Answer:
3 different committees
Step-by-step explanation:
after 3 committees are formed there will be one extra boy however without any more girls another committee cannot be formed.hope this helps!!!
Number of committees of 3 boys and 4 girls formed from the group of 10 boys and 12 girls = 59400
What is combination?The combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” The combination means “Selection of things”, where the order of things has no importance.
Number of combinations of taking x items out of total n items
ⁿCₓ = n!/x!(n-x)!
Given,
Number of girls in group = 12
Number of boys in group = 10
Selecting 3 boys from the group
= ¹⁰C₃
= ¹⁰C₃
= 10!/3!(10 - 3)!
= 10!/3!×7!
= (10 × 9 × 8 × 7!)/(3 × 2 × 1 × 7!)
= 10 × 3 × 4
= 120
Selecting 4 girls from group
= ¹²C₄
= 12!/4!(12 - 4)!
= 12!/4!×8!
= (12 × 11 × 10 × 9 × 8!)/(4 × 3 × 2 × 1 × 8!)
= 3 × 11 × 5 × 3
= 495
Total number of committees of 3 boys and 4 girls formed from the group
= ¹⁰C₃ × ¹²C₄
= 120 × 495
= 59400
Hence, 59400 different committees can be formed from the group.
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All of the scatter plots below display the data correctly, but which one of them displays the data best? By convention, a good scatter plot uses a reasonable scale on both axes and puts the explanatory variable on the xxx-axis.
To determine which scatter plot displays data most effectively, it is crucial to ensure that the explanatory variable is positioned on the x-axis and that the plot uses a scale that makes it easy to identify trends without obscuring data points. The best scatter plot will clearly demonstrate the relationship between two variables and indicate potential patterns that may suggest a correlation or relationship worthy of linear regression analysis.
Explanation:The question revolves around determining which scatter plot displays data most effectively, adhering to the guidelines of using a reasonable scale on both axes and positioning the explanatory variable on the x-axis. An essential aspect of a scatter plot is that it should clearly indicate the relationship between two variables, allowing for pattern identification and assessment of potential for linear regression.
By convention, data visualization practices dictate that the x-axis should represent the independent variable (explanatory variable), which is the variable that is presumed to cause changes in another variable. The y-axis should depict the dependent variable, whose changes are investigated to be a result or effect of the independent variable. A good scatter plot employs a scale that accurately encompasses all data points without distorting the visual perception of their distribution, making it easier for viewers to identify trends, clusters, or patterns that might suggest a correlation or relationship worthy of linear regression analysis.
In selecting the best scatter plot, one must also consider the clarity of the plot in demonstrating data distribution and potential correlations. The plot must be fine-tuned to avoid too large or too small scales, which can obscure data trends or require unnecessarily large graphical space. Additionally, attention should be paid to ensuring the number of significant figures on the axis values does not exceed those in the measurements. The ideal scatter plot employs a scale and plotting strategy that maximizes visualization efficiency, facilitating easy analysis and interpretation of the data's underlying patterns.
Graph A has explantory variable on x axis and response variable on y- axis also their scale is reasonable here.
How to determine the x and y axes of scatter diagram.
Scatter diagram: graph showing data points in 2D, revealing relationships between variables; useful for identifying patterns and correlations.
Here, Age act as explanatory variable and internets use as response variable ,because how much time they spend on internet it directly dependent on their age .
for a good scatter plot, the variable that might be considered an explanatory variable is plotted on the x axis, and the response variable is plotted on the y axis and scale should be reasonable .
Graph A has explanatory variable on x axis and response variable on y- axis also their scale is reasonable here.
Complete question
Nate wants to predict how long people use the internet each day based on their age. The table below shows the age (in years) and average daily internet usage (in hours) for a sample of people.
All of the scatter plots below display the data correctly, but which one of them displays the data best?
By convention, a good scatter plot uses a reasonable scale on both axes and puts the explanatory variable on the xxx-axis.
Please help me now plz
I will mark you brainliest
Answer:
theta = 24.4 degrees
Step-by-step explanation:
This is a right triangle.
sin theta = opp/ hyp
sin theta = 33/80
Take the inverse of each side
sin^-1 sin(theta) = sin^-1 (33/80)
theta =24.36197794
To the nearest tenth
theta = 24.4 degrees
When April made tortillas for the first time, she used all the dough to make 10 tortillas. After making quesadillas, she decided that the tortillas were not large enough. The next time, using the same amount of dough, she made each tortillas the same thickness for 25% larger. How many tortillas did April make the second time? If the area of each tortilla in the second batch is 201 in2, what was the area of each tortilla in the first batch?
