Two representatives are chosen one at a time, at random, from a group of 80 students that has 40 boys and 40 girls. What is the probability that both representatives are girls
The probability of both representatives being girls is 39/158, or approximately 0.247.
To find the probability of both representatives being girls, we first need to find the probability of selecting a girl as the first representative, and then the probability of selecting another girl as the second representative, given that the first one was a girl.
The probability of selecting a girl as the first representative is 40/80, or 1/2, since there are 40 girls in the group of 80 students.
Once a girl has been chosen as the first representative, there will be 39 girls left in the group of 79 students (since one student has already been chosen), so the probability of selecting another girl as the second representative is 39/79.
To find the probability of both events occurring (selecting a girl as the first representative and then selecting another girl as the second representative), we multiply the probabilities together:
1/2 x 39/79 = 39/158
Therefore, the probability is 39/158, or approximately 0.247.
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Practical difficulties such as undercoverage and _____ in a sample survey cause additional errors.
Practical difficulties such as undercoverage and nonresponse in a sample survey cause additional errors. These errors can affect the accuracy and representativeness of the survey results.
Undercoverage refers to when certain groups or individuals in the target population are not adequately represented in the sample. This can lead to biased estimates and inaccurate conclusions. Nonresponse occurs when selected participants choose not to respond to the survey, which can introduce bias and decrease the precision of the results.
To minimize these errors, researchers can use appropriate sampling techniques, employ effective survey design, and implement strategies to increase response rates. It is important to address these practical difficulties in order to obtain reliable and valid data in a sample survey.
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Malala is following this recipe for bread rolls.
She uses 200 g of flour.
How much of each of the other ingredients does she use?
Recipe: Makes 15 bread rolls
500 g flour
10 g salt
8 g yeast
30 mL oil
350 mL water
Answer:
She will use:
4g salt
3.2g yeast
12 ml oil
140 ml water
Step-by-step explanation:
Since 200 is 40% of 500 we calculate 40% of all the other ingredients and you get your answer
Write as an algebraic expression: the difference of 27 and 5
The algebraic expression of the statement given as the difference of 27 and 5 is 27 - 5
How to write the statement as an algebraic expression?The statement is given as:
the difference of 27 and 5
Difference means minus.
The minus sign is represented as -
This means that the statement given as: the difference of 27 and 5
Can be represented as
27 minus 5
So, have
27 - 5
Hence, the algebraic expression of the statement given as the difference of 27 and 5 is 27 - 5
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helppppppppppppp i suck at math
Answer:
i suck at math to, but i know this one
Step-by-step explanation:
you go on -7 and go <-------- that way. the arrow < is pointing that way and this arrow > is pointing this way.
5. Guests are given a random goodie bag at a party. There are less than 15 bags, but more than 8. Part A: How many bags were prepared? Explain your answer. * Goodie bag contents ½ of the bags contain money ⅙ of the bags contain candy ⅓ of the bags contain a toy
Answer:
12 bagsStep-by-step explanation:
Number of the bags = between 8 and 15 and
1/2 of bags contain money 1/6 of bags contain candy 1/3 of bags contain a toyAs per above the number is divisible by 2, 3 and 6. LCM of the three numbers is 6.
The number between 8 and 15 and divisible by 6:
This number is 6*2 = 12So the number of bags is 12
HELP PLEASE
Select the correct answer.
Twenty students in Class A and 20 students in Class B were asked how many hours they took to prepare for an exam. The data sets represent
their answers.
Class A: (2, 5, 7, 6, 4, 3, 8, 7, 4, 5, 7, 6, 3, 5, 4, 2, 4, 6, 3, 5)
Class B: (3, 7, 6, 4, 3, 2, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 2, 2, 5, 6)
Answer:
B
Step-by-step explanation:
Class A: (2, 5, 7, 6, 4, 3, 8, 7, 4, 5, 7, 6, 3, 5, 4, 2, 4, 6, 3, 5)
Mean = (2 + 5 + 7 + 6 + 4 + 3 + 8 + 7 + 4 + 5 + 7 + 6 + 3 + 5 + 4 + 2 + 4 + 6 + 3 + 5)/20 = 4.8
Median: 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8
The two middle numbers are 5 and 5.
