A small barrel can hold 2041.11 cubic centimeters sand. The radius of a barrel is 7 cm, what is the height of the barrel? Use 3.14 for pi. Round your answer to the nearest hundredth

Using the trigonometric ratios:

(1). sinA = 5/13, cosA = 12/13 and tanA = 5/13. And by Pythagoras rule:

(2). x = √116

(3). x = 90

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

(1). sinA = 5/13 {opposite/hypotenuse}

cosA = 12/13 {adjacent/hypotenuse}

tanA = 5/13 {opposite/adjacent}

By Pythagoras rule

(2). x = √(4² + 10²)

x = √(16 + 100)

x = √116

(3). 106² = x² + 56²

x² = 106² - 56²

x = √(11236 - 3136)

x = √8100

x = 90

Therefore, using trigonometric ratios:

(1). sinA = 5/13, cosA = 12/13 and tanA = 5/13. And by Pythagoras rule;

(2). x = √116

(3). x = 90

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Answer:

It depends if you need to simplify or find the factor. If its to simply the answer is 3a^3+3a^3+9a+3

if you need the factor the answer is

3(a^3+a^2+3a+1)

Answer:

19/20 , 1 1/4 , 1 4/5

Step-by-step explanation:

1.8 = 1 4/5 (fraction)

1.8 converts to 18/10. This can be simplified twice, firstly by making it 9/5 since both 18 and 10 are divisible by two, but can be simplified further to 1 4/5

1.25 = 1 1/4 (fraction)

1.25 converts to 125/100. This can be simplified to 5/4 or 1 1/4

0.95 = 19/20 (fraction)

0.95 converts to 95/100. This can be simplified to 19/20

Ascending Order (smallest to largest)

smallest - 19/20

middle - 1 1/4

largest - 1 4/5

I believe this is the right answer, but haven't done fractions in a while so may want to double check to make sure

a. C = 5.00 + 0.75t

b. It will cost Elaine $23.00 to park her car for a full 24 hours at the parking lot.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we can use the following equation:

C = 5.00 + 0.75t

In this equation, the constant term 5.00 represents the flat fee for parking, and the term 0.75t represents the additional cost per hour based on the number of hours (t) the car is parked. By adding the flat fee to the hourly cost, we get the total parking cost for t hours.

(b) To find out how much it will cost Elaine to park her car for a full 24 hours, we can substitute t = 24 into the equation:

C = 5.00 + 0.75 * 24

Calculating this expression, we get:

C = 5.00 + 18.00

C = 23.00

Therefore, it will cost Elaine $23.00 to park her car for a full 24 hours at the parking lot.

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Answer:

\(\log_{10}\sqrt{a} -\dfrac{3}{4}=\dfrac{1}{2}\log_{10}a-\dfrac{3}{4}\)

Step-by-step explanation:

Given:

\(x=\dfrac{\sqrt{10a\sqrt{0.1}}}{10}\)

Therefore:

\(\implies \log_{10}x=\log_{10}\left(\dfrac{\sqrt{10a\sqrt{0.1}}}{10} \right)\)

\(\textsf{Apply the log quotient law}: \quad \log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay\)

\(\implies \log_{10}\sqrt{10a\sqrt{0.1}}-\log_{10}10\)

\(\textsf{Apply log law}: \quad \log_aa=1\)

\(\implies \log_{10}\sqrt{10a\sqrt{0.1}}-1\)

\(\textsf{Apply radical rule: $\sqrt{ab}=\sqrt{a}\sqrt{b}$, \quad assuming $a \geq 0,\;b\geq 0$}\)

\(\implies \log_{10}\left(\sqrt{10}\sqrt{a}\sqrt{\sqrt{0.1}}}\right)-1\)

\(\textsf{Apply the log product law}: \quad \log_axy=\log_ax + \log_ay\)

\(\implies \log_{10}\sqrt{10} + \log_{10}\sqrt{a} + \log_{10}\sqrt{\sqrt{0.1}}}\right)-1\)