Answer:
Second time: 8 tortillas
Area of tortillas in the first batch: 160.8 in2
Step-by-step explanation:
Let's say that the amount of dough to make a tortilla is x.
So, in the first time, the amount of dough used is 10 * x = 10x
Then, she made the tortillas 25% larger, so the amount of dough used for each tortilla now is 1.25x
So, using the same amount of dough (10x), the amount of tortillas she can make is:
10x / 1.25x = 8 tortillas
If the area of the larger tortilla is 201 in2, and this tortilla is 25% larger than the ones in the first batch, to find the area of the inicial tortillas we just need to divide this new area by 1.25:
Area of first tortillas = 201 / 1.25 = 160.8 in2
Help ASAP
Zero product property
1. 100-x²=0
2. 3x²-75=0
3. 0=2x²+20x+50
4. 2x²-5x-12=0
Answer:
1. x=10,-10
2. x = 5
x = -5
3. x=-5
4. x ∈ {4,- 3/2}
Step-by-step explanation:
Two parallel lines are cut by a transversal and angles 1 and 7 are alternate exterior angles. If angle 1 measures 120 degrees , how does angle 7 compare with angle 1?
A.Angle 7 is supplementary with angle 1
B.Angle 7 and angle 1 are congruent.
C.The angles cannot be compared.
Answer: B.Angle 7 and angle 1 are congruent.
Step-by-step explanation:
Alternate angles means that the angles are formed on the alternating sides of the transversal. The term "exterior" means that the alternate angles are formed outside the parallel lines.
Since the parallel lines are cut by a transversal and angles 1 and 7 are alternate exterior angles, it means that angles 1 and 7 are equal or congruent. This is because of the rule in geometry stating that two alternate exterior angles are congruent. Therefore, the correct option would be
B. Angle 7 and angle 1 are congruent.
Answer: The correct option is B; Angle 7 and angle 1 are congruent
Step-by-step explanation: Please refer to the picture attached for more details. The parallel lines AB and CD have been drawn and a transversal line have also been drawn to cut both lines as shown in the picture.
Since both lines are parallel, the angles formed by the transversal would be equal.
A careful observation would show that the interior angle formed by the transversal (which is the supplement of angle 120), is equal or congruent to the interior angle formed at angle 7. These are commonly referred to as "z angles" by virtue of the shape formed. Angle 1 and angle 7 are the exterior alternate angles formed by the transversal and they are both congruent, that is, they both have the same measurement.
The angles cannot be described as supplementary, because supplementary angles add up to 180 degrees. That is, if angle A plus angle B equals 180, then angles A and B are both supplementary. This does not apply to angle 1 and angle 7.
of the 800 participants in a marathon 120 are running to raise money for a cause. How many participants out of 100 are running for a cause
Answer:
divide 120 by 800 should give you the answer 15/100
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
i-ready okurrr
The radius of a circle is 15 inches.
Enter the area of the circle, in square inches. Round your answer to the nearest tenth and use 3.14 for pi.
______ square inches
Answer:
706.5
it's saying i need to fill in twenty characters to answer
so here is my twenty characters
Answer:
[tex]706.5 {in}^{2} [/tex]
Step-by-step explanation:
[tex]area \\ = \pi {r}^{2} \\ = 3.14 \times 15 \times 15 \\ = 706.5 {in}^{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
What kind of salad do snowmen eat? Punchline 73 answer key
Answer:
Coldslaw
Step-by-step explanation:
The Haskins family spends $600 per month on groceries for their family. If this is 15% of their monthly budget, , then what is their monthly budget?
Hi
15/100 = 600 / X
X = 600 *100 /15 = 4000
monthly budget =4000
Answer:
Their monthly budget is $600
How does the coefficient of a affect the way the parabola opens?
Triangles A and B are right angled.
a) show that the two shorter sides in triangle A have the same length as the two shorter sides in triangle B.
b) explain why the two triangles are congruent.
Answer:
13²-12²
169-144
=25
√25
=5
The 2 shortest sides are 5cm and 12cm
Let the sides of the triangles be a, b and c. According to Pythagoras theorem;
[tex]c^2=a^2+b^2[/tex] where:
a is the hypotenuse (longest side)
For triangle A:
c = 13
b = 12
Get "a"
[tex]13^2=12^2+b^2\\169=144+b^2\\b^2=169-144\\b^2=25\\b=5cm[/tex]
Similarly for triangle B:
[tex]c^2=5^2+12^2\\c^2=25+144\\c^2=169\\c^2=\sqrt{169} \\b=13cm[/tex]
We can see that the two shorter sides have the same length which is 5cm
Since all the sides of the triangle are the same, hence the two triangles are congruent.
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Simplify 9 to the power of 2 over 9 to the power of 7 someone help please
1. 9 over 5
2. 1 over 9 to the power of 9
3. 1 over 9 to the power of negative 5
4. 1 over the 9 to the power of 5
Answer:
4. 1 over the 9 to the power of 5
Step-by-step explanation:
When you divide exponents with the same bases, you essentially subtract the exponents. So 9^2 / 9^7 = 9^-5. To change to a positive exponent, take the reciprocal. 9^-5 = 1 / 9^5
Find the area of a regular octagon (8 sides) that has an apothem of 12.1 meters and a side length of 10 meters.
Encuentra el área de un octágono regular (8 lados) que tiene una apotema de 12.1 metros y una longitud lateral
de 10 metros.
0
m2
1
2
3
0 1
0
4.
5
6
+
7
8
-
a lo
0
.
A baker purchases flour each week from a wholesale warehouse. The chart shows the quantities and prices available this week. If the best deal last week for flour was $1.60 per pound. What is the difference between the unit price for last week's best deal and this week's best deal?
The chart showing the quantities and prices is;
Best Deal 1
Quantity of Flour Price
3 pounds $5.25
5 pounds $9.75
7 pounds $12.60
10 pounds $14.20
12 pounds $18.24
Answer:
difference between last weeks best deal = $0.3
Step-by-step explanation:
Let's calculate the unit price for each of the quantities in the chart.
For quantity of 3 pounds;
We have; unit price = 5.25/3 = $1.75
For 5 pounds;. Unit price = 9.75/5 = $1.95
For 7 pounds; unit price = 12.6/7 = $1.8
For 10 pounds; unit price = 14.2/10 = $1.42
For 12 pounds; unit price = 18.24/14 = $1.3
Thus, last weeks best deal is the lowest = $1.3
Thus; difference between last weeks best deal is given as;
= this weeks best deal - last weeks best deal
This gives;
$1.6 - $1.3 = $0.3
Answer:
0.18
Step-by-step explanation:
Eric put several CD's in a case. Four CDs are country, six are rap and ten are pop. If Eric picks one CD from the case without looking, what is the probability that he will pick a country CD?
Probability that Eric will pick a country CD is 0.2.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given that,
Number of CD's which are country = 4
Number of CD's which are rap = 6
Number of CD's which are pop = 10
Total number of CD's = 4 + 6 + 10 = 20
Probability = Number of likely outcomes / Total number of outcomes3
Probability of getting country CD = 4 / 20
= 1/5
= 0.2
Hence the required probability is 0.2.
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Randy has 4 pennies , 3 nickels , and 3 dimes in his pocket if he randomly chooses 2 coins without replacement what is the probility they are both dimes.
[tex]3 \div 10 \times 2 \div 9 = 1 \div 15[/tex]
the probability of drawing one dime is 3/10. if you don't replace the coin, there are only 9 left, 2 of which are dimes. so multiple the to probabilities and there you have it
Answer:
0.09
Step-by-step explanation:
A sphere has radius of 3 cm. What is the volume of the sphere?
Answer: 113.04 cm³
Step-by-step explanation: To find the volume of a sphere, start with the formula for the volume of a sphere which is shown below.
[tex]V = \frac{4}{3} \pi r^{3}[/tex]
Here, we are given that our sphere has a radius of 3 centimeters.
So plugging into the formula, we have [tex](\frac{4}{3})(\pi)(3 cm)^{3}[/tex].
Start by simplifying the exponent.
(3 cm)³ is equal to 3 centimeters · 3 centimeters ·
3 centimeters or 27 cm³.
So we have [tex](\frac{4}{3})(27 cm^{3})(\pi)[/tex].
Notice that we can cross-cancel 3 and 27 to 1 and 9.
