what’s the equation of this red line?

The area of the shaded region is  4 cm².

The area of the shaded region is calculated by applying Cavalieri's principle.

Cavalieri's principle states that if two three-dimensional objects have the same cross-sectional area along a height and the same height, then the figures have the same volume.

The area of the shaded figure is calculate as follows;

from the diagram the width of the shaded region = 2 cm

The height of the shaded region = 2 cm

Area = 2 cm x 2 cm = 4 cm²

Thus, the area of the shaded region is determined by considering Cavalieri's principle.

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The rule of the z-score is

μ is the mean

σ is the standard deviation

Since the average of the height of an adult male is 70 inches, then

Since the standard deviation is 3 inches, then

We need to find the percentage of the height of the adult males between 65 and 75 inches, then

We will find the z-score of them

We will use the given table to find their areas

We will subtract both values to find the answer

The correct statement is: the volume of the cylinder is 8 cubic inches more than that of the cone.

The volume of cone (V) = 1/3 * πr²h

Volume of cylinder (V) = πr²h

Where, r is the radius of their bases.

The base area formula for the cone = πr²

Calculate the area of the base of the cone that has a radius (r) of 2.5 in:

Area of the base of the cone = π(2.5)² ≈ 19.6

The volume of the cone (V) = 1/3 * πr²h = 1/3 * π * 2.5² * 6.5

≈ 42.5 cubic inches

Volume of cylinder (V) = πr²h = π * 2² * 4

≈ 50.3 cubic inches

The difference in volume = 50.3  - 42.5

= 7.8 ≈ 8 cubic inches

Therefore, the only statement that is true is: the volume of the cylinder is 8 cubic inches more than that of the cone.

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According to the question The height of the cone that can be created by rolling one of the congruent sectors is approximately 6.32 cm.

To find the height of the cone that can be created by rolling one of the congruent sectors of the circular sheet, we need to calculate the circumference of the base of the cone.

The circumference of the base is equal to the length of the sector's arc, which can be calculated using the formula:

\(\[ \text{Arc Length} = \left(\frac{\text{Central Angle}}{360^\circ}\right) \times \text{Circumference of the Circle} \]\)

Since the sector is one-third of the circle, the central angle of the sector is  \(\( 120^\circ \) (\( \frac{360^\circ}{3} \)).\)

The circumference of the circle is given by the formula:

\(\[ \text{Circumference} = 2 \pi \times \text{radius} \]\)

Substituting the values, we have:

\(\[ \text{Circumference} = 2 \pi \times 6 \, \text{cm} = 12\pi \, \text{cm} \]\)

Now, we can calculate the arc length:

\(\[ \text{Arc Length} = \left(\frac{120^\circ}{360^\circ}\right) \times 12\pi \, \text{cm} = 4\pi \, \text{cm} \]\)

When the sector is rolled to form a cone, the arc length becomes the circumference of the base of the cone.

The circumference of the base of the cone is also equal to \(\( 2\pi \times \text{radius of the cone} \).\)

Therefore, we can equate the two circumferences and solve for the radius of the cone:

\(\[ 2\pi \times \text{radius of the cone} = 4\pi \, \text{cm} \]\)

Dividing both sides by \(\( 2\pi \)\), we find:

\(\[ \text{Radius of the cone} = 2 \, \text{cm} \]\)

Now, the height of the cone can be calculated using the Pythagorean theorem:

\(\[ \text{height}^2 = (\text{radius of the cone})^2 + (\text{radius of the base})^2 \]\)

\(\[ \text{height}^2 = 2^2 + 6^2 = 4 + 36 = 40 \]\)

Taking the square root of both sides, we get:

\(\[ \text{height} \approx \sqrt{40} \approx 6.32 \, \text{cm} \]\)

Therefore, the height of the cone that can be created by rolling one of the congruent sectors is approximately 6.32 cm.