median = (5 + 5)/2 = 5
range = 8 - 2 = 6
Class B: (3, 7, 6, 4, 3, 2, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 2, 2, 5, 6)
Mean = (3 + 7 + 6 + 4 + 3 + 2 + 4 + 5 + 6 + 7 + 2 + 2 + 2 + 3 + 4 + 5 + 2 + 2 + 5 + 6)/20 = 4
Median: 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7
The two middle numbers are 4 and 4.
median = (4 + 4)/2 = 4
range = 6 - 3 = 3
Summary:
Class A: mean = 4.8; median = 5
Class B: mean = 4; median = 4
B is true.
Answer:
The answer is B
Step-by-step explanation:
edmentum
d = 10.2 ft, r = 0.5 ft/h find t
Answer:
20.4
Step-by-step explanation:
If you are using D = r × t
10.2 = 0.5(t)
10.2/0.5 = t
20.4 = t
Alandra's rectangular cake pan is 33cm by 23 cm. She has enough cake batter to fill it to a depth of 3 cm. Instead, Alandra wants to pour the batter into ice cream cones. She plans to fill each cone to a depth of 9 cm with a diameter of 4 cm. How many whole cones can Alandra fill?
Answer:
Alandra can fill 60 whole cones
Step-by-step explanation:
The volume of a rectangular prism is V = L × W × H, where
L is its lengthW is its widthH is its heightThe volume of the cone is V = \(\frac{1}{3}\) π r² h, where
r is the radius of its baseh is its height∵ Alandra's rectangular cake pan is 33 cm by 23 cm
∴ L = 33 cm and W = 23 cm
∵ She has enough cake batter to fill it to a depth of 3 cm.
∴ H = 3 cm
→ Find the volume of the batter using the 1st rule above
∵ V = 33 × 23 × 3
∴ V = 2277 cm³
∵ Alandra wants to pour the batter into ice cream cones
∵ She plans to fill each cone to a depth of 9 cm with a diameter of 4 cm
∴ h = 9 cm
∵ r = \(\frac{1}{2}\) diameter = \(\frac{1}{2}\) (4)
∴ r = 2 cm
→ Substitute them in the 2nd rule above to find the volume of each cone
∵ V = \(\frac{1}{3}\) (π) (2)² (9)
∴ V = 12π cm³
→ To find the number of cones divide the volume of the batter by
the volume of each cone
∵ Number of cones = 2277 ÷ 12π
∴ Number of cones = 60.3993
→ We will take the whole number only because we need the whole cones
∴ Alandra can fill 60 whole cones
What is Precession? Group of answer choices
Deviations in the circularity of the orbit
Changes in the rate of Earth's Spin
Changes in the magnitude of the angle of tilt
Changes in the orientation of the axis of rotation
Precession is a phenomenon that refers to the gradual and continuous change in the orientation of the Earth's rotational axis over long periods of time.
This shift in the orientation of the axis of rotation results in changes in the position of the celestial pole with respect to the stars, which causes a shift in the apparent position of stars over time. The precession of the Earth's axis is caused by the gravitational forces of the Sun, Moon, and other planets in the solar system.
Precession is characterized by changes in the magnitude of the angle of tilt, which causes changes in the rate of the Earth's spin. As the axis of rotation moves, it causes the length of the day to change over time. Additionally, deviations in the circularity of the orbit also affect the precession of the Earth's axis.
Precession is a significant phenomenon in astronomy and has been observed for thousands of years. It has important implications for studies of astronomy, geology, and climate change. For instance, precession affects the timing of the seasons and has a significant impact on the Earth's climate. It also affects the orientation of the Earth's magnetic field, which has important implications for navigation and communication systems.
In conclusion, precession is the gradual change in the orientation of the Earth's rotational axis, caused by the gravitational forces of the Sun, Moon, and other planets. It results in changes in the magnitude of the angle of tilt, changes in the rate of Earth's spin, and deviations in the circularity of the orbit. Precession has significant implications for various fields of study, including astronomy, geology, and climate change.
