Assume that you have laid out the namecards for 14 people, and you want to hide 4 golden tickets, at most one under each namecard. The total number of ways = 784
From the question, we have
The total number of people in each party = 8
The total number of winners in each party = 2
The total number of ways of selecting two winners from 8 people = P(8,2) = 28
The total number of ways of selecting two winners from each political party = 28*28 = 784
The total number of ways = 784
Multiplication:
To determine the sum of two or more numbers, mathematicians multiply the numbers. It is a basic mathematical procedure that is widely used in daily life. Multiplication is used when we need to mix groups of like sizes. Multiplication is a representation of the underlying idea of adding the same number repeatedly.
The outcome of multiplying two or more numbers is referred to as the product of those numbers, and the factors are the quantities that are multiplied. Multiplying the numbers makes it simpler to add the same number repeatedly.
Complete question:
In celebration of Chinese new year, you are arranging name cards for 16 people to sit around this table. Since the cards are placed on the rotating lazy Susan, the specific chair of a guest does not matter, only who is to their left and right. That is, two namecard arrangements are considered different iff there is a guest whose person on their right or left changes. Now when you hide four golden tickets under the placed name cards, you want to ensure that each party has two winners. In how many ways can you choose to do so?
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the salaries of physicians in a certain speciality are approximately normally distributed. if 25 percent of these physicians earn less than $180,000 and 25 percent earn more than $320,000, approximately what fraction earn
Answer:
We know P(x<$180,000)=.25 and P(x>$320,000)=.25
Using the formula for normal distributions, we can find the mean and standard deviation (z = (x-mean)/SD) using the given info. Then you'll have two equations with two unknowns.
Finally when finding part a, make sure to do a continuity correction [P(x<$200,000) = P(x≤$200,000.5) = ?]
Step-by-step explanation:
the number of hits on the campus ready website follows a poisson process with a rate of 3 per minute. what is the probability that more than a minute foes by without a hit
The probability that more than a minute foes by without a hit is 0.0498.
Let X denote the waiting time in minutes until the next hit.
From the question, we have
The probability density function of exponential distribution is,
f(x)=λe^(-λ*) λ>0
Probability =
P(X>1) =∫_1^∞ 3e^(-3x) dx
=3(e^(-3z)/(-3))_1^∞
=e^(-3)
=0.0498
Probability = 0.0498
Probability:
Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.
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Find the volume of a right circular cone that has a height of 6.5 cm and a base with a radius of 8.5 cm. Round your answer to the nearest tenth of a cubic centimeter.
The volume of the right circular cone is 122.94754 in³.
What is the right circular cone?
The axis of a right circular cone is the line joining the vertex and the base's center.
In other words, a right angle is formed at the place where the apex of the cone and the center of the circular base meet.
Following is the correct circular cone volume formula:
V=1/3hπr²
Diameter = 8.5 in
Radius = 8.5/2 = 4.25 in
Now calculate the volume as follows:
V = 1/3hπr²
V = 1/3(6.5)π(4.25)²
V = 122.94754 in³
Therefore, the volume of the right circular cone is 122.94754 in³.
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4/9 + 1/4 less or greater than 1/2
Answer:
greater than
Step-by-step explanation:
4/9+1/4
16/36+9/36
25/36
25/36>18/36
Evaluate 11.5x + 10.9y when x = 6 and y =7
Answer: 145.3
Step-by-step explanation:
the solution for the given expression 11.5x + 10.9y is 145.3
What is an Equations?
Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) symbol. It demonstrates how the expressions written on the left and right sides are equivalent. Equations can be solved to find the value of a variable that represents an unknown quantity. If there is no "equal to" symbol in a statement, it is not an equation. It will be viewed as a phrase.
11.5x + 10.9y
Here x = 6 and y = 7
11.5*6 + 10.9*7 = 145.3
Hence, the solution the given expression is 145.3
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Write the following expression without negative exponents and without parentheses. -6x^{-2} −6x −2
Answer:
[tex]-\frac{6}{x^{2} } -6x-2[/tex]
Step-by-step explanation:
[tex]x^{-2}[/tex] is equivalent [tex]\frac{1}{x^{2} }[/tex]
Then, that is multiplied by the coefficient of -6
Thus [tex]-6x^{-2}[/tex] becomes [tex]-\frac{6}{x^{2} }[/tex]
6. In right triangle ABC, angle C is a right angle, AB is 25 units long, and BC is 24 units
Mong. What is the length of AC?
A. 1
B.2
C. 7
D. 49
Answer:
C. 7
Step-by-step explanation:
Draw out the triangle if you want.
You’ll notice you’ll have a hypotenuse and one other side.
Use Pythagoras’ theorem: a^2 + b^2 = c^2
c = the hypotenuse
24^2 + b^2 = 25^2
solve for b:
576 + b^2 = 625
b^2 = 625 - 576
b^2 = 49
b = 7
What is the meaning of closure property in mathematics?
The closure property states that any operation performed on the numbers of a set will be closed under that very state.
This means that in any mathematical operation like multiplication, addition, subtraction, or division when performed on two or more numbers of a particular set, the result will belong to that very set.
For example, addition is closed under whole numbers. This means tat the sum of any 2 whole numbers will always be a whole number.
For example, the sum of whole numbers 10 and 20 is 0, a whole number.
Another case is that of subtraction, which is closed under integers.
For example- the difference between integers 30 and 40 is -10, which is an integer.
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what are the differences between the predicted values and actual values called in a regression analysis?
The difference between the predicted regression value and the actual value is called the residual.
Let's assume a simpler model: Y= β₀+ β₁X + E. For linear regression, let ε∼N(0,σ2). The most important thing here is that ϵ is a normal random variable. This makes Y a normal random variable with mean β0+β1X and variance σ₂.
Regression Analysis:
Regression analysis is a set of statistical techniques used to estimate the relationship between a dependent variable and one or more independent variables. It can be used to assess the strength of relationships between variables and model future relationships between variables.
Assumptions:
One of the main assumptions of regression analysis is that residuals with mean equal to 0 are normally distributed. Residuals must be both positive and negative. If this condition is not met (residuals are only positive or negative, i.e. the model is either consistently Regardless, it means that it has not been properly selected for prediction.
Poor predictions are due to (i) the regression model should contain non-linear terms rather than only linear terms, (ii) multicollinearity of the independent variables, and (iii) missing important predictor variables (features). Poor understanding of the problem and data, (iv) non-constant data variance, or (v) extrapolation (prediction) far beyond the range of the independent variables used to estimate the parameters of the model.
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A study indicated that the citizens of Washington wasted 7,470 gallons of water last year. This year, they wasted 30% less. How many gallons did the citizens waste this year?
Answer:
2,241
Step-by-step explanation:
7470 x 0.3
How can we use the distributive property to find an expression equivalent to 15(x+2)? place the steps in order.
We can use the distributive property to find an expression equivalent to 15(x+2) as 15x + 30.
The given equation is 15(x+2).
The distributive property can be used on the component outside of the brackets, that is 15.
Therefore, we would multiply 15 by each term inside the rounded brackets.
It becomes, 15 times x = 15x and 15 times 2 = 30
That is, 15*(x+2) = 15* x +15* 2 = 15x + 30
Hence, the equation 15(x+2) becomes 15x + 30.
By using the distributive property, expression equivalent to 15(x+2) is 15x + 30
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ortwo flocks of birds are 210 miles apart and heading directly toward each other. one flock is flying at a rate of 25 miles per hour. in comparison, the other flock is flying at a rate of 37 miles per hour. in how much time will the two flocks meet?
If one flock is flying at a rate of 25 miles per hour and the other flock is flying at a rate of 37 miles per hour then both the flocks will meet each other after 3.39 hours.
Given, two flocks of birds are 210 miles apart and heading directly toward each other. one flock is flying at a rate of 25 miles per hour.
