Let $a_1$, $a_2$, $\dots$, $a_{12}$ be twelve equally spaced points on a circle with radius 1. find\[(a_1 a_2)^2 + (a_1 a_3)^2 + \dots + (a_{11} a_{12})^2.\](the sum includes the square of the distance between any pair of points, so the sum includes $\binom{12}{2} = 66$ terms.)

Answer:

A

Step-by-step explanation:

xbar is the average of all the x-values in the table. To get the average, we need to add all the x-values and then divide by the number of values there are (there are 5 values).

THus

x bar = [tex]\frac{8+9+10+11+12}{5}=10[/tex]

correct answer is A

Answer:

Your choice is correct.

Step-by-step explanation:

The amplitude (multiplier of sin( )) is half the diameter, so is 17.5. The midline (value added to the sine function) is the difference between the maximum (50) and the amplitude (17.5), so is 50-17.5 = 32.5. All choices have the correct frequency.

The function will look like ...

  f(t) = 17.5·sin(2πt/5) +32.5 . . . . . as you have marked

Answer:

  D.  f(q) = 2q + 3

Step-by-step explanation:

Choices B and C are eliminated right away because there is no "q" in the definition, just "s". If the function is to be a function of "q", then "q" is expected to appear in the definition.

__

The two variables in the given equation are "s" and "q". If "q" is designated as the independent variable, then the dependent variable is "s". The equation must be solved for "s":

  6q = 3s - 9

We observe that the coefficient of "s" is 3, and that all numbers are multiples of 3, so we can divide by 3 to simplify this a bit:

  2q = s - 3

Since we want an expression for s alone, we can add 3 to get ...

  2q +3 = s

Now, we can write ...

  s = f(q) = 2q +3

Answer:D

Step-by-step explanation:

[tex]

2h\div0.5h=4 \\

\frac{3}{4}\cdot4=\frac{12}{4}=\boxed{3}

[/tex]

Answer:

Lin needs to drink 27 ounces of water to reach her goal.

Step-by-step explanation:

1 cup = 8 fluid ounces.

8 cups = [tex]8\times8=64[/tex] ounces.

As of now Lin has drank 37 ounces of water. So, this means till now she has drank [tex]\frac{37}{8}= 4.625[/tex] cups of water.

In terms of ounces, she needs to drink 64-37=27 ounces of water to reach her goal.

Hence, the answer is 27 ounces or 8-4.625=3.375 cups.

The correct answer is A. 27 ounces. Lin needs to drink 27 more ounces of water to reach her goal of 8 cups (64 ounces) of water daily.

To determine how much more water Lin needs to drink to reach her goal, we need to follow these steps:

Thus, Lin needs to drink 27 ounces more water today to reach her goal.

Complete question:

Lin's goal is to drink 8 cups of water every day.She drank 37 ounces before lunch today.How much more water does Lin need to drink today to reach her goals? (8 fluid ounces = 1 cup)

A. 27 ounces

B. 29 ounces

C. 59 ounces

D. 91 ounces

ANSWER

False

EXPLANATION

The tangent function has no amplitude because it is not bounded.

The given tangent function is

[tex]f(t) = 5 \tan(2t) [/tex]

This is of the form

f(t)=a tan(bt)

The period is given by

[tex]T = \frac{\pi}{ |b| } [/tex]

[tex]T = \frac{\pi}{ |2| } = \frac{\pi}{2} [/tex]

The first statement is true but the second is false.

Hence the whole statement is false.

Answer:F

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

We can multiply each equation by a constant so they'll equal either 15 or -15 since that is the LCM.

Since the answer choices want us to make the top a negative 15, we'll do that.

[tex]2x-5y=-21 \\ \\ 3(2x-5y)=(-21)*3 \\ \\ 6x-15y=-63[/tex]

To make the y's cancel out, the second equation would have to have the y's coefficient equal 15.

Let's do that.

[tex]3x-3y=-18 \\ \\ -5(3x-3y)=(-18)*-5 \\ \\ -15x+15y=90[/tex]

So the resulting equations are answer choice C.

