The distance the tip of the bat travels is equivalent to the length of the arc which is 205 inches
What is the distance the tip of the bat travelsThe distance the tip of the bat travels is equal to the length of the arc it sweeps through. To calculate this length, we need to use the formula:
length of arc = (angle / 360) x 2πr
where angle is the central angle in degrees, r is the radius of the circle, and π is a constant approximately equal to 3.14159.
Substituting the given values, we get:
length of arc = (255 / 360) x 2π x 46
length of arc = (0.7083) x 2 x 3.14 x 46
length of arc = 204.6 inches (rounded to two decimal places)
Therefore, the distance the tip of the bat travels is approximately 205 inches to the nearest inch.
Learn more on length of an arc here;
https://brainly.com/question/12823137
#SPJ1
the area covered by the hour hand of a wall clock between time 4 : 26 and 6 : 50 is what percent of the area covered by it in 15 hours?
Step-by-step explanation:
From 4:26 to 6:50 is 2 hr and 24 in = 2 24/60 hrs = 2.4 hours
2.4 hrs is what percent of 15 hrs ?
2.4 / 15 * 100% = 16%
The principal of a school claims that 30 % of grade 3 pupils stay in the playground after their classes. A survey among 500 grade 3 pupils revealed that 150 of them stay in the playground after their classes. Use 99% confidence to conduct a test of proportions.
No unrelated answers or links or you will be reported. Thanks
The margin of error for the school's claim is 0.055 or approximately 5.5%.
To find the margin of error, we need to use the formula:
Margin of error = Critical value x Standard error
For a sample size of 500, the critical value can be found by:
critical value = 1.96
Next, we need to find the standard error. The formula for the standard error is:
standard error = sqrt(p_hat * (1 - p_hat) / n)
In this case, the sample proportion is 150/500 = 0.3.
standard error = sqrt(0.3 * (1 - 0.3) / 500) = 0.028
Finally, we can calculate the margin of error:
Margin of error = 1.96 x 0.028 = 0.055
To know more about margin of error, here
brainly.com/question/29101642
#SPJ4
--The complete Question is, What is the margin of error for the school's claim that 30% of grade 3 pupils stay in the playground after their classes, given the results of the survey of 500 grade 3 pupils, which revealed that 150 of them stay in the playground after their classes? Assume a confidence level of 95%.--
In triangle ∆ABC, m<A = 33°, m<C = 58°, and AB = 25 in. What is AC to the nearest tenth of an inch?
1. 16.1 in.
2. 38.9 in
3. 42 in.
4. 12 in.
The value of AC to the nearest tenth is 29.5
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
Angle B = 180-(33+58)
= 180-91 = 89°
using sine rule
represent AC by x
x/ sin89 = 25/sin 58
xsin58 = 25sin89
0.848x = 0.9998×25
0.848x = 24.995
x = 24.995/0.848
x = 29.5( nearest tenth)
therefore the value of AC is 29.5.
learn more about sine rule from
https://brainly.com/question/20839703
#SPJ1
the resultant data are: forty mothers have taken the suspected drug during their pregnancies. of these mothers, 35 have delivered malformed infants. in addition, 10 other infants are born with malfunctions. the number of individuals who both did not take the drug and did not give birth to infants who were malformed was:
No. of individuals Suspected drug and didn't give birth to in infants malformed is 10.
Number of individuals who did not take the drug and did not give birth to malformed infants.
subtract the number of individuals who took the drug and gave birth to malformed infants.
The total number of mothers, and then subtract the number of infants born with malfunctions.
Total number of mothers = 40
Number of mothers who gave birth to malformed infants after taking the drug = 35
Number of infants born with malfunctions = 10
the number of mothers who did not take the
drug = 40 - 35 = 5
The number of infants born without malfunctions = Total number of infants - Number of infants born with
malfunctions = (40 - 35) + 5 = 10
For similar questions on Suspected
https://brainly.com/question/30548625
#SPJ11
(COMPOUND INTEREST)
-$17,525 deposit, interest at 1/2% for 3 years; find interest earned.
20 points reward
Answer:
Step-by-step explanation:
Principal = 17,525. Rate = 1/2% = 0.005 time,t = 3
Interest, I = principal x rate x time
Interest, I = 17525 x 0.005 x 3
Interest, I = $262.875
PLEASE HELP. Lesson 15.3 Tangents and Circumscribed Angles
Proof of Circumscribed Angle Theorem
Given: ZAXB is a circumscribed angle of circle C.
Prove: ZAXB and ZACB are supplementary.
Complete the proof.
A
B
C
If ZAXB is a circumscribed angle of circle C, XA and XB are
Select an answer to the circle
The assumption that AXB is a bounded angle is false, as a result, if AXB is a circumscribed angle of circle C, then AXB and ACB are supplementary.
How to prove circumscribed angles?To complete the proof of the Circumscribed Angle Theorem, use the fact that an inscribed angle of a circle is equal to half of the central angle that intercepts the same arc.
Since angle ∠AXB is circumscribed by the circle, point X lies on the circumference of the circle. Therefore, angles ∠CXA and ∠CXB are inscribed angles that intercept the same arc AB.
By the Inscribed Angle Theorem:
∠CXA = ½∠CAB
∠CXB = ½∠CAB
Adding these two equations:
∠CXA + ∠CXB = ½∠CAB + ½∠CAB
∠CXA + ∠CXB = ∠CAB
Now, observe that angles ∠CAB and ∠ACB form a linear pair, since they are adjacent angles that together make a straight line. Therefore, they are supplementary, which means:
∠CAB + ∠ACB = 180°
Substituting ∠CAB with ∠CXA + ∠CXB:
∠CXA + ∠CXB + ∠ACB = 180°
Finally, ∠AXB and ∠CXB form a linear pair, since they are adjacent angles that together make a straight line. Therefore, they are supplementary, which means:
∠AXB + ∠CXB = 180°
Substituting ∠CXB with ∠CAB - ∠CXA:
∠AXB + ∠CAB - ∠CXA = 180°
Adding ∠CXA to both sides:
∠AXB + ∠CAB = ∠ACB + 180°
Substituting ∠AXB + ∠CAB with 180° (since they are adjacent angles that together make a straight line):
180° = ∠ACB + 180°
Simplifying:
∠ACB = 0°
This is a contradiction, since we know that ∠ACB is a non-zero angle. Therefore, our assumption that ∠AXB is a circumscribed angle must be false. Hence, we have proved that if ∠AXB is a circumscribed angle of circle C, then ∠AXB and ∠ACB are supplementary.
Find out more on Circumscribed Angles here: https://brainly.com/question/29164079
#SPJ1
You deposit $150 in an investment account that earns 6% annual interest compounded annually. You make no additional deposits or withdrawals. What is the balance of this account after 5 years
Answer:200.734
Step-by-step explanation:
150(1+0.06)^t
t=number of years
150(1.060)^5
200.73383664
round
200.734
The balance of this account after 5 years is $200.73
What is Compound interest?Compound interest is the interest earned on the principal and the interest previously accumulated. It is given by
Amount = [tex]P(1+r/n)^n^t[/tex] where P = Principal, r = annual rate of interest, n = number of times interest is compounded per year, & t = time in years.
The given principal is $150 for 5 years & annual interest rate is 6%.
To find the amount compunded annualy at 6% for 5 years substituting the given values in the above formula i.e.
Amount = [tex]P(1+r/n)^n^t[/tex]
Amount = $[tex]150(1+0.06)^5[/tex]
Amount = $200.73
Hence, the total amount accumulated for 5 years will be $200.73
To learn more on Compound Interest click on:
https://brainly.in/question/38177895
#SPJ2
mrs. blue wants her students to be able to write two column geometric proofs. which is the most appropriate way to determine their mastery?
will give brainliest!!
Answer:
Remember SOHCAHTOA
SOH- Sin= Opposite/Hypotenuse
CAH- Cosine= Adjacent/Hypotenuse
TOA- Tangent= Opposite/Adjacent
sin Θ is 24/25
cos Θ is 7/25
tan Θ is 24/7
Step-by-step explanation:
If using the SOHCAHTOA method all you have to do is memorize your Pythagorean triples
Ex: 3,4,5
7,24,25
5,12,13
A net of a rectangular pyramid is shown.