In comparison, the other flock is flying at a rate of 37 miles per hour.
We have to find in how much time will the two flocks meet.
Let, both take t hours to meet,
now, according to the question
first flock will travel the distance, 25t
and similarly second flock will travel the distance, 37t
so, 25t + 37t = 210
62t = 210
t = 3.39
So, both the flocks will meet each other after 3.39 hours.
Hence, if one flock is flying at a rate of 25 miles per hour and the other flock is flying at a rate of 37 miles per hour then both the flocks will meet each other after 3.39 hours.
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Aaron starts riding a bike at a rate of 3 mi/h on a road toward a store 20 mi away. Zhang leaves the store when aaron starts riding his bike, and he rides his bike toward aaron along the same road at 2 mi/h. How many hours will pass before they meet?.
2 hours will pass before they meet.
"Information available from the question"
In the question:
Aaron starts riding a bike at a rate of 3 mi/h on a road toward a store 20 mi away.
Zhang leaves the store when Aaron starts riding his bike, and he rides his bike toward Aaron along the same road at 2 mi/h.
Now, According to the question:
Total distance = 20mi
Aaron starts riding a bike at a rate of = 3mi/h
Zhang rides his bike toward Aaron along the same road at = 2mi/h
Let y be the number of hours for them to meet.
The expression is given as
3y + 2y = 20
solving for y, we have
5y = 20
y = 20/5
y = 4hrs
Therefore, 2 hours will pass before they meet.
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Help me please !!!!
Answer:
Step-by-step explanation:
2.) 143 7/23
3.) 291 46/48
4.) 220
5.) 56
6.) 1292 63/4
Write an equation of the line that passes through (4, -3) and is
perpendicular to y = - x - 2
Answer:
y=-3x+5
Step-by-step explanation:
As the new line is perpendicular to the original line, the gradient of the new line (m) will be -1 ÷ gradient of original line = -1 ÷ 1/3 =3
I need help thanks for your help…
The perimeter of the given right-angle triangle is 40 cm.
What is Pythagoras's theorem?In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
We also know that the perimeter of a triangle is the sum of the lengths of all the sides.
First, we need to figure out the length of the base of the right-angle triangle.
Assuming the base to be 'x'.
∴ 17² = 15² + x².
x² = 17² - 15².
x² = 64.
x = ± 8.
So, The base of the triangle is 8 cm.
∴ The perimeter of the triangle is (17 + 15 + 8) = 40 cm.
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16. Consider the inequalities -2.x < 10 and -6 < -2x.
a. Is x = 0 a solution to both inequalities?
b. Is x = 4 a solution to both inequalities?
c. Find another value of x that is a solution to both inequalities.
a) The value of x=0 will be a solution for both the inequalities .
b) One equality is false and only one in correct when value of x = 4
What is inequalities?
In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.a) x =0
i) -2.x < 10
-2(0) < 10
0 < 10
ii) -6 < -2x
-6 < -2(0)
-6 < 0
The value of x will be a solution for both the inequalities .
b) x = 4
i) -2.x < 10
-2(4) < 10
-8< 10
ii) -6 < -2x
-6 < -2(4)
-6 < -8
Hence, one inequality is false and only one in correct when the value of x =4.
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6 são quantos por cento de 8?
Answer: .48
Step-by-step explanation:
A circle has a diameter of 4 inches. Which statement about the area and circumference of the circle is true?
A comparison of the area and circumference of the circle is not possible because there is not enough information to find both.
The numerical values of the circumference and area are equal.
The numerical value of the circumference is greater than the numerical value of the area.
The numerical value of the circumference is less than the numerical value of the area.
Answer:
Option B is correct
The numerical values of the circumference and area are equal.
Step-by-step explanation:
Circumference(C) and Area (A)of the circle is given by:
....[1]
......[2]
where, r is the radius of the circle.
As per the statement:
A circle has a diameter of 4 inches.
