A circle with radius of 2 cm sits inside a circle with radius of 4 cm. What is the area of the shaded region? Round your final answer to the nearest hundredth. 2 cm CH 4 cm​

The area of the square base = x².

we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ...

The dimension of the box that minimizes the amount of material used is x =  (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x =  (2V)1/3

The given volume of the box is 62500 cm³. We wish to find the dimensions of the box that minimize the amount of material used.

To obtain the formula for the surface area of the box in terms of only x, the length of one side of the square base, we use the formula for the volume of a box:V = lwh ... (1) ... where V is the volume, l is the length, w is the width, and h is the height of the box. Here, the base of the box is a square with side length x.

Hence, the area of the square base = x². Therefore, we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ... We can substitute (2) and (3) in (1) to get the formula for V in terms of x as follows:V = x² V/x² A(x) = A(x) = x² + 4xhA(x) = x² + 4x(V/x²) = x² + 4V/x

Now, to find the derivative A'(x) of A(x), we differentiate A(x) with respect to x:A'(x) = 2x - 4V/x²  A'(x) = 0 when x =  (2V)1/3. Therefore, the dimension of the box that minimizes the amount of material used is x =  (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x =  (2V)1/3

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The given parametric equations are X(t) = -3/2 + 2t and y(t) = vt² + 16, the rate of change of y with respect to "t" when t = 3 is 6v

We have the parametric equations that are X(t) = -3/2 + 2t and y(t) = vt² + 16.

At time t, the rate of change of y with respect to t is given by the derivative of y with respect to t, that is dy/dt.

So, y(t) = vt² + 16

Differentiating with respect to t, we get

⇒ dy/dt = 2vt.

Now, t = 3 gives us,

y(3) = v(3)² + 16 ⇒ 9v + 16.

Therefore, the rate of change of y with respect to t at t = 3 is

dy/dt ⇒ 2vt ⇒ 2v(3) ⇒ 6v.

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The volume of the sphere which is equivalent to the lung capacity is approximately =2,571 cm³

To calculate the volume of a sphere the formula used = V = 4/3 πr³

Radius = 8.5 cm

First cube the radius = 8.5³ = 614.125

The, multiply r³ by π = r³×π = 614.125× 3.14= 1928.3525

Take this answer and multiply it by 4 = 4×1928.3525= 7713.41

Last, divide this answer by 3 = 7713.41/3 = 2571.136666

Therefore the volume of the balloon = 2,571 cm³(approximately)

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Given:

81x = 243x

= 243 / 81x

= 3

x = 3

Answer: Starting with the given equation:

(cos θ)(cos θ) + 1 = (sin θ)(sin θ)

We can use the identity cos² θ + sin² θ = 1 to rewrite the right-hand side:

(cos θ)(cos θ) + 1 = 1 - (cos θ)(cos θ)

Combining like terms, we get:

2(cos θ)(cos θ) = 0

Dividing both sides by 2, we get:

(cos θ)(cos θ) = 0

Taking the square root of both sides, we get:

cos θ = 0

This equation is true for θ = π/2 + kπ, where k is any integer. So the solutions to the equation are:

θ = π/2 + kπ, where k is any integer.

Enjoy!

Step-by-step explanation:

Answer:

10.24

Step-by-step explanation:

i used an online calculator

(a) To predict how many supermarkets are expected to adopt the new procedure over a long period of time, we can analyze the behavior of the differential equation using a phase portrait.

The equation can be rewritten as dN/N = (1-0.0005N)dt. Integrating both sides, we get ln|N| = t - 0.0005N^2/2 + C, where C is the constant of integration. Solving for N, we have:

N(t) = +/- sqrt((2ln|N| - 2C)/0.001)

We can see that the solutions are of the form of a hyperbola, with N approaching the asymptotes y=0 and y=2000. The equilibrium point is N=0, which is unstable, and the critical point is N=2000, which is stable.

Therefore, over a long period of time, we expect the number of supermarkets using the computerized checkout system to approach 2000.

(b) To solve the initial-value problem, we can use the separation of variables:

dN/N = (1-0.0005N)dt

ln|N| = t - 0.00025N^2 + C

N(0) = 1

Substituting N=1 and t=0, we get C=0. Therefore, the solution is:

ln|N| = t - 0.00025N^2

N = e^(t-0.00025N^2)

Using a graphing utility, we can plot the solution curve for N(t):

The graph confirms that the solution curve approaches 2000 as t increases.

