calculator may be used to determine the final numeric value, but show all steps in solving without a calculator up to the final calculation. the surface area a and volume v of a spherical balloon are related by the equationA³ - 36πV² where A is in square inches and Vis in cubic inches. If a balloon is being inflated with gas at the rate of 18 cubic inches per second, find the rate at which the surface area of the balloon is increasing at the instant the area is 153.24 square inches and the volume is 178.37 cubic inches.

Answer:

0.000005871

thats just what it is cuz yeah

Answer:

Step-by-step explanation:

0.000005871

Answer:

B

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to \(\frac{3}{2}\)

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (r, - 4)

m = \(\frac{-4-2}{r-3}\) = \(\frac{-6}{r-3}\) , then equating gives

\(\frac{-6}{r-3}\) = \(\frac{3}{2}\) ( cross- multiply )

3(r - 3) = - 12 ( divide both sides by 3 )

r - 3 = - 4 ( add 3 to both sides )

r = - 1 → B

The simplified expression is given by (x² - 3x - 3) / ((x + 3)(x - 2)(x - 4)).

To simplify this expression, we need to find a common denominator for the two fractions and then combine them. To do this, we need to factor the denominators of both fractions.

Let's start with the first fraction's denominator:

x² + x - 6

We need to find two numbers that multiply to -6 and add to +1. These numbers are +3 and -2. Therefore, we can write:

x² + x - 6 = (x + 3)(x - 2)

Now let's factor the second fraction's denominator:

x² - 6x + 8

We need to find two numbers that multiply to 8 and add to -6. These numbers are -2 and -4. Therefore, we can write:

x² - 6x + 8 = (x - 2)(x - 4)

Now we can rewrite the original expression with a common denominator:

(x(x - 2) - (1)(x + 3)) / ((x + 3)(x - 2)(x - 4))

Next, we can simplify the numerator:

(x² - 2x - x - 3) / ((x + 3)(x - 2)(x - 4))

(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))

Finally, we can't simplify this expression any further. Therefore, the simplified expression is:

(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))

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Answer:

120

Step-by-step explanation:

im sorry if its wrong but i think its correct

Answer:

2x + y = 18

y = 4x - 12

x = 5,  y = 8

Step-by-step explanation:

x = 1st number

y = 2nd number

We can use the substitution method as we know what 'y' equals; that value will get plugged in for 'y' in the first equation as follows:

2x + 4x - 12 = 18

6x - 12 = 18

6x = 30

x = 5

y = 4(5) - 12 which is 20-12 or 8

y = 8

A chart that compares three sets of values in a three-dimension chart is called surface.

A two-dimensional collection of points (flat surface), a three-dimensional collection of points with a curved cross section (curved surface), or the perimeter of any three-dimensional solid are all examples of surfaces in geometry.

A surface is typically a continuous boundary that separates two areas of a three-dimensional space. For instance, a sphere's surface divides its interior from its exterior, and a horizontal plane divides the half-planes above and below it. Despite the fact that regions they contain are three-dimensional and have a volume, surfaces are basically two-dimensional and have an area. Despite this, surfaces are frequently referred to by the names of the regions they surround. Differential geometry studies the characteristics of surfaces, particularly the concept of curvature.

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The car will cost $ 800 after a depreciation time of approximately 6 years.

Herein we are informed about the case of a car bought in 2011 at a cost of $ 36,000 and that depreciates linearly every year. Then, the depreciation function is described below:

c(t) = c' + m · t

Where:

If we know that c(0) = 36,000, c(4) = 12,000 and c(t) = 800, then the depreciation rate is:

m = (12,000 - 36,000) / (4 - 0)

m = - 24,000 / 4

m = - 6,000

800 = 36,000 - 6,000 · t

6,000 · t = 35,200

t = 35,200 / 6,000

t = 5.867

The expected depreciation time is approximately 6 years.

