what is the difference between 6x2 and 6²

16π/5 is the area enclosed by the curve r= 8sin(5θ)

The given curve is polar curve and hence the area of the polar curve is given by:

Let A be the area of the curve so,

A = [tex]\int\limits^a_b {\frac{1}{2} r^2 } \, d\theta[/tex]

where a and b is the boundary at which r=0

so after equation r=0

8sin(5θ) =0

=> sin(5θ) =0

=> 5θ = 0,π

=> θ = 0, π/5

so a=0 , b= π/5

now  

   A = [tex]\int\limits^a_b {\frac{1}{2} r^2 } \, d\theta[/tex]    ------(i)

 so   [tex]r^2[/tex] = (8sin(5θ))^2

=> 64 [tex]sin^2[/tex] ( 5θ )

ans we know that

cos(2α) = 1 -  2[tex]sin^2[/tex] α

so   [tex]r^2[/tex]  =32 (1- cos(10θ) )

putting the value of r in the equation (i) we get :-

A = [tex]\int\limits^a_b {\frac{1}{2} *32(1-cos(10\alpha ) } \, d\alpha[/tex]

=> 16 * [tex]\int\limits^a_b {(1-cos(10\alpha ) } \, d\alpha[/tex]

here a=0 and b=π/5

after putting the value and solving the integral

A = 16π/5

so A is the area enclosed by r=8sin(5θ) is 16π/5

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The closest volume of ball would be 321.4

What is Volume of sphere?

The volume of a sphere is a measure of the space occupied by the sphere, and can be calculated by the formula V = 4/3πr³, where r is the radius of the sphere. In other words, the volume can be found by multiplying 4/3 by π (3.14) by the cube of the radius of the sphere. For example, if the radius is 5, the volume of the sphere would be 4/3π x 5³, or approximately 523.60.

Solution:

Given that:

diameter = 8.5 in

hence, radius would be 4.25 in

                    [tex]Volume\ of \ ball = \frac{4}{3} \pi r^{3} \\\\Volume\ of \ ball = \frac{4}{3} \pi (4.25)^{3}\\\\Volume\ of \ ball = 321.4[/tex]

Hence, The closest volume of ball would be 321.4

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A lurking variable is an explanatory variable that was not examined in a study but has an effect on the value of the study's response variable.

A concealed variable affects both the dependent and independent variables, resulting in an incorrect connection. Confounding is a causal concept that cannot be expressed using correlations or linkages. Confounders have a significant quantitative role in explaining why correlation does not imply causation.

In the case of risk assessments assessing the degree and form of threat to human health, it is critical to account for confounding in order to isolate the impact of a specific hazard such as a food additive, pesticide, or new drug. It is difficult to recruit and screen volunteers with the same background (age, diet, education, geography, etc.) for prospective studies, and historical investigations can have similar variability.

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After a transformation of each coordinate point, the correct code are as follows;

A. (-4, -2).

I. (0, 1).

C. (5, 0).

E. (0, 0).

In Mathematics, the translation a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

Next, we would apply a translation to each of the points as follows;

Point 1 (1, 2) →  (x - 5, y - 4) = (1 - 5, 2 - 4) = Point 1' (-4, -2).

Point 2 (2, 4) →  (x - 2, y - 3) = (2 - 2, 4 - 3) = Point 2' (0, 1).

Point 3 (4, 4) →  (x + 1, y - 4) = (4 + 1, 4 - 4) = Point 3' (5, 0).

Point 4 (3, 2) →  (x - 3, y - 2) = (3 - 3, 2 - 2) = Point 4' (0, 0).

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At the rate of 135 containers per minute, it will take approximately 7.4 minutes to fill 1000 containers.

To determine the time it takes to fill 1000 containers, we need to divide the number of containers by the rate at which they are filled. In this case, we have 1000 containers and a filling rate of 135 containers per minute, so we divide 1000 by 135 to find the time it takes to fill the containers:

1000 containers / 135 containers/minute = 7.40740740740741 minutes

Since a minute cannot be divided into fractions, we must round the result to the nearest whole number. This means that it will take approximately 7.4 minutes to fill 1000 containers at a rate of 135 containers per minute.

The machine will take 7.41 minutes (approx) to fill 1000 Containers.

Time taken to fill 135 Containers= 1 minute ...............(Given)

Time taken to fill 1 Container= 1/135 minute

Time taken to fill 1000 Containers = 1000 × 1/135 minutes

                                                         = 1000/135 minutes

                                                         = 200/27 minutes

                                                         ≈ 7.41 minutes​.

Thus, The machine will take 7.41 minutes (approx) to fill 1000 Containers.

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Answer:

x = [tex]\frac{15-4y}{3}[/tex]

Step-by-step explanation:

3x + 4y = 15 ( subtract 4y from both sides )

3x = 15 - 4y ( isolate x by dividing both sides by 3 )

x = [tex]\frac{15-4y}{3}[/tex]

3 15/8 = 39/8 = 4 7/8

2 13/6 = 25/6 = 4 1/6

1.shade 3 full 8/8 circles 2. Shade 15 little slices in the rest 3. You done with the first one 1. Shade 2 full 6/6 circles 2. Shade 13 more little slices in the rest 3. TADAAA you done

Step-by-step explanation:

An angle is formed when two straight lines or rays meet at a common endpoint.

The common point of contact is called the vertex of an angle. The word angle is from a Latin word that means ‘angulus,’ meaning “corner.”

There are many examples of an angle, such as cloth hangers, arrowheads, scissors, etc.

Symbol of Angle:

The symbol ∠ represents an angle. Angles are measured in degrees (°) using a protractor.

For example, 45 degrees is represented as 45°

Parts of Angles:

Vertex: A vertex is a corner of an angle, a point where two lines/sides meet.

Arms: The two sides of the angle, joined at a common endpoint.

Initial Side: It is also known as the reference line, a straight line from where an angle is drawn.

Terminal Side: The side up to which the angle measurement is done.

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Answer: $43.43

Step-by-step explanation:

Take 9.65 times 4.5 = $ 43.425

Round up; we will get the answer $43.43

Answer: x = 14

Step-by-step explanation:

3x+9x-5=163

12x-5=163

12x=163+5

12x=168

x=14

Answer:

Step-by-step explanation:

This is a trick question,  about the red marks again.   those marks are important b/c they tell you that the lengths are the same, so that the angles MUST also be the same.  That is  ,  D and E are equal

so set up your equations with that info

180 = 84 +2p

now use your algebra skillz to solve

180-84 / 2 = p

96/2 = p

48 = p

see??

The fraction of the people surveyed that said that they buy neither product p nor product q is 1/6.

It is given to us that -

A survey is conducted with the number of people buying products p and q

We have to find out the fraction of the people surveyed said that they buy neither product p nor product q.

From the given information, the total number of products can be represented as -

[Total products bought] = [p products bought] + [q products bought] - [both p and q bought] + [neither p and q bought] ---- (1)

We have to find out -

[neither p and q bought]/[Total products bought]

Let us assume that the total products bought = 6

It is known that 1/3 of the people surveyed said that they buy product p but not product q.

=> [p products bought] - [both p and q bought] = 1/3 * 6

=> [p products bought] - [both p and q bought] = 2 ------ (2)

From equation (1), we can say that -

[Total products bought] = [p products bought] + [q products bought] - [both p and q bought] + [neither p and q bought]

=> 6 = ([p products bought] - [both p and q bought]) + [q products bought] + [neither p and q bought]

From equation (2), we can write the above equation as -

=> 6 = 2 + [q products bought] + [neither p and q bought]

=> [q products bought] + [neither p and q bought] = 4  ------ (3)

Again, it is also known that 1/2 of the people surveyed said that they buy product q.

=> [q products bought] = 1/2 *6

=> [q products bought] = 3 ---- (4)

From equation (3) and equation (4), we can say that -

[q products bought] + [neither p and q bought] = 4

=> 3 + [neither p and q bought] = 4

=> [neither p and q bought] = 1  ------ (5)

From equation (5) and the total number of products bought, we can say that -

[neither p and q bought]/[Total products bought] = 1/6

(Since, the total number of products bought = 6)

Therefore, the fraction of the people surveyed that said that they buy neither product p nor product q is 1/6.

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The given population is 10%.

If the 10 % condition is met, a binomial distribution can be used to approximate the number of successes in a simple random sample. The 10% condition requires that the sample represents less than 10% of the population. Despite the fact that the sample size is far too tiny in comparison to the population, it is reasonable to infer that the trials of occurrences are independent. This suggests that the sample size n must be smaller than 10% of the population size N in this situation.

According to the 10% condition, sample sizes shouldn't exceed 10% of the population. Check the condition whenever samples are involved in statistics to make sure your findings are reliable. If you want to employ a typical normal model, some statisticians contend that a condition of 5% is preferable to a condition of 10%.

Hence we get the required answer.

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y=6x+6 is the equation of the tangent line to the curve at point (0,6)

In order to fing the equation of tangent of any graph we need 2 things.

i . A point on the graph at which tangent need to be drawn.

ii . Slope a line on that point.

solpe of line = [tex]y^'[/tex]  =[tex]\frac{d(y)}{dx}[/tex]

=> d(6[tex]e^xcosx[/tex])/dx

in order to differentiate the above equation we have to use by parts

=> 6([tex]e^xcox-e^xsinx[/tex])

finding the slope at point(0,6)

[tex]y^'[/tex] = 6*(1*1-1*0)

=>6

so slope is 6

now equation of line with slope 6 and point (0,6)

=> y-6 = 6(x-0)

=> y = 6x+6

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Step-by-step explanation:

The equations of axes of ellipse:

y

+

3

=

0

&

x

−

2

=

0

Plot the axes of ellipse. Specify the center

(

2

,

−

3

)

, vertices & focii on the corresponding axes. Draw a free hand curve passing through the vertices & the points of intersection of ellipse with coordinate axes to get graph.

The probability that exactly two of thirteen fireworks are blue ones out of total 4 selections is 63/143.

The stated data;

You want 2 of the 7 items she selects to be blue, leaving 2 to be red.

Selecting 2 blue out of 7 blues is ⁷C₂ = 7!/(5!.2!)  =  21

Selecting 2 red out of 6 red = ⁶C₂ = 6!/(4!2!) = 15

Selecting total of 4 out of 13 ; ¹³C₄ = 13! / (9!.4!) = 715

Thus, probability that exactly two of them are blue ones;

P(2 blue) = 21 x 15 / 715

P(2 blue) = 63/143

Thus, probability that exactly two of them are blue ones out of total 4 selections is 63/143.

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The volume of cylinders [tex]x^2 + y^2 = 4r^2[/tex] and [tex]y^2 + z^2 = 4r^2[/tex] is 88[tex]r^3[/tex]/3.

The volume of cylinders can be calculated using integrals from the top curve subtract the bottom curve. For expression above we can convert to find the dimensions of cylinders using Fubini's Theorem. So,

x^2 + y^2 = 4r^2 to x^2 = 4r^2 - y^2

y^2 + z^2 = 4r^2 to z^2 = 4r^2 - y^2

Thus, the volume of the given solid is,

v = [tex]\int r-r\int\sqrt{4r^2-y^2}-\sqrt{4r^2-y^2}\times 2\sqrt{4r^2-y^2} dx dy[/tex]

= [tex]2\int r-r(x\sqrt{4r^2-y^2})(\sqrt{4r^2-y^2})-\sqrt{4r^2-y^2}dy[/tex]

= [tex]2\int r - r[(4r^2-y^2)+(4r^2-y^2)]dy[/tex]

= [tex]2\int r - r[2(4r^2-y^2)]dy[/tex]

= [tex]4\int r - r(4r^2-y^2)dy[/tex]

= [tex]4(4r^2y-y^3/3)r-r[/tex]

= [tex]4(4r^2(r+r)-(r^3+r^3)/3)[/tex]

= [tex]4((4r^2)(2r)-2r^3/3)[/tex]

= [tex]8(4r^3-r^3/3)[/tex]

= [tex](8)(12r^3-r^3)/3[/tex]

= 88[tex]r^3[/tex]/3

Thus, the volume of cylinders is (88r^3)/3.

You question is incomplete, but most probably your full question was

find the volume of the given solid. bounded by the cylinders [tex]x^2 + y^2 = 4r^2[/tex], [tex]y^2 + z^2 = 4r^2[/tex]

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Answer:

She has carved 4 times as many bird figures

Answer:

d = 21

Step-by-step explanation:

Given equation:

[tex]5^d \div 5^3=5^{18}[/tex]

Multiply both sides by 5³:

[tex]\implies 5^d=5^{18} \times 5^3[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies 5^d=5^{18+3}[/tex]

[tex]\implies 5^d=5^{21}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies d=21[/tex]

The distance traveled by light in 1 minute = 18 million kilometers and the distance traveled by light in 1 second = 0.3 million kilometers.

We are given that -

The distance traveled by light in 10 minutes = 180 million km.

Now we have to find the distance traveled by light in 1 minute.

Using the unitary method, we get -

Distance traveled by light in 1 min = 180000000 / 10

Distance traveled by light in 1 min = 18 million kilometers

Now we have to find the distance traveled by light in 1 second.

We know that 1 minute= 60 seconds,

Thus, In 60 seconds light travels a distance of = 18 million kilometers. (from above)

therefore, in 1 second light would travel a distance of = 18 million / 60

                                                                                         = 0.3 million km

Hence, the distance traveled by light in 1 second = 0.3 million kilometers.

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The complete question is -

Light travels about 180 million kilometers in 10 minutes. How far does it travel in one minute? How far does it travel in one second?

The congruence theorem that would best prove the congruence of the triangles is SAS that is Side-Angle-Side.

What is congruence theorem?

Congruent refers to something that is "absolutely equal" in terms of size and form. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, then stack them on top of one another.

The figure, in this case a triangle, is congruent if and only if the corresponding sides and angles are equal in measurement. In this case we have BC being common to both triangles. Thus, one pair of corresponding sides is equal. Next, we have another pair of corresponding sides that are equal, AC and DC. Lastly, we have the included angles being equal to each other. Thus, the congruence theorem that would best prove the congruence of the triangles is SAS that is Side-Angle-Side.