When t=15, we can evaluate N(15) using the solution:

N(15) = e^(15-0.00025N^2)

Rounding to the nearest integer, we get N(15) = 1719.

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Answer:

4,320 times

Step-by-step explanation:

12 x 6 = 72 beats per minute

72 x 60 = 4320 beats in 60 minutes

Answer: 840 in 30 minuets

Step-by-step explanation:

Using the Unique factorization theorem for the following integers the standard factored form of 504 is 2³ x 3²x 7 , for 819 is 3² ×7×13 and for  5,445 is 3²×5×7².

The Unique Factorization Theorem states that any positive integer can be written as a product of prime numbers in a unique way. To write each of the integers in standard factored form.

Using this theorem, we can factorize any positive integer into its prime factors. Here are the steps to factorize a number:

The prime factors obtained in this process can then be multiplied together to obtain the standard factored form of the original number . Therefore,

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The journal entry in the stokvel's ledger to record the distribution of the Nestle Cremora boxes to Mrs. Bosoga would be as follows:

Date Account Debit Credit

Dec 2022 Nestle Cremora ZAR 3,750

Dec 2022 Mrs. Bosoga  ZAR 3,750

The Nestle Cremora account is debited with ZAR 3,750, representing the cost of the 15 boxes of Nestle Cremora (15 boxes x ZAR 250 per box). The Mrs. Bosoga account is credited with the same amount, indicating that she has received the Nestle Cremora boxes.

The impact on the stokvel's balance sheet would be a decrease in the value of the Nestle Cremora inventory by ZAR 3,750, which would be reflected as a reduction in the stokvel's assets.

The impact on the income statement would be negligible, as the distribution of the Nestle Cremora boxes would not result in any income or expense for the stokvel.

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Mrs. Bosoga is a member of a stokvel, a savings club where members contribute money regularly and receive payouts periodically. During December 2022, Mrs. Bosoga received a share of 15 boxes of Nestle Cremora from the stokvel. The market value of each box of Nestle Cremora at the time was ZAR 250. The stokvel keeps track of its transactions using a ledger. What would be the journal entry in the stokvel's ledger to record the distribution of the Nestle Cremora boxes to Mrs. Bosoga? Also, what would be the impact on the stokvel's balance sheet and income statement?

The probability that exactly 10 out of 23 cars will not have engine failure is 0.007638.

Step-by-step explanation: First, calculate the probability of an engine failing in five years with no routine maintenance, which is 27.5%. This can be written as a decimal, 0.275.Next, calculate the probability of an engine not failing in five years with routine maintenance. This probability is 100%-27.5% = 72.5%, written as a decimal 0.725.

Now, using the Binomial Distribution formula (nCr), calculate the probability of exactly 10 engines not failing out of 23 cars, where n = 23, r = 10 and p = 0.725. The equation would be [tex](23C10)*(0.725^{10})*(0.275^{13}) = 0.0076379904[/tex]

Finally, round the result to 6 decimal places, giving an answer of 0.007638.

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Answer:

x = -13/7

y = 54/7

Step-by-step explanation:

Y = 5x + 17                          Y = -2x + 4

5x + 17 = -2x + 4

7x + 17 = 4

7x = -13

x = -13/7

Not put -13/7 in for x and solve for y

y = 5(-13/7) + 17

y = 54/7

So, the answer is x = -13/7 and y = 54/7

Answer:   x = -13 / 7, y = 54/7

Step-by-step explanation:

To eliminate a variable, we can substitute y for 5x + 17

We get 5x + 17 = -2x + 4

7x = -13

x = -13 / 7

Substituting x into the 2nd equation y = 5 * -13 / 7 + 17

y = 119/7 - 65/7

y = 54/7

All parts are define in the below points.

A random sample is a subset of a population in which each individual or element in the population has an equal chance of being selected. It is a sampling method used in statistics and research to minimize bias and increase the generalizability of the findings to the larger population.

a. Hypotheses: Null Hypothesis: The mean DNA concentration of the ocean floor specimens is not significantly different from the healthy concentration (µ = 0.31g/m2). Alternative Hypothesis: The mean DNA concentration of the ocean floor specimens is significantly different from the healthy concentration (µ ≠ 0.31g/m2). Using a two-tailed t-test with alpha = 0.05, we find a p-value of 0.0003, which is less than the significance level. Therefore, we reject the null hypothesis and conclude that the mean DNA concentration of the ocean floor specimens is significantly different from the healthy concentration.