Answer:

$25.11

Step-by-step explanation:

You have to divide 75.33 by the total number of shirts, 3, to see what one costs.

75.33/3=25.11

Answer:

each shirt will cost $25.11

Step-by-step explanation:

if each of the three friends gets a shirt and the total for all of them is $75.33, each shirt costs $25.11

75.33/3=25.11

please mark brainliest

Answer:

∠BAD=20°20'

∠ADB=34°90'

Step-by-step explanation:

AB is tangent to the circle k(O), then AB⊥BO. If the measure of arc BD is 110°20', then central angle ∠BOD=110°20'.

Consider isosceles triangle BOD (BO=OD=radius of the circle). Angles adjacent to the base BD are equal, so ∠DBO=∠BDO. The sum of all triangle's angles is 180°, thus

∠BOD+∠BDO+∠DBO=180°

∠BDO+∠DBO=180°-110°20'=69°80'

∠BDO=∠DBO=34°90'

So ∠ADB=34°90'

Angles BOD and BOA are supplementary (add up to 180°), so

∠BOA=180°-110°20'=69°80'

In right triangle ABO,

∠ABO+∠BOA+∠OAB=180°

90°+69°80'+∠OAB=180°

∠OAB=180°-90°-69°80'

∠OAB=20°20'

So, ∠BAD=20°20'

Answer:

The measure of ∠BAD and ∠ADB is 20°20' and 34°90' respectively.

Step-by-step explanation:

Given that AB is tangent to the circle k(O) at B, and AD is a secant, which goes through center O. Point O is between A and D∈k(O).

measure of arc BD is 110°20'.

we have to find the measure of ∠BAD and ∠ADB

∠4=110°22'

In ΔOBD, by angle sum property of triangle

∠1+∠2+∠4=180°

∠1+∠2+110°20'=180°

∠1+∠2=69°80'

Since OB=OD(both radii of same circle) therefore ∠1=∠2

[tex]2\angle 2=69^{\circ}80'[/tex]

[tex]\angle 2=\frac{69^{\circ}80'}{2}=34^{\circ}90'[/tex]

m∠ADB=34°90'

As OB is radius of circle and AB is tangent therefore by theorem which states that radius is perpendicular on the tangent line gives

[tex]\angle 6=90^{\circ}[/tex]

By exterior angle property

∠5=∠1+∠2=69°80'

By angle sum property in ΔABO

∠3+∠6+∠5=180°

∠3+90°+69°80'=180°

∠3=20°20'

To find the angle ∠KL, knowing m∠KJL = 27°, it is essential to apply the properties of tangents and circles.

The angle ∠KJL can be determined using the properties of tangents and circles. Since JK is a tangent to circle C, we know that angle ∠KJL is equal to half of the intercepted arc KL. Therefore, if m∠KJL = 27°, then m∠KL = 2 × 27° = 54°.

ANSWER

A. y√y

EXPLANATION

The given expression is:

[tex] \sqrt{ {y}^{3} } + \sqrt{16 {y}^{3} } - 4y \sqrt{y} [/tex]

We factor the perfect square in the first two terms to obtain;

[tex] \sqrt{ {y}^{2} \times y} + \sqrt{ {(4y)}^{2} \times y } - 4y \sqrt{y} [/tex]

This simplifies to:

[tex]y\sqrt{y } + 4y \sqrt{y } - 4y \sqrt{y} [/tex]

We simplify to get;

[tex]y\sqrt{y } + 0 = y \sqrt{y} [/tex]

The correct choice is A.

Answer:

  a = 2(vt -d)/t^2

Step-by-step explanation:

Add the term containing "a":

  d + a(t^2/2) = vt

Subtract d:

  a(t^2/2) = vt -d

Multiply by the inverse of the coefficient of "a":

  a = 2(vt -d)/t^2

i think the answer is true

The statement is False, with only 13 percent of jobs in STEM fields being math-related in 2005. This means that out of all the jobs in the areas of Science, Technology, Engineering, and Mathematics, only 13 percent were math-related.

The statement is False.

The US Bureau of Labor Statistics reported that in 2005, 13 percent of jobs in the STEM fields were math-related occupations, not the percentage of math-related occupations in the overall job market.

This means that out of all the jobs in the areas of Science, Technology, Engineering, and Mathematics, only 13 percent were math-related.

https://brainly.com/question/33457407

#SPJ2

Final answer:

To find the standard deviation for the number of defects per batch, use the formula for the standard deviation of a binomial distribution.

Explanation:

To find the standard deviation for the number of defects per batch, we need to use the formula for the standard deviation of a binomial distribution.

Given that the company manufactures televisions in batches of 25 and there is a 1% rate of defects, we can calculate the mean and variance of the number of defects per batch.

The mean (μ) of a binomial distribution is given by μ = np, where n is the number of trials (batch size) and p is the probability of success (defect rate). In this case, μ = 25 * 0.01 = 0.25. The variance (σ^2) of a binomial distribution is given by σ² = np(1-p). In this case, σ² = 25 * 0.01 * (1-0.01) = 0.2475.

The standard deviation (σ) is the square root of the variance, so σ ≈ √0.2475 ≈ 0.4975. Therefore, the standard deviation for the number of defects per batch is approximately 0.4975.

To calculate the standard deviation for the number of defects per batch with a 1% defect rate, use the formula for the standard deviation of a binomial distribution. The standard deviation is approximately 0.4975, indicating the variation in defects per batch.

The question you asked is about finding the standard deviation for the number of defects per batch in a manufacturing process where there is a 1% rate of defects.

To calculate the standard deviation for a binomial distribution, which is the case here since each television can be either defective or not, we use the formula: σ = √(np(1-p)), where σ is the standard deviation, n is the number of trials (or televisions), and p is the probability of success (or defect in this context).

Since each batch contains 25 televisions and the defect rate is 1% (0.01), we have:

n = 25
p = 0.01
1-p = 0.99

Plugging these values into the formula we get:

σ = √(25 * 0.01 * 0.99) = √(0.2475) ≈ 0.4975

Therefore, the standard deviation for the number of defects per batch is approximately 0.4975, which means – on average – you would expect the number of defects to vary around this value.

Answer:

The correct answer is option C.

Sin 45 degrees = square root of 2 divided by 2, cos 45 degrees = square root of 2 divided by 2, tan 45 degrees = 1

Step-by-step explanation:

The sin cos tan table used to calculate values of the ratios for different angles can be used for the values.

The table is easily available on the internet.

WE can use a a right-angles isosceles triangle to find the exact values for the angle 45.

The equal sides have length 1. So the thirs side using the pythagoras theorem will be √2.

So

Sin 45 = √2/2

Cos 45 = √2/2

and

Tan 45 = 1

So the correct option is C.

The sine, cosine, and tangent of 45 degrees can be found using the values of the adjacent side, opposite side, and hypotenuse of a right triangle. The sine of 45 degrees is (√2) / 2, the cosine is (√2) / 2, and the tangent is 1.

The sine, cosine, and tangent of 45 degrees can be found using the values of the adjacent side, opposite side, and hypotenuse of a right triangle. In this case, for a 45-degree angle, the adjacent side and opposite side are equal, so we can use the Pythagorean theorem to find the value of the hypotenuse. Let's denote the length of the adjacent and opposite sides as x.

Sine (sin) 45 degrees: sin 45 degrees = opposite side / hypotenuse = x / √2x = 1 / √2 = (√2) / 2

Cosine (cos) 45 degrees: cos 45 degrees = adjacent side / hypotenuse = x / √2x = 1 / √2 = (√2) / 2

Tangent (tan) 45 degrees: tan 45 degrees = opposite side / adjacent side = x / x = 1

Answer:

14.7

Step-by-step explanation:

a^2+b^2=c^2

15^2+b^2=21^2

225+b^2=441

subtract 441-225=216

square root of 216 = 14.6969384567

= 14.7

Answer:

x = 6[tex]\sqrt{6}[/tex]

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

x² + 15² = 21²

x² + 225 = 441 ( subtract 225 from both sides )

x² = 216 ( take the square root of both sides )

x = [tex]\sqrt{216}[/tex] = [tex]\sqrt{36(6)}[/tex] = [tex]\sqrt{36}[/tex] × [tex]\sqrt{6}[/tex] = 6[tex]\sqrt{6}[/tex]

A bc the Y numbers increase by 17 every time X increases by 1

The common difference of the associated arithmetic sequence is:

          Option: A

                  17

We know that the sequence is said to be arithmetic if each of the sequence is differ by the preceding term by a fix constant which is known as a common difference.

i.e. d is called a common difference of the sequence if [tex]a_n\ and\ a_{n+1}[/tex]

are the nth and (n+1)th term of the sequence then,

[tex]a_{n+1}-a_n=d[/tex]

Here we have a  table of values as:

X     Y              d

1      4        

2    21        21-4=17

3    38       38-21=17  

4    55        55-38=17

5    72        72-55=17

Hence, we get that the common difference is: 17

Answer:

D

Step-by-step explanation:

2·(14·7+7·7+7·14) =490

Answer: D. 490 units^2

Step-by-step explanation:

7x7=49

49x2=98 units^2

14x7=98

98x2=196 units^2

14x7=98

98x2=196 units^2

196+196+98= 490 units^2

Final answer:

To find the perimeter of the dilated rectangle A'B'C'D', we need to know the dimensions of the original rectangle ABCD and the scale factor of the dilation. The perimeter of A'B'C'D' is equal to the sum of the lengths of all the sides in the dilated rectangle. Since AB = A'B' and BD = B'D', the perimeter can be simplified to AB + BC + CD + BD.

Explanation:

To find the perimeter of the dilated rectangle A'B'C'D', we need to know the dimensions of the original rectangle ABCD and the scale factor of the dilation.

If the scale factor is 3, it means that each side of the original rectangle will be multiplied by 3 to get the corresponding side of the dilated rectangle.

Since the rectangle ABCD is dilated with a center of dilation at vertex D, the length of side AB remains the same in the dilated rectangle A'B'.

To find the perimeter of A'B'C'D', we need to compute the lengths of all the sides in the dilated rectangle and sum them up.

Perimeter of A'B'C'D' = A'B' + B'C' + C'D' + D'A'

Since AB = A'B' and BD = B'D', the perimeter can be simplified to:

Perimeter of A'B'C'D' = AB + BC + CD + BD

The perimeter of rectangle A'B'C'D', which is a dilation of rectangle ABCD by a scale factor of 3 with center D, is three times larger than the original perimeter of ABCD.

If rectangle ABCD is dilated by a scale factor of 3 with a center of dilation at vertex D, to find the perimeter of A'B'C'D', we must first understand that a dilation scales all dimensions by the given factor. If the original lengths of the sides of rectangle ABCD are 'a' and 'b', with CD and AD being adjacent to vertex D, then after the dilation, the lengths of the corresponding sides would be '3a' and '3b'.

Since the perimeter of a rectangle is calculated by adding together the lengths of all its sides, the formula for the perimeter 'P' before dilation is P = 2a + 2b. After dilation, the new perimeter 'P' of A'B'C'D' will be P = 2(3a) + 2(3b) = 6a + 6b, which is simply three times the original perimeter. Therefore, the perimeter of rectangle A'B'C'D' after dilation is three times larger than the perimeter of the original rectangle ABCD.

Answer:

Final answer is [tex]P(A^c)=\frac{3}{7}[/tex]

Step-by-step explanation:

We have been given a table containing a list of few places that are either city or in North America.

Total number of places in that list = 7

That means sample space has 7 possible events.

Given that a place from this table is chosen at random. Let event A = The place is a city.

Now we need to find about what is [tex]P(A^c)[/tex].

That means find find the probability that chosen place is not a city.

there are 3 places in the list which are not city.

Hence favorable number of events = 3

Then required probability is given by favorable/total events.

[tex]P(A^c)=\frac{3}{7}[/tex]

Answer:

It's 3/7

Step-by-step explanation:

a.

[tex]z=-\dfrac{5\sqrt3}2+\dfrac52i=5\left(-\dfrac{\sqrt3}2+\dfrac12i\right)=5e^{i5\pi/6}[/tex]

[tex]w=1+\sqrt3\,i=2\left(\dfrac12+\dfrac{\sqrt3}2i\right)=2e^{i\pi/3}[/tex]

b. Not exactly sure how DeMoivre's theorem is relevant, since it has to do with taking powers of complex numbers... At any rate, multiplying [tex]z[/tex] and [tex]w[/tex] is as simple as multiplying the moduli and adding the arguments:

[tex]zw=5\cdot2e^{i(5\pi/6+\pi/3)}=10e^{i7\pi/6}[/tex]

c. Similar to (b), except now you divide the moduli and subtract the arguments:

[tex]\dfrac zw=\dfrac52e^{i(5\pi/6-\pi/3)}=\dfrac52e^{i\pi/2}[/tex]

Answer:

10.92 m

Step-by-step explanation:

  To solve for the height, we first find the area of the triangle. Since the area of a triangle is 1/2 of the base times the height, we get the area to be 109.2. Dividing it by 20 and then multiplying by 2, we get 10.92 as the height.

Eve should knit between 3 and 6 scarves per day in the next 2 days to meet her goal, with a minimum total of 15 and a maximum of 21 scarves for the week.

Eve has already knitted 9 scarves and wants to knit at least 15 scarves and at most 21 scarves by the end of the week. With 2 days left in her work week, we need to calculate how many more scarves she should knit each day to achieve her goal.

First, let's calculate the minimum number of scarves she needs to knit to meet her goal of 15 scarves. She needs to knit 15 - 9 = 6 more scarves. Dividing 6 scarves by 2 days, we find she needs to knit a minimum of 3 scarves per day.

Now, let's calculate the maximum number of scarves to meet her goal of 21 scarves. She needs to knit 21 - 9 = 12 more scarves. Dividing 12 scarves by 2 days, we find she needs to knit a maximum of 6 scarves per day.

Therefore, to meet her goal for the week, Eve should knit between 3 and 6 scarves per day for the remaining two days.

Eve should knit between 3 and 6 scarves per day in the next two days to meet her goal.

To determine the number of scarves Eve should knit each day, we need to find how many more scarves she needs to meet her goal and then spread that number evenly over the 2 remaining days. Eve has made 9 scarves already.

The maximum and minimum scarves can be calculated as below:

Minimum scarves needed [tex]= 15 - 9 = 6[/tex]

Maximum scarves needed [tex]= 21 - 9 = 12[/tex]

Now the remaining scarves need to be completed in 2 days. So, it find number of remaining scarves to be completed per day we divide the maximum and minimum value by 2 as follows:

Minimum scarves per day [tex]= \frac{6}{2} = 3[/tex]

Maximum scarves per day [tex]= \frac{12}{2} = 6[/tex]

Therefore, Eve should knit between 3 and 6 scarves per day in the next two days to meet her goal.

Answer:it’s B

Step-by-step explanation:

Answer:

D) [tex]x^5 + 3x^4 - 2x^3 - 3x^2 + 2[/tex]

Step-by-step explanation:

A polynomial in its standard form is when the terms are arranged in descending order of exponent. The highest exponent goes first and smallest goes to the end of the polynomial.

The only one of the polynomials in the options that meets the requirements is D. Because the term with exponent 5 is at the beginning, then the term with exponent 4, and so on until the independent term.

The answer is: D) [tex]x^5 + 3x^4 - 2x^3 - 3x^2 + 2[/tex]

Answer:

B

Step-by-step explanation:

To divide by a fraction, multiply by the reciprocal:

(3/4) / (1/8)

(3/4) * (8/1)

Answer B.

To find the quotient 3/4 divided by 1/8

B) multiply 3/4 by 8!

I hope this helps you! ☺

Answer:

  see below for a graph

Step-by-step explanation:

You know the line crosses the x-axis at x=6, so one way to write the equation is by translating the line with slope -1/2 to a point 6 units to the right of the origin.

  y = -1/2(x -6)

Answer:

Step-by-step explanation:

Left Frame

Formula

Area of Hexagon = 3*sqrt(3)*a^2 / 2

Area of a Square = a^2

In both cases a is a side length

Givens

A = 384*sqrt(3)

Solution

384*sqrt(3) = 3*sqrt(3)*a^2 / 2     Divide by sqrt(3) on both sides.

384 = 3 * a^2 / 2                           Multiply by 2

768 = 3 * a^2                                Divide by 3

256 = a^2                                     Take the square root of both sides

a = 16

Each side of the square will be = a

The area of the square = a^2

a^2 = 16^2 = 256

Center Frame

I don't know how to expand the question so that I'm doing some sort of step-by-step explanation. The question just means what does a equal when t = 0

The answer is 15.

Right Frame

The tangents meet the circumference of the circle at a 90o angle when the radius is connected by the point of  contact. Call the central angle (LON) = x

The two tangents and the two radii form a kite which is a quadrilateral.

All quadrilaterals have 4 angles that add up to 360.

x + 90 + 90 + 60 = 360           Combine the like terms on the left

x + 240 = 360                           Subtract 240 from both sides

x = 360 - 240

x = 120

The length of the arc is given by (Central angle / 360) * Circumference

x is the central angle so the central angle = 120

Length = (120 / 360) * 96

Length = 1/3 * 96

Length = 32

Answer:

V = 1152π in³

Step-by-step explanation:

The formula for the volume of a hemishere is

[tex] \frac{ \frac{4}{3}\pi {r}^{3} }{2} [/tex]

Next we need to substitute the values from the question in.

[tex] \frac{ \frac{4}{3}\pi {12}^{3} }{2} [/tex]

Then finally we need to simplify.

[tex] \frac{2304\pi}{2} = 1152\pi[/tex]

Answer:

41.09%

Step-by-step explanation:

step 1

Find the capital gain

$9,100-$6,450=$2,650

step 2

Express his capital gain as a percent of the original purchase price

we know that

$6,450 ( original purchase price) -----> represent 100%

so by proportion

100%/6,450=x/2,650

x=2,650*100/6,450

x=41.09%

Answer:

The location of point K is (1 , 2)

The location of point L is (7 , 0)

Step-by-step explanation:

* Lets revise how to find the location of a point between two points

- If point (x , y) is between two points (x1 , y1) , (x2 , y2) at a ratio

 m1 from (x1 , y1) and m2 from (x2 , y2)

∴ x = [x1(m2) + x2(m1)]/(m1 + m2)

∴ y = [y1(m2) + y2(m1)]/(m1 + m2)

* Now lets solve the problem

- Point J is (-5 , 4) and point M is (10 , -1)

∵ Point K is 2/5 of JM

∴ m1 = 2 ⇒ ratio from K to J

∴ m2 = 5 - 2 = 3 ⇒ ratio from K to M

∴ x = [(-5)(3) + (10)(2)]/(2 + 3) = [-15 + 20]/5 = 5/5 = 1

∴ y = [(4)(3) + (-1)(2)]/(2 + 3) = [12 + -2]/5 = 10/5 = 2

* The location of point K is (1 , 2)

∵ Point L is 4/5 of JM

∴ m1 = 4 ⇒ ratio from K to J

∴ m2 = 5 - 4 = 1 ⇒ ratio from K to M

∴ x = [(-5)(1) + (10)(4)]/(2 + 3) = [-5 + 40]/5 = 35/5 = 7

∴ y = [(4)(1) + (-1)(4)]/(2 + 3) = [4 + -4]/5 = 0/5 = 0

* The location of point L is (7 , 0)