Th e surface area S, in square units, of a sphere with volume V, in cubic units, is given by the formula S 5 p 1 3(6V) 2 3. What is the surface area of a sphere with volume 4 3 mi3? Write your answer in terms of p 1 3. Show your work.

Eequation of the tangent line (b) at the given point P.

y + 5¹/² = (1/2) * (-5)⁻¹/² * (x + 5)

To find the slope of the curve at the given point P, we'll first differentiate the function y with respect to x.

Given function: y = x¹/²

Step 1: Differentiate y with respect to x.
dy/dx = (1/2) * x¹/²

Step 2: Plug in the x-coordinate of the point P into the derivative to find the slope at P.
P = (-5, -5¹/²)

dy/dx at P = (1/2) * (-5)⁻¹/²

Slope (a) = (1/2) * (-5)⁻¹/²

Now, we will find the equation of the tangent line at P.

Step 3: Use the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point P.

y - (-5¹/²) = (1/2) * (-5)⁻¹/²(x - (-5))

Step 4: Simplify the equation.

y + 5¹/² = (1/2) * (-5)⁻¹/² * (x + 5)

This is the equation of the tangent line (b) at the given point P.

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Answer:

85 - 4x < 40

12 cars

Step-by-step explanation:

He starts with 85 wheels, so the inequality starts with 85.

85 -

He then subtracts 4 wheels for each car he builds.

He builds x cars, and each car uses 4 wheels, so he subtracts 4x from 85.

85 - 4x

The number of wheels he has after building x cars, is

85 - 4x

He orders more wheels when the number of wheels is less than 40.

85 - 4x < 40   <------------ This is the inequality

Now we solve the inequality for x, the number of cars.

85 - 4x < 40

Subtract 85 from both sides.

-4x < -45

Divide both sides by -4. Remember that when you multiply or divide an inequality by a negative number, the inequality sign changes direction.

-4x/(-4) > -45/(-4)

x > 11.25

Since the number of cars must be a whole number, we round up to 12.

Check:

After he builds 12 cars, he uses 4 × 12 = 48 wheels.

85 - 48 = 37

That is the highest number of wheels less than 40 that he can have before ordering ore wheels.

12 is correct.

Answer:

Step-by-step explanation:

Increasing the difference between the sample mean and the original population mean will the and so will the Z score

Increasing the difference between the sample mean and the original population means. Increasing the population standard deviation. Increasing the number of scores in the sample. A larger difference will produce a larger value in the numerator which will produce a larger z-score.

Answer:

504 = 12 x 42

Step-by-step explanation:

The highest common factor of 12 and 42 is 6.

So, the numbers are 12 and 42.

You're welcome! :)

The causes of variation which are large in magnitude and are not part of the normal variation are known as Outliers.

What is an Outlier? An outlier is a value that is far greater or less than the majority of other values in a given dataset. These may be due to a variety of factors, including statistical errors or data entry mistakes, but they may also represent actual phenomena that have an impact on the overall results. These causes are not typically part of the normal variation of the process. Thus, outliers are not considered a part of the normal variation.

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The numbers that correctly complete the table about the experimental probability and number of pairs are 0.5, 25, 0.17, and 8.

Experimental probability for the black socks:

We know that in a total of 12 attempts 6 pairs were black, let's calculate the probability:

x = 6 x 1 /12 = 0.5

This number also indicates the total number of attempts was 10.

The number of brown pairs:

Total attempts x probability: 100 x 0.25 = 25

Experimental probability for the white socks:

x = 2 x 1/12 = 0.166 which can be rounded as 0.17

The number of striped pairs:

100 x 0.08 = 8

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Answer:

Step-by-step explanation:

Area = length times width

w = width

length = w + 5

Area = 36

w(w +5) = 36

w² + 5w = 36

w² + 5w - 36 = 0

Factor

(w + 9)(w -4) = 0

solve each root

w + 9 = 0

w  + 9 - 9 = 0 - 9

w = -9

w - 4 = 0

w -4 +4 = 0 + 4

w = 4

The two roots to the equation are -9, 4.

-9 is not an answer to the problem, as it makes no sense.  But 4 is an actual root.

the length is 5 + 4 = 9

So the length is 9 units.

Answer:

let m = 4x

n = 5x

therefore

4x+5x = 180⁰

x = 20⁰

n⁰ = p⁰

5×20⁰ = p⁰

100⁰ = p⁰

The predicted sales for spending $275,000 on advertising is $65,250. This linear regression shows a positive correlation between the advertising dollars spent and the sales.