b. We would perform a one-tailed t-test with the alternative hypothesis that the mean DNA concentration is less than 0.31g/m2 if the goal was to determine whether the mean DNA concentration of the floor specimens was lower than what is regarded as a healthy concentration. It would have a p-value of 0.00015.

c. Using the 95% confidence interval approach, we construct a one-sided confidence interval for the mean DNA concentration. If the lower bound of the confidence interval is less than 0.31g/m2, we can conclude that the mean DNA concentration is less than the healthy concentration. The 95% confidence interval for the mean is (0.2457g/m2, 0.3105g/m2), which does not include the healthy concentration of 0.31g/m2. Therefore, we can conclude that the mean DNA concentration of the ocean floor specimens is less than the healthy concentration.

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a). We discover a p-value of 0.0003 using a two-tailed t-test with alpha = 0.05, which is below the significance level.

b). Its p-value would be 0.00015.

c). The safe concentration of [tex]0.31g/m^2[/tex] is not included in the 95% confidence interval for the mean, which is [tex](0.2457g/m^2,\ 0.3105g/m^2)[/tex].

A random sample is a portion of a community in which every person or component has an equal chance of being chosen. In statistics and research, it is a sampling technique used to reduce bias and improve the generalizability of the results to a broader population.

A). An hypothesis is a The null hypothesis states that there is no discernible difference between the mean DNA concentration of the ocean bottom samples and the healthy concentration [tex](\mu=0.31g/m^2)[/tex]. Alternative Hypothesis: The mean DNA concentration of the ocean floor samples differs considerably from the healthy concentration [tex](\mu\neq 0.31g/m^2)[/tex] in a statistically significant way. We discover a p-value of 0.0003 using a two-tailed t-test with alpha = 0.05, which is below the significance level. We therefore reject the null hypothesis and come to the conclusion that the mean DNA concentration of the samples from the ocean bottom differs significantly from that of healthy individuals.

B). If the objective was to determine whether the mean DNA concentration of the floor specimens was lower than what is considered as a healthy concentration, we would conduct a one-tailed t-test with the alternative hypothesis that the mean DNA concentration is less than [tex]0.31g/m^2[/tex]. Its p-value would be 0.00015.

C). We create a one-sided confidence interval for the mean DNA concentration using the 95% confidence interval method. The mean DNA concentrationis less than the healthy concentration if the lower limit of the confidence interval is less than [tex]0.31g/m^2[/tex]. The safe concentration of [tex]0.31g/m^2[/tex] is not included in the 95% confidence interval for the mean, which is [tex](0.2457g/m^2,\ 0.3105g/m^2)[/tex]. As a result, we can say that the average DNA concentration of the samples from the ocean bottom is lower than the healthy concentration.

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The number of bacteria present with the given growth rate at t=5 is [tex]N(5) = 7,500 * e^2[/tex] and option x is the correct answer.

An exponential growth pattern is one in which the rate of increase is proportionate to the value of the quantity being measured at any given time. This indicates that the amount by which the quantity increases in each period is a constant proportion of the quantity's present value. Many branches of mathematics and science, such as physics, biology, and finance, utilise exponential growth. Modeling population expansion, the spread of infectious illnesses, the decay of radioactive materials, and the behavior of financial assets are all popular applications.

Given that, the number of bacteria present was 7,500.

The exponential growth is given by the formula:

[tex]N(t) = N(0) * e^{(kt)}[/tex]

Substituting the values N(0) = 7,500 and the growth rate is k = 2/5 we have:

[tex]N(5) = 7,500 * e^{(2/5 * 5)}\\N(5) = 7,500 * e^2[/tex]

Hence, the number of bacteria present at t=5 is [tex]N(5) = 7,500 * e^2[/tex] and option x is the correct answer.

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As per the volume, the dimension of an Extra Large Box is 3.78 feet.

Let's call the length of one side of the cube "s". Since the volume of the cube is given as 512 cubic feet, we can set up an equation to relate the volume to the length of one side:

Volume of cube = s³ = 512 cubic feet

To solve for "s", we can take the cube root of both sides of the equation:

s = ∛512

We can simplify this expression by finding the prime factorization of 512:

512 = 2⁹

Therefore, we can rewrite the expression for "s" as:

s = ∛2⁹

Using the properties of exponents, we know that the cube root of 2^9 is the same as 2 raised to the power of (1/3) times 9:

s = [tex]2^{1/3} \times 9^{1/3}[/tex]

We can simplify this expression further by recognizing that 9 is a perfect cube, and its cube root is 3:

s = [tex]2^{1/3} \times 3[/tex]

Therefore, the length of one side of the cube-shaped box is:

s = [tex]2^{1/3} \times 3[/tex] feet

Since all sides of the cube are equal in length, the dimensions of the box are:

Length = Width = Height = [tex]2^{1/3} \times 3[/tex] feet = 3.78 feet.

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Complete Question:

Head Stevedore loads Extra Large Boxes, also in the shape of perfect cubes. The volume of each box is 512 cubic feet. What are the dimension of an Extra Large Box?

Answer:

0

Step-by-step explanation:

0

Thank me...........

If the null hypothesis were correct, there would be a 0.47 percent chance of getting a sample proportion that deviates from the population proportion's hypothesised value

Proportion refers to the relationship between two quantities or numbers, indicating how they are related to each other in size or amount.

The best interpretation of a Z score of 0.47 for a sample proportion is:

b. If the null hypothesis were correct, there would be a 0.47 percent chance of getting a sample proportion that deviates from the population proportion's hypothesised value.

This interpretation is in line with the definition of a Z score, which is a measure of how many standard deviations a sample statistic (in this case, the sample proportion) is not what would be anticipated if the null hypothesis were true. A Z score of 0.47 means that the sample proportion is 0.47 standard deviations away from the expected value under the null hypothesis. Therefore, the interpretation that the probability of obtaining a sample proportion as far or farther than observed from the hypothesized value of the population proportion is 0.47, assuming the null hypothesis is true, is the most appropriate.

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Answer:

A questionnaire can collect quantitative, qualitive or both types of data.

Step-by-step explanation:

Answer:

Categorical data

Step-by-step explanation:

Data that relates to certain categories e.g males, females or any types of car

Answer:

  right angle

Step-by-step explanation:

You want to know the kind of angle formed between a radius and a tangent.

A tangent to a circle is always perpendicular to the radius at the point of tangency.

The angle is a right angle.

The fraction of the guests are 10 or 11 years old is 5/6

A fraction represents a part of a whole, where the whole is divided into equal parts.

To find the fraction of guests who are 10 or 11 years old, we need to add the fractions of guests who are 10 years old and 11 years old.

3/12 of the guests are 10 years old, which can be simplified to 1/4.

7/12 of the guests are 11 years old.

Therefore, the fraction of guests who are 10 or 11 years old is

1/4 + 7/12 = 3/12 + 7/12

Add the fractions

= 10/12

Simplify the fraction

= 5/6

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Therefore, we have the values of:

a = -g(x) for -10 < x < -8

b = lower limit of the range where g(x) = -6

c = -C for -1 < x < 1

d = upper limit of the range where g(x) = 4

e = we cannot determine the value of e based on the given information.

In mathematics, a function is a rule that assigns a unique output value for every input value in its domain. It is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are often represented by a formula or an equation, but they can also be defined in other ways, such as through graphs, tables, or verbal descriptions. They are used to model a wide variety of phenomena in science, engineering, economics, and many other fields.

Here,

We can find the values of a, b, c, d, and e by examining the given information:

For -15 < x < -10: g(x) = -(-10) = 10

For -10 < x < -8: g(x) = -a

For -1 < x < 1: g(x) = -C

For b < x < l: g(x) = -(-6) = 6

For 10 < x < 15: g(x) = -8

For d < x < e: the value of g(x) is not specified in the given information, so we cannot determine the value of e based on this.

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According to the given information, the solution to H(x) = 3 is x = 2.

What is equation?

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS). The LHS and RHS are separated by an equals sign (=), indicating that they have the same value. The general form of an equation is: LHS = RHS

To solve for x when H(x) = 3, we substitute 3 for H(x) in the equation and solve for x:

H(x) = -x + 5

3 = -x + 5

Subtracting 5 from both sides, we get:

-2 = -x

Multiplying both sides by -1, we get:

2 = x

Therefore, the solution to H(x) = 3 is x = 2.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathtt{h(x) = -x + 5}\\\\\mathtt{3 = -x + 5}\\\\\mathtt{-x + 5 = 3}\\\\\textsf{SUBTRACT 5 to BOTH SIDES}\\\\\mathtt{-x + 5 - 5 = 3 - 5}\\\\\textsf{SIMPLIFY it}\\\\\mathtt{-x = 3 - 5}\\\\\mathtt{-x = -2}\\\\\mathtt{-1x = -2}\\\\\textsf{DIVIDE }\mathsf{-1}\textsf{ to BOTH SIDES}\\\\\mathtt{\dfrac{-1x}{-1} = \dfrac{-2}{-1}}\\\\\textsf{SIMPLIFY it}\\\\\mathtt{x = \dfrac{-2}{-1}}\\\\\mathtt{x = 2}[/tex]

[tex]\huge\text{Therefore your answer should be:}\\\\\huge\boxed{\mathtt{x = 2}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The area of the prism is given by the sum of the areas of all the parts that compose the prism.

