We need 9 sophomore girls to make sex and class independent when a student is selected at random.
No. of freshman boys (fb) = 4
No. of freshman girls (fg) = 6
No. of sophomore boys (sb) = 6
Let, the no. of sophomore girls = sg
The total number of students in the class T = fb + fg + sb +sg
T = 4+6+6+sg
T = 16 + sg
The probability of selecting a girl is P(G) = (fg + sg) / T
= (6+sg)/(16+sg)
The probability of selecting a sophomore is P(S) = (sb + sg)/T
= (6+sg)/(16+sg)
As the events are independent, the probability of selecting a sophomore girl is P(sg) = P(G)*P(S)
sg/(16+sg) = (6+sg)*(6+sg)/(16+sg)(16+sg)
sg(16+sg) = (6+sg)(6+sg)
16sg + [tex]sg^{2}[/tex] = 36 + 6sg + 6sg + [tex]sg^{2}[/tex]
4sg = 36
sg = 9
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double d, then subtract 6 from the result
Do not simplify any part of the expression.
Answer:
2d-6
Step-by-step explanation:
Since the d is doubled you are multipling then subtracting 6 from the result
Zainab runs her own business where she leads guided day-long tours for small groups of tourists
in her city. Each tour has a maximum of 3 guests. Let X represent the number of customers
Zainab gets on a randomly chosen day. Based on previous data, here is the probability
distribution of X along with summary statistics:
X = # of customers
P(X)
Hy =
What are the mean and standard deviation of Y?
σy ≈
1
0.20 0.10
It costs Zainab $5 each day to pay for her own transportation to her business, and then each
customer she gets pays her $60. Let Y represent Zainab's net gain on a randomly chosen day.
dollars
dollars
2
0.40
Mean:
Standard deviation:
3
0.30
4x = 1.8
x 1.08
The mean of Y is 103 dollars. The standard deviation of X is 64.8 dollars
How to solve for the mean and the standard deviationThe mathematical expression that we would have to use i the representation of Y is Y = 60X - 5.
How to solve for the mean of Y
Y = exp(Y)
= 60 * EXP(X) - 5
the expected value of x is 1.8
= 60 * 1.8 - 5
= 103 dollars
then we have to solve for the standard deviation of Y
standard deviation of x = 1.08
= 60 * 1.08
= 64.8 dollars
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A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students. Ice Cream Candy Cake Pie Cookies 81 9 72 36 27 Which statement is the best prediction about the slices of pie the college will need? The college will have about 480 students who prefer pie. The college will have about 640 students who prefer pie. The college will have about 1,280 students who prefer pie. The college will have about 1,440 students who prefer pie.
The college will have about 640 students who prefer pie. We can calculate percentages based on the student sampling of 225 students (assuming it was a completely random sample, and not one taken just from a specific group, such as football players at half-time).
What is random sample?
A simple random sample is a subset of a statistical population where each member has an equal chance of being selected. Unbiased representation of a group is what a straightforward random sample is supposed to be.The researcher uses simple random sampling, a type of probability sampling, to randomly select a subset of individuals from a community. Every member of the population has the same chance of being selected.A random experiment has a result known as a sample. One particular value is chosen at random from a pool of potential values when we sample a random variable.A sample is that specific value. The probability distribution of the random variable specifies the possible values and their probabilities.To make a prediction, we need to assume that the preferences of the 225 students surveyed are representative of the entire student population of 4,000. We can use the proportion of students who prefer pie in the sample to make an estimate.
The proportion of students who prefer pie in the sample is:
36/225 = 0.16
We can use this proportion to estimate the number of students who prefer pie in the entire population:
4,000 x 0.16 = 640
Therefore, the best prediction about the slices of pie the college will need is that the college will have about 640 students who prefer pie. So the option "The college will have about 640 students who prefer pie" is the correct statement.
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Using the omission strategy, what value would be placed in the missing observation in x1?
x1x2
76
22
82
91
32
41
88
Options:
84
No value because excluded
83
90
The values in the missing observation are:
X1 X2
76 22
82 25
91 32
101 41
88 28
What is an expression?An expression contains terms with addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
x1 x2
76 22
82 __
91 32
__ 41
88 28
The difference between each row are:
76 - 22 = 54
82 - 25 = 57
91 - 32 = 59
101 - 41 = 60
88 - 28 = 60
We see that,
57 - 54 = 3
59 - 57 = 2
60 - 59 = 1
60 - 60 = 0
So,
The difference between the numbers is consecutive as 3, 2, 1, 0.