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Find the perimeter of the polygon Direct lines are for measurement references only and don’t affect the perimeter. If a polygon Appears to be regular you can assume it is
Recall that the perimeter of a figure is the sum of the lengths of its sides.
From the given diagram, we get that the figure has
\(12\text{ sides,}\)and each side measures 5.75 m.
Therefore, the perimeter of the figure is:
\(12*5.75m.\)Finally, we get that the perimeter is:
\(69m.\)Answer: \(69m.\)What is the answer to 2 + 2?
The answer of 2 + 2 = 4.
What is Addition?Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.
The process of doing addition is also called as finding the sum.
The given addition problem is 2 + 2.
We have to add the two numbers.
We know that addition is the method of counting the numbers.
2 + 2 means that 2 is added to 2.
When 2 is added to 2, we get 4.
Hence the answer to 2 + 2 is equal to 4.
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plz help ill give 15 points
the answer should be 90° since it is adjacent to the 90° on the other side :)
Answer:
90 degrees
Step-by-step explanation:
180-90 degrees would be 90!
I hope this helped!
Solve the system using substitution (1 point)
x + y = 8
y = 3x
(A). (4, 12)
(B). (2, 6)
(C). (1/2, 3/2)
(D). (-4, -12)
The solution to the system is x = 2 and y = 6, represented as the ordered pair (2, 6). This corresponds to option (B) in the answer choices.
To solve the system using substitution, we'll substitute the value of one variable from one equation into the other equation and solve for the remaining variable.
Given the system:
x + y = 8
y = 3x
Substituting the value of y from the second equation into the first equation, we have:
x + (3x) = 8
4x = 8
x = 2
Now, substitute the value of x into the second equation to solve for y:
y = 3(2)
y = 6
Therefore, the solution to the system is (2, 6). Option (B) is the correct answer.
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On an algebra test, I had seven times as many correct answers as
incorrect ones. There were 120 items on the test, how many did I get right?
Answer:
105 were correct
Step-by-step explanation:
120 divided by 8 = 15. 15 questions were wrong.
15 times 7 = 105.
5x-19y= 14
How do you put this is slope intercept form
In parallelogram lmno, what is the measure of angle m? 20° 60° 80° 100°
In parallelogram lmno measure of angle m m∠M = 80°
In a parallelogram, opposite sides and opposite angles are congruent to each other.
⇒ m∠N = m∠L and m∠M = m∠O ..........(1)
Also, the sum of any two consecutive angles of a parallelogram is supplementary that is 180°
⇒ m∠M + m∠L = 180° ...........(2)
Now, using equation (1)
m∠N = m∠L
⇒ 5x = 3x + 40
⇒ 5x - 3x = 40
⇒ 2x = 40
⇒ x = 20
⇒ m∠N = m∠L = 5x = 100°
Now, from equation (2)
m∠M + m∠L = 180°
⇒ m∠M + 100 = 180
⇒ m∠M = 80°
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Why are 3/4 and 8/12 NOT equivalent? Thanks!
Answer:Does this help?
Step-by-step explanation:
3/4 needs to have the same denominator as 8/12 so you can do this by multiplying the denominator by 3 and the top by 3 you get 9/12 When you convert them to percents you get , 3/4= 75% and 8/12= 66.666%
Help please due today
Answer:
68
Step-by-step explanation:
the square shape on the corner means it is a right angle, which is 90 degrees
--> that means the value which comes out when you subtract 22 from 90 is the angle left, which is "a" in this case.
90-22=68
People leaving a movie were randomly asked their age. The results are show below. What graph would best display the data, if you were only concerned about the shape and spread of the data, and not specific data? Select all that apply.
7, 37, 45, 78, 24, 97, 12, 17, 43, 56, 69, 63, 76, 23, 50, 38, 45, 57, 4
dot plot
box plot
stem-and-leaf plot
histogram
The graphs to use are box plots, histogram and dot plots
How to determine the graph?From the question, the most important factors are:
Shape of distributionSpread of dataUsing the box plots, histogram and dot plots, one would see the shape and the spread.
While the stem and leaf plot would show specific data values
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(a) (i) What conditions should be satisfied to use image averaging method for noise reduction? (ii) Using mathematical expressions, characterize the noise in the resultant image when K images are averaged, as K becomes large. (iii) Would you select spatial averaging or temporal image averaging when either method can be used for noise reduction? Explain your selection in detail.
(a)image averaging is a very effective method of reducing noise in images. Image averaging reduces noise by adding multiple images of the same scene together and then dividing by the number of images added.The conditions that must be fulfilled for the image averaging method are as follows:-
(i) The background of the image must not move between each image capture.- The noise present in the image must be random.- The source of the noise must be consistent.
(ii)The mathematical expression that characterizes the noise in the resultant image when K images are averaged, as K becomes large is given by;sigma_n^2/K
Where;sigma_n^2 is the variance of the noise and K is the number of images that have been averaged.
Therefore, as K increases, the variance of the noise in the resultant image reduces, and thus, the noise reduces.When either method can be used for noise reduction, the temporal image averaging method would be the preferred method to select.
(iii)This is because it uses a sequence of images that are taken at different times, usually at high speeds, to produce a single image that is free of noise. This method is best when dealing with fast-moving objects, and it can be used in situations where the camera cannot be stabilized and is experiencing unwanted vibration or shaking.
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you are in Hawaii walking around a circular volcano.it has a diameter of 25 miles. you got tired and only walked 1/4 of the way around how far did you walk?
Answer:
19.625 miles
Step-by-step explanation:
The diameter of the circle is 25 miles, so the circumference is 25 x pi = 78.5.
78.5 x 1/4 (0.25) = 19.625 miles
Feng wants to ride his bicycle 45.6 miles this week. He has already ridden 20 miles. If he rides for 4 more days, write and solve an equation which can be used to determine mm, the average number of miles he would have to ride each day to meet his goal.
The average number of miles he would have to ride each day to meet his goal is 6.4 miles
Writing an EquationFrom the question, we are to determine the average number of miles Feng would have to ride each day to meet his goal
Let x represent the average number of miles he would have to ride each day to meet his goal
From, the given information,
"Feng wants to ride his bicycle 45.6 miles this week"
and
"He has already ridden 20 miles"
Then,
The equation that represents the average number of miles he would to ride for 4 more days is
x = (45.6 - 20)/4
x = 25.6/4
x = 6.4 miles
Hence, the average number of miles he would have to ride each day to meet his goal is 6.4 miles
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What is the solution of the system?
prove that
tan x / (1 +secx) + (1+secx)/tanx = 2 csc x
The trigonometric expression \(\left(\dfrac{tan( x)}{1+sec( x)} +\dfrac{1+sec( x)}{tan( x)}\right)\) can be simplified to prove that it equals 2·csc(x), by plugging in \(\left(tan(x) = \dfrac{sin(x)}{cos(x)}\right)\),
\(\left(sec(x) = \dfrac{1}{cos(x)}\right)\) and \(\left(csc(x) = \dfrac{1}{sin(x)}\right)\) to give the following
trigonometric identity;
\(\dfrac{tan( x)}{1+sec( x)} +\dfrac{1+sec( x)}{tan( x)} = 2\cdot csc(x)\)What are trigonometric identities?Trigonometric identities are equations of trig functions which are valid for all values of the input variable at which the expressions on both sides of the equality are defined.
The trigonometric expression in the question is simplified as follows;
\(\dfrac{tan( x)}{1+sec( x)} +\dfrac{1+sec( x)}{tan( x)} = \dfrac{tan( x)}{1+\dfrac{1}{cos(x)} } +\dfrac{1+\dfrac{1}{cos(x)}}{tan( x)}\)
\(\dfrac{tan( x)}{1+\dfrac{1}{cos(x)} } +\dfrac{1+\dfrac{1}{cos(x)}}{tan( x)} = \dfrac{cos(x)\times tan( x)}{cos(x)+1} } +\dfrac{cos(x)+1}{cos(x)\times tan( x)}}\)
\(\dfrac{cos(x)\times tan( x)}{cos(x)+1} } +\dfrac{cos(x)+1}{cos(x)\times tan( x)}} = \dfrac{sin(x)}{cos(x)+1} } +\dfrac{cos(x)+1}{sin( x)}}\)
\(\dfrac{sin(x)}{cos(x)+1} } +\dfrac{cos(x)+1}{sin( x)}} = \dfrac{sin^2(x)+(cos(x)+1)^2}{sin( x)\cdot (cos(x)+1)} }\)
\(\dfrac{sin^2(x)+(cos(x)+1)^2}{sin( x)\cdot (cos(x)+1)} }=\dfrac{sin^2(x)+cos^2(x)+2\cdot cos(x)+1}{sin( x)\cdot (cos(x)+1)}\)
\(\dfrac{2\cdot cos(x)+2}{sin( x)\cdot (cos(x)+1)} =\dfrac{2\cdot (cos(x)+1)}{sin( x)\cdot (cos(x)+1)} = \dfrac{2}{sin( x)}\)
\(\dfrac{2}{sin( x)} = 2\cdot csc(x)\)
\(\therefore \dfrac{tan( x)}{1+sec( x)} +\dfrac{1+sec( x)}{tan( x)} =2\cdot csc(x)\)
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PLEASE HELP ME! I will mark you as BRAINLIEST if you answer this correctly.
Answer:
0.92
Step-by-step explanation:
Each year, the value declines. This eliminates choices A and D.
The decline from 33000 to 30360 is slightly less than 10%, so the multiplier from one year to the next is slightly more than 1 -10% = 90%. The only choice in range is ...
0.92 . . . . the third listed choice
What is the solution to this system of linear equations?
y − x = 6
y + x = −10
a. (−2, −8)
b. (−8, −2)
c. (6, −10)
d. (−10, 6)
Answer:
B: (-8,-2)
you add the equation to solve the first variable, then plug in the values to the other equation to find the last variable
good Luck!!!
jared has a wooden board 11 ft long. he wants to cut it into two pieces so that the longer piece is 4 ft less than 4 times the length of the shorter piece. how long will each piece of board be? enter your answers in the boxes.
On solving we got that. he shorter pieces will therefore be 3 feet long and the longer pieces will therefore be 8 feet long.
What is equation?Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.
The lengths of the shorter and longer pieces of a board should be determined.
the case
Let's say that the shorter parts are x in length.
as stated
Jared has an 11-foot wooden board with him.
In order for the longer piece to be 4 feet less than 4 times as long as the shorter piece, he wants to cut it into two pieces.
The length of the longer pieces is then equal to 4x - 4.
The equation then becomes
\(x + 4x - 4 = 11\\ 5x = 11 + 4\\ 5x = 15\\ x = 3 ft\)
The shorter pieces will therefore be 3 feet long.
The longer pieces' length -
\(4x - 4\\ = 4 X 3 - 4\\ = 12 - 4\\ = 8 ft\)
The longer pieces will therefore be 8 feet long.
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It is known that 2x-3/x = x + 1 What is the value of x^2 -x + 3
The value of the equation x² - x + 3 is 37/9.
We have,
We can start by multiplying both sides of the equation by x:
2x - 3/x = x + 1
2x - 3 = x^2 + x
Rearranging and simplifying, we get:
x^2 - x + 3 = (2x - 3) + x^2
x^2 - x + 3 = x^2 + 2x - 3
-x + 3 = 2x - 3
5 = 3x
x = 5/3
Now we can substitute x into the equation x^2 - x + 3:
x^2 - x + 3 = (5/3)^2 - 5/3 + 3
x^2 - x + 3 = 25/9 - 15/9 + 27/9
x^2 - x + 3 = 37/9
Therefore,
The value of x² - x + 3 is 37/9.
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The chance of having either a boy or a girl is 50%. What is the probability of the Smiths having two girls?
pls help asap :)
Based on the fact that the chance of having a boy or a girl is 50%, the probability of the Smiths having two girls is 25%.
What is the probability of having two girls?When you are faced with two independent events happening one after the other, the way to find their probability is:
= Probability of first event x Probability of second event
The probability of the Smiths getting two girls is therefore:
= 50% x 50%
= 25%
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