Rewrite the radicals:

\(\implies \log_{10} \left(10\right)^{\frac{1}{2}} + \log_{10}\sqrt{a} + \log_{10}\left(0.1\right)^{\frac{1}{4}\right)-1\)

\(\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax\)

\(\implies \dfrac{1}{2}\log_{10} 10 + \log_{10}\sqrt{a} + \dfrac{1}{4}\log_{10}0.1-1\)

\(\textsf{Apply log laws}: \quad \log_aa=1 \quad \textsf{and} \quad \log_a\dfrac{1}{a}=-1\)

\(\implies \dfrac{1}{2}(1) + \log_{10}\sqrt{a} + \dfrac{1}{4}(-1)-1\)

\(\implies \dfrac{1}{2}+ \log_{10}\sqrt{a} -\dfrac{1}{4}-1\)

\(\implies \log_{10}\sqrt{a} -\dfrac{3}{4}\)

If you want to simplify further:

\(\implies \log_{10}\left(a\right)^{\frac{1}{2}} -\dfrac{3}{4}\)

\(\implies \dfrac{1}{2}\log_{10}a-\dfrac{3}{4}\)

Answer:

56

Step-by-step explanation: 10a+10 0.1 -=

Answer:    20,736

Step-by-step explanation:

Math and History and Chemistry and Biology and Subjects

  3!     x        4!        x          3!          x        1!          x        4!       = 20,736

Answer:

Step-by-step explanation:

5

The equation of line passes through the point (-4, -2) will be;

⇒ 3x - 4y = - 4

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (-4, -2).

And, The parallel line is,

⇒ 3x - 4y = 7

⇒ y = 3/4x - 7/4

Now,

Since, The equation of line passes through the point (- 4, -2).

So, We need to find the slope of the line.

Since, The slope of the parallel line is same.

Hence, Slope of the line is,

⇒ y = 3/4x - 7/4

m = dy/dx = 3/4

m = 3/4

Thus, The equation of line with slope 3/4 is,

⇒ y - (-2) = 3/4 (x - (-4))

⇒ y + 2 = 3/4 (x + 4)

⇒ y + 2 = 3/4x + 3

⇒ y = 3/4x + 3 - 2

⇒ y = 3/4x + 1

⇒ 4y = 3x + 4

⇒ 3x - 4y = - 4

Therefore, The equation of line passes through the point (-4, -2) will be;

⇒ 3x - 4y = - 4

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The number of acres that are not federally owned = 3089.98 million

Land or other assets that are legally owned by the government or a government agency are referred to as government-owned property.

Federal, state, or local governments may be the owners of government-owned land, which may or may not be open to the general public without restriction.

If 14% of the land is federally owned, then 100 -14  = 86% of the land is not federally owned.

(14 *3593 ) / 100

50302 / 100 = 503.02

Federal owned land is 503.02 million acres of land.

3593 - 503.02 = 3089.98 =  (86× 3593) ÷ 100

Land not owned by Federal Government = 3089.98 million acres of land.

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With the conversion factor from tries to seconds, the time taken to to complete the average number of random tries is 24 minutes.

Your information is incomplete. Therefore, an overview will be given based on the values. Let's assume that the number of tries for 10 amino acids is 2 minutes.

Therefore, the duration for 120 amino acids will be:

= (120/10) × 2

= 12 × 2

= 24 minutes.

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The number of inches the bicycle tires travel in 75 rotations is 3,768 inches. Therefore, option C is the correct answer.

The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle. The circumference of a circle is the product of the constant π and the diameter of the circle.

Given that, the tires on a bicycle each have a diameter of 16 inches.

So, radius =16/2 =8 inches

We know that, the circumference of a circle =2πr

= 2×3.14×8

= 50.24 inches

The bicycle tires travel in 75 rotations is

75×50.24

= 3768 inches

Therefore, the distance traveled by bicycle is 3768 inches.

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The informal negation for each of the following statements:

1) No dog is ferocious.