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Answer: r=0

Step-by-step explanation: Hope this help :D

We know

\(\boxed{\sf \star TSA_{(Cylinder)}=2\pi r(h+r)}\)

\(\\ \sf\longmapsto TSA_{(Old\:Cylinder)}=2\times \dfrac{22}{7}\times 4(8+4)\)

\(\\ \sf\longmapsto TSA_{(Old\:Cylinder)}=\dfrac{176}{7}(12)\)

\(\\ \sf\longmapsto TSA_{(Old\:Cylinder)}=\dfrac{2112}{7}\)

\(\\ \sf\longmapsto TSA_{(Old\:Cylinder)}=301.7cm^2\)

Now

\(\\ \sf\longmapsto TSA_{(New\:Cylinder)}=2\times \dfrac{22}{7}\times 8(16+8)\)

\(\\ \sf\longmapsto TSA_{(New\:Cylinder)}=\dfrac{352}{7}(24)\)

\(\\ \sf\longmapsto TSA_{(New\:Cylinder)}=\dfrac{8448}{7}\)

\(\\ \sf\longmapsto TSA_{(New\:Cylinder)}=1204.7cm^2\)

So

\(\\ \sf\longmapsto \dfrac{TSA_{(New\:Cylinder)}}{TSA_{(Old\:Cylinder)}}=\dfrac{1204.7}{301.7}\)

\(\\ \sf\longmapsto \dfrac{TSA_{(New\:Cylinder)}}{TSA_{(Old\:Cylinder)}}=\dfrac{4}{1}\)

\(\\ \sf\longmapsto\underline{\boxed{\bf{ {TSA_{(New\:Cylinder)}}:{TSA_{(Old\:Cylinder)}}=4:1}}}\)

Hence our correct option is Option C

\(\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &200\\ t=\textit{elapsed time}\dotfill &14325\\ h=\textit{half-life}\dotfill &5730 \end{cases} \\\\\\ A=200\left( \frac{1}{2} \right)^{\frac{14325}{5730}}\implies A=200\left( \frac{1}{2} \right)^{\frac{5}{2}}\implies A\approx 35.36\)

The latest time for pickup, found by converting the 150 minutes maximum time provided by the school, from minutes to hours is about 5:45 pm

Minutes can be converted into hours by dividing the number of minutes by 60, which is the number of minutes in an hour.

The time that school ends = 3:15 pm

The latest time for pick up after school care = 150 minutes after school ends

Therefore, the latest time for pick up after school care = 3:15 pm + 150 minutes

60 minutes = 1 hour

150 minutes = (1/60) × 150 = 2.5

The latest for pick up = 3:15 pm + 2.5 hours = 5:45 pm

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We must solve for n the following equation:

1) First, we assume n ≠ 0 and multiply both sides by √n, we get:

2) Now, we divide both sides by E:

3) Finally, taking the square on both sides, we get:

Answer:

D. The money that Kai started with before he mowed any lawns.

Step-by-step explanation:

We Know

The equation is y = mx + b

The x represents the number of lawns that Kai mows.

What does the y-intercept represent in this equation?

The y-intercept is when the x = 0, meaning the y-intercept is the amount of money he has when mowing 0 lawn. So, the answer is D.

Answer:

The Answer is D

Step-by-step explanation:

The area of the rectangle is \($\sqrt{20} \times \sqrt{5} = \sqrt{100} = 10$\) square units. Thus, the answer is option D: 10 square units.

What is area of rectangle?

The area of a rectangle is the measure of the region enclosed by its sides, and is calculated by multiplying the length and the width of the rectangle. The unit of area is typically expressed in square units, such as square meters (m²) or square feet (ft²).

The area of rectangle can be calculated using the distance formula to find the length and width of the rectangle, and then multiplying them. Let A(2,1), B(1,3), C(5,5), and D(6,3) be the coordinates of the rectangle's vertices.