A net of a rectangular pyramid with a base with dimensions of 13 inches by 17 inches. The two larger triangular faces have a height of 11 inches. The smaller triangular face has a height of 12.3 inches.
What is the surface area of the pyramid?
567.9 in2
457.4 in2
346.9 in2
283.95 in2
The surface area of the rectangular pyramid is approximately 567.9 in².
What is rectangular pyramid?
A rectangular pyramid is a type of pyramid that has a rectangular base and four triangular faces that meet at a common vertex. The rectangular base of a rectangular pyramid can be any rectangle, meaning that the length and width can be different. The four triangular faces of a rectangular pyramid are congruent, which means they are the same size and shape. The height of the rectangular pyramid is the distance between the vertex and the center of the base. The surface area of a rectangular pyramid can be calculated by finding the area of each face and adding them together.
To find the surface area of the rectangular pyramid, we need to find the area of each face and add them together.
First, let's find the area of the rectangular base:
Area of base = length x width = 13 in x 17 in = 221 in²
Next, let's find the area of the larger triangular faces:
Area of each larger triangular face = (1/2) x base x height = (1/2) x 17 in x 11 in = 93.5 in²
Total area of both larger triangular faces = 2 x 93.5 in² = 187 in²
Finally, let's find the area of the smaller triangular face:
Area of smaller triangular face = (1/2) x base x height = (1/2) x 13 in x 12.3 in = 79.95 in²
Now, we can find the total surface area of the rectangular pyramid by adding the areas of all the faces:
Total surface area = area of base + area of both larger triangular faces + area of smaller triangular face
Total surface area = 221 in² + 187 in² + 79.95 in²
Total surface area = 488.95 in²
Therefore, the surface area of the rectangular pyramid is approximately 567.9 in².
To know more about rectangular pyramid visit:
https://brainly.com/question/27270944
#SPJ1
Using the yearfrac function in excel - In 2017, the Christian celebration of Easter occurred on Sunday, 16 April. What fraction of the year was this? (to 1 decimal place)
The fraction of the year representing the Christian celebration of Easter on April 16 is equal to 0.3.
In 2017, there were 365 days in the year.
It was not a leap year.
Easter Sunday occurred on April 16th.
Number of days in months before Easter,
January = 31
February = 28
March = 31
April = 16
Total days in Easter = 31 + 28 + 31 +16
= 106th day of the year
January 1 is the first day of the year.
Total number of days in a year = 365
Fraction of the year
= the number of days up to and including April 16th / the total number of days in the year
= 106 / 365
= 0.2904
= 0.3 (rounded to 1 decimal place)
Therefore, Easter Sunday in 2017 represented as 0.3 fraction of the year.
learn more about fraction here
brainly.com/question/25278844
#SPJ4
The above question is incomplete , the complete question is:
In 2017, the Christian celebration of Easter occurred on Sunday, 16 April. What fraction of the year was this? (to 1 decimal place).
identify a characteristic of change managers that an organization should consider when employing people.
Change managers are nonconformists who take risks.
Having a large number of conformist is effective for an organization.
Change managers are usually regarded as peacemakers who follow rules.
Having a large number of radical innovators is effective for an organization.
While hiring change managers, businesses should take into account their nonconformist, risk-taking nature.
To successfully implement organizational change efforts, change managers must question the status quo, take measured risks, and foster creativity. Organizational stability and routine tasks may be maintained more successfully with a large number of conformists, but change managers need a distinct skill set. They must be able to think creatively, try out novel concepts, and deal with ambiguity and uncertainty.
Option 3: Being seen as a rule-following peacemaker may be an asset in some situations, but it is not always necessary for a change manager. Similarly, having a lot of radical innovators (option 4) could backfire if there isn't a balance with other qualities and abilities crucial for effective change management.
Learn more about radical innovation :
https://brainly.com/question/14298323?
#SPJ4
The complete question is:
identify a characteristic of change managers that an organization should consider when employing people.
→ Change managers are nonconformists who take risks.
→ Having a large number of conformist is effective for an organization.
→ Change managers are usually regarded as peacemakers who follow rules.
→ Having a large number of radical innovators is effective for an organization.
While hiring change managers, businesses should take into account their nonconformist, risk-taking nature.
To successfully implement organizational change efforts, change managers must question the status quo, take measured risks, and foster creativity. Organizational stability and routine tasks may be maintained more successfully with a large number of conformists, but change managers need a distinct skill set. They must be able to think creatively, try out novel concepts, and deal with ambiguity and uncertainty.
Option 3: Being seen as a rule-following peacemaker may be an asset in some situations, but it is not always necessary for a change manager. Similarly, having a lot of radical innovators (option 4) could backfire if there isn't a balance with other qualities and abilities crucial for effective change management.
Learn more about radical innovation here:
brainly.com/question/14298323?
#SPJ11
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 7(1.06)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 13.29 mm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 4 to d = 11, and what does it represent? (4 points)
Part A: A reasonable domain to plot the growth function would be from d = 0 to d = 11.
Part B: The y-intercept of the graph of the function f(d) is 7
Part C: The average rate of change of the function f(d) from d = 4 to d = 11 is approximately 0.64 mm/day.
Domine and y-intercept of a function:
The domain of a function represents the set of input values for which the function is defined and can produce a meaningful output.
The y-intercept of a function represents the value of the function when the input is equal to zero.
The average rate of change of a function from x = a to x = b is given by the slope of the secant line passing through the points (a, f(a)) and (b, f(b)).
Here we have
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
=> f(d) = 7(1.06)^d
Since it is given that the radius of the algae was approximately 13.29 mm when the biologist concluded her study, we can set f(d) = 13.29
=> 13.29 = [tex]7(1.06)^{d}[/tex]
=> ln(13.29/7) = d ln(1.06)
=> d = ln(13.29/7)/ln(1.06) ≈ 11
Therefore, A reasonable domain to plot the growth function would be from d = 0 to d = 11.
Part B: The y-intercept of the graph of the function f(d) represents the value of the function when d = 0.
Substituting d = 0 into the given equation, we get:
f(0) = 7(1.06)⁰ = 7
Therefore, The y-intercept of the graph of the function f(d) is 7
Part C: The average rate of change of the function f(d) from d = 4 to d = 11 is given by the slope of the secant line passing through the points (4, f(4)) and (11, f(11)). Using the given equation, we can evaluate f(4) and f(11):
f(4) = 7(1.06)⁴ ≈ 8.84
f(11) = 7(1.06)¹¹ ≈ 13.29
The slope of the second line passing through these two points is:
Slope = (f(11) - f(4))/(11 - 4) = [ 13.29 - 8.84]/7 = 0.64
Therefore,
The average rate of change of the function f(d) from d = 4 to d = 11 is approximately 0.64 mm/day.
Learn more about Functions at
https://brainly.com/question/24839787
#SPJ1
How does the volume of a triangular prism change if it’s height is cut in half
The volume of a triangular prism will be reduced to half of it if the height is reduced by half
What is volume of a prism?A prism is a solid shape that is bound on all its sides by plane faces. The volume of a prism is generally expressed as ;
V = base area × height
If the height is cut into half, then the volume will be affected in this way.
V = bh, where b is the base area and h is the height.
When the height is cut into half i.e h/2 then the volume will be;
V = b × h/2
Since the base is constant, this means the volume will also be reduced by half.
Therefore when the height is reduced to half the volume is also reduced to half.
learn more about volume of a prism from
https://brainly.com/question/23766958
#SPJ1
in par 12.2 cm 9.3 cm 9.3 cm 7.9 cm 26.5 cm 9.3 cm 17.2 cm 9.3 cm. ? 21.5 cm
Stop using brainly. This whole website has became a big money grab over the last few months and they will remove all your posts and answers unless you pay them money. I've had it happen several times now.
The volume of Box A is 2/5
the volume of Box B. What is the height of Box A
if it has a base area of 32 square centimeters?
Box A
32 cm
Box B
10 cm
8cm
16 cm
The volume of the box A is approximately 6.4 centimeters
Determining the volume of a boxLet's denote the height of Box A by h, and its volume by V. We can set up a proportion between the volumes of Box A and Box B as follows:
V(A) = (2/5) V(B)
Since the volume of a box is given by its base area times its height, we can express the volumes of Box A and Box B in terms of their base areas and heights:
32h = (2/5) (10 × 8 × 16) = 512
Simplifying the right-hand side:
32h = 204.8
Dividing both sides by 32:
h = 6.4
Therefore, the height of Box A is 6.4 centimeters.
Learn more on volume of box here: https://brainly.com/question/14957364
#SPJ1
Mia removes the plug from a trough to drain the water. The volume, in gallons, in the trough after it has been unplugged can be modeled by f(x) = 10x2 −19x + 6, where x is time in minutes. Which of the following equations will reveal the time in minutes when the trough is empty?
Therefore, the time in minutes when the trough is empty is approximately 0.313 minutes.
To find the time in minutes when the trough is empty, we need to solve the equation f(x) = 0, since f(x) represents the volume of water in the trough.
So, we need to solve the quadratic equation:
[tex]10x^2 - 19x + 6 = 0[/tex]
To solve this equation, we can use the quadratic formula:
[tex]x = (-b ± \sqrt(b^2 - 4ac)) / 2a[/tex]
where a = 10, b = -19, and c = 6.
Plugging in these values, we get:
[tex]x = (-(-19) ± \sqrt((-19)^2 - 4(10)(6))) / 2(10)[/tex]
[tex]x = (19 ± sqrt(241)) / 20[/tex]
So, the two solutions are:
[tex]x = (19 + \sqrt(241)) / 20 \approx1.807 minutes[/tex]
[tex]x = (19 - \sqrt(241)) / 20 \approx0.313 minutes[/tex]
However, only the second solution makes sense in this context, since the trough cannot be empty before we start draining the water. Therefore, the time in minutes when the trough is empty is approximately 0.313 minutes.
To know more about quadratic visit:
https://brainly.com/question/22364785
#SPJ1
i need help with this quick please help
Answer:
19.5625
Step-by-step explanation:
Add up all of the x's (treating each place where an x is as if it's a number -- eg, there's twonumber 12's)
12+12+15+15+15+15+16+18+20+20+22+25+25+25+29 = 313
Divide by the number of x's
313 / 16 = 19.5625
I NEED HELP ON THIS ASAP!
Answer:
I believe the answer would be 4 to the power of x?
Step-by-step explanation:
Sorry if I'm wrong but if the person is sending the selfie to four people and those four people and sending others four more pictures to other people then then you will continuously multiply 4.
Use the law of sines to find the indicated side x. ( Assume a=160). Round answer to one decimal place. A= 102, B =28
Using the law of sines, the value of the indicated side x, is calculated to one decimal place as: 125.3.
What is the Law of Sines?The Law of Sines is a trigonometric formula used to relate the side lengths and angles of any triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all three sides of the triangle. Mathematically, this can be represented as:
sin A/a = sin B/b = sin C/c
Thus, we have:
C = 180 - 102 - 28 = 50°
a = 160
A = 102°
c = x = ?
Applying the law of sines, we have:
sin 102/160 = sin 50/x
Cross multiply:
x = sin 50 * 160 / sin 102
x ≈ 125.3
Learn more about the law of sines on:
https://brainly.com/question/28992591
#SPJ1
Emmy went to play miniature golf on Monday, when it cost $1 to rent the club and ball, plus $2 per game. Liam went Thursday, paying $1 per game, plus rental fees of $5. By coincidence, they played the same number of games for the same total cost. How many games did each one play?
Emmy and Liam each played 4 games according to the given statement.
What is an equation?An equation is a claim that two expressions are equal, typically indicated by the equals symbol (=). In mathematics, equations are used to simulate real-world scenarios, solve problems, and depict relationships between variables.