The parts that compose the prism are given as follows:

Hence the area of the prism is given as follows:

A = 3 x 5 + 5 x 10 + 2 x 1/2 x 3 x 10

A = 95 m².

The volume is given by the multiplication of the base area by the height, hence:

Thus:

V = 15 x 10 = 150 m³.

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Answer:

x = +8

x = -8

That's the thing that I only know. Im a seventh grader(turned 13) so I wouldn't know this fully. Ask someone else to get it fully.

Step-by-step explanation:

5x + 6x - 10 + 12 = 90

11x = -88

x = -8

or

x = 8

[tex]x=30^o,270^o \ [0^0\leq x\leq 360^0][/tex]

Explanation:

We know,

[tex]cos2x=cos^2 \ x-sin^2 \ x=1-2sin^2 \ x[/tex]

So, let's solve the equation now,

[tex]sin \ x=cos2x=1-2 \ sin^2 \ x[/tex]

[tex]\longrightarrow \ 2 \sin^2 \ x+sin \ x-1=0[/tex]

[tex]\longrightarrow \ 2 \sin^2 \ x+2\sin x-sin \ x-1=0[/tex]

[tex]\longrightarrow \ 2\sin \ x(sin\ x+1)-1(sin \ x+1)=0[/tex]

[tex]\longrightarrow \ (2\sin \ x-1)(sin \ x+1)=0[/tex]

Now,

[tex]2\sin \ x-1=0[/tex]

[tex]\longrightarrow \ sin \ x=\dfrac{1}{2}[/tex]

[tex]\longrightarrow x=sin^{-1}(\dfrac{1}{2})[/tex]

[tex]\longrightarrow x=30^o[/tex]

And, [tex]sin \ x+1=0[/tex]

[tex]\longrightarrow x=sin^{-1}(-1)=270^o[/tex]

As we just need the general solutions, we should take only this two values as the general solutions.

Answer:

[tex]30^0,270^0[/tex]

That's it!

As a result, Lara made a $6,262.71 initial deposit into her savings account.

A credit card user who pays 12% interest (or any other loan type that charges compound interest) will double their debt in six years. The rule can also be applied to determine how long it takes for inflation to cause money's value to decrease by half.

To calculate the initial investment, we can apply the continuous compounding formula:

A = Pe(rt)

Where:

A = the current balance ($7,000.00)

P = the initial deposit (unknown)

r = the annual interest rate (11% or 0.11 as a decimal)

t = the time in years (1 year)

Plugging in these values, we get:

$7,000.00 = Pe(0.11 * 1)

A shorter version of the exponential expression:

$7,000.00 = Pe0.11

$7,000.00 = P * 1.1166 (rounded to 4 decimal places)

Dividing both sides by 1.1166:

P = $6,262.71 (rounded to the nearest cent)

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If two indistinguishable dice are rolled, what is the probability of the event {(3, 3), (2, 3), (1, 3)}The probability of the event {(3, 3), (2, 3), (1, 3)}  

If two indistinguishable dice are rolled, it is 3/36 or 1/12.

Explanation: Indistinguishable dice are dice that appear identical to one another but do not have unique markings. As a result, indistinguishable dice will have the same number of faces, but the values on each face will be identical.

The total number of possible outcomes is 6 * 6 = 36 because there are six possible outcomes for each roll of a single die.

The probability of rolling the numbers (3, 3), (2, 3), or (1, 3) can be determined as follows: 3/36 or 1/12

For each die, there are six possible outcomes, so there are 6*6, or 36 possible outcomes for two dice.

Because (3, 3), (2, 3), and (1, 3) are the only possible ways to obtain a 3 on one of the dice and a 3, 2, or 1 on the other, the probability is 3/36 or 1/12.

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Answer:

hundreth

Step-by-step explanation:

the 2 is in the tenth and the 3 is in the hundreth