The probability that the hand contains exactly 3 face cards is 0.1503.
Combinations of 7 cards out of a choice of 52.
52!/(45! *7!)= 52*51*50*49*48*47*46/7*6*5*4*3*2 = 133,784,560
Combinations of 3 face cards out of 12
12*11*10/3*2 = 220
Combinations of 4 non-face cards out of 40
40*39*38*37/4*3*2 = 91,390
Combinations of 5 face cards and 2 non-face cards
220 * 91,390 = 20,105,800
So the probability is 20,105,800/133,784,560 or 0.1503
About ProbabilityProbability theory is the theory used to model uncertainty. Probability value o events show how likely it is the event will occur with an interval of values between zero up to one. However, probability theory can only used for events that have information that complete.
For events that have no information complete can be represented by imprecise probability. One model of imprecise probability is the set-valued probability. Probability worth the set is the non-empty set with every the elements are the results of the probability selector mapping.
Then a set-valued measure is constructed which is constructed by set-valued probabilities.
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what happens to fst when two finite populations are connected by migration (say 2% chance of migration per organism per generation, and no selection)? group of answer choices fst increases to 1 fst decreases to 0 fst stays moderate, near 0.5 fst wanders around randomly between 0 and 1 forever
When two finite populations are connected by migration , then (b) Fst decreases to 0 .
The Fixation Index denoted as Fst , is a measure of population differentiation, which is used to quantify the level of genetic differentiation between two populations.
The Fst ranges from 0 to 1, where 0 indicates complete gene flow between two populations and 1 indicates complete genetic isolation.
If the migration rate is 2% per organism per generation, over time this will lead to a reduction in genetic differentiation between the populations, and the Fst value will decrease towards 0.
This is because the exchange of genetic material will reduce the amount of variation that is unique to each population, which leads to an increase in the genetic similarities between the populations.
The given question is incomplete , the complete question is
What happens to Fst when two finite populations are connected by migration (say 2% chance of migration per organism per generation, and no selection) ?
(a) Fst increases to 1
(b) Fst decreases to 0
(c) Fst stays moderate, near 0.5
(d) Fst wanders around randomly between 0 and 1 forever .
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what will it cost to carpet a rectangular floor measuring 9 feet by 18 feet if the carpet costs $12.75 per square yard? if needed, round your answer to the nearest penny.
The cost of carpeting a rectangular floor measuring 9 feet by 18 feet is 18 square yards x 12.75 = 228.50. If needed, this can be rounded to the nearest penny, which is 228.50.
The formula to calculate the cost of carpeting a rectangular floor is Area of the floor x Cost of carpet per square yard.
The area of the floor is calculated by multiplying the length and the width, which in this case is 9 feet x 18 feet = 162 square feet.
To convert 162 square feet into square yards, divide 162 square feet by 9, which equals 18 square yards.
Therefore, the cost of carpeting a rectangular floor measuring 9 feet by 18 feet is 18 square yards x 12.75 = 228.50. If needed, this can be rounded to the nearest penny, which is 228.50.
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what is the correct way to report the length of the rectangle in centimeters? a ruler is adjacent to the rectangle. one edge of the rectangle is at the 0 cm mark. the other edge of the rectangle is between the 15.5 and 15.6 centimeter marks. select one: 15.6 cm highlight off info 15.600 cm 16 cm 15.60 cm
The length of the rectangle in centimeters is 15.60 cm.
The correct way to report the length of the rectangle in centimeters is 15.60 cm. To calculate the length of the rectangle, we must first calculate the distance between the two edges of the rectangle. To do this we can use the formula Distance = Final Position - Initial Position. Therefore, the distance between the two edges of the rectangle is 15.600 cm - 0 cm = 15.600 cm. This is the length of the rectangle, so the correct way to report the length of the rectangle in centimeters is 15.60 cm.
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PLEASE HELP ASAP
Which of the following tables represents a linear relationship that is also proportional? x −3 0 3 y −4 −2 0 x −2 0 2 y 0 3 6 x −3 0 3 y −4 −3 −2 x −3 0 3 y −2 0 2
The table that represents a proportional relationship is given as follows:
x −3 0 3
y −2 0 2
(which is the last option).
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
From the definition, we have that a proportional relationship is a linear function with an intercept of zero, meaning that when x = 0, y = 0.
The last option is the only option for which the intercept of zero condition is satisfied, hence it is the correct option.
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1. The Carmona Construction Company is laying a brick patio. Thirty rows of bricks have been installed. Twenty more rows are needed to finish the job. If 600 bricks have already been used, how many will be used for the entire job? write a proportion which can be solved for x.
The number of bricks that will be used for the entire job would be = 1000 bricks.
How to calculate the quantity of bricks needed?The amount of bricks which will be used by the Carmona Construction Company for brick patio can be calculated as follows;
The amount of rows that has been installed = 30 rows
The amount of bricks that makes up the installed rows = 600 bricks.
The amount of uninstalled rows = 20
The amount of bricks that would be required to install the remaining 20 rows ;
30 rows = 600
20 rows = X
Make X the subject of formula
X = 20×600/30
X = 12000/30
X= 400 bricks
Therefore, the total brick that will be required = 400+600 = 1000 bricks.
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Geometry help please. It’s due tomorrow
Points G, H, and I It seems to be the vertices of a triangle, forming the triangle GHI. Triangle GHI resembles triangle ABC.
What exactly is a triangle?A triangle is a three-sided polygon that is also known as the trigon. Every triangle has three sides and three angles, which might be different. In geometry, a triangle is a three-sided polygon with three edges and three vertices. The sum of a triangle's internal angles equals 180 degrees, which is its most important characteristic. This is known as a triangle's angle sum property.
Here,
Point G, H, I looks like the vertices of triangle making triangle GHI. Triangle GHI is similar to triangle ABC.
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Help!!!! 9.a) is the one I need help with please!!!
The perimeter of the playground is 92 meters
How to determine the perimeter of the figureThe figure is added as an attachment
To calculate the perimeter, we simply add the side lengths of the playground
i.e. Perimeter = Sum of side lengths
Using the above as a guide, we have the following:
Perimeter = 10 + 14 + 10 + 10 + 6 + 6 + 6 + 14 + 6 + 10
Evaluate the like terms
Perimeter = 92
Hence, the perimeter is 92 meters
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Find the marginal profit function if cost and revenue are given by C(x) = 292 +0.9x and R(x) = 9x -0.02x².
Answer:
The marginal profit function can be found by subtracting the marginal cost from the marginal revenue. The marginal cost is given by the derivative of the cost function, and the marginal revenue is given by the derivative of the revenue function.
The derivative of the cost function is:
C'(x) = dC(x)/dx = 0.9
The derivative of the revenue function is:
C'(x) = dC(x)/dx = 0.9
The derivative of the revenue function is:
R'(x) = dR(x)/dx = 9 - 0.04x
Therefore, the marginal profit function is:
P'(x) = R'(x) - C'(x) = 9 - 0.04x - 0.9 = 8.1 - 0.04x
The length of a runway is 1/2 of a mile. The area of it is 3/4 miles squared. What is the width?
Answer:
3/2 of a mile
Step-by-step explanation:
The equation is 1/2 times something = 3/4 (because length times width is area)
you would divide 1/2 on both sides to get an unknown number(that represents the width)
3/4 divided by 1/2 is 3/2 of a mile !
Identify the given statement as either true or false.The standard deviation is a resistant measure of spread.a. Falseb. True
The given statement: The standard deviation is a resistant measure of spread is true.
Standard deviation is the measure of how spread out numbers are. It is a measure that is used to quantify the amount of variation or dispersion of a set of data values.
The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability. When data points are closely spaced from the mean, there is a little variation, and when they are far spaced from the mean, there is a large variation. The standard deviation determines how much the data deviate from the mean.
When outliers are included, resistant statistics don't change (or vary very little). Resistance does not imply that anything is immobile; that would be "immovable." It implies that your results could fluctuate a bit, but not much.
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mean of 8,12,4,3,14,1,9,13
Answer:
The mean is 8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
add all numbers together and divide by how many numbers there are so:
8+12+4+3+14+1+9+13=64
64÷8=8
Feel free to ask me any questions if you don't understand it :)
the area of a triangle is one half the base times the height. if the area of the triangle is 16 square inches and the bas is 8 inches, what is the height?
Answer:
4 inches
Step-by-step explanation:
Let b = base length
h = height
A = area
[tex]A = \dfrac{1}{2}\cdot b \cdot h\\\\[/tex]
Multiply throughout by 2
[tex]2 \cdot A = 2\cdot \dfrac{1}{2}\cdot bh\\\\2A = bh\\\\h = \dfrac{2A}{b}[/tex]
We are given A = 16 in² and b = 8 inches
So, h = 2(16)/8 = 32/8 = 4 inches
Check to see if this is correct
A = (1/2)(8)(4) = (4)(4) = 16
# 2. A mountain in Marion County is losing
elevation at a rate of 6% every decade. If the
current elevation is 1200 meters, how tall will the
mountain be after 7 decades
To answer this question, you cannot do it all at once. Since the percentage will change every year because of how percents work, you must do seven calculations for each of the seven decades.