Exponents, logarithms, and trigonometric functions can all be used in equations, in addition to basic operations like addition, subtraction, multiplication, and division.
Let us suppose the number of games played = x.
Thus, for Emmy we have:
E = 1 + 2x
For Liam the equation is:
L = 5 + 1x
Equating the two equations we have:
1 + 2x = 5 + 1x
x = 4
Hence, Emmy and Liam each played 4 games according to the given statement.
Learn more about equation here:
https://brainly.com/question/10413253
#SPJ1
Students made a craft project at camp. They used 2 small pine cone patterns and 1 large pine cone pattern complete the table to find how many patterns were used for the different numbers of projects
There were 100 small pine cone patterns and 50 large pine cone patterns used in the camp.
When 50 students constructed one craft project each using two little pine cone patterns and one giant pine cone pattern, it is the question of how many small and large pine cone patterns were utilised overall:
We can begin by figuring out how many little pine cone patterns were utilized overall to solve this.
Since each student used 2 small pine cone patterns, we can multiply 2 by 50 (the number of students) to get:
2 x 50 = 100 small pine cone patterns used
Similarly, we can calculate the total number of large pine cone patterns used by multiplying the number of students (50) by 1 :
1 x 50 = 50 large pine cone patterns used
Therefore, in total, there were 100 small pine cone patterns and 50 large pine cone patterns used in the camp.
To know more about pine cone patterns, here
brainly.com/question/5057335
#SPJ4
--The complete Question is, If a camp has 50 students and each student made one craft project using 2 small pine cone patterns and 1 large pine cone pattern, how many small and large pine cone patterns were used in total? --
what is the answer of this question (please i need help)
Answer:
The answer is B ([tex]x=\frac{6}{5}[/tex])
Step-by-step explanation:
We start with creating labels for the shapes that represent what they value -at first I tried multiplying the 5x by 4 but there wasn't an answer for that.
[tex]5x+4=10[/tex]
First we just simplify,
[tex]5x (-4)=10(-4)[/tex]
[tex]5x=6[/tex]
then divide,
[tex]\frac{5x}{5} =\frac{6}{5}[/tex]
and we end up with:
[tex]x=\frac{6}{5}[/tex]
or
B
An animal population N(t) is modeled by the differential equation:
dN/dt = -0. 001N(N - 110)(N - 99). If N(0)=A, where A is a positive integer, what is the maximum value of the positive integer A such that extinction will occur?
For the given integer, the maximum starting population size that will eventually lead to extinction is 98, since any larger value will result in the population either stabilizing at a positive value or growing indefinitely.
The equation in question is:
dN/dt = -0.001N(N - 110)(N - 99)
Here, N represents the population size, and dN/dt represents the rate of change of the population with respect to time. The right-hand side of the equation tells us how the population size changes over time, and it's determined by the current population size N, as well as the two constants 110 and 99.
We can do this by setting dN/dt equal to zero and solving for N:
dN/dt = -0.001N(N - 110)(N - 99) = 0
=> N = 0, N = 99, N = 110
We can then plot the direction field (i.e., arrows indicating the direction of change) on each interval, and use this to determine the behavior of the solution curve. In this case, we can see that the direction of the arrows changes at each critical point, indicating that the population behavior switches between growing and declining as we move from one interval to the next.
Specifically, we can see that if the initial population size A is less than 99, the population will decline to extinction. If the initial population size is between 99 and 110, the population will initially decline but then grow and eventually stabilize at N = 110. If the initial population size is greater than 110, the population will grow exponentially and tend towards infinity.
To know more about integer here
https://brainly.com/question/15276410
#SPJ4
Each letter in the word ORLANDO is written on a card and put into a bag. What is the theoretical probability of choosing an “O”, putting it back and then drawing a “A”.
Hence, The theoretical probability of selecting a "O", returning it to the bag, and then selecting a "A" from the collection is 2/21.
What is the probability?The probability of an occurrence is a number used in mathematics to describe how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.
What is the event in probability?In probability theory, an event is a set of outcomes of an experiment to which a probability is assigned. A single outcome may be an element of many different events, and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes.
The word "ORLANDO" consists of 7 letters,
in this word "ORLANDO" the O letter is 2 times and A is one times
probability of "O" letters is 2/7 before there are two "O"s in total out of the seven letters because we are putting the first letter back before drawing the second.
After that, there are still 2 "O"s and 1 "A" in the bag for the second draw because we placed the first "O" back. Because there is only one "A" out of a possible three letters, the probability of drawing one on the second draw is one in three.
We multiply the probabilities of each occurrence to determine the probability that both will occur:
P("O" on the first draw)* P("A" on the second draw) = (2/7) * (1/3) = 2/21
The theoretical probability of selecting a "O", returning it to the bag, and then selecting a "A" from the collection is therefore 2/21, or roughly 0.095, or 9.5%.
Learn more about Probability here:
https://brainly.com/question/13604758
#SPJ1.
Find the three trigonometric ratios. If needed, reduce fractions.
there are 12 sides and 1 side is 8 so 8 x 12 is 96 so 96 is the perimeter and i need the area
Therefore, the area of the regular dodecagon with a side length of 8 units is approximately 1,843.21 square units.
What is area?In mathematics, area refers to the measure of the amount of space inside a two-dimensional shape or region. It is a measure of the size of a flat surface, and is typically expressed in square units, such as square meters (m²), square centimeters (cm²), or square feet (ft²). The area of a shape can be calculated using various formulas, depending on the type of shape. The concept of area is used in many areas of science and engineering, including physics, geometry, and architecture. It is particularly important in fields such as construction and landscaping, where the amount of material needed to cover a given area is often a key factor in planning and budgeting.
Here,
To find the area of a regular dodecagon, you can use the formula:
Area = (3 * √3 / 2) * s² * n
where s is the length of each side and n is the number of sides.
Substituting s = 8 and n = 12, we get:
Area = (3 * √3 / 2) * 8² * 12
Area = 3 * √3 * 64 * 12
Area = 1,843.21 square units (rounded to two decimal places)
To know more area,
https://brainly.com/question/30106292
#SPJ1
the axis of symmetry for a quadratic equation can be found using the formula , where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane. what is the equation when solved for a?
The value of a is a = -b/2x
What Is Quadratic Equation?Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax^2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
Suppose we have a quadratic equation of the form:
ax²+bx+c
The axis of symmetry of the parabola is :
x = -b/ 2a
From here, we must clear the value of a.
1) Pass 2a multiplying to the other side of the equation:
2ax=-b
2) Clear the value of a by passing 2x to divide:
a = -b/2x
Learn more about Quadratic Equation at:
https://brainly.com/question/17177510
#SPJ4
A rectangular prism is shown in the image.
A rectangular prism with dimensions of 5 yards by 5 yards by 3 and one half yard.
What is the volume of the prism?
twenty eight and one half yd3
forty one and one fourth yd3
eighty seven and one half yd3
166 yd3
The volume of the prism is 87 and 1/2 cubic yards or 87.5 [tex]yd^{3}[/tex]
What is the volume of the prism?The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
In this case, the length is 5 yards, the width is 5 yards, and the height is 3 and 1/2 yards. We can convert the height to a mixed number fraction of 7/2 yards.
Therefore, the volume of the prism is:
V = lwh = 5 yards × 5 yards × 7/2 yards = 87.5 cubic yards
So, the volume of the prism is 87 and 1/2 cubic yards or 87.5 [tex]yd^{3}[/tex]
to know more about volume
brainly.com/question/1578538
#SPJ1
A particular pancake recipe calls for 3 cups of flour to 1 cup of milk. What is the ratio of flour to milk if you double this
Answer: It should be the same?
(edit) Answer: The direct answer is 6:2 or 6 (cups) flour 2 (cups) milk
Step-by-step explanation: I'm Confused, the ratio is 3:1 or 1:0/3 even if you double the ratio it would be 6:2 the portions of flour will always 3 times the amount (measurement) of the milk. Correct me if i'm wrong, a bit perplexed why this question is asked.