2) Noboby is sad.

4) No suspicions were unsubstantiated.

5) No estimate is incorrect.

It is sometimes necessary in mathematics to determine the inverse of a given mathematical statement. This is commonly known as "negating" a statement. Keep in mind that if a statement is true, then its negation is false (and if a statement is false, then its negation is true). A conditional statement's negation is logically equivalent to a conjunction of the antecedent and the negation of the consequent. The logical negation symbol or is one of the statement connectives or operators that can be used to combine two or more statements to form new compound statements. It simply flips the truth value of any statement it appears in front of.

Here,

Each of the following statements has an informal negation:

1) No dog is ferocious.

2) Noboby is sad.

4) No suspicions were unsubstantiated.

5) No estimate is incorrect.

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Answer:

1/2=10

Step-by-step explanation:

it depends upon the area of the triwngle

Answer:

No. It is not proportional.

Answer:

7

Step-by-step explanation:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

The significance level is set at 5% and the probability of the result is 3.6% which is less than the significance level. The result is statistically significant

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true

The probability of the treatment group’s mean being greater than the control group’s mean by 8 points or more will be:

= (26 + 8 + 2)/1000

= 36/1000

= 0.036

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Answer:

The baker would need 47. 25 cups of floor

We need to know that proportion is a form of mathematical comparison with two equations made equal to each other.

From the information given, we have that;

baker used 33 3/4 cups of flour to make 15 batches of cookies

This is represented as;

Convert to improper fractions

135/4 cups = 15 batches of cookies

Then, x cups = 21 batches of cookies

cross multiply the values

15x = 708. 75

Divide both sides by the coefficient of x, we have ;

x = 708. 75/15

x = 47. 25 cups of floor

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Answer:

1a)Confidence Interval: (77.936,82.064)

b)Confidence Interval: (79.020, 80.980)

c)Confidence Interval: (79.510, 80.490)

d) As the sample size increases, the confidence interval for the lower class (bound) increases while that of the upper class(bound) decreases.

2a)Confidence Interval: (491.609

, 502.797)

b)Confidence Interval: (483.218, 516.782)

c)Confidence Interval: (466.436,533.564)

d)As the standard deviation increases, the confidence interval for the lower class (bound) decreases while that of the upper class(bound) increases.

Step-by-step explanation:

1 a) A random sample of 25 was drawn from a normal distribution with a standard deviation of 5. The sample mean is 80.

The formula for confidence Interval is:

C.I = Mean ± z score × Standard deviation/√n

Note to apply the formula above n greater than or equal to 30

a) Determine the 95% confidence interval estimate of the population mean.

For a, the confidence interval formula above cannot be applied because n is less than 30, so we use the t score confidence interval value

C.I = Mean ± t score × Standard deviation/√n

Mean = 80

Standard deviation = 5

n = 25

Degree of freedom = 25 - 1 = 24

Hence, 95% confidence interval degree of freedom t score = 2.064

Hence, Confidence Interval =

80 ± 2.064 × 5/√25

80 ± 2.064 × 1

80 ± 2.064

Confidence Interval =

80 - 2.064

= 77.936

80 + 2.064

= 82.064

Confidence Interval: (77.936, 82.064)

b) Repeat part (a) with a sample size of 100.

C.I = Mean ± z score × Standard deviation/√n

Mean = 80

Standard deviation = 5

n = 100

z score for 95% confidence interval = 1.96

C.I = 80 ± 1.96 × 5/√100

C.I = 80 ± 1.96 × 5/10

C.I = 80 ± 1.96 × 0.5

C.I = 80 ± 0.980

Confidence Interval =

80 - 0.980

= 79.020

80 + 0.980

= 80.980

Confidence Interval: (79.020, 80.980)

c) Repeat part (a) with a sample size of 400.

C.I = Mean ± z score × Standard deviation/√n

Mean = 80

Standard deviation = 5

n = 400

z score for 95% confidence interval = 1.96

C.I = 80 ± 1.96 × 5/√400

C.I = 80 ± 1.96 × 5/20

C.I = 80 ± 1.96 × 0.25

C.I = 80 ± 0.490

Confidence Interval =

80 - 0.490

= 79.510

80 + 0.490

= 80.490

Confidence Interval: (79.510, 80.490)

d) As the sample size increases, the confidence interval for the lower class (bound) increases while that of the upper class(bound) decreases.

2a) The mean of a sample of 25 was calculated as ¯x=500. The sample was randomly drawn from a population with a standard deviation of 15.

For a,b and c the confidence interval formula above cannot be applied because n is less than 30, so we use the t score confidence interval value

C.I = Mean ± t score × Standard deviation/√n

a) Mean = 500

Standard deviation = 15

n = 25

Degree of freedom = 25 - 1 = 24

Hence, 99% confidence interval degree of freedom t score = 2.064

Hence, Confidence Interval =

500 ± 2.797 × 15/√25

500 ± 2.797 × 15/5

500 ± 2.797 × 3

Confidence Interval =

500 - 8.391

= 491.609

500 + 8.391

= 508.391

Confidence Interval: (491.609, 508.391)

b) Repeat part (a) changing the population standard deviation to 30

Hence, Confidence Interval =

500 ± 2.797 × 30/√25

500 ± 2.797 × 30/5

500 ± 2.797 × 6

500 ± 16.782

Confidence Interval =

500 - 16.782

= 483.218

500 + 16.782

= 516.782

Confidence Interval: (483.218, 516.782)

c) Repeat part(a) changing to the population standard deviation to 60.

Hence, Confidence Interval =

500 ± 2.797 × 60/√25

500 ± 2.797 × 60/5

500 ± 2.797 × 12

500 ± 33.564

Confidence Interval =

500 - 33.564

= 466.436

500 + 33.564

= 533.564

Confidence Interval: (466.436,533.564)

d)As the standard deviation increases, the confidence interval for the lower class (bound) decreases while that of the upper class(bound) increases.

Answer:

C

Step-by-step explanation:

cot²θ = 1/tan²θ

plug this in to get

1/(1/tan²θ + 1)

1/tan²θ + 1 = 1/tan²θ + tan²θ/tan²θ = (1+tan²θ)/tan²θ

we then have

1/((1+tan²θ)/tan²θ)

1/(x/y) = y/x, so this is equal to

tan²θ/(1+tan²θ)

tan²θ = sin²θ/cos²θ, so plug this in to get

(sin²θ/cos²θ)/(1+sin²θ/cos²θ)

1+sin²θ/cos²θ = cos²θ/cos²θ + sin²θ/cos²θ

sin²θ + cos²θ = 1, so we have

(cos²θ+sin²θ)/cos²θ = 1/cos²θ. plug this in to get

(sin²θ/cos²θ)/(1/cos²θ)

(a/b)/(c/d) = (d/c) * (a/b), so we have

(sin²θ/cos²θ)/(1/cos²θ)  = cos²θ/1 * sin²θ/cos²θ = sin²θ

We got x = 16.54 by using Pythagorean theorem .

What is the Pythagorean theorem in plain English?

angle of semicircle is always be 90° .

   18² = 7.1² + x²

    324 = 50.41 + x²

     x² = 324 - 50.41

          = 273.59

    x = √ 273.59

    x = 16.54

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The potential roots of the function p(x) = x² - 9x² - 4x + 12 are x = 1, -1.5, and 12.

Degree of a polynomial is the highest power of the variable in that polynomial. For example, in a cubic polynomial, the variable [\(\bold{x}\)] has the highest power of 3.

Given is the following function with degree of 2 as -

We will plot the graph and find the roots of this function. The number of x - intercepts [coordinates where the graph cuts the x axis] will give us the roots or zeroes of the polynomials. Refer to the graph attached, it shows that the graph intercepts the x - axis at three different coordinates which are → x = 1, x = -1.5, and x = 12. Hence, these three values of [x] are the potential roots of the function p(x) = x² - 9x² - 4x + 12.