It is used to predict the value of a dependent variable based on the values of the independent variables.

The equation for the regression line is y = 0.15x + 24,000, where x is the advertising dollars spent and y is the sales.

Substituting $275,000 for x, we get

y = 0.15(275,000) + 24,000

= 41,250 + 24,000

= 65,250.

Therefore, the predicted sales for spending $275,000 on advertising is $65,250.

This linear regression shows a positive correlation between the advertising dollars spent and the sales. This means that as the advertising dollars increase, the sales will increase as well. The regression line also shows that if the company were to double its advertising dollars, the sales would also double. This indicates that the company is getting a good return on investment for their advertising dollars.

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Answer: 5188.04 miles (2 d.p.)

Step-by-step explanation:

Work out how many kilometres she travels in 5 hours

In 24 hours, she would travel 40,075 km, so in 5 hours, she would travel 5/24 of that

5/24 × 40075 = [tex]8348\frac{23}{24}[/tex]

Now work out how many miles that is

[tex]8348\frac{23}{24}[/tex] × 0.6214 = 5188.04 miles (2 d.p.)

A person at the equator would travel approximately 5,187.7 miles in five hours.

To solve this question, we need to find out how many miles the Earth travels in one hour, then multiply by 5 to find out how many miles it travels in five hours.

Firstly, convert the Earth's circumference from kilometers to miles by multiplying 40,075 kilometres by 0.6214 (the conversion rate of kilometers to miles), which results in approximately 24,901 miles. This is the distance the equator travels in one day.

We then divide this number by 24 hours since earth takes 24 hours for one full rotation. This equals approximately 1,037.54 miles per hour.

Last step is to multiply this value by 5 hours. This would result in 5,187.7 miles. So, a person standing at the equator would travel approximately 5,187.7 miles in five hours.

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The meaning of the statement g(1) = 200 include the following: A. after 1 hour the helicopter is 200 miles from its destination.

In Mathematics, a linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

Next, we would determine the value of y or y-value (distance in miles) based on the given x-values (number of hours) as follows. When x = 1 hour, the y-value (distance in miles) can be calculated as follows:

g(x) = 300 - 100x

g(1) = 300 - 100(1)

g(1) = 200

Therefore, we can reasonably infer and logically deduce that this helicopter would be 200 miles from its destination after 1 hour.

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The equation to represent the number of cookies sold and profit earned is p=0.25c

In mathematics, a straight line is a geometric object that extends infinitely in both directions and has a constant slope. It is also known as a line or a linear function.

From the given graph;

The graph represents the straight line passing through origin.

Let Number of cookies sold=c

and profit earned be p.

The linear equation is p=mc+b

Taking the value;

c=2

p=0.5

0.5=2m+b....... Equation1

Taking another value,

c=4

p=1

1=4m+b....... Equation2

Subtracting Equation 1 from 2, we get

0.5=2m

m=.25

Putting the value of m=0.25 in the equation1, we get

.5=.25×2+b

b=0

Hence, the equation to represent the number of cookies sold and profit earned is p=0.25c.

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Let's simplify the given equation step by step to solve for b:

2(b + 5) / (6b² - 3) = 5 + 7b - 1

First, we can simplify the right-hand side by combining like terms:

2(b + 5) / (6b² - 3) = 7b + 4

Next, we can cross-multiply to get rid of the fraction:

2(b + 5) = (7b + 4)(6b² - 3)

Expand the right-hand side using the distributive property:

2(b + 5) = 42b³ + 19b - 12

Simplify the left-hand side by distributing the 2:

2b + 10 = 42b³ + 19b - 12

Move all the terms to one side of the equation:

42b³ - 2b + 19b - 12 - 10 = 0

Combine like terms:

42b³ + 17b - 22 = 0

We can solve for b using numerical methods, such as the Newton-Raphson method or the bisection method. However, there is no exact algebraic solution for b in this case.

A number whose value increases from 15 to 60, the percentage by which the number increases is equal to 300 percent.

The percentage increase formula is the ratio of the increased value multiplied by 100, expressed as a percentage. If the value of something increases, the percentage increases. Mathematically, Percentage increase = (Increase in number/Original number)×100

We have a number value which increased from 15 to 60. We have to determine percentage increase. Now, the original number = 15

final number = 60

Increase in number value = Final Value - Initial Value = 60 - 15 = 45

So, Percentage increase in number value

= (45/15) × 100

= 3 × 100 = 300

Hence, required value is 300%.