The distance between A and B is \(\sqrt{(1-2)^2 + (3-1)^2} = \sqrt{1+4} = \sqrt{5}$.\)

The distance between B and C is \(\sqrt{(5-1)^2 + (5-3)^2} = \sqrt{16+4} = \sqrt{20}$.\)

So, the length of the rectangle is \(\sqrt{20}$ units.\)

The distance between A and D is \(\sqrt{(6-2)^2 + (3-1)^2} = \sqrt{16+4} = \sqrt{20}$.\)

The distance between C and D is \(\sqrt{(6-5)^2 + (3-5)^2} = \sqrt{1+4} = \sqrt{5}$.\)

Therefore, the width of the rectangle is \(\sqrt{5}$ units.\)

Hence, the area of the rectangle is \($\sqrt{20} \times \sqrt{5} = \sqrt{100} = 10$\) square units. Thus, the answer is option D: 10 square units.

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Answer:

ok

Step-by-step explanation:

i dont even know

Answer:To verify the Divergence Theorem, the surface integral of F · dS can be evaluated as a surface integral, and the triple integral of div(F) can be evaluated as a triple integral. However, the given function F(x, y, z) = xzi + zyj + 2z²k does not match the provided surface description, so it cannot be used to verify the Divergence Theorem.

Step-by-step explanation:

To verify the Divergence Theorem, we need to evaluate both the surface integral and the triple integral involving the given vector field F(x, y, z) = xzi + zyj + 2z²k.

The surface S is described as being bounded by the equation z = 16 - x² - y² and z = 0. However, the given vector field F does not match this surface description, as it has z terms that do not match the z equation of the surface. Therefore, we cannot use this vector field to verify the Divergence Theorem for the given surface.

In order to properly verify the Divergence Theorem, we would need a vector field that matches the surface description, i.e., one that has z = 16 - x² - y² as the z equation. With the correct vector field, we could evaluate the surface integral of F · dS and the triple integral of div(F) over the region enclosed by the surface.

Without the correct vector field and surface description, it is not possible to proceed with the verification of the Divergence Theorem for the given problem.

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Answer:

\( \sqrt{72} \)

\( \sqrt{201} \)

\( \sqrt{52} \)

These are surd

so A and D are not surd

Step-by-step explanation:

A surd is an expression that includes a square root, cube root or other root symbol. Surds are used to write irrational numbers precisely – because the decimals of irrational numbers do not terminate or recur, they cannot be written exactly in decimal form.

The limit of \(L_n\) as n approaches infinity is 1/2, and it can be expressed as the definite integral of x from 0 to 1.

To express the limit of \(L_n\) as n approaches infinity as a definite integral, we can use the fact that the limit of a Riemann sum is equal to the corresponding definite integral. Thus, we can rewrite \(L_n\) as:

\(L_n\) = 1/n * (0 + 1 + 2 + ... + (n-1))

This is a Riemann sum for the integral:

\(\int\limits^1_0 {x} \, dx\)

with n subintervals of width 1/n. Therefore, we can write:

\(\lim_{n \to \infty} L_n = \lim_{n \to \infty} 1/n * (0 + 1 + 2 + ... + (n-1)) = \int\limits^1_0 {x} \, dx = [x^2/2] \ from \ 0 \ to \ 1 = 1/2\)

So, the limit of Ln as n approaches infinity is 1/2, and it can be expressed as the definite integral of x from 0 to 1.

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The quadratic equation y = 6x²+ 19x -20 has the same standard form as Ax+By +C = 0.

what is quadratic equation ?

A quadratic polynomial in an independent condition is represented by the expression x ax²+bx+c=0. a 0. Since this equation is of second order, the Fundamental Theory of Algebra requires that it has at best one solution. There can be both simple and complex solutions.

A quadratic equation is just that—quadratic. This indicates that which has at least yet another word that has to be squared. One of the often cited solutions for differential calculus is "ax² + bx + c = 0." where X is an undefined parameter and a, b, and c are mathematical coefficients or constants.

y=(6x-5)(x+4)

y = 6x² - 5x + 24x - 20

y = 6x² + 19x -20

The quadratic equation y = 6x² + 19x -20 has the same standard form as Ax+By +C = 0.

