Rays QR and QS are tangents to circle P at R and S. If Q measures to 54°, find RS

The required bearing angle of town B from Thomas is 75°.

We have,

Bearing is basically an angle that is measured clockwise from the north. Bearing are generally written in three figure.

Given that

Thomas is facing towards town A, which is at a bearing of 300°.

Implies that town A is 300° from north.

If Thomas turns 135° clockwise, then he faces towards town B,

The bearing angle will be 300+135 = 435°

Since, one complete round makes angle 360°, therefore

The required bearing angle = 435 - 360 = 75

The bearing angle of town B from Thomas is 75°.

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The length of arc EG is approximately 7.35 units.

To find the length of arc EG, we need to use the formula:

length of arc = (central angle/360°) × 2πr

where r is the radius of the circle and the central angle is in degrees.

We are given that m∠EFG = 58°, and EF = 6 units. Since EF is a chord of the circle, we can use the chord-chord angle theorem to find that m∠EGF = ½(180° - 58°) = 61°.

Now, we can use the Law of Cosines to find the length of GE:

GE² = EF² + FG² - 2(EF)(FG)cos(∠EGF)

GE² = 6² + FG² - 2(6)(FG)cos(61°)

Since FG = 2r (because it is the diameter of the circle),

GE² = 36 + (2r)² - 12r cos(61°)

We can simplify this to:

GE² = 4r² - 12r cos(61°) + 36

GE² = 4(r² - 3r cos(61°) + 9)

Now, we can use the formula for the length of the arc:

length of arc EG = (m∠EGF/360°) × 2πr

length of arc EG = (61/360) × 2πr

length of arc EG = (61/180) × πr

Substituting the expression for GE² in terms of r, we get:

length of arc EG = (61/180) × π √[4(r² - 3r cos(61°) + 9)]

We can now use a calculator to find the approximate value of the length of arc EG.

Rounded to the nearest hundredth, the length of arc EG is approximately 7.35 units.

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Answer:

35 boys

25 girls

Step-by-step explanation:

you will the total number of volunteers and divide that by the total number of "parts" in the ratio (7+5=12)

60 / 12 = 5

you then will multiply your answer (in this case, 5) to each part of the ratio (7 to find the number of boys, & 5 to find the number of girls)

5x7=35 boys

5x5= 25 girls

HOPE THIS HELPS!!!

The value of x , y and z in the parallel line is 50 degrees.

When parallel lines are crossed by a transversal line, angle relationships are formed such as vertically opposite angles, alternate interior angles, alternate exterior angles, adjacent angles, corresponding angles etc.

Therefore, let's use the angle relationships to find the angle, x, y and z as follows:

Therefore,

x = 360 - 310(sum of angles in a point)

x = 50 degrees

Therefore,

x = y(alternate interior angles)

Alternate interior angles are congruent.

Hence,

y = 50 degrees

Therefore,

x = z(alternate interior angles)

z = 50 degrees.

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Therefore, the component form of vector v is (7.7551, 2.0664) (rounded to four decimals).

To find the component form of a vector v given its magnitude and the angle it makes with the positive x-axis, we can use trigonometric functions to determine the x-component (v_x) and y-component (v_y) of the vector. In this case, we are given the magnitude of the vector ‖v‖ = 8 and the angle θ = 15°. The formulas for finding the components are:

v_x = ‖v‖ * cos(θ)

v_y = ‖v‖ * sin(θ)

Plugging in the given values, we have:

v_x = 8 * cos(15°)

v_y = 8 * sin(15°)

By evaluating these trigonometric functions, we can calculate the values:

v_x ≈ 8 * cos(15°) ≈ 7.7551

v_y ≈ 8 * sin(15°) ≈ 2.0664

These values represent the x-component and y-component of the vector v, respectively. So, the component form of vector v is approximately (7.7551, 2.0664) (rounded to four decimals).

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To calculate the 90% confidence interval for the average EPS of all industrials listed on the DJIA, we will use the formula:

Confidence interval = sample mean ± (critical value * standard deviation / √sample size)

Step 1: Find the critical value.
Since we want a 90% confidence interval, the corresponding critical value can be obtained from the z-table. The critical value for a 90% confidence level is 1.645.

Step 2: Calculate the margin of error.
The margin of error is given by (critical value * standard deviation / √sample size).
Substituting the values, we get: 1.645 * 0.395 / √9 = 0.29175.

Step 3: Calculate the confidence interval.
The confidence interval is given by the sample mean ± margin of error.
Substituting the values, we get: 1.85 ± 0.29175.

The 90% confidence interval for the average EPS of all industrials listed on the DJIA is (1.55825, 2.14175).

We can be 90% confident that the true average EPS of all industrials listed on the DJIA falls within the range of 1.55825 to 2.14175.

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The tendency of group members to exert less effort when they work in groups than they would exert if they were acting alone is known as social loafing.

Social loafing is a common phenomenon that occurs when individuals feel that their individual effort will not significantly affect the group's overall performance or when they believe that other group members will compensate for their lack of effort.

This phenomenon can be observed in various group settings, such as in work teams, sports teams, and even in classroom group projects. The lack of accountability and the diffusion of responsibility that occur in groups can contribute to social loafing.

Social loafing can have negative consequences on group performance, as it can decrease the overall quality of the group's output and reduce motivation among group members.

To mitigate social loafing, it is important to establish clear roles and responsibilities for each group member and to provide regular feedback and recognition for individual contributions.

Additionally, creating a sense of collective identity and establishing group goals can also help to combat social loafing by promoting a sense of shared responsibility and commitment to the group's success.

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Answer:

option 6b):) is correct

Answer: $2.12

Step-by-step explanation: Subtract $2.65 from 34.45 and then divide that number by 15.

Answer:21

Step-by-step explanation:

There are 360 black counters and 306 white counter in 20:17 ratio.

Let's denote the number of black counters by B and the number of white counters by W. We know that the ratio of black to white counters is 20:17, which means that:

B/W = 20/17

We also know that there are 54 more black counters than white counters, which means that:

B = W + 54

We can use substitution to solve for B. Substituting the second equation into the first equation, we get:

(W + 54)/W = 20/17

Cross-multiplying, we get:

17(W + 54) = 20W

Expanding the left side, we get:

17W + 918 = 20W

Subtracting 17W from both sides, we get:

918 = 3W

Dividing both sides by 3, we get:

W = 306

Now we can use the second equation to find B:

B = W + 54 = 306 + 54 = 360

Therefore, there are 360 black counters in the bag.

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Answer:

\(MN = 18\)  

Step-by-step explanation:

Given

\(AB = 9\)

\(BD = x + 1\)

\(MB = x - 1\)

\(BN = 15\)

See attachment

Required

Determine MN

The products of the segments of two chords that intersect are always, equal.

So, we have:

\(AB * BD = MB * BN\)

\(9 * (x + 1) = (x - 1) * 15\)

Open bracket

\(9x + 9 = 15x - 15\)

Collect like terms

\(15x - 9x = 9 + 15\)

\(6x = 24\)

Solve for x

\(x = \frac{24}{6}\)

\(x = 4\)

The length of MN is calculated as:

\(MN = MB + BN\)

\(MN = x - 1 + 15\)

Substitute \(x = 4\)

\(MN = 4 - 1 + 15\)

\(MN = 18\)  

Answer:

C. 18 units

Step-by-step explanation:

Answer:

.25 dollars

Step-by-step explanation:

divide everything by 4 to get .25

Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

Answer:

−4x + 10 < 26

Step 1: Subtract 10 from both sides.

−4x + 10 − 10 < 26 − 10

−4x < 16

Step 2: Divide both sides by -4.

-4x/−4  <  16 /−4

x > −4

Answer:

x > −4

assuming you're solving for x:

solve using pemdas backwards, so basically sadmep :)

first subtract 10, and you end up with the equation -4x < 16.

Next is dividing the -4. Remember dividing by a negative number switches the sign direction, so the < becomes a >. So, your answer would be x > -4

The requried value of the expression \(\sum_{n=11}^{30}n-\sum_{n=1}^{10}n\) is 355.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
To evaluate the expression:

\(\sum_{n=11}^{30}n-\sum_{n=1}^{10}n\)

we can first simplify each summation separately and then subtract the second summation from the first.

\(\sum_{n=11}^{30}n\)= 11 + 12 + 13 + ... + 29 + 30

We can use the formula for the sum of an arithmetic series to simplify this expression:

S = (n/2)(a + l)

In this case, a = 11, l = 30, and n = 20 (since we're summing 20 terms).

So, we have:

S = (20/2)(11 + 30)

S= 410

Similarly,

\(\sum_{n=1}^{10}n\) = 1 + 2 + 3 + ... + 9 + 10

S = 55

Finally, we can subtract the second summation from the first:

= 410 - 55 = 355

Therefore, the value of the expression is 355.

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Answer:

cosA = \(\frac{5}{13}\)

Step-by-step explanation:

cosA = \(\frac{adjacent}{hypotenuse}\) = \(\frac{AC}{AB}\) = \(\frac{5}{13}\)

The value of the fractions in the mixed fraction form is 3(⁷/₉), 4(⁷/₉), and 6(²/₅) respectively.

A mixed fraction is a fraction that is created by fusing a fraction with a whole number. The fraction is defined as the division of the whole part into an equal number of parts.

The given fractions 34/9, 43/9, and 32/5 can be written in the form of the mixed fraction as below:-

To write the fractions in the form of the mixed fraction first divide the fraction by the complete number and put the remainder on the numerator.

34/9 = 3(⁷/₉)

43/9 = 4(⁷/₉)

32/5 = 6(²/₅)

Therefore, the value of the fractions in the mixed fraction form is 3(⁷/₉), 4(⁷/₉), and 6(²/₅) respectively.

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Answer:

x=8 and QNR= 63°

Step-by-step explanation:

90+8x-1+27=180

116+8x=180

8x=64

x=8

Answer:

8, m<QNR=63 degrees

Step-by-step explanation:

So, lets go over what we know:

The angle that makes up (8x-1) and 27 degrees is a right angle.

A right angle is 90 degrees.

So, to solve for angle m<QNR and for x, we must subtract and solve using 27 degrees, and (8x-1).

Lets put this into equation form:

(8x-1)+27=90

Lets subtract 27 from both sides to get the (8x-1) alone:

(8x-1)=63.

So lets stop here real quick.

We need to find angle M<QNR. This is (8x-1)

So looking at what we have solved so far, angle M<QNR must be 63 degrees.

Now, lets solve further to find out what x is:

(8x-1)=63

Lets add x to both sides to get 8x alone:

(8x)=64

We dont need the parethese, for they do not have a function, so:

8x=64

Finally, lets divide 8 from both sides so we can make 8x into just x:

x=8

So x is equal to 8.

Overall:

x = 8

Angle m<QNR = 63

Hope this helps! :)

Answer:

1

Step-by-step explanation: 1

The cost of one earring is 15.50.

The first step is to determine the total cost of the three sets of earrings. Total cost of the three sets of earrings = total amount spent - total cost of the scarves

Total cost of the scarves = cost of one scarf x total number of scarves bought

18 x 2 = $36

Total cost of the three sets of earrings = 82.50 - 36 = 46.50

Cost of one set of earring = total cost of the three sets of earrings / number of sets bought

46.50 / 3 = 15.50

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Answer:

4

Step-by-step explanation:

(25-18+5)/4=4

(insert the variables)

The z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

The z-scores will not change if you convert the height measurements from inches to centimetres or vice versa. The z-score is a standard score representing the number of standard deviations, a value above or below the mean of a normal distribution.

The z-score is calculated using the formula z = (x - mean)/standard deviation, where x is the value being compared to the mean and standard deviation of the distribution.

Converting the height from inches to centimetres or vice versa will only change the units of measurement, but the relative position of a value within the distribution will remain unchanged.

Therefore, the z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

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Step-by-step explanation:

Given angle of elevation = angle ACB.

angle ACB + angle ABC + angle BAC = 180(sum of angles in a triangle)

angle ACB + 90 + 58 = 180

angle ACB = 180 - 90 - 58

=32

Answer:

? = 32 degrees

Step-by-step explanation:

since the angles inside a triangle has to add up to 180 degrees then we can use this equation to find the missing angle:

58° + 90° + ? = 180°

The required solutions are as follows,
1. Angle e = Angle a
2. Angle f = Angle c
3. Ange a, b, and c add up to 180°.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

here.
Angle e = Angle and as they are alternate angles,
Angle f = Angle c as they are alternate angles,

Ange a, b, and c add up to 180°. as they lie on a straight line.
Therefore angles e, f, and b also be added to  180°

Thus, the solution of the angles is shown above.

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The slope of the tangent line at (4, 54) is 45. So the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54) is y = 45x - 126.

To find the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54), we need to use calculus. First, we find the derivative of the function:

y' = 3x^2 - 3

Next, we plug in x = 4 to find the slope of the tangent line at that point:

y'(4) = 3(4)^2 - 3 = 45

So the slope of the tangent line at (4, 54) is 45. To find the equation of the line, we use the point-slope form of the equation:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point on the line. Plugging in our values, we get:

y - 54 = 45(x - 4)

Simplifying, we get:

y - 54 = 45x - 180

y = 45x - 126

So the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54) is y = 45x - 126.

To find the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54), we need to first find the derivative of the function and then use the point-slope form of a line.

1. Find the derivative of the function with respect to x:
y'(x) = d/dx (x^3 - 3x + 2) = 3x^2 - 3

2. Evaluate the derivative at the given point (4, 54) to find the slope of the tangent line:
m = y'(4) = 3(4)^2 - 3 = 3(16) - 3 = 48

3. Use the point-slope form of a line (y - y1 = m(x - x1)):
y - 54 = 48(x - 4)

4. Simplify the equation:
y - 54 = 48x - 192
y = 48x - 138

So, the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54) is y = 48x - 138.

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Answer:

7x-34 because...

product means multiply the variable x by 7

7x

decreased mean we subtract 34 from 7x

7x-34

If Brad has $272 now and lent his friend Jorge $10, his monthly allowance is $47.00

What is the total monthly allowance over 6 months?

Brad total monthly allowance over 6 months is the sum of the amount lent to Jorge and the balance Brad has currently which is $272

total allowances for 6 months=$272+$10

total allowances for 6 months=$282

monthly allowance=total allowances for 6 months/6 months

monthly allowance=$282/6

monthly allowance=$47.00

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Answer:

A. C. And D.

Step-by-step explanation:

I searched it up for you, cause... I'm not good at this XD. I hope this helps :D

The probability that exactly 4 out of the 5 randomly selected employees are cashiers is approximately 0.00549 or 0.549%

To calculate the probability that exactly 4 out of the 5 employees selected to work on Labor Day are cashiers, we need to use the concept of combinations and probabilities.

First, let's determine the total number of ways to select 5 employees out of the 22. This can be calculated using the combination formula:

C(n, k) = n! / (k!(n-k)!)

where n is the total number of employees (22) and k is the number of employees selected (5).

C(22, 5) = 22! / (5!(22-5)!)

= 22! / (5! * 17!)

= (22 * 21 * 20 * 19 * 18) / (5 * 4 * 3 * 2 * 1)

= 22,957

So, there are a total of 22,957 ways to select 5 employees out of the 22.

Next, let's determine the number of ways to select exactly 4 cashiers out of the 9 cashiers. This can also be calculated using combinations:

C(9, 4) = 9! / (4!(9-4)!)

= 9! / (4! * 5!)

= (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1)

= 126

Now, let's calculate the probability of selecting exactly 4 cashiers out of the 5 employees randomly selected for overtime pay:

P(4 cashiers) = Number of ways to select 4 cashiers out of 9 / Total number of ways to select 5 employees from 22

= C(9, 4) / C(22, 5)

= 126 / 22,957

≈ 0.00549

Therefore, the probability that exactly 4 out of the 5 randomly selected employees are cashiers is approximately 0.00549 or 0.549%

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