Thus,
The missing values of X1 and X2 are 101 and 25.
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Find the area of an isosceles triangle whose one side is 10 cm greater than each of its equal sides and perimeter is 100 cm.
Answer:
the area of the isosceles triangle is approximately 104.49 cm^2.
Step-by-step explanation:
The perimeter of the triangle is 100 cm, so we can write an equation using the lengths of the sides:
x + x + (x + 10) = 100
3x + 10 = 100
3x = 90
x = 30
So the equal sides of the triangle have length 30 cm and the side that is 10 cm greater has length 40 cm.
To find the area of the triangle, we can use the formula for the area of an equilateral triangle:
Area = (sqrt(3) / 4) * (side length)^2
Area = (sqrt(3) / 4) * 30^2
Area = (sqrt(3) / 4) * 900
Area = (sqrt(3) / 4) * 30 * 30
Area = (sqrt(3) / 4) * 900
Area = (30 * sqrt(3)) / 2
Area = 45 sqrt(3)
a card is drawn from a standard deck of 52 playing cards. what is the probability that the card will be a diamond or a seven? express your answer as a fraction or a decimal number rounded to four decimal places.
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
Total cards = 52
Total diamond cards = 13
So, probability of getting a card of diamond,
P(diamond) = 13/52 = 1/4
Now,
Total cards with number seven = 4
So, probability of getting a seven,
P(seven) = 4/52 = 1/13
Hope it helps~
A line is drawn tangent to a circle of radius 8 with the origin as its center, passing through the paint (12,0). Find the point where the line touches the circle. NOTE: the tangent line will be perpendicular to the radical line from the origin to the tangent point. Use the relation between the slopes to find the point
The radius line intersects the circle at (4, 8) because the tangent line's slope, which is -1/3, is perpendicular to the radius line's slope of (0, 8), which is 0.
1. Use m = 0 to calculate the slope of the line through point (12, 0).
2. Calculate the radical line's angle between the origin and the tangent point: m = ∞
3. To determine the location where the line touches the circle, use the relationship between the slopes: M2 = -1/M1 = -1/0 = - since M1 M2 = -1
4. To determine a point's coordinates, use the equation for a circle: (x - 8)2 + (y - 8)2 = 82, so (4, 8) (4, 8)
We can use the relationship between the slopes of the tangent line and the radical line from the origin to the tangent point to determine the location where the line contacts the circle. Since the tangent line crosses through point (12,0), its slope is equal to zero. Since the radical line slopes at m2 =, m1 m2 = -1. Accordingly, m2 = -1/m1 = -1/0 = -∞.The coordinates of the spot where the line touches the circle can then be determined using the equation for a circle. (x - 8)2 + (y - 8)2 = 82 is the equation for a circle having the origin as its center and a radius of 8. The coordinates of the place where the line intersects the circle are (4, 8), which can be obtained by substituting in the values for m1 and m2.
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A quadrilateral has two angles that measure 100° and 90°. The other two angles are in a ratio of 7:10. What are the measures of those two angles?
The measures of angles C and D are 70° and 100°, respectively.
Understanding angles is a fundamental concept in geometry. A quadrilateral is a polygon with four sides, and its angles are essential to determining its properties.
Let's start by labeling the angles in the quadrilateral. We know that two angles measure 100° and 90°, so let's label them as A and B, respectively. The other two angles, which we are trying to find, can be labeled as C and D.
Now, we are given that the ratio of angles C and D is 7:10. This means that we can write the following equation:
C/D = 7/10
We can use this equation to solve for one of the angles. Let's choose angle C. We can rewrite the equation as:
C = (7/10)D
We also know that the sum of the angles in a quadrilateral is 360°. Therefore, we can write another equation:
A + B + C + D = 360°
We can substitute the values we know into this equation and solve for angle D:
100° + 90° + (7/10)D + D = 360°
Simplifying the equation:
(17/10)D = 170°
D = 100°
Now that we know the value of angle D, we can use the equation we derived earlier to find the value of angle C:
C = (7/10)D = (7/10) x 100° = 70°
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The stemplot shows the years of experience for several teachers at Sycamore High School.
A stemplot titled Teaching Experience. The values are 2, 4, 5, 5, 5, 7, 9, 10, 12, 14, 15, 15, 18, 20, 24.
What is the IQR of the data?
6 years
10 years
12 years
22 years
The IQR of the data is 10 years and option B is the correct answer.
What is IQR?The dispersion of the middle 50% of the sample is measured by the interquartile range, or IQR, which is the difference between the top and lower quartiles.
