Find the potential inside and outside a sphere shell that carries a uniform surface charge $\sigma_0$, using results of Ex. 3.9

Step-by-step explanation:

A + B = 188

A = 188 - B - (1)

Now,

A - B = 34

188 - B - B = 34 (Substituting eqn 1 in A)

188 - 34 = 2B

154 = 2B

• B = 77 tons

Now

A = 188 - B

A = 188 - 77

A = 111 tons

The area under the curve y = 1/ (x^2 + 6x -16) from x = t to x = 6 is 1/10( ln(4) - 1/10 ln(t+8))

To find the area under the curve y = 1/ (x^2 + 6x -16) from x = t to x = 6, where t > 2, we need to evaluate the definite integral:

∫[t,6] 1/ (x^2 + 6x -16) dx

To solve this integral, we can use partial fraction decomposition. First, we factor the denominator:

x^2 + 6x -16 = (x+8)(x-2)

Then, we can write:

1/ (x^2 + 6x -16) = A/(x+8) + B/(x-2)

Multiplying both sides by (x+8)(x-2), we get:

1 = A(x-2) + B(x+8)

Setting x = -8, we get:

1 = A(-10)

So, A = -1/10.

Setting x = 2, we get:

1 = B(10)

So, B = 1/10.

Therefore, we can write:

1/ (x^2 + 6x -16) = -1/10(x+8) + 1/10(x-2)

Substituting this into the integral, we get:

∫[t,6] 1/ (x^2 + 6x -16) dx = ∫[t,6] (-1/10(x+8) + 1/10(x-2)) dx

Integrating, we get:

= [-1/10 ln|x+8| + 1/10 ln|x-2|] from t to 6

= 1/10 ln|6-2| - 1/10 ln|t+8|

= 1/10 ln(4) - 1/10 ln(t+8)

Therefore, the area is: 1/10( ln(4) - 1/10 ln(t+8))

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_____The given question is incomplete, the complete question is given below:

begin by finding the area under the curve from to y = 1/ (x^2 + 6x -16) from x = t to x = 6, t>2 this area can be written as the definite integral

Answer:

x²

Step-by-step explanation:

[tex]{ \tt{ \frac{ {x}^{ - 3} . {x}^{2} }{ {x}^{ - 3} } }} \\ \\ \dashrightarrow{ \tt{x {}^{( - 3 + 2 - ( - 3))} }} \\ \dashrightarrow{ \tt{ {x}^{( - 3 + 2 + 3)} }} \: \: \: \: \\ \dashrightarrow{ \boxed{ \tt{ \: \: \: \: {x}^{2} \: \: \: \: \: \: }}} \: \: \: \: [/tex]

Answer:

A

Step-by-step explanation:

because___________________________________

Answer:

B) True

Step-by-step explanation:

SSS or Side-Side-Side is used to prove two triangles are congruent.

Answer: The total cost of buying 5 balls individually is $2.00 x 5 = $10.00.

The box costs $8.50, which means it is $10.00 - $8.50 = $1.50 cheaper to buy the box.

To calculate the percentage difference, we can use the formula:

% difference = (difference ÷ original value) x 100%

In this case, the difference is $1.50, and the original value is $10.00.

% difference = ($1.50 ÷ $10.00) x 100%

% difference = 0.15 x 100%

% difference = 15%

Therefore, it is 15% cheaper to buy the box than to buy 5 individual balls.

Step-by-step explanation:

a) The standard error of mean for this data set is approximately 0.141.

b) The approximate 95% margin of error is approximately 0.282.

c) The approximate 95% confidence interval for the population mean age is 19.824 to 20.376.

a) The standard error of mean (SEM) is given by the formula: SEM = s / sqrt(n), where s is the sample standard deviation and n is the sample size. Plugging in the values given, we have:

SEM = 1.8 / sqrt(163) ≈ 0.141

So the standard error of the mean is approximately 0.141.

b) The approximate 95% margin of error (MOE) can be calculated using the formula: MOE ≈ 2 * SEM. Plugging in the SEM value from part 1, we get:

MOE ≈ 2 * 0.141 ≈ 0.282

So the approximate 95% margin of error is approximately 0.282.

c) The approximate 95% confidence interval (CI) for the population mean age can be calculated using the formula: CI = x ± (z*SEM), where x is the sample mean, z is the critical value from the standard normal distribution corresponding to the desired level of confidence (95% in this case), and SEM is the standard error of the mean. The critical value for 95% confidence is approximately 1.96. Plugging in the values, we get

CI = 20.1 ± (1.96 * 0.141) ≈ 19.824 to 20.376

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Answer: c

Step-by-step explanation: i dont have one

1/2 x (6.08 - 2) (6.08 - 2) is the correct numerical expression for "one-half the difference of 6 and 8 hundredths and 2 " .

An expression, as used in computer programming, is a grouping of values, variables, operators, and/or function calls that the computer evaluates to produce a final value. For instance, the equation 2 + 3 combines the numbers 2 and 3 using the + operator to produce the number 5. Similar to this, the equation x * (y + z) produces a value based on the current values of the variables x, y, and z by combining the variables x, y, and z with the * and + operators.

given

In terms of numbers, the phrase "one-half the difference of 6 and 8 hundredths and 2" is expressed as follows:

1/2 x (6.08 - 2) (6.08 - 2)

1/2 x (6.08 - 2) (6.08 - 2) is the correct numerical expression for "one-half the difference of 6 and 8 hundredths and 2 " .

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Option B: The ratio of the volume of soil to the volume of sand is 1:4.

Looking at the table, we can see that for every 100 m³ increase in soil, the sand volume increases by 25 m³. This gives us a ratio of 4:1, which means that the volume of sand is one-fourth of the volume of soil. Therefore, option B is correct.

Option D: The equation y = 4x models the relationship.

We can see that the volume of sand is always one-fourth of the volume of soil. Therefore, we can write y = (1/4)x or y = 0.25x. This equation is the same as y = 4x. Therefore, option D is also correct.

So, the correct statements are B and D.

In mathematics, a graph is a visual representation of data or a mathematical function. It consists of a set of points or vertices connected by lines or curves called edges or arcs, which represent the relationships between the points. Graphs can be used to show trends, patterns, and relationships in data, and they are commonly used in fields such as statistics, economics, and computer science. Some common types of graphs include line graphs, bar graphs, pie charts, scatterplots, and network graphs.

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The table mentioned in the question has been attached below.

The expression (x < y) && (y == 5) is an alternative way of writing the original expression, and it will be true only if two conditions are met: first, x is smaller than y, and second, y is equal to 5.

The expression !(!(x < y) || (y != 5)) is equivalent to:

(x < y) && (y == 5)

To see why, let's break down the original expression:

!(!(x < y) || (y != 5))

= !(x >= y && y != 5) (by De Morgan's laws)

= (x < y) && (y == 5) (by negating and simplifying)

So, the equivalent expression is (x < y) && (y == 5). This expression is true if x is less than y and y is equal to 5.

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Complete question:

Assume that x and y have been defined and initialized as int values. The expression

!(!(x < y) || (y != 5))

is equivalent to which of the following?

(x < y) && (y = 5)

(x < y) && (y != 5)

(x >= y) && (y == 5)

(x < y) || (y == 5)

(x >= y) || (y != 5)

Answer:

B) 33 times.

Step-by-step explanation:

The total amount of pebbles is 50. There is 22 yellow pebbles.

Note that 3/2 * 50 is 75. 3/2 * 22 = 33.

He should expect to choose a yellow pebble B) 33 times.

Answer: 37.5

Step-by-step explanation:

75 - 180 = 105

105 degrees = the obtuse angle, bottom triangle.

75/2= 37.5 (since both sides of the bottom triangle are equal angles)

As the two triangles are congruent to each other, using that we can get the value of x = 13 and y = 9.

Whether two or more triangles are congruent depends on the size of the sides and angles. As a result, a triangle's three sides and three angles determine its size and shape.

Two triangles are said to be congruent if their respective side and angle pairings are both equal.

Now in the given question,

The triangles are congruent so,

ED = QR

5y -7 = 38

⇒ 5y = 38+7

⇒ y = 45/5

⇒ y = 9

Now as the sum of angles in a triangle are 180°,

∠E +∠D +∠F = 180°

⇒ ∠F = 180 - 123 - 29

⇒ ∠F = 28°

As per congruency,

(2x+2) ° = 28°

⇒ 2x = 28-2

⇒ x = 26/2

⇒ x = 13

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The complete question is:

Find the values of x and y. ADEF = AQRS

(5y-7) ft

D

E

123⁰

F

S

S

(2x + 2)° R

= 0, y =

Q

38 ft

P

Answer:

There were 8 bears

Step-by-step explanation:

Letting L = number of lions, T = number of tigers and B = number of bears

L : T = 3 : 2

We can rewrite this as
L/T = 3/2

Cross multiply:
L x 2 = 3 x T

Divide by 3 to get
T = 2/3 L

Since L = 9

T = 2/3 x 9 = 6

In the other ratio we have
T : B = 3 : 4 which we can write as
T/B = 3/4

Cross multiply to get

4T = 3B

B = 4/3 T

Since T = 6, B = 4/3 x 6 = 8

Check
L : T = 9 : 6 = 3: 2 (by dividing both sides of : by 3)
T : B = 6 : 8 = 3:4 (by dividing both sides of : by 2)

Answer:

Step-by-step explanation:

The theoretical probability of getting the same side every time in a single coin toss is 1/2. Since we have five independent coin tosses, we can calculate the probability of getting the same side every time by multiplying the probability of getting the same side in each toss:

(1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32

Therefore, the theoretical probability of getting the same side every time in five coin tosses is 1/32, which is equivalent to 0.03125. So, the answer is (C) 0.03125.

Answer:

x = 52.2

Step-by-step explanation:

Add 4x - 4y^2 = 36 and x + 2y^2 = 225

x + 2y^2 + 4x - 4y^2 = 225 + 36

5x = 261

x = 261/5=52.2

The unique solution to the initial value problem of differential equation is y(t) = -t^2 + 2t + 3sin(3t) - 1 with e(t) = -t^2 + 2t + 3sin(3t) - 9, a = 2, and B = -21.

To find the solution to the initial value problem, we first need to solve the differential equation.

Taking the derivative of y(t), we get:

y'(t) = -2t + a

Taking the derivative again, we get:

y''(t) = -2

Substituting y''(t) into the differential equation, we get:

y''(t) + 2y'(t) + 10y(t) = 20sin(3t)

Substituting y'(t) and y(t) into the equation, we get:

-2 + 2a + 10(-2t + a) = 20sin(3t)

Simplifying, we get:

8a - 20t = 20sin(3t) + 2

Using the initial condition y(0) = 2, we get:

y(0) = -2(0) + a = 2

Solving for a, we get:

a = 2

Using the other initial condition y'(0) = 21, we get:

y'(0) = -2(0) + 2(21) + B = 21

Solving for B, we get:

B = -21

Therefore, the solution to the initial value problem is:

y(t) = -t^2 + 2t + 3sin(3t) - 1

Thus, we have e(t) = y(t) - 8, so

e(t) = -t^2 + 2t + 3sin(3t) - 9

and a = 2, B = -21.

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_____The given question is incomplete, the complete question is given below:

Consider the initial value problem >= [22. 2.1]+20). 361) = [2] Suppose we know that (t) = -2t + a 21? + is the unique solution to this initial value problem. Find e(t) and the constants and B. a = B= 8(t) =

In response to the stated question, we may state that Hence, the 95% CI function for u is (16.72, 19.48), rounded to two decimal places in increasing order.

In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.v

We use the following formula to create a confidence interval around the population mean u:

CI = x ± z*(s/√n)

where x represents the sample mean, s represents the sample standard deviation, n represents the sample size, z represents the z-score associated with the desired degree of confidence, and CI represents the confidence interval.

Because the degree of confidence is 95%, we must calculate the z-score that corresponds to the standard normal distribution's middle 95%. This is roughly 1.96 and may be determined with a z-table or calculator.

CI = 18.1 ± 1.96*(4.1/√34)

CI = 18.1 ± 1.96*(0.704)

CI = 18.1 ± 1.38

Hence, the 95% CI for u is (16.72, 19.48), rounded to two decimal places in increasing order.

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Step-by-step explanation:

Please mark as brainliest

Answer:

57

57

123

123

57

57

123

that's all.

Answer:

m<1 = 57°

m<2 = m<1 = 57°

m<3 = x = 123°

m<4 = x = 123°

m<5 = m<1 = 57°

m<6 = m<5 = 57°

m<7 = m<4 = 123°

Step-by-step explanation:

[tex]{ \tt{m \angle 1 + x = 180 \degree}} \\ { \colorbox{silver}{corresponding \: angles}} \\ { \tt{m \angle 1 = 180 - 123}} \\ { \tt{ \underline{ \: m \angle 1 = 57 \degree \: }}}[/tex]

Answer:

V=lwh

=2×2×2=8

720÷8=90

90 cubes

By answering the presented question, we may conclude that Therefore, 1  expressions cm on the map corresponds to a real distance of 3.2 km. 

In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

Scale 1:

320000 means that 1 unit on the map represents his 320000 units in the real world.

To find the actual distance represented by 1 cm on the map, you need to convert the units to the same scale.

1 kilometer = 100000 cm

So,

1 unit on the map = 320000 units in the real world

1 cm on the map = (1/100000) km in the real world

Multiplying both sides by 1 cm gives:

1 cm on the map = (1/100000) km * 320000

A simplification of this expression:

1 cm on the map = 3.2 km

Therefore, 1 cm on the map corresponds to a real distance of 3.2 km. 

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Answer:

the answer would be 100 I guess

The set of all x-values that are at a distance of 13 or less from the number 8 in the interval notation is given by  [ -5, 21 ].

The distance between x and 8 is |x - 8|.

Find all the values of x such that |x - 8| ≤ 13.

This inequality can be rewritten as follow,

|x - 8| ≤ 13

⇒ -13 ≤ x - 8 ≤ 13

Now,

Adding 8 to all sides of the inequality we get,

⇒  -13 +  8 ≤ x - 8 + 8 ≤ 13 + 8

⇒ -5 ≤ x ≤ 21

Therefore, all the x-values which are at a distance of 13 or less from the number 8 represented in the interval notation as [ -5, 21 ].

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Answer:

30, rational

Step-by-step explanation:

[tex]3\sqrt{20}\cdot\sqrt{5}=3\sqrt{4}\sqrt{5}\cdot\sqrt{5}=(3\cdot2)\cdot5=6\cdot5=30[/tex]

The result is rational because it can be written as a fraction of integers.

Answer:

Step-by-step explanation:

We can use the formula for the future value of an annuity to determine how much Marcia needs to invest today to meet her retirement goal of $90,000. The formula for the future value of an annuity is:

FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)

where:

FV = future value of the annuity

PMT = payment (or deposit) made at the end of each compounding period

r = annual interest rate

n = number of compounding periods per year

t = number of years

In this case, we want to solve for the PMT (the amount Marcia needs to invest today). We know that:

Marcia wants to retire in 15 years (when she is 65), so t = 15

The interest rate is 10% per year, compounded semiannually, so r = 0.10/2 = 0.05 and n = 2

Marcia wants to have $90,000 in her retirement account

Substituting these values into the formula, we get:

$90,000 = PMT x [(1 + 0.05/2)^(2*15) - 1] / (0.05/2)

Simplifying the formula, we get:

PMT = $90,000 / [(1.025)^30 - 1] / 0.025

PMT = $90,000 / 19.7588

PMT = $4,553.39 (rounded to the nearest cent)

Therefore, Marcia needs to invest $4,553.39 today in order to meet her retirement goal of $90,000, assuming an interest rate of 10% per year, compounded semiannually.

Answer:

To find the yield percentage of the fillets, we need to divide the weight of the fillets by the weight of the dressed mahi-mahi and then multiply by 100 to get a percentage:

Yield percentage = (Weight of fillets / Weight of dressed mahi-mahi) x 100%

First, we need to convert the weights to a common unit, such as ounces:

Weight of dressed mahi-mahi = 30 lb. 4 oz. = 484 oz.

Weight of fillets = 13 lb. 12 oz. = 220 oz.

Now we can calculate the yield percentage:

Yield percentage = (220 oz. / 484 oz.) x 100% = 45.45%

So the yield percentage of the fillets is 45.45%.

To find the per pound cost of the fillets, we need to divide the total cost of the dressed mahi-mahi by its weight in pounds, and then multiply by the yield percentage to get the cost per pound of fillets:

Total cost of dressed mahi-mahi = 30.25 lb. x $5.85/b. = $176.96

Weight of dressed mahi-mahi in pounds = 30.25 lb.

Weight of fillets in pounds = 13.75 lb.

Cost per pound of fillets = (Total cost of dressed mahi-mahi / Weight of dressed mahi-mahi) x Yield percentage / 100%

Cost per pound of fillets = ($176.96 / 30.25 lb.) x 45.45% = $3.04/lb.

Therefore, the per pound cost of the fillets is $3.04/lb.

The correct interpretation of the confidence interval is We are 95 percent confident that the mean cost of a hospital visit for all parrot owners in the state is between $44.99 and $80.27 that is option A.

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific degree of confidence, this is the range of values you anticipate your estimate to fall inside if you repeat the test. In statistics, confidence is another word for probability.

Given,

Confidence interval, CI = 62.63 +/- 17.64

CI = ( 44.99 , 80.27 )

The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level. In other words, a limitless number of independent samples are used to calculate the confidence intervals at the specified degree of assurance. in order for the percentage of the range that includes the parameter's real value to be equal to the confidence level.

Most of the time, the confidence level is chosen before looking at the data. 95% confidence level is the standard degree of assurance. Nevertheless, additional confidence levels, such as the 90% and 99% confidence levels, are also applied.

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Complete question:

To investigate hospital costs for pets in a certain state, researchers selected a random sample of 46 owners of parrots who had recently taken their parrot to an animal hospital for care. The cost of the visit for each parrot owner was recorded and used to create the 95 percent confidence interval $62.63±$17.64.

Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval?

The given prescription lacks important information about the frequency and route of administration. Knowing how often a medication should be taken and how it should be administered is crucial for ensuring that patients receive the appropriate dose and achieve the desired therapeutic effect.

Without the frequency information of how (e.g., orally, intravenously, etc.) and when  (e.g., daily, twice daily, etc.)  to take medicine on prescription, patients may take the medication incorrectly or miss doses, potentially leading to ineffective treatment or adverse effects.

Healthcare providers should always provide clear and complete instructions for medication use to ensure patient safety and optimal treatment outcomes.

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The chance that both numbers drawn are even numbers is 8/21.

The probability refers to the measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.

There are 4 even numbers and 3 odd numbers in the first box, and 2 even numbers and 1 odd number in the second box.

The probability of drawing an even number from the first box is 4/7, and the probability of drawing an even number from the second box is 2/3.

By the multiplication rule of probability, the probability of drawing an even number from both boxes is

(4/7) × (2/3) = 8/21

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Answer:

[tex]a = \frac{20}{3}[/tex]

Step-by-step explanation: