WC is tangent to circle O at point W. If the radius of the circle is 32, and the tangent segment WC = 27, what is the length of CO? Round your answer to two decimal places.​

The probability of the baseball player getting exactly 4 hits out of 10 times at bat is approximately 0.161, or 16.1%.

To calculate the probability of a baseball player getting exactly 4 hits out of 10 times he was up at bat, we need to use the binomial probability formula.

The binomial probability formula is given by:P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) is the probability of getting exactly k hits

n is the total number of trials (in this case, the player's 10 times at bat)

k is the number of successful trials (in this case, 4 hits)

p is the probability of success in a single trial (in this case, the player's batting average, 0.298)

(1 - p) is the probability of failure in a single trial

Plugging in the values:

P(X = 4) = C(10, 4) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Using the combination formula C(n, k) = n! / (k! * (n - k)!):

P(X = 4) = 10! / (4! * (10 - 4)!) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Calculating the values:

P(X = 4) ≈ 0.161

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Answer:

1885.0

Explanation:

The surface area of a cylinder is given by

where r is the radius and h is the height of the cylinder.

Now in our case, r = 10 cm and h = 25 cm; therefore,

which is our answer!

Answer:

If x is the length of the square tomato patch, then the width of the tomato patch is also x, since it is a square.

According to the problem, the length of the rectangular vegetable garden must exceed three times the length of the tomato patch by 2 feet, so the length of the garden is:

3x + 2

The width of the rectangular vegetable garden must exceed the width of the tomato patch by 5 feet, so the width of the garden is:

x + 5

To find the area of the garden, we multiply its length by its width:

Area of garden = length x width

Area of garden = (3x + 2)(x + 5)

To find the area of the tomato patch, we note that it is a square with side length x, so its area is:

Area of tomato patch = x²

Therefore, the area of the vegetable garden that is not taken up by the tomato patch is:

(3x + 2)(x + 5) - x²

And the total area of the vegetable garden, including the tomato patch, is:

x² + (3x + 2)(x + 5)

Simplifying:

x² + (3x² + 17x + 10)

4x² + 17x + 10

So the total area of the garden is 4x² + 17x + 10 square feet.

Answer:

a. Expected frequency of losses per semester = 0*0.08 + 5*0.16 + 10*0.28 + 15*0.32 + 20*0.14 + 25*0.02

Expected frequency of losses per semester = 11.7 losses per semester

b. Variance = (0-11.7)²*0.08 + (5-11.7)²*016 + (10-11.7)²*0.28 + (15-11.7)²*0.32 + (20-11.7)²*0.14 + (15-11.7)²*0.02

Variance = 10.9512 + 7.1824 + 0.8092 + 3.7848 + 9.6446 + 3.5378

Variance = 35.61

c. As losses equal $60, expected losses per semester = 11.7*$60 = $702

d. Expected losses of all textbooks per semester = 250*11.7*$60 = $175,500

If wheel on a scooter completes 124 revolutions and travels 22.4 meters then  diameter of the wheel is 57 mm

Each revolution of the wheel covers a distance equal to the circumference of the wheel.

The diameter of the wheel "d".

The distance covered in 124 revolutions is:

distance = 124 x circumference

= 124 x pi x d

= 124 x 3.14 x d

We know that this distance is equal to 22.4 meters, so we can set up an equation:

124 x 3.14 x d = 22.4

Simplifying and solving for d:

d = 22.4 / (124 x 3.14)

d = 0.057 meters

As we know that 1 meter is equal to thousand millimeters so multiply by 1000 to get in millimeters

d = 57 millimeters

Therefore, the diameter of the wheel is approximately 57 mm.

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N= number of nickels

D= number of dimes

from the part of the question that says: "Your piggy bank has 50 coins" we know that N+D=50

and from the part that says: "worth a total of $4.55" and since the nickel is $0.05 and the dime is $0.10 then 0.05N+0.10D=4.55

now we have a system of two equations, let's solve it:

1. multiply the first equation by -0.05, obtaining

2. add the previous equation to the second one:

then there will be 41 dimes in the piggy bank, and replacing D for this value in the first equation, we obtain that N=9 then there will be 9 nickels in the piggy bank:

a.i) The number of inches per minute that the Galapagos tortoise walks are 216 inches (6 x 36).

a.ii) The time it would take a Galapagos tortoise to walk across the U.S. in hours is 2,933 hours (1,056,000/(6 x 60).

b.i) The Hare runs 31,680 inches per minute (1,900,800/60).

b.ii) The time it would take the Hare to complete the race across the U.S. in hours is 20 hours (600/30).

c.) For the Tortoise to pass the Hare, the Hare needs to sleep for 2,913 hours (2,933 - 20) or 121.4 days (2,933/24).

In this exercise, the following equivalent values are used for computing the distance and speed:

Speed of Galapagos Tortoise per minute = 6 yards/ min (60 yards in 10 minutes)

Speed of Hare = 30mph

30 miles = 52,800 yards (30 x 1,760)

52,800 yards = 1,900,800 inches (52,800 x 36)

= 880 yards per minute (52,800/60)

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let's firstly convert the mixed fractions to improper fractions.

\(\stackrel{mixed}{3\frac{2}{3}}\implies \cfrac{3\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{11}{3}}~\hfill \stackrel{mixed}{2\frac{1}{4}} \implies \cfrac{2\cdot 4+1}{4} \implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{11}{3}-\left( \cfrac{9}{4} \right)\implies -\cfrac{11}{3}+\cfrac{9}{4}\implies \cfrac{-(4)11~~ + ~~(3)9}{\underset{\textit{using this LCD}}{12}} \\\\\\ \cfrac{-44+27}{12}\implies \cfrac{-17}{12}\implies {\Large \begin{array}{llll} -1\frac{5}{12} \end{array}}\)

Answer: ite will be 3 bc i done that all ready

Step-by-step explanation:

The number of individuals that work for the company is 272 workers.

Given,

The Parker company employs 68 part-time workers.

This represents 4% of the total workforce.

We need to find out how many individuals work for the company.

Percentage is a fraction or a ratio in which the value of whole is always 100.

Find the total workforce.

Total workforce = 100%

We have,

4% = 68 workers

Multiply 25 on both sides.

25 x 4% = 4 x 68 workers

100% = 272 workers.

This means the number of individuals that work for the company is 272 workers.

Thus the number of individuals that work for the company is 272 workers.

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Answer:

Simple it would be 76x - 1 whatever that is, and 72x + 3 which u shuld get like uh 75x, and 75x again on both so its 75x

PLEASE DONT QUOTE ME ON THIS

Xoxo~May

Step-by-step explanation:

Answer:

3.78

Step-by-step explanation:

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

Work Shown for problem 1

P(pink, then violet) = P(pink)*P(violet given 1st was pink)

= (4/14)*(2/13)

= 8/182

= 4/91

------------------------------

Work Shown for problem 2

P(gray, then gray)

= P(gray)*P(gray given 1st was gray)

= (3/14)*(2/13)

= 6/182

= 3/91

-------------------------------

Work Shown for problem 3

P(not yellow, not yellow)

= P(not yellow)*P(not yellow given 1st was not yellow)

= (9/14)*(8/13)

= 72/182

= 36/91

-------------------------------

Work Shown for problem 4

P(yellow, not yellow)

= P(yellow)*P(not yellow given 1st was yellow)

= (5/14)*(9/13)

= 45/182

Answer:

V = 262.61 m³

Step-by-step explanation:

Given: Slant height of the cone is 9 inches, the diameter is 6.2 inches.

Formula: The formula for the volume of a cone is V = 1/3hπr².

Solve: V = 262.610935 m³

The image after the reflection over the line x = 2 is (11, -3)

Here we have the point T which has coordinates (-7,  -3), and we apply a refletion across the line x = 2.

This reflection will only chane the value of x in our point, such that the initial value x = -7

Is at the same distance of the line x = 2 than the final x-value

The distance between these values is:

d = |-7 - 2| = 9

Then the new x-value will be:

x = 2 + 9 = 11

Thus, the image after the reflection is (11, -3)

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Answer:

volume=60cm3, surface area=96cm2

Step-by-step explanation:

volume=1/3×(6×6)×5

=60cm3

surface area= 4(1/2×6×5)+(6×6)

=96cm2

Based on the given graph, the expression that best defines f(x) is option 2) 5(2^x). It aligns with the exponential growth pattern shown in the graph.

To determine the expression that defines f(x) based on the given graph, we need to analyze the behavior and characteristics of the graph.

Looking at the options provided:

2x: This expression represents a linear function with a constant slope. However, the given graph does not exhibit a linear pattern or a constant slope, so this option is not a suitable representation for f(x).

5(2^x): This expression represents an exponential function with a base of 2 and a vertical scaling factor of 5. The graph shows an exponential growth pattern that aligns with this expression, so it is a plausible representation for f(x).

5(2^x/2): This expression represents an exponential function with a base of 2, but it includes a division by 2 in the exponent. This modification would alter the growth rate of the function and result in a different graph shape compared to what is shown. Thus, this option does not match the given graph.

5(2^2x): This expression represents an exponential function with a base of 2 and an exponent of 2x. The graph of f(x) does not exhibit a quadratic growth pattern, so this option does not accurately represent the given graph.

Based on the analysis, option 2) 5(2^x) is the most suitable expression that defines f(x) based on the given graph.

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Answer:

x = 8

Step-by-step explanation:

12 : 36

1 : 3

the distance is 3×, so

x = 26 ÷ 3

= 8

After 4.5 seconds, the baseball will have dropped approximately 99.35 meters.

To find out how far the baseball will have dropped after 4.5 seconds, we need to use the free fall formula.

The terms involved in this calculation are:
Time (t): 4.5 seconds.

Acceleration due to gravity (g): 9.81 m/s² (approximated)
Distance dropped (d)
The free fall formula is:
\(d = (1/2) \times g \times t^{2}\)
Now, we will plug in the given values and solve for d:
Substitute the values
\(d = (1/2) \times 9.81 \times  (4.5)^{2}\)
Calculate the square of time
\(d = (1/2) \times 9.81 \times 20.25\)
Multiply the values
d = 99.3525.

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Answer:

B. -18

Step-by-step explanation:

In order to find the fourth term of the sequence, first find second term, next, third term and finally fourth term.

\(a_n = - 6 + a_{(n - 1)} \\ \\ \implies \: a_2 = - 6 + a_{(2 - 1)} = - 6 + a_1 = - 6 + 0 \\ \\ \implies \: \pink{a_2 = - 6} \\ \\\: a_3 = - 6 + a_{(3 - 1)} = - 6 + a_2 = - 6 + ( - 6) \\ \\ \implies \: \purple{ a_3 = - 12}\\ \\\: a_4= - 6 + a_{(4 - 1)} = - 6 + a_3 = - 6 + ( - 12) \\ \\ \implies \: \huge { \red{a_4 = - 18}}\)

Another way:

\(a_1=0\)

\(a_2=-6\)(Calculated above)

\(a_3=-6+a_2=-6-6=-12\)

\(a_4=-6+a_3=-6-12=-18\)

Answer:

20 pizzas

Step-by-step explanation:

An equation of the line that goes through the point (-1, -3) and (3, 5) is y = 2x - 1.

An equation of the line in slope-intercept form that is perpendicular to the equation for obstacle 1 is y = -x/2 + 3.

In Mathematics, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁) or \(y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\)

Where:

At data point (-1, -3), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

\(y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - (-3) = \frac{(5- (-3))}{(3-(-1))}(x -(-1))\\\\y +3 = \frac{(5+3)}{(3+1)}(x +1)\)

y + 3 = 2(x + 1)

y = 2x + 2 - 3

y = 2x - 1

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

2 × m₂ = -1

m₂ = -1/2.

At point (-4, 5), an equation of the line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -1/2(x + 4)

y = -x/2 - 2 + 5

y = -x/2 + 3

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The direction of rotation used to create the image is 90°  counterclockwise rotation. To determine the direction and degree of rotation used to create the image, we can compare the positions of the vertices of the original triangle ABC with the corresponding vertices of the image triangle A' B' C'.

Let's analyze the changes in the coordinates of the vertices.

Original Triangle ABC:

A(-4, -4)

B(3, -3)

C(0, -10)

Image Triangle A' B' C':

A'(4, -4)

B'(3, 3)

C'(10, 0)

By comparing the coordinates, we can observe that the image triangle has undergone a 90° counterclockwise rotation.

To determine this, we can focus on a single vertex, such as A. The original point A(-4, -4) has been rotated counterclockwise by 90° to its new position A'(4, -4). This rotation is evident in the change of sign for the y-coordinate (-4 to -4) and the swapping of the x-coordinate (-4 to 4). This pattern is consistent across all three vertices.

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Answer:

Counterclockwise rotation of 90° about the origin

Answer:

See the image for marked congruences.

1. JM ≅ LM                           |      Given

2. △JML is isosceles          |      definition of isosceles

3. ∠MJL ≅ ∠MLJ                  |       isosceles triangle theorem

4. m∠MJL = m∠MLJ             |      definition of ≅

5. JK ≅ LK                            |      Given

6. △JKL is isosceles           |      definition of isosceles

7. m∠KJL = m∠KLJ              |       isosceles triangle theorem

8. m∠MJL + m∠KJM = m∠KJL                         |  adjacent angle theorem

9. m∠MLJ + m∠KMJ = m∠KLJ                         |  adjacent angle theorem

10. m∠MJL + m∠KJM = m∠MLJ + m∠KLM      |   transitive property of =

11. m∠MJL + m∠KJM = m∠MJL + m∠KLM      |   substitution

12. m∠KJM = m∠KMJ          |        subtraction

13. ∠KJM ≅ ∠KLM                |        definition of ≅

14. △KJM ≅ △KLM             |        SAS theorem

15. ∠JKM ≅ ∠LKM                |        CPCTC

16. KM bisects ∠JKL            |        definition of bisector

Answer: m<2= 126 and is supplementary angle

We have the following:

solving:

which means that the following intervals are not a solution

Answer:

-6

Step-by-step explanation:

djhcjici4n c rncinr

for the question the answer will be -6

Answer:

(1.5, 0.5)

Step-by-step explanation:

(5, 3) and (-2, -2)

5 - 2 / 2 = 1.5

-2 + 3 / 2 = 0.5