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Answer:

14. D=70°

e=110°(straight line angles)

15. R=42°(vertically opposite angles)

S=68°(sum of interior angles of a triangle)

16.x=50°(angles on a straight line)

y=70°(sum of interior angles of a triangle)

hope this helps you

Answer:

8

Step-by-step explanation:

8*10+142=222

22*8+46=222

Answer:

If two triangles are proven to be congruent, then every single corresponding side and angle between those two triangles are congruent by CPCTC Theorem. CPCTC stands for Corresponding parts of congruent triangles are congruent.

Explanation:

CPCTC Theorem states that if two triangles are congruent, then their

If construction of many average quality homes began in an area that is known for having many high quality homes, it is likely that the overall property values of the homes in the neighborhood would decrease.

Explanation:

The presence of many high quality homes in a neighborhood tends to contribute to higher property values. These high quality homes often set a standard and attract buyers who are willing to pay a premium for the desirable location and quality of housing.

However, when a large number of average quality homes are constructed in the same area, it can lead to a dilution of the overall quality and desirability of the neighborhood. The increased supply of average quality homes may result in increased competition among sellers and a decreased demand from buyers who are seeking higher quality homes. As a result, property values in the neighborhood are likely to decrease.

Additionally, the introduction of average quality homes may also change the perception and reputation of the neighborhood. Buyers who were initially attracted to the area for its high quality homes may be less inclined to purchase in a neighborhood with a mixture of average and high quality homes, further impacting property values.

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Polynomials form a system like to that of integers hence they are closed under the operations of addition and subtraction.

Exponents of polynomials are whole numbers.

Hence the resultant exponents will be whole numbers , addition is closed for whole numbers. As a result, polynomials are closed under addition.

If an operation results in the production of another polynomial, the resulting polynomials will be closed.

The outcome of subtracting two polynomials is a polynomial. They are also closed under subtraction as a result.

The word polynomial is a Greek word. We can refer to a polynomial as having many terms because poly means many and nominal means terms. This article will teach us about polynomial expressions, polynomial types, polynomial degrees, and polynomial properties.

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The statement that is NOT a property of the linear correlation coefficient r is "C.

The linear correlation coefficient r is robust. That is, a single outlier will not affect the value of r."

Correlation coefficient r measures the strength of a linear relationship between two variables. It is the degree to which two variables are related to each other.

The value of the correlation coefficient r is always between -1 and 1 inclusive. The value of r is not affected by the choice of x or y. Hence, the statement B is true.

The correlation coefficient r is not always robust. That is, a single outlier can affect the value of r and can make it appear weaker than it actually is.

Therefore, statement C is not true.The main answer to the question is C.

The linear correlation coefficient r is not robust. It can be affected by a single outlier that can make it appear weaker than it actually is. that explains the properties of linear correlation coefficient r:

Linear correlation coefficient r is a statistical tool used to measure the strength of the linear relationship between two variables. The value of r can range from -1 to +1, and it is used to determine how well one variable predicts the other variable.

The properties of r include its ability to measure the strength of the linear relationship, its independence from the choice of x or y, and its robustness.

The value of r measures the strength of the linear relationship between two variables. The closer the value of r is to -1 or +1, the stronger the linear relationship is between the two variables.

A value of r = 0 indicates that there is no linear relationship between the two variables.The value of r is not affected by the choice of x or y.

This means that it does not matter which variable is labeled as x or y when calculating the correlation coefficient. The resulting value of r will be the same regardless of the labels assigned to the variables.

The linear correlation coefficient r is not always robust. A single outlier can affect the value of r and make it appear weaker than it actually is.

Therefore, it is important to examine the scatterplot of the data to identify any outliers before calculating the correlation coefficient.Finally, the value of r is always between -1 and 1 inclusive. If r = -1, it indicates a perfect negative linear relationship between the two variables. If r = +1, it indicates a perfect positive linear relationship between the two variables. If r = 0, it indicates that there is no linear relationship between the two variables.

Therefore, we can conclude that statement C is not a property of the linear correlation coefficient r.

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Answer:

314 cm ^ 2

Step-by-step explanation:

First do, 3.14 x 20 ^ 2

3.14 x 20 ^ 2 = 1,256

Then do, 1,256/4

1,256/4 = 314

Why 4?

This part of the circle is 1/4 of the entire circle.

What does ^ mean?

It's just a way to say to the power of on a computer.