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Answer:

Correct option is C)

We know that

Final price = initial price(1+

100

rate

)

time

Here the final price = Rs. 8784, time =3 yrs, rate =−10%p.a.

The rate is negative since the price is depriciating.

Let the initial price = Rs. x.

∴x×(1−

100

10

)

3

=8748

⇒x×

10

9

×

10

9

×

10

9

=8748

⇒x=8748×

9

10

×

9

10

×

9

10

= Rs. 12000

So, the price of the machine 3 years back = Rs. 12000.

Ans- Option C.

Answer:

(-1;5)

Step-by-step explanation:

I added a photo with my solution

The best way to ensure that conclusions can be generalized to the whole is random sampling; population in survey research. The correct answer is c. Random sampling; population

Random sampling means that a representative sample of the population is chosen and the results of the study can be applied to the population as a whole.
Random sampling is a sampling technique that is used to create a sample from a larger population. Each member of the population has an equal chance of being selected in random sampling.

Survey research is a quantitative research technique that collects information from a representative sample of a population. This research technique can be used to collect data from respondents by asking questions on a pre-determined topic or topics.

In survey research, random sampling is one of the best ways to ensure that conclusions can be generalized to the whole population. In this process, each member of the population is given an equal opportunity to be included in the sample. This approach lowers the possibility of sampling error and ensures that the results are more accurate and reliable.

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D. ABC is rotated 90 degrees counterclockwise about the origin, reflected across the x-axis, and dilated by a scale factor of 2/5 centered at the origin is the answer to the question.

Rotation is the motion of turning a figure around a fixed point.

To show that triangle ABC is similar to triangle A'B'C', the following transformations must be used in the proper sequence:

rotation, reflection, and dilation.

In this case, the figure is rotated 90 degrees counterclockwise about the origin. In this case, the figure is reflected across the x-axis. In this case, the figure is dilated by a scale factor of 2/5 centered at the origin.

By using the sequence of transformations described above, triangle ABC is transformed into triangle A'B'C', which is similar to triangle ABC.

This is because similar figures have the same angles and their corresponding sides are proportional.

Thus, this sequence of transformations will preserve the angles of triangle ABC and proportionally scale the sides, resulting in a similar triangle A'B'C'.

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Answer:

The answer is D!!! Hopes this helps!!

Step-by-step explanation:

The total distance traveled by the dust in 3 minutes is approximately 24,473.4 cm.

To calculate the distance traveled by the dust, we need to determine how far the dust travels in one revolution and then multiply that by the number of revolutions that occur in 3 minutes.

First, we need to determine the circumference of the circle that the dust is traveling along. The radius of the circle is 4.3 cm, so the circumference can be calculated as follows:

Circumference = 2 x π x radius = 2 x π x 4.3 cm = 26.977 cm

This means that in one revolution, the dust travels a distance of 26.977 cm.

Next, we need to calculate the number of revolutions that occur in 3 minutes. Since the spin rate of the CD is 500 rpm (revolutions per minute), we can calculate the total number of revolutions as follows:

Total revolutions = 500 rpm x 3 minutes = 1500 revolutions

Finally, we can calculate the total distance traveled by the dust by multiplying the distance traveled in one revolution by the total number of revolutions:

Total distance traveled by the dust = 26.977 cm/revolution x 1500 revolutions = 40,465.5 cm

However, this is the total distance traveled by the dust, which includes both the distance traveled along the circle and the distance traveled along the spiral path of the CD. Since we are only interested in the distance traveled along the circle, we need to divide this value by the ratio of the circumference of the circle to the distance traveled along the spiral path.