So we have (4)(9 cm³) which is equal to 36 cm³.
So we have 36π cm³.
So the volume of the sphere is 36π cm³.
Remember that π is approximately equal to 22/7 or 3.14 so we can estimate the value of the volume by plugging in 3.14 for π.
So we have (36)(3.14) which is equal to 113.04 which means
that the volume of approximately equal to 113.04 cm³.
Which graph represents this equation?
Y=3/2x^2-6x
The parabola is passing through (0, 0) and (9, 0). Then the correct option is C.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
The equation of the parabola is given below.
y = (3/2)x² - 6x
Then the factor of the equation will be
y = 3x (x / 2 - 3)
Then the zeroes of the function will be
y = 0
x = 0, 9
Then the correct option is C.
The graph is given below.
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Suppose a parabola has vertex (–8, –7) and also passes through the point (–7, –4). Write the equation of the parabola in vertex form.
A bag contains 666 red jelly beans, 444 green jelly beans, and 444 blue jelly beans. If we choose a jelly bean, then another jelly bean without putting the first one back in the bag, what is the probability that the first jelly bean will be green and the second will be red?
Answer:
12/91
Step-by-step explanation:
The question is not properly formatted, here is how it should be formatted.
A bag contains 6red jelly beans, 4 green jelly beans, and 4 blue jelly beans. If we choose a jelly bean, then another jelly bean without putting the first one back in the bag, what is the probability that the first jelly bean will be green and the second will be red
Step one
This is selection without replacement.
Sample space
6red jelly beans,
4 green jelly beans, and
4 blue jelly beans.
S= 6+4+4= 14
Probability that the first jelly bean will be green = 4/14= 2/7
Without replacement, Probability that the second jelly bean will be red = 6/13
Hence for the two selections the probability is= 2/7*6/13= 12/91
URGENT!!!!! Mai conducted an experiment by flipping a fair coin 200 times. The coin landed heads up 110 times. Which statement about the coin landing heads up in Mai’s experiment is correct.
A. The experimental probability of the coin landing heads up is One-half and the theoretical probability of the coin landing heads up is StartFraction 11 over 20 EndFraction.
B. The experimental probability of the coin landing heads up is StartFraction 11 over 20 EndFraction and the theoretical probability of the coin landing heads up is One-half.
C. The experimental probability of the coin landing heads up is StartFraction 11 over 20 EndFraction and the theoretical probability of the coin landing heads up is StartFraction 11 over 20 EndFraction.
D. The experimental probability of the coin landing heads up is One-half and the theoretical probability of the coin landing heads up is One-half.
Answer:
B
Step-by-step explanation:
the statement is correct
Answer:
b
Step-by-step explanation:
mia wants to earn 2500 in her job at a bycicle store she is paid 55 for every bycicle she tunes up the minimum number of bycicles mia needs to tune up to reach her goal of 2500
Mia needs to tune up at least 46 bicycles at $55 each to reach her goal of $2500, as she cannot tune up a fraction of a bicycle.
To calculate the minimum number of bicycles Mia needs to tune up to reach her goal of $2500, we must divide her goal amount by the amount she earns per bicycle. Thus, the calculation is as follows:
Number of bicycles = Total goal amount / Earnings per bicycle
Number of bicycles = $2500 / $55
When we divide 2500 by 55, we get approximately 45.4545. Since Mia cannot tune up a fraction of a bicycle, she will need to tune up a whole number of bicycles. Therefore, she needs to tune up at least 46 bicycles to reach or exceed her goal of $2500.
Karen is on a game show. She will choose a box to see if she wins a prize. The odds in favor of Karen winning a prize are 5/7. Find the probability of Karen winning a prize
Answer:
0.71
Step-by-step explanation:
P(Karen wins a prize) = 5/7 = 0.71
tan(pi/2) =
A)1
B) -1
C)0
D) Undefined
Answer:
D) Undefined
Step-by-step explanation:
[tex] \tan \: \bigg( \frac{\pi}{2} \bigg) = \infty \: or \: undefined\\ [/tex]
5: Un músico golpea un tambor una vez cada 24 segundos exactamente, mientras que otro lo hace cada 14 segundos. Suponiendo que acaban de golpear ambos a la vez, ¿cuándo volverán a coincidir?
Answer:
168 seconds
Step-by-step explanation:
To find out when they coincide again, the least common multiple between both numbers must be calculated:
24 14 | 2
12 7 | 2
6 7 | 2
3 7 | 3
1 7 | 7
1 1
Therefore the least common multiple is:
2 * 2 * 2 * 3 * 7 = 168
This means that they will coincide again at 168 seconds, when the first musician has struck 7 times (168/24) and the other 12 times (168/14)
5. (8 pts) Compute the derivative of h(x) = x^3+x^2/e^3x
and simplify your answer.
Answer:
h'(x) = (-3x^3 +2x)/e^(3x)
Step-by-step explanation:
The formula for the derivative of a quotient is ...
(u/v)' = (vu' -uv')/v²
Using u = (x^3 +x^2) and v = e^(3x), this becomes ...
h'(x) = (e^(3x)(3x^2 +2x) -(x^3 +x^2)(3)(e^(3x))/e^(6x)
h'(x) = (-3x^3 +2x)/e^(3x)
I really need help. I need to get this done by the end of this week otherwise i will fail the class. PLEASE HELP ME!! THANK YOU!!
x=7th root of 30=1.6256
Justification=a process that is both individual and social undetermined in developing
And you have to subtract in the math
Answer:
1. Subtraction property of equality; multiplication property of equality; division property of equality
For this question, you simply have to state the operation that is occurring.
2. To solve this, simplify the equation so that it is in y=mx+b form. From the equation, find two points so that you can plot a line.
4x + y = 6x - 1
y = 2x - 1
-1 is the y-intercept. This means that you can place a point at (0,-1) which is the -1 on the y (vertical) axis.
For the second point, you can plug any number for the x-value that will stay within the given graph. I am going to use 2.
y = 2(2) - 1
y = 4 - 1
y = 3
This gives you the point (2, 3). Plot the points (0, -1) and (2, 3). You will be able to draw a line from that.
3.(a) 1200 represents the population of bacteria at the beginning, or when t is equal to 0.
(b) 1.8 represents the factor by which the bacteria increases each hour.
(c) 1000 represents the beginning population. The difference means that the total amount of bacteria will increase more slowly than the population that began with 1200.
The circumference of a circle is 7.7mm.
Find the length of the diameter.
Give your answer rounded to 3 SF.
PLZ HELP!!!!!!
Answer:
D = 2.45 mm
Step-by-step explanation:
D = C ÷ π
D = 7.7 ÷ 3.14
D = 2.4509
D = 2.45 mm
To find the length of the diameter of a circle when the circumference is given, divide the circumference by π.
Explanation:To find the diameter of a circle when only the circumference is given, divide the circumference by π (approximately 3.1416). The formula to find the diameter is:
Diameter = Circumference / π
In this case, the circumference is 7.7mm. So, the diameter would be:
Diameter = 7.7mm / 3.1416 ≈ 2.448mm
Therefore, the length of the diameter, rounded to 3 significant figures, is approximately 2.45mm.
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Please I need help ASAP!!
Answer:
I think 3%
Step-by-step explanation:
Hope this helps:)
Answer:
33.3%
Step-by-step explanation:
I had answered another question first. This is the answer for this problem. Sorry!
hope this helps :)
An airline finds that 6% of the people who make reservations on a certain flight do not show up for the flight. If the airline sells 190 tickets for a flight with only 185 seats, use the normal approximation to the binomial distribution to find the probability that a seat will be available for every person holding a reservation and planning to fly. (Round your answer to four decimal places.)
Answer:
0.9826 = 98.26% probability that a seat will be available for every person holding a reservation and planning to fly.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
6% of the people who make reservations on a certain flight do not show up for the flight. So 100-6 = 94% show up, which means that [tex]p = 0.94[/tex]
190 tickets, so [tex]n = 190[/tex]
So
[tex]\mu = E(X) = np = 190*0.94 = 178.6[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{190*0.94*0.06} = 3.27[/tex]
Find the probability that a seat will be available for every person holding a reservation and planning to fly.
At most 185 people show up.
Using continuity correction, we have to find [tex]P(X \leq 185 + 0.5) = P(X \leq 185.5)[/tex], which is the pvalue of Z when X = 185.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{185.5 - 178.6}{3.27}[/tex]
[tex]Z = 2.11[/tex]
[tex]Z = 2.11[/tex] has a pvalue of 0.9826
0.9826 = 98.26% probability that a seat will be available for every person holding a reservation and planning to fly.