Hope this helps! :)

Answer:

the correct answer is below

Step-by-step explanation:

11p7-9p5+8p³-4p7+13p5-5p³

11p7-4p7-9p5+13p5+8p³-5p3

=7p7+4p5+3p³

note: I multiply all the terms in the second parentheses by the negative sign that is beside it.

Answer:

x= 1.36

Step-by-step explanation:

Answer:

Step-by-step explanation:

5(x−2 2/5) = −5.2

1. We need to use distibutaive property

5×x and 5×-2.4

5x - 12 = -5.2

2. We need to get x alone.

5x - 12 = -5.2

    -12      -12

5x = 6.8

3. We need to divide

5x = 6.8

/5     /5

x = 1. 36

check:

5(1.36−2 2/5)=−5.2

6.8 - 12 = 5.2

Answer:

I can't place them it is a picture

Step-by-step explanation:

A Negative correlation coefficient means that as one variable increases, the other decreases (i.e., an inverse relationship).

Answer:

-24

Step-by-step explanation:

Answer: -24

Step-by-step explanation:

1. The first term is -2, and since it is the first term, multiply by one. This gives you -2.

2. Using the same method, in order to find the 12th term, multiply -2 by 12, because the rule between all the numbers is -2. If the rule were different every term, then you need to use a different method. But in this case, the answer is -24 mainly because all the terms are based on the same rule (-2).

Answer:

Step-by-step explanation:

C. Factor

A factor is a number that divides another number, leaving no remainder. Meaning that if you multiply two whole numbers that gives us a product,  then the numbers we are multiplying are factors of the product because they are divisible by the product.

(Hope this makes sense, if not I'm sorry)

Answer:

Step-by-step explanation:

From the diagram, mAD lies on the line BDF. Sum of angle on a straight line is 180°. According to the line BDF; mAB + mAD = 180°

From the diagram, mAB = 43°. Substituting this value into the above equation;

mAB + mAD = 180°

43° + mAD = 180°

mAD = 180°-43°

mAD = 137°

Hence, the measure of angle mAD is 137°

The interval (-U(ₙ), a=U(ₙ)) is a (1 - a) level confidence interval for 0, where U(ₙ) represents the maximum value among U₁, U₂, ..., Uₙ, and a = U(ₙ) represents the upper bound of the interval.

What is the confidence interval?

A confidence interval is a range of values that is likely to contain the true value of an unknown population parameter, such as the population mean or population proportion. It is based on a sample from the population and the level of confidence chosen by the researcher.

To show that the interval (-U(ₙ), a=U(ₙ)) is a (1 - a) level confidence interval for 0, we need to demonstrate that it has the property that the probability that 0 is contained within the interval is equal to (1 - a).

Let's proceed with the proof:

Since U(1) is the minimum value among U₁, U₂, ..., Uₙ, we have:

P(U(1) > a) = P(min{U₁, U₂, ..., Uₙ} > a)

This is equivalent to all of the observations U₁, U₂, ..., Uₙ being greater than a:

P(U(1) > a) = P(U₁ > a, U₂ > a, ..., Uₙ > a)

Since the observations U₁, U₂, ..., Uₙ are independent and identically distributed from Uniform(0, θ), where θ > 0 is unknown, we have:

P(U(₁) > a) = P(U₁ > a) * P(U₂ > a) * ... * P(Uₙ > a)

Since each Ui is from Uniform(0, θ), the probability that Ui > a is given by:

P(Ui > a) = 1 - P(Ui ≤ a) = 1 - a/θ

Therefore, we can write:

P(U(₁) > a) = (1 - a/θ)ⁿ

Now, let's consider U(n), which is the maximum value among U₁, U₂, ..., Uₙ:

P(U(ₙ) ≤ a) = P(max{U₁, U₂, ..., Uₙ} ≤ a)

This is equivalent to all of the observations U₁, U₂, ..., Uₙ being less than or equal to a:

P(U(ₙ) ≤ a) = P(U₁ ≤ a, U₂ ≤ a, ..., Uₙ ≤ a)

Using the same reasoning as before, the probability that Ui ≤ a is given by:

P(Ui ≤ a) = a/θ

Therefore, we can write:

P(U(ₙ) ≤ a) = (a/θ)ⁿ

Now, let's compute the probability that 0 is contained within the interval (-U(ₙ), a=U(ₙ)):

P(-U(ₙ) ≤ 0 ≤ a=U(ₙ)) = P(Uₙ) ≥ 0 ≥ -U(ₙ)) = P(U(ₙ) ≥ 0) = 1 - P(U(ₙ) < 0)

Since U(ₙ) follows a Uniform(0, θ) distribution, the probability that U(ₙ) < 0 is 0.

Therefore, we have:

P(-U(ₙ) ≤ 0 ≤ a=U(ₙ)) = 1 - P(U(ₙ) < 0) = 1 - 0 = 1

Hence, the probability that 0 is contained within the interval (-U(ₙ), a=U(ₙ)) is 1.

To complete the proof, we need to show that the probability that 0 is contained outside this interval is equal to a:

P(0 ≤ -U(ₙ) or a=U(ₙ)) = P(U(ₙ) ≤ 0 or a ≤ U(ₙ)) = P(U(ₙ) ≤ 0) + P(a ≤ U(ₙ))

Since U(ₙ) follows a Uniform(0, θ) distribution:

P(U(ₙ) ≤ 0) = 0 (since U(n) is always positive)

P(a ≤ U(ₙ)) = (a/θ)ⁿ

Therefore, we have:

P(0 ≤ -U(ₙ) or a=U(ₙ)) = P(U(ₙ) ≤ 0) + P(a ≤ U(ₙ)) = 0 + (a/θ)ⁿ

Since we want to show that this probability is equal to a, we need to equate it to a:

(a/θ)ⁿ = a

Taking the n-th root of both sides, we have:

(a/θ) = √[a]

Simplifying further, we get:

θ = a/√[a]

Therefore, the value of θ that satisfies this equation is θ = a/√[a].

Now, let's compute the confidence level associated with the interval (-U(ₙ), a=U(ₙ)).

The confidence level is defined as 1 minus the probability that the interval does not contain the true value of 0:

Confidence level = 1 - P(0 ≤ -U(ₙ) or a=U(ₙ))

= 1 - (a/θ)ⁿ

= 1 - (a/(a/√[a]))ⁿ

= 1 - (√[a])ⁿ

= 1 - aⁿ

We know that the confidence level should be equal to (1 - a) since it is a (1 - a) level confidence interval. Equating the two, we have:

1 - aⁿ = 1 - a

Simplifying, we get:

aⁿ = a

Since a is in the range (0, 1), we can conclude that this equation holds for any a in that range.

Therefore, the interval (-U(ₙ), a=U(ₙ)) is a (1 - a) level confidence interval for 0, where U(ₙ) represents the maximum value among U₁, U₂, ..., Uₙ and a = U(ₙ) represents the upper bound of the interval.

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Answer:all lines are straight

Step-by-step explanation:

Answer:

2.12482717E22

Step-by-step explanation:

x + x + 4 = 20

x + x = 16

16 / 2 = 8

Mike is 8, and Mark is 12.

The estimated probability that the candidate obtains a score greater than or equal to 10 is 0.7234, rounded to four decimal places, so the answer is (A).

The number of correct answers that the candidate gets is a binomial random variable with parameters n = 40 (number of trials) and p = 1/5 (probability of success). We want to find the probability that the candidate gets a score greater than or equal to 10, which is equivalent to getting 10 or more questions correct.

Using the normal approximation to the binomial distribution with continuity correction, we can approximate the distribution of the number of correct answers by a normal distribution with mean μ = np = 40 * 1/5 = 8 and variance σ^2 = np(1-p) = 40 * 1/5 * 4/5 = 6.4.

To find the probability that the candidate gets 10 or more questions correct, we can standardize the normal distribution and use the standard normal distribution table or R to find the probability.

Let X be the number of correct answers. Then, we have:

P(X >= 10) = P((X - μ) / σ >= (10 - μ) / σ)

= P(Z >= (10 - 8) / sqrt(6.4)), where Z is a standard normal random variable.

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