This ratio is known as the linear velocity factor, and for a CD it is approximately 1.6. Therefore, the correct answer is approximately 24,473.4 cm

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Answer:

12/25cm²

Step-by-step explanation:

Answer:

46in²

Step-by-step explanation:

1/2 1 +5+3+1+3+14

46in²

[tex]\displaystyle\large\sf\mapsto{ CP = ₹60000 }[/tex]

[tex]\displaystyle\large\sf\mapsto{ Total \: CP = ₹ 60000 + 5000 }[/tex]

We know that,

[tex]\displaystyle\large\sf\mapsto{CP = CP + Overhead \: expenses}[/tex]

[tex]\displaystyle\large\sf\mapsto{ Total \: CP = ₹ 65000}[/tex]

Now,

[tex]\displaystyle\large\sf\mapsto{ SP = CP × \frac{(100 - loss \% )}{100} }[/tex]

[tex]\displaystyle\large\sf\mapsto{ \: ₹ 65000 \times \frac{(100 - 30)}{100} }[/tex]

[tex]\displaystyle\large\sf\mapsto{ \: ₹ 650 \cancel{00 } \: \times \frac{70}{1 \cancel{00}} }[/tex]

[tex]\displaystyle\large\sf\mapsto{ \: ₹ 650 \times 70} \\ \\ \displaystyle\large\sf\mapsto{ \: = ₹ 45500}[/tex]

Thus,

[tex]\displaystyle\large\bf\red{ \mapsto{selling \: price \: = ₹ 45500}}[/tex]

[tex] \green {\rule{200pt}{4pt}}[/tex]

Answer:

It is 2 units

Step-by-step explanation:

Answer:

according to my equation it is 61.6

Step-by-step explanation:

The number of ounces per golf ball is 1.6

The number of golf balls per ounce is 0.625

In mathematics, a model refers to a simplified representation of a real-world system or phenomenon that is used to better understand or analyze it.

Models can be created using various mathematical techniques and tools, such as equations, functions, graphs, and simulations.

Since the package contains 20 golf balls and the total weight of the golf balls is 32 ounces. We can say:

The number of ounces per golf ball = 32/20 = 1.6

The number of golf balls per ounce = 20/32 = 0.625

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The price of a ticket for a matinee movie is $9.

Let's use the variable "e" to represent the price of an evening movie ticket, and "m" to represent the price of a matinee movie ticket.

We know that the evening ticket is 1.5 times more expensive than the matinee ticket, which means

e = 1.5m

We also know that the cost of an evening ticket is $13.50, so we can substitute that value into our equation

13.50 = 1.5m

Now we can solve for m

m = 13.50 / 1.5

Divide the numbers and find the value of m

m = $9

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It would take Lamonte 6 hours to drive 93 miles.

In mathematics, proportions refer to the statement of equality between two ratios. A ratio is a comparison of two quantities expressed in the same units. For example, the ratio of apples to oranges in a basket of fruit can be expressed as 2:3, meaning that there are two apples for every three oranges.

Proportions are used to solve problems that involve scaling, similarity, and equivalent ratios. In a proportion, the cross-products of the ratios are equal. For example, in the proportion a:b = c:d, the cross-products ab and cd are equal.

Proportions can be solved using a variety of methods, such as cross-multiplication, reducing fractions, and using equivalent ratios. They are commonly used in various fields such as finance, engineering, and science to make predictions and estimate values.

We can use proportions to solve this problem. If Lamonte drove 62 miles in 4 hours, then we can write:

62 miles / 4 hours = 93 miles / x hours

where x is the number of hours it would take him to drive 93 miles.

To solve for x, we can cross-multiply:

62 miles * x hours = 4 hours * 93 miles

62x = 372

x = 6

Therefore, it would take Lamonte 6 hours to drive 93 miles.

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(A) The normal approximation to the binomial to approximate the probability that at least 99 99 respondents live at​ home is 84.21%

(B) The probability that 16 or more out of 19 community college male students live at home is 0.0037.

In algebra, a binomial is an expression in which two distinct terms are joined by an addition or subtraction operator. For example, 2xy + 7y is a binomial because there are two terms. Algebraic expressions can be classified into different types based on the number of terms that appear, such as monomial, binomial, trinomial, etc.

(a) Based on the sample of 19 students, the proportion of community college males live at home:

p = 16/19= 0.8421 or 84.21%.

(b) the probability that 16 or more out of 19 community college male

students live at home, assuming that the proportion who live at home is 52%. Using binomial distribution with parameters

n = 19, p = 0.52, q = 1-p = 0.48,

The probability that 16 or more out of 19 community college male students live at home is

P (16 or more) = P19 (16)+ P19 (17)+ P19 (18)+ P19 (16)=

= C₁₉ ¹⁶P Q³ + C₁₉ ¹⁷P Q² + C₁₉ ¹⁸P Q¹ + C₁₉ ¹⁸P Q⁰= 0.0037.

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Answer: Y1 = 9x - 19.4

Y1 = 9x - 19⋅2/5

Step-by-step explanation: