Which members are in the sample

Recall that the area of an equilateral triangle with side length [tex]s[/tex] is [tex]\dfrac{\sqrt3}4s^2[/tex].

In the [tex]x-y[/tex] plane, the base is given by two equations:

[tex]x^2+y^2=9\implies y=\pm\sqrt{9-x^2}[/tex]

so that for any given [tex]x[/tex], the vertical distance between the two sides of the circle is

[tex]\sqrt{9-x^2}-\left(-\sqrt{9-x^2}\right)=2\sqrt{9-x^2}[/tex]

and this is the side of length of each triangular cross-section for each [tex]x[/tex]. Then the area of each cross-section is

[tex]\dfrac{\sqrt3}4(2\sqrt{9-x^2})^2=\sqrt3(9-x^2)[/tex]

and the volume of the solid is

[tex]\displaystyle\int_{-3}^3\sqrt3(9-x^2)\,\mathrm dx=\boxed{36\sqrt3}[/tex]

Answer:

(x - 4)² + (y + 7)² = 53

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (4, - 7), so

(x - 4)² + (y + 7)² = r²

The radius is the distance from the centre to a point on the circle.

Use the distance formula to calculate r

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (4, - 7) and (x₂, y₂ ) = (- 3, - 5)

r = [tex]\sqrt{(-3-4)^2+(-5+7)^2}[/tex]

  = [tex]\sqrt{(-7)^2+2^2}[/tex] = [tex]\sqrt{49+4}[/tex] = [tex]\sqrt{53}[/tex]

Hence r² = ([tex]\sqrt{53}[/tex] )² = 53

(x - 4)² + (y + 7)² = 53 ← equation of circle

Answer:

tallest man height is more extreme.

Step-by-step explanation:

Given:

Heights of men at that time had a mean of 173.73 cm and a standard deviation of 8.65 cm.

Concept used:

Convert height into z scores for comparison of deviation from the mean.

Solution:

Tallest man height = 265 cm

[tex]Z_{tall} =\frac{265-173.73}{8.65} \\=10.55[/tex]

Shortest man height = 109.1 cm

[tex]Z_{short} =\frac{109.1-173.73}{8.65} \\=-7.47[/tex]

Thus we find that tallest man is 10.55 std deviations from the mean to the right and shortest man is 7.47 std deviations from the mean to the left.

Hence tallest man height is more extreme.

The tallest living man at one time had a more extreme height compared to the shortest living man at that time.

In this question, we are given the heights of the tallest and shortest living men at a specific time, as well as the mean and standard deviation of heights at that time. To determine which man had a more extreme height, we need to compare their heights to the mean and see how many standard deviations away they are.

The tallest man had a height of 265 cm, which is 265 - 173.73 = 91.27 cm above the mean.

The shortest man had a height of 109.1 cm, which is 173.73 - 109.1 = 64.63 cm below the mean.

Since the tallest man's height is significantly farther away from the mean compared to the shortest man's height, we can conclude that the tallest man had a more extreme height.

Answer:

Step-by-step explanation:

4 miles = 1hour

5miles = 1hour and 25 minutes

10miles = 2 hours and 50 min

15miles = 4hours and 15min

x miles = 5 hours

20 miles = 5 hours

tell me if i got it wrong sry

Answer:

[tex]\frac{32m^{15}}{x^3-x^2}[/tex]

Step-by-step explanation:

The given expression is: [tex]\frac{4m^{12}}{x-1}\div \frac{x^2}{8m^3}[/tex]

We multiply by the reciprocal of the second fraction:

[tex]\frac{4m^{12}}{x-1}\times \frac{8m^3}{x^2}[/tex]

We cancel out the common factors to get;

[tex]\frac{32m^{12+3}}{x^2(x-1)}[/tex], where [tex]x\ne0[/tex] and [tex]m\ne0[/tex]

We simplify to get:

[tex]\frac{32m^{15}}{x^3-x^2}[/tex]

Answer:

To simplify all that its D

Step-by-step explanation:

Step-by-step explanation:

h = -490t² + 1470t

When h = 980:

980 = -490t² + 1470t

Simplifying:

0 = -490t² + 1470t - 980

0 = t² - 3t + 2

Factoring:

0 = (t - 1) (t - 2)

t = 1, 2

There are two solutions because the rocket first reaches the height of 980 cm as it's going up at 1 second, then it reaches that height again as it's coming down at 2 seconds.

The rocket reaches a height of 980 cm at 1 second and 2 seconds. The equation is factored to find these solutions, symbolizing the ascent and descent of the rocket.

To find when the height of the rocket is 980 cm, we set the height formula equal to 980 cm:

h = -490t² + 1470t = 980.

We then solve the equation by factoring:

-490t² + 1470t - 980 = 0
Divide by -10:
t²- 3t + 2 = 0
Factor:
(t - 1)(t - 2) = 0

Setting each factor to zero gives us the solutions:

t = 1 second

t = 2 seconds

There are two solutions because the rocket reaches 980 cm twice: once on its way up and once on its way down. This is demonstrated by the positive and negative components of the parabolic trajectory represented by the quadratic equation.

Answer:

jnd8663393765422345678

Step-by-step explanation:

nhbkjnm.l,n aels ewdlasmjDQLKd

Answer:

B

Step-by-step explanation:

2 || 1   -   4     6    -   4

              2    -4       4

==================

     1       -2    2

x^2 - 2x + 2 with no remainder.

Looks like the answer is B

Note: Note that the two in x - 2 changes sign. That always happens when using synthetic division as long the number in front of the x is positive.

1.63

4.89 divided by 3 = 1.63

1.63 just divided the total by 3

Final answer:

A number that can be expressed as a ratio of two integers is called a fraction. Ratios compare quantities and can be written in various forms, like fractions or with a colon. Proportions represent the equivalence of two ratios and are widely used in both mathematics and science.

Explanation:

Any number that can be written as a ratio of two integers is known as a fraction. A fraction is a type of ratio where one integer, the numerator, is divided by another integer, the denominator. For instance, 5/8 is a fraction because it represents 5 parts out of a total of 8.

A ratio can compare any two quantities, not just parts of a whole. These can be written as fractions, with a colon, or with the word 'to'. Examples include 2/3, 2:3, . Ratios are often used to compare dimensions, such as on a map where a unit scale is provided. For example, a map might state that 1 inch represents 100 feet, which is a ratio written as 1 inch/100 ft. Ratios are also essential in the health sciences, for instance, when describing solutions with a certain proportion like 1:1000.

In more complex applications, proportions are used to express equivalences between two ratios. For example, 1/2 is equivalent to 3/6, and this relationship forms a proportion. Proportions are useful in various fields, for setting up equivalencies and solving for unknown quantities.

Answer:

Correct: A, D, F

Step-by-step explanation:

Consider right triangle EFG.

By the definition of the cosine function,

[tex]\cos \angle E=\dfrac{EG}{EF}\\ \\\cos 30^{\circ}=\dfrac{EG}{EF}\\ \\\dfrac{\sqrt{3}}{2}=\dfrac{EG}{EF}\\ \\EG=\dfrac{\sqrt{3}}{2}EF[/tex]

Option F is correct.

By the definition of the sine function,

[tex]\sin \angle E=\dfrac{FG}{EF}\\ \\\sin 30^{\circ}=\dfrac{GF}{EF}\\ \\\dfrac{1}{2}=\dfrac{GF}{EF}\\ \\GF=\dfrac{1}{2}EF\\ \\EF=2FG[/tex]

Option D is correct.

By the definition of tangence,

[tex]\tan \angle E=\dfrac{FG}{EG}\\ \\\tan 30^{\circ}=\dfrac{GF}{EGF}\\ \\\dfrac{1}{\sqrt{3}}=\dfrac{GF}{EG}\\ \\GF=\dfrac{1}{\sqrt{3}}EGF\\ \\EG=\sqrt{3}FG[/tex]

Option A is correct

Rewriting [tex]z[/tex] in polar form makes this trivial.

[tex]z=|z|e^{i\mathrm{arg}(z)}[/tex]

We have

[tex]|z|=\sqrt{(-1)^2+(-\sqrt3)^2}=2[/tex]

[tex]\mathrm{arg}(z)=\tan^{-1}(-1,-\sqrt3)=-\dfrac{2\pi}3[/tex]

(not to be confused with the standard inverse tangent function [tex]\tan^{-1}x[/tex]. Here [tex]\tan^{-1}(x,y)[/tex] is the inverse tangent function that takes into account position in the coordinate plane; look up "atan2" for more information)

So we have

[tex]z=-1-\sqrt3\,i=2e^{-2\pi/3\,i}[/tex]

Then

[tex]z^6=2^6\left(e^{-2\pi/3\,i}\right)^6=64e^{-4\pi\,i}=64[/tex]

so that [tex]a=64[/tex] and [tex]b=0[/tex].

Answer:

5x-(3x+1) or 2x-1

Step-by-step explanation:

The difference (subtraction) between five times x (5x) and one more (+1) than three times x (3x.) 5x-(3x+1)

Simplified, 5x-3x-1=2x-1.

Answer:

The box of 32oz is cheaper by 2 cents per ounce.

Step-by-step explanation:

1. 3.84/24 ($0.16/oz)

2. 4.48/32 ($0.14/oz)

___

Hope this helps you! :)

Answer:

Add the five terms.

Use the formula for the fifth partial sum.

The fifth partial sum represents the total amount of money the athlete earns over the first five years.

Step-by-step explanation:

Add the five terms.

Use the formula for the fifth partial sum.

The fifth partial sum represents the total amount of money the athlete earns over the first five years.

Answer:  The fifth partial sum = 2210

The fifth partial sum represent the sum of the first 5 terms in the sequence.

Step-by-step explanation:

We know that he partial sum of a sequence gives the sum of the first n terms in the sequence.

Thus, the fifth partial sum represent the sum of the first 5 terms in the sequence.

The given geometric sequence : $400, $420, $441, $463, and $486.

Now, the fifth partial sum of the above sequence will be :

[tex]S_5=\$400+ \$420+ \$441+ \$463+\$486=\$2210[/tex]

For this case we have that by definition, the circumference of a circle is given by:

[tex]C = \pi * d[/tex]

Where:

d: It is the diameter of the circle

They tell us that:

[tex]d = \frac {35} {2}\\\pi = \frac {22} {7}[/tex]

Substituting:

[tex]C = \frac {22} {7} * \frac {35} {2}\\C = \frac {770} {14}\\C = 55 \ cm[/tex]

Thus, the circumference of the circle is 55 centimeters.

Answer:

Option B

Answer:

55 im not sure

Step-by-step explanation:

Answer:

(x + 5)² + (y + 8)² = 49

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (- 5, - 8), so

(x - (-5))² + (y - (- 8))² = r², that is

(x + 5)² + (y + 8)² = r²

The radius is the distance from the centre to a point on the circle

Use the distance formula to calculate r

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 5, - 8) and (x₂, y₂ ) = (2, - 8)

r = [tex]\sqrt{(2+5)^2+(-8+8)^2}[/tex] = [tex]\sqrt{7^2+0^2}[/tex] = [tex]\sqrt{49}[/tex] = 7

r = 7 ⇒ r² = 7² = 49

Hence

(x +5)² + (y + 8)² = 49 ← equation of circle

These 5 numbers can be written as [tex]x,x+2,x+4,x+6,x+8[/tex], so their sum is

[tex]x+(x+2)+(x+4)+(x+6)+(x+8)=5x+20=310[/tex]

[tex]\implies5x=290[/tex]

[tex]\implies x=58[/tex]

Then the numbers are 58, 60, 62, 64, and 66.

Answer:

  D)  If Jack drives 200 miles, it will cost anywhere between $30 and $42

Step-by-step explanation:

The cost is said to be a range of possibilities. The first three answer choices seem to assume the cost is at one extreme or the other. They incorrectly interpret the statement of cost.

Answer:

D. 158

Step-by-step explanation:

Fill in the x's with a 15:

[tex]y=-2(15)^2+40(15)+8[/tex]

so y = 158

The best prediction for the number of new cases in year 15 is 158.

Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power solve for x in the quadratic equation.

Here, Given quadratic equation

                 y = -2x² + 40x + 8

 at put the value of x = 15, we get

               y(15) = -2 X (15)² + 40 X 15 + 8

               y(15) = -2 X 225 + 600 + 8

               y(15) = -450 + 600 + 8

              y(15) = 150 + 8

              y(15) = 158

Thus, the best prediction for the number of new cases in year 15 is 158.

Learn more about Quadratic Equation from:

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After 5 weeks, Brian will have completed 445 sit-ups, and Christina will have completed 425 sit-ups.

To calculate the total number of sit-ups Brian and Christina will have done after 5 weeks, we can use arithmetic progressions since the number of sit-ups increases by the same amount each week after the first.

For Brian:

For Christina:

Therefore, after 5 weeks, Brian will have done 445 sit-ups and Christina will have done 425 sit-ups.

Answer:

[tex]\large\boxed{2\sqrt7}[/tex]

Step-by-step explanation:

Look at the picture.

ΔADC and ΔACB are similar. Therefore the corresponding sides are in proportion:

[tex]\dfrac{AC}{AD}=\dfrac{AB}{AC}[/tex]

We have

[tex]AC=x,\ AD=2,\ AB=2+12=14[/tex]

Substitute:

[tex]\dfrac{x}{2}=\dfrac{14}{x}[/tex]           cross multiply

[tex]x^2=(2)(14)\\\\x^2=28\to x=\sqrt{28}\\\\x=\sqrt{4\cdot7}\\\\x=\sqrt4\cdot\sqrt7\\\\x=2\sqrt7[/tex]

Answer:

  6

Step-by-step explanation:

In order for 132* to be a multiple of 2, the digit * must be even.

In order for 132* to be a multiple of 3, the sum of all digits must be a multiple of 3. That is (1 +3 +2 + *) = 6+* is a multiple of 3. Since 6 is already a multiple of 3, then * must be a multiple of 3.

Single-digit values of * that are both even and a multiple of 3 are 0 and 6. We know that any number ending in 0 will be a multiple of 5, so we cannot use that digit.

The only possible digit that makes 132* a multiple of 2 and 3, but not 5, is 6.

Answer:

Step-by-step explanation:

5

The average yield per plant is 4.00 pints, and the standard deviation is approximately 0.35 pints.

To calculate the average yield per plant:

1. Add up all the yields: 4 + 3.5 + 4.5 + 4.2 + 3.8 = 19.0 pints.

2. Divide the total yield by the number of plants (5): 19.0 / 5 = 3.8 pints per plant.

To calculate the standard deviation:

1. Find the mean (average) yield per plant, which we already calculated as 3.8 pints.

2. Calculate the squared differences from the mean for each yield:

  - Plant 1: [tex](4 - 3.8)^2[/tex] = 0.04

  - Plant 2:[tex](3.5 - 3.8)^2[/tex] = 0.09

  - Plant 3: [tex](4.5 - 3.8)^2[/tex] = 0.49

  - Plant 4:[tex](4.2 - 3.8)^2[/tex] = 0.16

  - Plant 5:[tex](3.8 - 3.8)^2[/tex] = 0

3. Calculate the average of these squared differences: (0.04 + 0.09 + 0.49 + 0.16 + 0) / 5 = 0.156.

4. Take the square root of the variance to get the standard deviation: √0.156 ≈ 0.35 pints.

The average yield per plant provides a measure of the central tendency of the data set, indicating the typical yield for one plant.

The standard deviation measures the spread or variability of the data points around the mean. A smaller standard deviation indicates that the data points are closer to the mean, while a larger standard deviation indicates more variability. In this case, the standard deviation of approximately 0.35 pints suggests that the yields are relatively close to the average of 3.8 pints per plant, with minimal variability.

Complete question

A homeowner has 5 cherry tomato plants in her garden. Over the course of the season the yields (in pints of tomatoes per plant) are: Plant 1 2 3 4 5 Yield 4 3.5 4.5 4.2 3.8 What is the average yield per plant, and what is the standard deviation (to two decimal places)?

Answer:

The custodian can make 128 pails.

Step-by-step explanation:

first, you convert 1/8 to 0.125.

then, you divide 16 by 0.125 to get 128.

Answer:

$219.6

Step-by-step explanation:

we know that

The sell price is equal to the cost price plus the profit

Let

C ----> the cost price

S----> the sell price

P ----> the profit

so

S=C+P

we have

C=$180

Find the profit

22%=22/100=0.22

P=0.22*(180)=$39.6

Find the sell price

S=$180+$39.6=$219.6

Using technology, the regression equation is

y=9.08292(1.09965)ˣ. 

The number of recommendations after 60 days is 2113.277 ≈ 2113.

Explanation

I used Desmos to graph the points, then entered the expression y₁~a*bˣ to calculate the regression.

I then substituted 60 in for x in the regression equation to get the answer of 2113.

Answer:

i am assuming 2 and 5 because they are the only ones that are not like the others

Step-by-step explanation:

Answer:

Angles 2 and 5

Step-by-step explanation:

Supplement angles are the angles which up to 180 degrees.

And all the angles shown are Vertically opposite angles and these angles are always the same.

Vertically opposite angles:

Angles  2 and 5

Angles 1 and 3

Angles 6 and 4

As shown in the picture, Angle 2 is 90 degrees and angle 5 being a vertically opposite angle, angle 5 is 90 degrees too.

90 + 90 = 180 degrees.

The option that shows a two-way conditional frequency table is option B as shown in the image attached.

A two-way conditional frequency table is a type of table that shows the frequency determined by two variables. In this case, the variables are:

Moreover, this table uses numbers from 0 to 1 to express frequency rather than percentages or numbers of people.

The correct option is option B because it meets the following requirements:

Learn more about variables in: https://brainly.com/question/787279

Answer:

Do you prefer dancing or playing sports?

 Playing sports Dancing Row totals

Male students 0.48 0.52 1

Female students 0.35 0.65 1

Step-by-step explanation:

This is the answer

Answer:

112560

Step-by-step explanation:

The total profit is the sale price of the helmet is $ 60 is:

                        $ 27,600

p denote the total profit and s denote the sale price.

The total profit in terms of the sale price is given by the function :

        [tex]p(s)=-24s^2+2200s-18000[/tex]

Now we are asked to find the value of p when the s=60

when s=60 we have:

[tex]p(60)=-24\times (60)^2+2200\times 60-18000\\\\\\p(60)=-24\times 3600+132000-18000\\\\\\p(60)=-86400+132000-18000\\\\\\p(60)=27600[/tex]

          Hence, the total profit when sale price is $ 60 is:

                              $ 27,600