Therefore, the potential roots of the function p(x) = x² - 9x² - 4x + 12 are x = 1, -1.5, and 12.

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The potential roots of the given polynomial equation are +4 and -3. These roots are found by factoring the equation, setting each factor equal to zero and solving for x.

To find the potential roots of the polynomial equation p(x) = x² - 9x - 12, we can set the equation to zero and solve for x: 0 = x² - 9x - 12.

Next, we look for the factors of 12 which when multiplied would give you -12 and when subtracted would give you 9. There we have -4 and +3. Therefore the factors of the equation are (x - 4)(x + 3) = 0.

So, Final answer:

The potential roots of the given polynomial equation are +4 and -3. These roots are found by factoring the equation, setting each factor equal to zero and solving for x.

To find the potential roots of the polynomial equation p(x) = x² - 9x - 12, we can set the equation to zero and solve for x:

0 = x² - 9x - 12.

Next, we look for the factors of 12 which when multiplied would give you -12 and when subtracted would give you 9. There we have -4 and +3. Therefore the factors of the equation are (x - 4)(x + 3) = 0.

So, potential roots of the equation are x = 4 and x = -3 if we set each factor equal to zero and solve for x. This means that from the given options, the potential roots to the equation would be +4 and -3 (though -3 is not mentioned). of the equation are x = 4 and x = -3 if we set each factor equal to zero and solve for x. This means that from the given options, the potential roots to the equation would be +4 and -3 (though -3 is not mentioned).

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Answer:

Initial value 4x and rate of change is 75

Step-by-step explanation:

Because the initial value is the value before something is taken or added to it. Rate of change is whats being taken from the initial value

The range is the best measure of variability for this data, and its value is 4.

The line plot displays the number of roses purchased per day at a grocery store, with the data values ranging from 0 to 4 (since there are no dots above 4).

The best measure of variability for this data is the range, which is the difference between the maximum and minimum values in the data set. In this case, the minimum value is 0 and the maximum value is 4, so the range is:

Range = Maximum value - Minimum value = 4 - 0 = 4

Therefore, the range is the best measure of variability for this data, and its value is 4.

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The distance between the points (-1, 5) and (-7, -3) is 10 units.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Point 1 (-1,5)

Point 2 (-7,-3)​

Plug the given values into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

D = √[(-7 - (-1))² + (-3 - 5)²]

D = √[(-7 + 1)² + (-3 - 5)²]

D = √[-6² + (-8)²]

D = √[36 + 64]

D = √100

D = 10

Therefore, the distance is 10 units.

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helloAnswer:

Step-by-step explanation:

Answer:

The margin of error M.O.E = 2.5%

Step-by-step explanation:

Given that;

The sample size = 1500

The sample proportion \(\hat p\) = 0.60

Confidencce interval = 0.95

The level of significance ∝ = 1 - C.I

= 1 - 0.95

= 0.05

The critical value:

\(Z_{\alpha/2} = Z_{0.05/2} \\ \\ Z_{0.025} = 1.96\) (From the z tables)

The margin of error is calculated by using the formula:

\(M.O.E = Z_{\alpha/2} \times \sqrt{\dfrac{\hat p(1 -\hat p)}{n}}\)

\(M.O.E = 1.96 \times \sqrt{\dfrac{\hat 0.60(1 -0.60)}{1500}}\)

\(M.O.E = 1.96 \times \sqrt{\dfrac{0.24}{1500}}\)

\(M.O.E = 1.96 \times \sqrt{1.6 \times 10^{-4}}\)

M.O.E = 0.02479

M.O.E ≅ 0.025

The margin of error M.O.E = 2.5%

Answer:

6/10

Step-by-step explanation:

Simplify 15/25 by dividing by 5/5

15/25 ÷ 5/5 = 3/5

Multiply 3/5 by 2/2 to convert to tenths

3/5 × 2/2 = 6/10