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Answer:

x = 7, -11

Step-by-step explanation:

(x + 2)^2 = 81

(7 + 2)^2 = 81      Take one value of x

9^2 = 81              Solve for the exponent

81 = 81                Final Answer

(x + 2)^2 = 81

(-11 + 2)^2 = 81   Take one value of x

9^2 = 81             Solve for the exponent

81 = 81

Understandings:

Understand how to solve for exponents

For example the ones that we used in this situation, in order to solve for an exponent, multiply the number by itself twice = 9 x 9 = 9^2 = 81

Answer:

x = 7 , x = - 11

Step-by-step explanation:

\((x+ 2)^2 = 81\\\\(x+2) = \sqrt{81}\\\\(x+2) = \pm 9\\\\x + 2 = 9 \ , \ x + 2 = - 9\\\\x = 9 - 2 \ , \ x = - 9 - 2\\\\x = 7 \ , \ x = -11\)

An interaction occurs when (D) the values of one independent variable influence how another independent variable influences a result.

A type of activity known as interaction takes place when two or more items have an impact on one another.

In contrast to a one-way causal effect, the idea of a two-way effect is crucial to the concept of interaction.

Interactivity and interconnection are closely related concepts; the latter deals with the interactions of interactions inside systems; combinations of numerous straightforward interactions might result in unexpected emergent phenomena.

In many sciences, interaction has numerous specialized meanings.

When the values of one independent variable affect how a result is affected by another independent variable, this is known as an interaction.

Therefore, an interaction occurs when (D) the values of one independent variable influence how another independent variable influences a result.

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Complete question:

An interaction occurs when:

a. a single independent variable changes the dependent variable, disregarding all other variables in the study

b. two independent variables both influence the dependent variable

c.the dependent variable does not depend on any of your independent variables

d. the effects of one of your independent variables depend on the level of the other independent variable

Given that, Edin has £3000 in his account.

The bank offers him a fixed 5% simple interest rate per annum, for three years. We need to calculate how much interest he will have earned after three years.

So,

Interest after 3 years = Principal × Rate × Time

= 3000 × 5% × 3

= £450

Therefore, Edin will have earned £450 in interest after three years at a fixed 5% simple interest rate per annum.

let's do it in more detail:

Simple interest is calculated based on the principal amount, the interest rate, and the time period. Let's break down the calculation step by step.

Given:

Principal (P) = £3000

Rate (R) = 5% = 0.05 (expressed as a decimal)

Time (T) = 3 years

The formula for calculating simple interest is:

Interest = Principal * Rate * Time

Plugging in the values from the given information:

Interest = £3000 * 0.05 * 3

First, we convert the percentage interest rate to a decimal by dividing it by 100. In this case, 5% becomes 0.05.

Next, we multiply the principal (£3000) by the decimal interest rate (0.05) and the time period (3 years).

Interest = £3000 * 0.05 * 3

= £150 * 3

= £450

Therefore, Edin will have earned £450 in interest after the three years. This means that his account balance will increase by £450 over the three-year period due to the interest earned on the principal amount.

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Answer:

(1, 6) (2, 12) (3, 24) (4, 48)

If you have to continue to graph, multiply your y value by 2 and just add 1 to your x value. Hope this helps.

find slope

5-4/3-2 = 1/1 = 1

choose a point

(y - 4) = 1(x-2)

The order of the differential equation d²y/dx² + 4x(dy/dx) = d³(cos(2x))/dx³ is 3.

The order of a differential equation is determined by the highest derivative present in the equation. In the given differential equation, the highest derivative is the third derivative, d³(cos(2x))/dx³. Since this is the highest derivative and there are no higher-order derivatives present, the order of the differential equation is 3. This means that the equation involves up to the third derivative of the dependent variable y with respect to the independent variable x.

