Use a half-angle identity to find the exact value of tan5π/12

The measure of ∠BPO is 48°.

Since PD bisects ∠BPA, we can say:

∠AOC = ∠BOC .

Thus, ∠ BOC = 42°

Since PB is tangent to the circle, PBO = 90°.

Looking at triangle PBO, we can say:

∠BPO + ∠PBO + ∠BOC = 180  (angles in a triangle add up to 180)

∠BPO + 90 + 42 = 180

∠BPO + 132 = 180

∠BPO = 180 - 32

∠BPO = 48°

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Complete Question

Check image attached

a) The percent of the scores are between 72 and 87 is 77.45%

b) The probability that a score is greater than 77 is 84.13%

c) The probability that a score is less than 82 or greater than 92 is 52.28%

d) About 5 students scored outside two standard deviations of the mean.

a) To find the percent of scores between 72 and 87, we first need to standardize these scores. We can do this by subtracting the mean (82) and dividing by the standard deviation (5). This gives us:

z = (72 - 82) / 5 = -2

z = (87 - 82) / 5 = 1

We can then use a table of standard normal probabilities (also called a z-table) to find the probability of a score being between -2 and 1. This probability is 0.7745, or 77.45%

b) To find the probability that a score is greater than 77, we again need to standardize the score:

z = (77 - 82) / 5 = -1

Using the z-table, we can find the probability of a score being greater than -1 (which is the same as the probability of a score being less than or equal to 77). This probability is 0.1587, or 15.87% (rounded to two decimal places). To find the probability of a score being greater than 77, we subtract this probability from 1:

P(score > 77) = 1 - P(score <= 77) = 1 - 0.1587 = 0.8413, or 84.13%

c) To find the probability that a score is less than 82 or greater than 92, we can break this into two separate probabilities:

P(score < 82) + P(score > 92)

We can standardize these scores as follows:

z = (82 - 82) / 5 = 0

z = (92 - 82) / 5 = 2

Using the z-table, we can find the probabilities associated with these z-scores:

P(score < 82) = P(z < 0) = 0.5 (from the symmetry of the standard normal distribution)

P(score > 92) = P(z > 2) = 0.0228

Adding these probabilities together gives us:

P(score < 82 or score > 92) = 0.5 + 0.0228 = 0.5228, or 52.28%

d) Two standard deviations from the mean in either direction would be:

82 - (2 x 5) = 72

82 + (2 x 5) = 92

So any score below 72 or above 92 would be considered outside two standard deviations. To find how many students scored outside this range, we need to find the total proportion of scores that fall outside this range and multiply by the total number of scores.

To find the proportion of scores outside the range, we can use the same approach as in part c):

P(score < 72 or score > 92) = P(z < -2 or z > 2) = P(z < -2) + P(z > 2)

Using the z-table, we find:

P(z < -2) = 0.0228

P(z > 2) = 0.0228

Adding these probabilities together gives us:

P(score < 72 or score > 92) = 0.0228 + 0.0228 = 0.0456

So 4.56% of scores fall outside the range of 72 to 92. To find the number of students who scored outside this range, we can multiply this proportion by the total number of scores:

0.0456 x 120 = 5.472 ≈ 5

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Answer: In one week, Nursen saves $5 and shares $3.75, so she has $5 + $3.75 = $8.75 per week.

She spends $4.95 on bus fare, so she has $8.75 - $4.95 = $3.80 per week to spend.

This week, Nursen earned $24 babysitting, so she has an additional $24 to spend.

Therefore, Nursen has $3.80 + $24 = $27.80 to spend.

Step-by-step explanation:

Answer:

True, a cone has an apex which is the point where the sides of the cone meet to form a tip.

It seems there are two numbers missing between "15 cm summ" and "12 cm". Please provide the complete values so I can help you solve the problem.

The new coordinates of dilated rectangle by scale factor of 1/4 are J(1, 2), K(3, 2), L(3, 1), and M(1, 1) we can draw figure.

We are given the coordinates of the vertices of a rectangle J(4,8), K(12,8), L(12,4), and M(4,4).

To dilate the rectangle by a scale factor of 1/4, we need to multiply each coordinate by 1/4.

Multiplying each x-coordinate by 1/4

x-coordinate of J: 4 * 1/4 = 1

x-coordinate of K: 12 * 1/4 = 3

x-coordinate of L: 12 * 1/4 = 3

x-coordinate of M: 4 * 1/4 = 1

Multiplying each y-coordinate by 1/4

y-coordinate of J: 8 * 1/4 = 2

y-coordinate of K: 8 * 1/4 = 2

y-coordinate of L: 4 * 1/4 = 1

y-coordinate of M: 4 * 1/4 = 1

Therefore, the coordinates of the dilated rectangle are: J(1,2), K(3,2), L(3,1), and M(1,1).

Using these new coordinates, we can draw the dilated rectangle by plotting the four vertices on a coordinate plane.

The dilated rectangle has the same shape and orientation as the original rectangle, but it has been reduced in size by a scale factor of 1/4.

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Answer: Linear

Step-by-step explanation:

I can tell from the table because there is a difference of 4 between each y value.

I dont know what the other blanks will be because i cant see the options. But it shouldnt be too hard to fill out

Answer:

The function that is a translation one unit right of the function f(x) = log x is k(x) = log(x - 1).

When we shift a function f(x) one unit right, we replace x with (x - a) where "a" is the amount of the shift. In this case, "a" is equal to 1. Therefore, the function becomes:

f(x - 1) = log(x - 1)

This means that the function k(x) = log(x - 1) is obtained by shifting the function f(x) one unit to the right.

since i don't see the graph ill go with... B The slope of the line is 24, which means that the swimmer must complete 24 laps in the race.

-24/6 = -4

Step-by-step explanation:

The slope of the line can be found using the formula:

slope = (change in y) / (change in x)

In this case, we can use the two given points on the line: (0, 24) and (6, 0).

Change in y = 0 - 24 = -24

Change in x = 6 - 0 = 6

Therefore, slope = -24/6 = -4

This means that for every minute that passes, the swimmer completes four laps. The swimmer's pace is steady and consistent throughout the race, gradually decreasing the number of laps remaining until they finish at 0 after six minutes.

Answer:

The slope of the line represents the rate of change in the number of laps remaining per unit of time (in this case, per minute). In other words, it tells us how quickly the swimmer is completing laps.

Since the slope of the line is -4, this means that the swimmer is completing 4 laps every minute. This could be interpreted as the swimmer's pace or speed in the race. The negative sign indicates that the number of laps remaining is decreasing over time, which is expected as the swimmer completes more and more laps.

It's worth noting that the slope is constant throughout the race, meaning that the swimmer is maintaining a consistent pace. This information could be useful for the swimmer and their coach in terms of planning and pacing the race.

Answer:

it is b got it right on my test

Step-by-step explanation:

The required graph that shows Ellen's steps where her mean steps for a week is 10000 is graph 2 where the data are as,

Day 1 = 11000 , Day 2 = 9000, Day 3 = 10000, Day 4 = 12000, Day 5 = 8000, Day 6 ≈ 10000, Day 7 ≈ 10000

Mean of ungrouped data is the average of all the values of the observation in the data set.

Mean = (Summation of all values in data set)/ (Number of observations)

Here there are 7 observations and the mean number of steps is 10000.

For graph 1 the values for each day of the week are as,

Day 1 = 8000 , Day 2 = 9000, Day 3 = 12000, Day 4 = 2000, Day 5 = 6000, Day 6 = 10000, Day 7 = 10000

Thus, the mean number of steps is = (8000+ 9000+ 12000+ 2000+ 6000+ 10000 + 10000) / 7

= 8143 (approximately) ≠ 10000

For graph 2 the values for each day of the week are as,

Day 1 = 11000 , Day 2 = 9000, Day 3 = 10000, Day 4 = 12000, Day 5 = 8000, Day 6 ≈ 10000, Day 7 ≈ 10000

Thus, the mean number of steps is = (11000+ 9000+ 10000+ 12000+ 8000+ 10000 + 10000) / 7

= 10000

For graph 3 the values for each day of the week are as,

Day 1 = 7000 , Day 2 = 14000, Day 3 = 11500, Day 4 = 10000, Day 5 = 4500, Day 6 = 6000, Day 7 = 11000

Thus, the mean number of steps is = (7000+ 14000+ 11500+ 10000+ 4500+ 6000 + 11000) / 7

= 9143 (approximately) ≠ 10000

For graph 4 the values for each day of the week are as,

Day 1 = 8000 , Day 2 = 9000, Day 3 = 9500, Day 4 = 10000, Day 5 = 9000, Day 6 = 7000, Day 7 = 11000

Thus, the mean number of steps is = (8000+ 9000+ 9500+ 10000+ 9000+ 7000 + 11000) / 7

= 9071 (approximately)  ≠ 10000

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The value of a in the equation 60°a = [? ]° is dependent on the value of [? ].

To solve for a in the equation 60°a = [? ]°, we need to isolate a on one side of the equation. We can do this by dividing both sides of the equation by 60°:

60°a / 60° = [? ]° / 60°

This simplifies to:

a = [? ]° / 60°

Since we don't have the value of [? ]°, we cannot determine the exact value of a. However, we can simplify the expression by canceling out the ° units:

a = [? ] / 60

Therefore, the value of a is dependent on the value of [? ].

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As pumpkins cost $0.60 per pound Diego will pay $7.68 for his pumpkin.

To find out how much Diego will pay for his pumpkin, we need to multiply the weight of the pumpkin by the cost per pound:

Cost = weight × cost per pound

In this case, the weight is 12.8 pounds and the cost per pound is $0.60:

Cost = 12.8 pounds × $0.60/pound

Simplifying the expression, we get:

Cost = $7.68

Therefore, Diego will pay $7.68 for his pumpkin.

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The total number of employees in the company is 297 if  ratio of union members to nonunion members working for a company is 4 to 7

The given ratio of union members to nonunion members, which is 4 to 7. This means that for every 4 union members, there are 7 nonunion members.

We are also given that there are 108 union members working for the company.

The total number of employees in the company be "x".

Let us from a proportional equation

4/11 = 108/x

To solve for x, we can cross-multiply and simplify:

4x = 1188

x = 297

Therefore, the total number of employees in the company is 297.

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Answer:

[tex]1 \frac{7}{20} [/tex]

Step-by-step explanation:

Well you should find a common denominator for 10, 4 and 5 first to be able to mix them. Let's take 20 because it's the smallest number we can convert 10, and 4 and 5 to.

So

[tex] \frac{3 \times 2}{10 \times 2} + \frac{1 \times 5}{4 \times 5} + \frac{4 \times 4}{5 \times 4} [/tex]

And you get

6/20 + 5/20 + 16/20 (now you can add them because they all have 20 as denominator) so = 27/20 = 1 7/20

The solid that is produced rotating the triangle about the line m is given as follows:

A cylinder with height of 2 units.

The cylinder has a circular base, hence we must start there, then we consider that;

Rotating the line, the features of the cylinder generated are given as follows:

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The discriminant value is 120 and 2 is the  x - intercept will have the graph of f.

The intercept of a line is the point on a graph where the line crosses an axis. There can be both x and y intercepts on a graph. The x-axis is the horizontal line on the graph, therefore the x-intercept can also be referred to as the horizontal intercept. This is the point where the line crosses the x-axis. At this point, the value of y is zero. The y-axis is the vertical axis on a graph. The y-intercept is the point where the line crosses the y-axis and x has a value of zero.

The function, we have:

[tex]f(x) = -7x^2 + 8x + 2[/tex]

We have to find the value of the discriminant of f and how many x- intercepts of the graph?

Firstly, We have to find the value of discriminant is

[tex]b^2 -4ac[/tex]

[tex]where ,ax^2 +bx+c[/tex]

a= -7,  b = 8, c=2

The discriminant is:

= [tex]8^2 - 4(-7) (2)[/tex]

= 64 +56

= 120

This will have 2 real x intercepts because 120 > 0

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1) Note the the linearization of th function f(X) at a =1 is l(x) = 2x-3
2) since l(x) = 2x-3, f(1.01) is = - 0.98

Linearization is the process of converting a nonlinear function's gradient with respect to all variables into a linear representation at that moment.

for the  above prompt , we have to use the formula:

l (x) =  f(a) + f' (a) (x-a)

where  (a) is the value fo the function at point a

and f' (a)  is the derivative of the function evaluated at point  a.


Using a =  1, f(a) becomes:


f(1)  = 2 (1) ⁵ - 8 (1) + 5

f (1) =-1


f(x) = 10x⁴ -8

So f' (1 ) when evalutated will give us the slope of the tangent line at x =1

Thus,

f (1 ) = 10 (1)⁴ -8

= 2

Hence substituting all the values into th e linearization formula we get:

l(x) = f( 1) + f '(1) (x-1)

= -1 + 2 *( x-1 )
= -1 + 2x - 2
= 2x -3

This means that the linearization of the function f(x ) at a= 1 is l(x) = 2x-3


b) Given the l(x) above, f(1.01) gives us:

l(x) = 2x -3
= 2 (1.01) -3
= - 0.98

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The frequency table is plotted and the order for the restaurant is given

Given data ,

A restaurant had 160 lunch customers last weekend.

90 ordered seltzer, 75 ordered a chicken sandwich, and 38 ordered both.

There were 45 customers who ordered seltzer and a veggie sandwich.

Eleven more people ordered a veggie sandwich than a tuna sandwich.

On simplifying the equation , we get

A = 90 - 38 - 45 = 7

B = 75 - 38 = 37

E = 160-90 = 70

C = D + 11

D + 11 + D = 70-37

2D = 33-11

D=22/2

D=11

Thus C = 22

F = 45 + C

F = 45 + 22

F = 22

G = A + D = 18

                  Chicken       Veggie             Tuna               Total

Seltzer            38                 45                     7                    90

Iced Tea           B                  22                     11                    70

Total                 75                 67                    18                    160

Hence , the frequency is completed

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The complete question is attached below :

A restaurant had 160 lunch customers last weekend. Of those, 90 ordered seltzer, 75 ordered a chicken sandwich, and 38 ordered both. There were 45 customers who ordered seltzer and a veggie sandwich. Eleven more people ordered a veggie sandwich than a tuna sandwich. Complete the two-way frequency table for the data.

1) The scale factor of dilation is 1/3

2) The orientation is preserved in dilation of A to A'

3) The congruence is not preserved in dilation of A to A'

We know that the scale factor is nothing but the ratio of the size of the transformed image to the size of the original image.

Here from the attached graph we can observe that the square A is transformed to A'

The side length of square A is 18 units and the side length of square A' is 6

So, the scale factor would be,

r = A' / A

r = 6/18

r = 1/3

We know that a dilation preserves the shape and orientation of the figure, but changes the size of he figure.

So, the dilations do not preserve congruence, as it changes the size of a figure.

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The probability that the  transferred jelly bean was green is P ( G ) = 0.636

Given data ,

Let the probability that the  transferred jelly bean was green be P ( G )

Now , There are 7 blue and 7 green jelly beans in the box, so the probability of selecting a green jelly bean from the box is 7/(7+7) = 0.5, and the probability of selecting a blue jelly bean from the box is also 0.5

A jelly bean is chosen from the box and then put in the bag. Say someone chooses a green jelly bean from the package and puts it in the bag. Currently, there are 6 + 1 = 7 green jelly beans and 4 + 0 = 4 blue jelly beans in the bag.

Now , Since there are 7 green jelly beans and 4 blue jelly beans in the bag, the probability of selecting a green jelly bean from the bag is P ( G )

where P ( G ) = 7/(7+4)

P ( G ) = 0.636

Hence , the probability is 0.636

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a) The total number of balls in a bag is 9.

b) The probability that the first ball chosen is orange is 1/3.

c) The probability that the 2nd ball is also orange is 1/4.

d) The probability that both balls are orange is 1/12.

Given that:

Balls, White = 6 and Orange = 3

a) The total of ping-pong balls in the bag at the start is calculated as,

Total ball = 6 + 3

Total ball = 9

b) The probability that the first ball chosen is orange is calculated as,

P(Orange) = 3/9

P(Orange) = 1/3

c) There will be 8 balls in the bag, of which 2 are orange if the first ball selected was an orange ball. Then the probability is calculated as,

P(Orange) = 2/8

P(Orange) = 1/4

d) The product rule of probability may be used to determine the likelihood that the first and second balls are both orange:

P(Orange and Orange) = 1/3 x 1/4

P(Orange and Orange) = 1/12

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The value of u -v is 6i - 10j.

We have,

u = 4i-3j, and v= -2i+ 7j.

So, u - v

= (4i - 3j) - (-2i + 7j)

= 4i - 3j + 2i - 7j

= (4i + 2i) + (-3j - 7j)

= 6i - 10j

Thus, the resultant vector is 6i - 10j.

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Using the statistical tool, the following were arrived at:

It should be noted that when arranged from lowest to highest, the IQR represents the central 50% of values.

Find the median (middle value) of the lower and higher half of the data to get the interquartile range (IQR).

These are the quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The difference between Q3 and Q1 is the IQR.

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Answer: Maryanne's conjecture could have been that the perimeter of the image of the triangle will be the same as the perimeter of the original triangle.

Step-by-step explanation:

The measure of WY using trigonometric identities is 5.4405.

We have,

Using trigonometric identities,

tan 33 = YW/√70

Now,

√70 = 8.37

tan 33 = 0.65

Substituting,

0.65 = YW/8.37

YW = 0.65 x 8.37

YW = 5.4405

Thus,

The measure of WY is 5.4405.

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Answer:

cm^3 can be used to represent volume.

The estimate of the population mean is 80 and the variability in the distribution is 120

Here, we have

The dot plots

From the dot plots, we can see that the data are normally distributed

This means that the mean, the median and the mode are equal

From the distribution of the random variable, we have the following readings

Hence, the estimate of the population mean is 80

Here, we use the range

So, we have

Variability = Highest - Least

This gives

Variability = 140 - 20

Variability = 120

So, the variability in the distribution is 120

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Answer:θ≈2.15

θ≈4.13 are correct

Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):

3u^2 - 2u - 2 = 0

We can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 3, b = -2, and c = -2. Substituting these values, we get:

u = (2 ± sqrt(4 + 24)) / 6

u = (2 ± 2sqrt(7)) / 6

Simplifying this expression, we get:

u = (1 ± sqrt(7)) / 3

Therefore, either:

Answer:

  0.67 million miles per day

Step-by-step explanation:

You want the average rate of change of the function d(t) = ∛(6t²) on the interval [4, 8], where d is in millions of miles, and t is in days.

The average rate of change of the function on the interval [a, b] is given by ...

  rate of change = (d(b) -d(a))/(b -a)

As the table in the attachment shows, this is approximately ...

  rate of change = (7.268 -4.579)/(8 -4) ≈ 0.67

The average rate of change on the interval 4 ≤ t ≤ 8 is about 0.67 million miles per day.

__

Additional comment

Mercury has an orbit of about 88 days at a distance of roughly 36 million miles from the Sun. Already at that distance, the General Theory of Relativity comes into play, making predictions from Newtonian physics somewhat problematic. It is unlikely this formula has any relation to reality for t much less than 200.

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Answer:

For this question, you can use the simultaneous equation to solve this problem.

Equation 1 reads: x + y = 34. (There are 34 notes in total.)

Equation 2: 5x + 10y = 235 (The notes are worth a total of $235.)

To find x in terms of y, we can apply equation 1:

x = 34 - y

When we use this expression to replace x in equation 2, we obtain:

5(34 - y) + 10y = 235

By condensing and figuring out y, we get at:

y = 15

There are 15 $10 bills in the wallet as a result.