The given data is: 2, 4, 5, 5, 5, 7, 9, 10, 12, 14, 15, 15, 18, 20, 24.
The median of the data is:
M = 15 + 1 /2 = 16/2 = 8th value.
M = 10
Ignoring the median divide the data into two parts.
The lower quartile median is 4th term:
Q1 = 5
The upper quartile median is 12th term:
Q2 = 15
IQR = Q2 - Q1
IQR = 15 - 5 = 10 years.
Hence, the IQR of the data is 10 years and option B is the correct answer.
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Sara can read 19 pages an hour. How many pages can Sara read in 95 min? Round to the nearest whole number.
Answer:
Step-by-step explanation:
Convers 95 min into hours
95/60 = 1.58 Hours
Sara can read 19 pages per hour
Total pages in 95 min or 1.58 hours =
19 * 1.58 = 30.02
Rounding off to nearest whole number- 30
Hope it helps
Mario has a box. He wants to determine how much the box can hold. Which measurement should he calculate?
O area
O length
O perimeter
O volume
In the diagram, BA BE and CE CD.
What is mZDAE?
m2DAE =
Submit
B
68⁰
52%
E
mZDAE is a line segment that connects the midpoints of line segments BA and CE. In the diagram, its coordinates are (66⁰, 52%).
which of the following approaches to building a multiple linear regression model involves taking all of the possible independent variables, and then systematically eliminating insignificant ones until only significant ones remain? forward selection. stepwise regression. backward elimination. back-checking for aic
The approaches to building a multiple linear regression model is option (C) Backward elimination
Here the multiple linear regression model involves taking all of the possible independent variables, and then systematically eliminating insignificant ones until only significant ones remain
We know the independent variable is the variable that does not depends on any other variables
Here the given elimination methods is eliminating insignificant ones until only significant ones remain
In the backward elimination method starts with explanatory variables in the regression model then starts to eliminates the least significant ones will eliminates one by one
Therefore, the suitable approach is backward elimination method
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Daniel has a goal to complete a triathlon. The race consists of a 0. 93
-mile swim, a 24. 8
-mile bike ride, and a 6. 2
-mile run. In training, Daniel can swim at an average pace of 2. 2mph. He rides his bike at an average of 17. 8mph
and runs at 5. 9mph. Estimate how long it will take his to complete the triathlon
It will take Daniel approximately 2 hours and 52 minutes (172.066 minutes) to complete the triathlon.
To estimate how long it will take Daniel to complete the triathlon, we can calculate the time it will take him to complete each leg of the race and add them together.
Swim:
Distance = 0.93 miles
Speed = 2.2 mph
Time = Distance / Speed = 0.93 miles / 2.2 mph = 0.4236 hours = 25.416 minutes
Bike:
Distance = 24.8 miles
Speed = 17.8 mph
Time = Distance / Speed = 24.8 miles / 17.8 mph = 1.3933 hours = 83.6 minutes
Run:
Distance = 6.2 miles
Speed = 5.9 mph
Time = Distance / Speed = 6.2 miles / 5.9 mph = 1.0508 hours = 63.05 minutes
Total time = Swim time + Bike time + Run time
Total time = 25.416 minutes + 83.6 minutes + 63.05 minutes
Total time = 172.066 minutes
Therefore, it took 172.066 minutes which is approximately equal to 2 hours and 52 minutes by Daniel to complete the triathlon.
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Joseph runs 212 miles on Monday. Each day after that, he runs the same 113 mile route every morning. His goal is to run at least 6 miles by the end of the week. Which inequality represents the least number of days after Monday that Joseph needs to run to reach his goal?
The inequality that represents the least number of days after Monday that Joseph needs to run to reach his goal is [tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{3}x[/tex] ≤ 6
Number of miles that Joseph run on Monday = [tex]2\frac{1}{2}[/tex] miles
Number of miles that Joseph run each day after that = [tex]1\frac{1}{3}[/tex] miles
The inequality is the mathematical statement that shows the relationship between two expression using an inequality symbol. The inequality symbols are less than, greater than, less than or equal and greater than or equal.
Then the inequality will be
[tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{3}x[/tex] ≤ 6
Where x is the number of days after Monday that Joseph needs to run to reach his goal
Therefore, the inequality is [tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{3}x[/tex] ≤ 6
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The height of a cone is 10 centimeters. The radius is 4 centimeters. What is the volume of this cone? Around your answer to the nearest hundredth. Do not include units in your answer
Answer: 167.55 cm.
Step-by-step explanation:
Cone volume formula is V=1/3hπr².
Substitute...
V= 1/3 (10) (π) (4)^2
V= 53 1/3 π
V= 167.55 cm
Hope this helps!
MM
Or
Mr. Mosley ordered pizzas for the volunteers at Highland School's fundraiser event. He ordered 12 large pizzas from the Roman Rounds pizzeria. Since this was a bulk order, Roman Rounds reduced the price of each large pizza by $2. The total came to $192. Which equation can you use to find the amount of money, p, Roman Rounds normally charges for a large pizza?
Equation that we can use to find the amount of money, p, Roman Rounds normally charges for a large pizza is 12(p - 2) = 192.
Let's use p to represent the normal price of a large pizza from Roman Rounds. Since Mr. Mosley ordered 12 large pizzas and received a $2 discount on each, he paid a total of $192. We can use this information to set up the following equation:
12(p - 2) = 192
In this equation, 12 represents the number of large pizzas that were ordered, and (p - 2) represents the discounted price of each pizza. The left side of the equation gives us the total amount that Mr. Mosley paid for the pizzas. By setting this expression equal to 192, we can solve for p, the normal price of a large pizza from Roman Rounds.
To solve for p, we first distribute the 12 on the left side of the equation:
12p - 24 = 192
Next, we add 24 to both sides of the equation:
12p = 216
Finally, we divide both sides of the equation by 12:
p = 18
Therefore, the normal price of a large pizza from Roman Rounds is $18.
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Nick buys a car for $15,000. He gives the car dealer $5,000 and borrows the rest of the money at 7% simple interest for 5 years. What is the total amount of interest he will have to pay on the loan?
Answer: $3,500
Step-by-step explanation: 15000-5000=10000
0.7*10,000=700.
700*5=$3,500
how to find the average value of a function on an interval?
To find the average value of a function on an interval dividing the definite integral [tex]\int\limits^a_b f{(x)} \, dx[/tex] by the length of the interval.
The definition of average value of a function is -"The average value of a function is the height of the rectangle that has an area that is equivalent to the area under the curve of the function."
When there's a need to find the average value of a function, rather than adding up numbers we can just integrate, and instead of dividing by the number of values we can just divide by the length of the interval.
Adding values → Integration
Number of values → Length of the interval
When we use the length of the interval it makes more sense as we all know intervals have an infinite number of values, so it is more appropriate to use the length of the interval instead.
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Mel uses one fourth of a yard of ribbon to make a hair bow. How many hair bows can Mel make with 1 yard of ribbon?
Answer:
it's simple 4 that is 100% the correct answer
Every week at the Cougar Scouts meeting, Jamal is in charge of the craft activity. This week, he decides to make pinecone bird feeders. At the meeting, Jamal divides a bag of birdseed evenly among 12 Cougar Scouts, and each scout gets 1/2 of a cup of birdseed. Use an equation to find the amount of birdseed in the bag.
To write a fraction, use a slash (/) to separate the numerator and denominator.
Rhetta started a typing program in hopes to speed up her typing skills. She started the program typing 40 words per minute. After two weeks, she can now type 56 words per minute. What was her percent of increase for typing?
Her percentage difference in programming in accordance with the statement is 40%.
What is the straightforward meaning of speed?It is discussing speed. the velocity at which the position of an object shifts in any direction. Speed is defined as the ratio of the distance traveled to the time required to cover that distance. Speed can be stated as a number since it just has to have 1 element and no magnitude.
You may use the following format to get Rhetta's increased typing speed in percentages:
(New Values - Originally Value) / (Original Value x 100) = Percent Increase
Calculating the percentage increase is as follows: Percentage Point Equals (56 - 40) / 40 x 100 Equals 40% in this instance, where the previous value was 40 words every minute and the new number was 56.
Rhetta was now 40% faster at typing.
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!URGENT HELP! 100 points to any who are willing ^-^
Consider the function f(x) = [tex]2^{x}[/tex]. Find b so that the graphs of each of the functions listed are the same as the graph of function f.
• [tex]g(x) = 4^{bx}[/tex]
• [tex]h(x) = 8^{bx}[/tex]
• [tex]j(x) = (\frac{1}{2}) ^{bx}[/tex]
Side note:
To whom it may concern!
I do deeply appreciate all your help if you did or were willing to help me! Thank you for taking the time out of your day and life to bring aid to my little situation! Bless your kind soul.
.
What is the coefficient in this expression?
-17+(-b)+(-25)
Answer:
In the expression -17 + (-b) + (-25), the coefficient is a number that multiplies a variable. In this case, the coefficients are -17, -1 (which multiplies the variable "b"), and -25.
Step-by-step explanation:
whats the middle product of (-2x+1)(-3x-5)
Answer:
7x
Step-by-step explanation:
That would be ( -2x )(-5) + -3x(1) = 10x - 3x = 7x
Abby loves riding Ferris wheels and
roller coasters. While visiting the Polk
County Fair, she first went on the
Ferris wheel 5 times and the roller
coaster 4 times, using a total of 26
tickets. Then, after taking a break and
having a snack, Abby went on the
Ferris wheel 5 times and the roller
coaster 3 times, using a total of 22
tickets. How many tickets does it take
to ride each attraction?
Answer:
ferris wheel: 2
roller coaster: 4
Step-by-step explanation:
Variables
y = ferris wheel tickets
x = roller coaster tickets
Two equations
5y + 4x = 26
5y + 3x = 22
Using Elimination (minus the top and bottom)
We get:
x = 4 (because 5y - 5y is zero, 4x - 3x is x, and 26 - 22 is 4)
Since the roller coaster price is know, you can sub it into any of the two equations and fine ferris wheel price.
5y + 3(4) = 22
5y + 12 = 22
5y = 10
y = 2
Therefore:
ferris wheel charges 2 tickets
roller coaster charges 4 tickets
Answer:
Step-by-step explanation:
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
Vince works in an amusement park and is helping decorate it with strands of lights. This morning, he used a total of 16 strands of lights to decorate 2 bushes and 1 tree. This afternoon, he strung lights on 3 bushes and 4 trees, using a total of 44 strands. Assuming that all bushes are decorated one way and all trees are decorated another, how many strands did Vince use on each?
Vince decorated every bush with
strands of lights and every tree with
strands.
Which of the following is NOT a characteristic of a plane?
The answer option which is not a characteristic of a plane include the following: C. thickness.
What is a plane?In Mathematics, a plane is sometimes referred to as a two-dimensional surface and it can be defined as a flat, two-dimensional surface with zero curvature and zero thickness, that extends indefinitely (infinitely). Additionally, two (2) planes intersect at a line.
What are the characteristics of a plane?Generally speaking, there are different characteristics of a plane and these include the following:
LengthFlat surface.Width.In this context, we can reasonably infer and logically deduce that thickness is not a characteristic of a plane.
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Complete Question:
Which of the following is NOT a characteristic of a plane?
A. length
B. flat surface
C. thickness
D. width
question which of the following must be true for an estimator of a population parameter to be unbiased? responses the sampling distribution of the estimator is normal. the sampling distribution of the estimator is normal. the expected value of the estimator is equal to the population parameter. the expected value of the estimator is equal to the population parameter. the sampling distribution of the estimator is the same shape as the distribution of the population parameter. the sampling distribution of the estimator is the same shape as the distribution of the population parameter. the variability of the sampling distribution of the estimator is equal to the variability of the population parameter. the variability of the sampling distribution of the estimator is equal to the variability of the population parameter. the variability of the sampling distribution of the estimator is less than the variability of the population parameter.
The second statement in your question is the correct response.
What is the sampling distribution?
A sampling distribution is the probability distribution of a statistic (such as the sample mean or sample proportion) based on all possible random samples of a fixed size from a population.
The following statement must be true for an estimator of a population parameter to be unbiased:
The expected value of the estimator is equal to the population parameter.
Hence, the second statement in your question is the correct response.
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three pieces of wood measuring 70m, 105m and 175m long have to be divided to planks of equal length what is the greatest possible length of each plank
Answer:
35 m
Step-by-step explanation:
I will assume the goal is not to waste any wood. We need to find a common length that will allow each piece of wood to be divided into whole pieces with nothing left over. The shortest plank is 70 m, but that length will cause a loss of 35 m on the 105m plank, and also 35m on the 175m plank after two 70m sections have been cut off (175 - 140 = 35).
Looking at the actual lengths, one might spot that they are all evenly divisible by 35. See the table below. The numbers under "35" are the result of the length divided by 35. They are all whole numbers. We can cut each plank into 35m sections and have none left over.
Length (m) 35 (factor)
70 2 planks
105 3 planks
175 5 planks
This will result in 10 35m planks.
No need to plank me.
look at attachment
The graph of the relation G is shown below.
Give the domain and range of G .
Write your answers using set notation.
please explain it too I dunno what I'm doing btw I set the point worth to 50 points
Answer:
The answer is 15 and 22
Step-by-step explanation:
KHAN