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Equation of the direct variation described

a. g(t) = 25t + 80

b. The domain of the function is all non-negative real numbers, since time and the amount of water in the pool cannot be negative.

c. The range of the function is all values of g(t) such that g(t) >= 80 since the pool started with 80 gallons of water and only increased from there.

d. No, the function is not one-to-one, since multiple values of t can correspond to the same value of g(t). For example, both g(0) and g(1.84) are equal to 80.

e. Yes, the function is an example of direct variation, since the rate at which water is added to the pool is constant (25 gallons per minute) and directly proportional to the amount of time that has passed since 9 A.M. (t). This can be seen in the equation g(t) = 25t + 80, which is in the form of y = kx, where k is the constant rate of change.

This relationship is expressed mathematically through the equation g(t) = 25t + 80, where g(t) represents the number of gallons of water in the pool at time t. The constant term 80 represents the initial amount of water in the pool when Christina started adding water at 9 A.M., and the coefficient 25 represents the constant rate of change, or the number of gallons of water added per minute.

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Complete Question:

Write an equation of the direct variation described. At 9 A.M., Christina began to add water to a swimming pool at the rate of 25 gallons per minute. When she began, the pool contained 80 gallons of water. Christina stopped adding water to the pool at 4 P.M. Let be the number of gallons of water in the pool and  be the number of minutes that have past since 9 A.M.

a. Write an equation for g as a function of t

b. What is the domain of the function?

c. What is the range of the function?

d. Is the function one-to-one?

e. Is the function an example of direct variation? Explain why or why not.

No, because P(A|B) = 0.79 and the P(A) = 0.48 they are not equal.

The probability formula defines the likelihood of the happening of an event. It is the ratio of favorable outcomes to the total favorable outcomes.

We have the information:

P(A)= 0.48  

P(B) = 0.42

P(A∩B) = 0.38

To find out if watching a movie and buying a popcorn are independent,

The formula is used:

P(A|B) = P(A∩B)/P(A)

Plug all the values in above formula:

P(A|B) = 0.38/0.48 = 0.79166

P(A|B) = 0.79

From the deductions above;

Hence, the answer is

No, because P(A|B) = 0.79 and the P(A) = 0.48 they are not equal.

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For complete question, to see the attachment

Therefore, The density of air enclosed in a sphere with a radius halved will be 9.6 kg/m3. This is because the volume reduces by a factor of 8, resulting in an increase in density by a factor of 8.

When the radius of the sphere is halved, the volume of the sphere reduces by a factor of 8. Since the mass of the air enclosed remains constant, the density of the air within the sphere will increase by a factor of 8. Therefore, the density of the air within the sphere will be 9.6 kg/m3 after compression.
The density of the air enclosed within a sphere is given as 1.2 kg/m3. When the radius of the sphere is halved, the volume of the sphere reduces by a factor of 8 (since volume is proportional to the cube of radius). However, the mass of the air enclosed remains constant. Therefore, the density of the air within the sphere will increase by a factor of 8, resulting in a new density of 9.6 kg/m3.


Therefore, The density of air enclosed in a sphere with a radius halved will be 9.6 kg/m3. This is because the volume reduces by a factor of 8, resulting in an increase in density by a factor of 8.

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Answer:

Karen expects the vehicle to depreciate by 600 each year.

Step-by-step explanation:

Given:

- initial value: 4400

- salvage value: 800

- another six years

It is expected to depreciate from 4400 to 800 in 6 years.

The depreciation per year is the ratio

depreciation per year = (total depreciation) / (number of years)

Total depreciation is the change in value, so the depreciation per year is

 (4400 - 800)/6 = 600

Answer: It is not.

Step-by-step explanation:

The salaries paid to the various departments of a company are usually different as some departments get paid more than others. For instance, in a manufacturing company, the R&D department would on average, get paid more than members of the Cleaning department.

Asking members of only one department therefore, about their pay satisfaction would not bring about a reasonable result because it would not be indicative of the thoughts of members of the other departments who are not being paid the same.

Answer:

There are 58 of 58.1 students in Ms.Smith's class.

Step-by-step explanation: