Step-by-step explanation:

Information given

0.082601, 0.082621, 0.082589, 0.082617, 0.082598

We can calculate the sample mean and deviation with the following formulas:

\( \bar X= \frac{\sum_{i=1}^n X_i}{n}\)

\(s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}\)

\(\bar X=0.0826052\) represent the sample mean

\(\mu\) population mean

s=0.000013424 represent the sample standard deviation

n=5 represent the sample size  

Part 1

The confidence interval for the mean is given by the following formula:

\(\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}\)   (1)

The degrees of freedom, given by:

\(df=n-1=5-1=4\)

The Confidence level is 0.95 or 95%, and the significance would be \(\alpha=0.05\) and \(\alpha/2 =0.025\), the critical value would be using the t distribution with 4 degrees of freedom: \(t_{\alpha/2}=2.776\)

Now we have everything in order to replace into formula (1):

\(0.0826052-2.776\frac{0.000013424}{\sqrt{5}}=0.082588\)    

\(0.0826052+2.776\frac{0.000013424}{\sqrt{5}}=0.0826219\)    

Part 2

The original margin of error is given by:

\( ME= 2.776\frac{0.000013424}{\sqrt{5}}=0.0000166653\)

And we want 2/3 of the margin of error so then would be: \( 2/3 ME = 0.00001111\)

The margin of error is given by this formula:

\( ME=z_{\alpha/2}\frac{s}{\sqrt{n}}\)    (1)

And on this case we have that ME =0.00001111016 and we are interested in order to find the value of n, if we solve n from equation (1) we got:

\(n=(\frac{z_{\alpha/2} s}{ME})^2\)   (2)

Replacing we got:

\(n=(\frac{2.776(0.000013424)}{0.00001111})^2 =11.25 \approx 12\)

So the answer for this case would be n=12 rounded up to the nearest integer

Answer: B C E

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

using the rule of exponents

\(a^{m}\) ÷ \(a^{n}\) = \(a^{(m-n)}\) , then

\(6^{9}\) ÷ 6³ = \(6^{(9-3)}\) = \(6^{6}\)

Not all intersecting lines are perpendicular.

Perpendicular lines require a 90-degree angle of intersection, creating the formation of right angles.

Nonetheless, unlike perpendicular lines that necessitate exactly 90 degrees of intersections, other types of driven lines can be at varying angles beside these.

As such, it is critical to highlight that in general intersecting lines come with different angles of intersection, and only those featuring exact 90-degree angle of intersection become normal cases of intersecting lines, becoming one among many subtypes existing today.

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2:5 = 2/5

2/5 x 150

2 x 30= 60km

Answer:

there are 2 Magnesium and Nitrogen

Step-by-step explanation:

Answer:

domain: all natural numbers greater than zero and less than or equal to 21

Step-by-step explanation:

You cannot go for zero nights, and the maximum number of nights you can stay is 21. You also cannot have fractional night, so your answer has to be in natural numbers.

The angle formed by the two hands have a measure less than 1/4 turn

From the question, we have the following parameters that can be used in our computation:

A clock with the hour hand at 12 and the minute hand at 2

The turn represented by the above is represened as

Turn = (2 * 30)/360

When simplified, we have

Turn = 1/6

Next, we have

Angle at the turn = 1/4

1/6 is less than 1/4

This means that the angle formed by the two hands have a measure less than 1/4 turn

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The distance across the lot, or the altitude of the trapezoid, is 60 feet.

Let's denote the length of the shorter base by x, and the length of the longer base by y. Then, we can use the formula for the area of a trapezoid:

Area = (x + y) * h / 2,

where h is the altitude (distance across the lot) and Area is given as 8,400 square feet.

We also know that the sum of the bases is 280 feet, so x + y = 280.

Now we can solve for h:

h = 2 x  Area / (x + y)

Substituting the given values, we get:

h = 2 x  8,400 / 280 = 60 feet.

Therefore, the distance across the lot, or the altitude of the trapezoid, is 60 feet.

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Answer:25.13

Step-by-step explanation:

use the formulas

C=2πr

d=2r

Solution:

Given:

The increase in price from 2003 to 2021 is;

The percent increase is gotten by;

Therefore, the percent increase is approximately 4.85%

Answer:

The graph that best represents the slope is Graph A.

Hope this helps!!

Ronald originally had $163

He spent a total of $123.45 on school clothes. The money he had left after the expenditure is $39.55 . The total money he had originally can be calculated as follows:

Therefore,

let

x = the original amount he had

Variable are numbers that are represented by letter in a mathematical equation,.

x - 123.45 = 39.55

x = 39.55 + 123.45

x = $163

The amount he originally had is $163

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The area A of the region between the two curves x = y^3–4y^2+3y and x+y=y^2 is 11.8334.

The graph of the question is given below:

We have to evaluate the integral needed to determine the area A of the region between the two curves x = y^3–4y^2+3y and x+y=y^2 i.e. x = y^2-y.

Now the area A of the given region is:

A = \(\int^1_{y=0}\left[g(y)-f(y)\right]dy+\int^4_{y=1}\left[g(y)-f(y)\right]dy\)

A = \(\int^1_{y=0}\left[(y^3-4y^2+3y)-(y^2-y)\right]dy+\int^4_{y=1}\left[(y^2-y)-(y^3-4y^2+3y)\right]dy\)

A = \(\int^1_{y=0}\left[y^3-4y^2+3y-y^2+y)\right]dy+\int^4_{y=1}\left[y^2-y-y^3+4y^2-3y)\right]dy\)

A = \(\int^1_{y=0}\left[y^3-5y^2+4y\right]dy+\int^4_{y=1}\left[5y^2-y^3-4y)\right]dy\)

Further simplification

A = \(\left[\frac{y^4}{4}-\frac{5y^3}{3}-\frac{4y^2}{2}\right]^1_{y=0}+\left[\frac{5y^3}{3}-\frac{y^4}{4}-\frac{4y^2}{2}\right]^4_{y=1}\)

A = \(\left[(\frac{1}{4}-\frac{5}{3}-2)\right-(0-0+0)]+\left[(\frac{320}{3}-64-32)\right-(\frac{5}{3}-\frac{1}{4}-2)]\)

A = (3-20+24)/12 + 320/3 - 96 - (20-3-24)/12

A = 7/12 + 32/3 + 7/12

A = (7+128+7)/12

A = 142/12

A = 11.8334

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Answer:

Step-by-step explanation:

The reading that separates the rejected thermometers from the others is given as follows:

1.175 ºC.

The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is obtained by the equation presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation for this problem are given as follows:

\(\mu = 0, \sigma = 1\)

The 12% higher of temperatures are rejected, hence the 88th percentile is the value of interest, which is X when Z = 1.175.

Hence:

1.175 = X/1

X = 1.175 ºC.

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A completely randomized design is an appropriate design to use in this situation because There is no blocking variable, and incentive plans will be randomly assigned to the workers.

A completely randomized design (CRD) is the simplest design for comparative experiments because it employs only two basic experimental design principles: randomization and replication.

By randomization, we mean that the experimental units' run sequence is determined at random.

Treatments are assigned to experimental units or plots in a completely random manner in CRDs. CRD can be used for either single-factor or multifactor experiments.

According to the question,

The quality control manager of a large factory wants to find out the number of defective items . For that 10 workers are selected Randomly and these worker will work on item according 3 incentive plans Means Replication is 3.

Hence , A completely randomized design is an appropriate design to use in this situation because There is no blocking variable, and incentive plans will be randomly assigned to the workers.

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Answer:

24a+6=12a

Step-by-step explanation:

6(4a+1)

24a+6

2a X 6= 12a

24a+6=12a

The answer is: Pm= pm/n

1 whole, 1 whole, 3/5, 1 whole,6/7, 1 whole,6/9, 8/10, 6/13, and 6/7 i think but im not positive

The Division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

To find the division of the sum of (7/8), (15/4), and (1/12) by their multiplication, we first need to calculate the sum and multiplication of the given fractions.

The sum of the fractions is:

(7/8) + (15/4) + (1/12)

To add these fractions, we need a common denominator. The least common multiple of 8, 4, and 12 is 24. Let's convert each fraction to have a denominator of 24:

(7/8) = (21/24)

(15/4) = (90/24)

(1/12) = (2/24)

Now we can add the fractions:

(21/24) + (90/24) + (2/24) = (113/24)

The multiplication of the fractions is:

(7/8) * (15/4) * (1/12)

To multiply fractions, we multiply the numerators and denominators:

(7*15*1) / (8*4*12) = (7/96)

Now we can divide the sum of the fractions by their multiplication:

(113/24) / (7/96)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

(113/24) * (96/7) = (2712/168)

Therefore, the division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

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The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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