Complete question: Triangles ABC and DBC have the following characteristics: BC is a side of both triangles ∠ACB and ∠DCB are right angles AC ≅ DC Which congruence theorem can be used to prove △ABC ≅ △DBC?

AAS

SSS

HL

SAS

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Answer:

A. 276 miles apart

Step-by-step explanation:

We have the information that if two cities are 1 inch apart then the distance between them is 24 miles.

If it is 11.5 inches apart, then we should multiply the 24 miles per inch by 11.5

24 miles / 1 inch

(24 miles / 1 inch) * 11.5 inches

Inches cancel so you are left with

24 * 11.5 = 276 miles

The equivalent equation is 2x - 3 = 4. Option A

An equivalent expressions are simply described as algebraic expression that have the same solution(s) but differ in the arrangement of their values.

These expressions are known to work in the same way but look different.

Two algebraic expressions are said to be equivalent, when the expressions have the same value when plugged in the same value(s) for specific variable(s).

From the information given, we have;

(6x-9) = 12

expand the bracket

6x - 9 = 12

Find the common factors

2x - 3 = 4

Hence, the equation is 2x -3 = 4

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The water level is rising at a rate of 0.0764 cm per second.

Using implicit differentiation, it is found that the water level is rising at a rate of 0.0764 cm per second.

The volume of a cone of radius r and height h is given by:

V = πr²h/3

Applying implicit differentiation, the rate of change is given by:

dV/dt = 2πr/3 dr/dt + πr²/3 dh/dt

In this problem:

The radius is constant, thus dr/dt = 0

Height of 5 cm and radius of 3 cm, thus h = 5, r=3.

Water poured at a rate of 2 cm³/s, thus dV/dt = 2

Then

dV/dt = 2πr/3 dr/dt + πr²/3 dh/dt

2 = 25π/3 dh/dt

dh/dt = 6/25π

dh/dt = 0.0764

The water level is rising at a rate of 0.0764 cm per second.

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Answer:

(18, -15)

Step-by-step explanation:

The vector AB is defined by its starting and endpoints. Usually, B would be at the end, but in this case A is. Since we are given its midpoint, that is, the point equidistant from both the coordinates A and B, we can find coordinate B by simply calculating the distance between A and the midpoint and reapplying this distance to the midpoint.

1. Finding the distance between the midpoint and A:

The distance between two coordinates, from what I can recall, is simply the final coordinate value minus the initial coordinate value, following the form (x2-x1, y2-y1). We know that A comes after the midpoint, because it is the endpoint (so it will be the final coordinate value). Applying this to the context of the question, (2-10, 13+1) = (-8,14).

2. Finding B using the distance between midpoint and A:

B will be the initial coordinate value because it comes before the midpoint. Therefore, giving B the values (x,y):   (10-x, -1-y) = (-8, 14). Separating into two equations (respective to each axis):

10-x=-8

-x=-18

x=18

-1-y=14

-y=15

y=-15

Therefore, the coordinate of B is (18, -15).

If new automobile prices are roughly regularly distributed, with a mean of $17,000 and a standard deviation of $500, then it means that the majority of the prices paid for the car will fall within a certain range.

Specifically, approximately 68% of the prices paid will be within one standard deviation of the mean, which in this case would be between $16,500 and $17,500.

Approximately 95% of the prices paid will be within two standard deviations of the mean, which would be between $16,000 and $18,000. And approximately 99.7% of the prices paid will be within three standard deviations of the mean, which would be between $15,500 and $18,500. This demonstrates that the prices paid for the cars are generally consistent, with only a tiny percentage deviating from the mean and standard deviation-defined range.

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The z-score of the blood pressure readings are:

a = 1.4

b = 0.6

c = 1.2

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

Mean = 121

Standard deviation = 15

The z-score is given as,

z = (x - mean) / Standard deviation

x = 142

z = (142 - 121) / 15

z = 21/15

z = 7/5

z = 1.4

x = 130

z = (130 - 121) / 15

z = 9/15

z = 3/5

z = 0.6

x = 103

z = (103 - 121) / 15

z = 18/15

z = 6/5

z = 1.2

Thus,

The readings are:

a = 1.4

b = 0.6

c = 1.2

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True. Adjusted R2 is always less than or equal to R2 in the multiple regression model.

A statistical method called regression links a response variable with one or more independence (explanatory) variables. A regression model can demonstrate whether changes in any or all of the independent variable are related to changes in the dependent variable.

Regress, from which the word "regression" is derived, means "to go back" in Latin (to something). Regression is the method that enables "going back" from muddled, challenging data to a simpler and more significant model in this manner. Forecasting, time series modeling, and determining the causal connection between variables are the three basic applications of regression analysis.

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