To decrease a number by 6%, you multiply it by 0.94, which is the same as finding 94% of that number, as you have taken 60% away.
1. 1200*0.94 = 1128
2. 1128*0.94 = 1060.32
3. 1060.32*0.94 = 996.7008
4. 996.7008*0.94 = 936.898752
5. 936.898752*0.94 = 880.68482688
6. 880.68482688*0.94 = 827.843737267
7. 827.843737267*0.94 = 778.173113031
You probably don't need 9 decimal places, so we can round to 778.17.
After seven decades, the mountain will be 778.17 meters.
I actually have no clue how to solve this please help me.
A Doctor's office is deciding between buying 2 different sized cups. the 2 cups are shown. Before deciding which size cup to buy, they determine how much water each size cup can hold. How much More water (in cubic inches) can the larger cup hold than the smaller cup.
*Round your answer to the nearest hundredth, and use 3.14 for PI in your calculations*
The larger cup can hold 144.51 in³ more water than the smaller cup.
How to obtain the volume of a cone?The volume of a cone of radius r and height h is given by one third of the multiplication of pi = 3.14 by the radius squared by the height, hence:
V = 3.14r²h/3
V = 1.0472r²h.
For the smaller cup, the dimensions are r = 2 in and h = 3 in, hence the volume is given as follows:
V = 1.0472 x 2² x 3
V = 12.57 in³.
For the larger cup, the dimensions are r = 5 in and h = 6 in, hence the volume is given as follows:
V = 1.0472 x 5² x 6
V = 157.08 in³.
Then the difference is of:
157.08 - 12.57 = 144.51 in³.
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Show that 8+√12/5+√3 can be written in the form a+√3/b where a and b are integers.
The expression (8+√12) / (5+√3) in the form of (a+√3) / b is given by (18 + √3) / 11, where a = 18 and b = 11
What is expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that, an expression (8+√12) / (5+√3) we need to convert it into
(a+√3) / b, where, a and b are integers.
The given expression is (8+√12) / (5+√3)
Rationalizing the expression by multiplying the numerator and denominator by changing the sign of the denominator, (5-√3)
Therefore, (8+√12) / (5+√3)
= (8+√12) / (5+√3) × (5-√3) / (5-√3)
= (40 - 8√3 + 5√12 - √36) / 5²-√3² [a²-b² = (a+b)(a-b)}
= (40 - 8√3 + 5× 2√3 - 6) / (25-3)
= (40 - 8√3 + 10√3 - 6) / 22
= (36 + 2√3) / 22
= (18 + √3) / 11
Hence, the expression (8+√12) / (5+√3) in the form of (a+√3) / b is given by (18 + √3) / 11, where a = 18 and b = 11
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a given insect population doubles every week. if 2 insects exist on the first week, how many weeks will pass until the insect population exceeds 10,000 insects? use a while loop to output the insect population each week until the population exceeds 10,000 insects. researchers have discovered that every 4 weeks a disease is killing 40% of the insect population after the population has reproduced. if 2 insects exist on the first week, how many weeks will pass until the insect population exceeds 10,000 insects? write a second do-while loop that outputs the insect population each week until the population exceeds 10,000 insects. decimal places will appear in the number of insects after removing 40% of the population on week 4.
It will take 14 weeks for the insect population to exceeds 10,000 insects. It will take 17 weeks for the insect population to exceeds 10,000 insects when 40% of the insect is killed by a disease every 4 week.
The code for this function of Java is : class InsectPopulation {
public static void main(String[] args) {
int week = 1;
double population = 2;
System.out.println("Week 1: 2 insects");
while (population <= 10000) {
population = population * 2;
week++;
if (week % 4 == 0) {
population = population - (population * 0.4);
}
System.out.println("Week " + week + ": " + String.format("%.2f", population) + " insects");
}
}
}
The second function for the loop is : class InsectPopulation {
public static void main(String[] args) {
int week = 1;
double population = 2;
System.out.println("Week 1: 2 insects");
do {
population = population * 2;
week++;
if (week % 4 == 0) {
population = population - (population * 0.4);
}
System.out.println("Week " + week + ": " + String.format("%.2f", population) + " insects");
} while (population <= 10000);
}
}
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While working at a soup kitchen, Suzie made 9 quarts of vegetable soup to serve 25 people. She gave each person an equal portion.
How much soup did each person get?
Write your answer as a proper fraction or mixed number.
Answer:
Each person gets .36 quarts of vegetable soup.
Step-by-step explanation:
If Suzie makes 9 quarts of vegetable soup to serve among 25 people, you must divide 25 by 9, doing so you get .36 .
naomi's school is having a spring carnival. when naomi carries a bin of water balloons outside for the balloon toss, she trips and breaks 13 balloons. she counts the remaining water balloons, and there are 15 left.which equation can you use to find the number of water balloons w in the bin before naomi trips?
Equation can use to find the number of water balloons w in the bin before Naomi trips is w - 13 = 15.
As per the given data, Naomi's carries a bin of water balloons outside for the balloon toss, she trips and breaks 13 balloons.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The number of water balloons w in the bin before Naomi trips.
She counts the remaining water balloons, and there are 15 left.
According to the question, the equation is
w - 13 = 15
⇒ w = 15 + 13
⇒ w = 28
Hence, equation which is used to find the number of water balloons w in the bin before Naomi trips is w - 13 = 15.
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(b) Work out the value of (2.4 x 10³) x (9.5 x 10³)
Give your answer in standard form.
Answer:
[tex]2.28*10^7[/tex]
Step-by-step explanation:
[tex](2.4*10^3)(9.5*10^3)=(2.4*9.5)(10^3*10^3)=22.8*10^6=2.28*10^7[/tex]
Answer:
228,000
Step-by-step explanation:
(2.4x10^3) x (9.5x10^3)
(2.4x100) x (9.5x100)
240x950
228,000
A triangle has vertices A(-2,-1), B(4,7) and C(-8,9). Find the length of AB.
Answer:
10
Step-by-step explanation:
Use the pythagorean theorem/distance formula.
AB = \sqrt{(4-(-2))^2+(7-(-1))^2} = \sqrt{36+64} = \sqrt{100} = 10
data from a poll conducted by travelocity led to the following estimates: approximately 44% of travelers check work email while on vacation, about 32% take cell phones on vacation in order to stay connected with work, and about 26% bring a laptop computer on vacation. are the given percentages population values or were they computed from a sample?
The estimates that is led from the data from a poll conducted by Travelocity , then the percentages are "computed from a sample" .
The Data from the poll conducted by Travelocity was computed from a sample of travelers and was used to estimate the proportion of travelers
The travelers have certain habits or behaviors, such as checking work email (44%) taking a cell phone (32%) , or bringing a laptop computer on vacation (26%) .
The sample estimates are used to make inferences about the population.
Therefore , the given percentages are that they were "computed from a sample" .
The given question is incomplete , the complete question is
Data from a poll conducted by Travelocity led to the following estimates:
Approximately 44% of travelers check work email while on vacation, about 32% take cell phones on vacation in order to stay connected with work, and about 26% bring a laptop computer on vacation.
Are the given percentages "population values" or were they "computed from a sample" ?
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The radius of a circle is 2 miles. What is the length of a 135% arc
what is the probability that after servicing twelve of these phones, phones of only two of the three types remain to be serviced?
The probability that after servicing twelve of these phones, phones of only two of the three types remain to be serviced can be calculated using combinatorics.
The number of ways to choose two types of phones out of three and the number of ways to arrange twelve phones of these two types need to be determined. The probability can then be calculated as the number of favorable outcomes divided by the total number of possible outcomes. This method can help determine the likelihood of a specific event happening in a given scenario.
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Pls help asap ! . . . . . . . . . . .
The equation that represents the total amount of kites for a given number will be y = 2x + 20.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The rate of the kite is $2 per kite and the shipping charge is $20.
Let 'x' be the number of kites and 'y' be the total amount. Then we have
y = 2x + 20
Then the table is completed below.
Number of kites Total amount
0 20
1 22
4 28
7 34
10 40
The equation that represents the total amount of kites for a given number will be y = 2x + 20.
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question some of the students enrolled at college t are part-time students and the rest are full-time students. by what percent did the number of full-time students enrolled at college t increase from the fall of 1999 to the fall of 2000 ? (1) there were 50 more full-time students enrolled at college t in the fall of 2000 than in the fall of 1999. (2) the total number of students enrolled at college t increased by 5 percent from the fall of 1999 to the fall of 2000.
As percent did the number of full-time students enrolled at college t increase from the fall of 1999 to the fall of 2000 is 25%.
A percentage is a fraction of a whole number expressed as a fraction of 100. It is often used to describe the change in a quantity over time or between different groups.
There were 50 more full-time students enrolled in the fall of 2000 than in the fall of 1999, we can calculate the change in the number of full-time students as follows:
Change in full-time students = 50
To calculate the percentage change, we need to know the initial number of full-time students in the fall of 1999. This information is not provided, so we will use the information that the total number of students enrolled at College T increased by 5 percent from the fall of 1999 to the fall of 2000.
Let's call the total number of students enrolled at College T in the fall of 1999 "x". Then, the total number of students enrolled at College T in the fall of 2000 would be x + 5% of x.
x + 5% of x = x + 0.05x = 1.05x
To find the number of full-time students in the fall of 2000, we can subtract the change in full-time students from the total number of students enrolled at College T in the fall of 2000:
Number of full-time students in fall of 2000 = 1.05x - 50
To calculate the percentage change, we divide the change in full-time students by the initial number of full-time students and multiply by 100:
Percentage change = (50 / x) * 100
Where the value of x as 2000, then the percentage is
=> (50/2000) * 100 = 25%.
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Graph the equation y-4=0.75(x-1)
Graph of the equation y-4=0.75(x-1) is in the attachment.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given equation is y-4=0.75(x-1)
y-4=0.75x-0.75
Add 4 on both sides
y=0.75x+3.25
The slope is 0.75 and y intercept is 3.25.
The graph is given in the attachment.
Hence, graph of the equation y-4=0.75(x-1) is in the attachment.
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Candace recently opened an online makeup
salon. Her sales in the first week were $86. After
starting an online advertising campaign, her
sales increased 20% the following week and
continued to increase at that rate. How much
were total sales in week 20 after beginning the
advertising campaign?
The total sales in week 20 after the beginning of the advertising campaign was $3297.03
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical expressions. Equations are classified based on degree as linear, quadratic, cubic
Her sales in the first week were $86. After starting an online advertising campaign, her sales increased 20% the following week. This expression can be represented in the form of an exponential function:
y = abˣ
Where a is the initial value and b is the multiplication factor
Let y represent the total sales after x weeks. Comparing with the expression:
a = $86, b = 100% + 20% = 1.2. Hence:
y = 86(1.2)ˣ
After 20 weeks:
y = 86(1.2)²⁰ = 3297.03
The total sales was 3297.03
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A box in the shape of a rectangular prism has the dimensions shown. To the nearest tenth of a centimeter, how many centimeters long is the interior diagonal of the box?
A rectangular prism with a base that measures 6 centimeters by 8 centimeters, and a height of 11 centimeters. A dashed diagonal line is drawn from one vertex of the base to the opposite vertex of the same base. Another dashed diagonal line is drawn from one vertex of the base to the opposite vertex of the other base.
The length of the dashed diagonal line is drawn from one vertex of the base to the opposite vertex of the same base is 10
The length of the dashed diagonal line is drawn from one vertex of the base to the opposite vertex of the other base is 14.87
How to find the interior diagonalThe interior diagonal is solved using the Pythagoras theorem is applicable to right angle triangle. the formula of the theorem is
hypotenuse² = opposite² + adjacent²
For same base
opposite = 6
adjacent = 8
plugging the values as in the problem
let x be the required distance
x² = 6² + 8²
x² = 36 + 64
x² = 100
x = √100
x = 10
dashed diagonal line is drawn from one vertex of the base to the opposite vertex of the other base
opposite = 11
adjacent = 10
let y be the required distance
y² = 10² + 11²
y² = 100 + 121
y² = 221
y = √221
y = 14.87
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Three boxes each contain a different number of marbles. Box A has 70 marbles, box B has 88 marbles, and box C has 80 marbles. Marbles are to be transferred from box B to box A. What is the least number of marbles that can be transferred so box C has the most marbles?
it A
Step-by-step explanation:
Judy charged $800 worth of furniture using noninstallment credit since her tax refund is due shortly. If she intends to pay off the entire amount of her purchase, how much will she have to come up with if her refund is $535?
If Judy's refund is $535, to pay for furniture worth $800, she will have to come up with $265, which is the difference.
What is the difference?The difference is the result of the subtraction operation.
The subtraction operation is one of the four basic mathematical operations.
Subtraction operations involve the minuend, subtrahend, the subtraction operator (-), the difference, and the equal symbol (=).
The cost of furniture = $800
Expected credit refund = $535
The difference between the cost and refund = $265 ($800 - $535)
Thus, Judy will bring $265 to make up for the purchase of the furniture.
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