We know:
Diameter = 2 (radius(r))
then;
4 = 2r
Divide both sides by 2 we have;
r = 2 inches
Substitute these in [1] and [2] we have;
Therefore, the numerical values of the circumference and area are equal i.e 12.56
Hell plsss
Solve;
Y>-x+1
Y<1/3x-3
Answer:
1/3 x -3
Step-by-step explanation:
will give brainliest!
find the slope of the line that passes through the given two points.
( -3, 3 ) and ( -9 , 5 )
and
find the slope of the line that passes through the given two points.
( 4 , -7 ) and ( 2 , -7 )
Answer:
The slope of the line passing through the points (-3,3) and (5,9) is 3/4
3/2 is the second one
1 ) y = - 1 / 3 x + 2
2 ) y = 0x - 7
To find the slope of the line you can use the equation.
m = y2 - y1 / x2 -x1 = tan(Ф)
Answer:
1 ) y = - 1 / 3 x + 2
2 ) y = 0x - 7
Step-by-step explanation:
To find the slope of the line you can use the equation...
m = y2 - y1 / x2 -x1 = tan(Ф)
Hope this helps! :)
Vickie deposited a $689.78 paycheck, a $200 stock dividend check, a $50 rebate check
and $140 cash into her checking account. Her original account balance was $103.45.
Assuming the checks clear. How much will be in her account after the deposits are
made?
WILL GIVE 50 POINTS
For real-world problems, the domain and range of functions can be constrained by situations that make sense. Janet records how far she runs each day in January. The domain of the function is the date in January. The range of the function is how far Janet runs. How are the domain and range of the function constrained?
Answer: The domain is constrained by the number of days in January, [1,31]. The range is constrained by how far she can run each day.
Step-by-step explanation:
Two numbers are in the ratio 4: 7. If their L.C.M. is 168, find the numbers.
Two numbers are in the ratio 4: 7. If their L.C.M. is 168,The numbers would be 56 and 98.
The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm) in mathematics and number theory. It can also be referred to as the lowest common multiple (lcm), or the smallest common multiple of two numbers (a and b).
The given ratio is 4:7, which can be written as 4/7.
To find the individual numbers, we can use the formula:
Number1 = LCM × Ratio1/ (Ratio1 + Ratio2)
Number2 = LCM × Ratio2/ (Ratio1 + Ratio2)
Therefore,
Number1 = 168 × 4/ (4 + 7) = 56
Number2 = 168 × 7/ (4 + 7) = 98
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you are given two boxes with a number inside each box. the two numbers are different but you have no idea what they are. you pick one box to open; read the number inside; and then guess if the number in the other box is larger or smaller. you win if you guess correctly, and lose otherwise. is there anyway that you can win the game with more than 50% chances no matter what the two numbers are?
The required chances to win the game is more than 50% no matter what two are.
What is probability?The probability is the proportion of the likelihood of an occasion to occur. It estimates the conviction of the occasion. The recipe for likelihood is given by; P(E) = Number of Ideal Results/Number of all out results.
According to question:
Allow the two numbers to be an and b, with a<b. Look at an acknowledgment of X (free of your decision of an or b) with the worth of the main number you see. Assuming that X is greater, switch, in any case keep the number.
The likelihood of winning can be registered as follows:
In the event that you pick a (with 12 possibility), you win assuming you switch, ie if X>a. This has prob. P(X>a).
Comparably assuming you pick b (with 12 possibility), you win on the off chance that you don't switch, ie if X≤b. This has prob. P(X≤b).
So the general likelihood of winning is 1/2+1/2P(a<X≤b), which is marginally bigger than 1/2 in view of our presumptions on X.
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Find the dimensions of a rectangle (in m) with perimeter 60 m whose area is as large as possible. (enter the dimensions as a comma-separated list. ).
The dimension of a rectangle is 15m and 15m.
Here we have to find the area of a rectangle as large as possible.
Data given:
Perimeter = 60m
The formula for the perimeter of the rectangle:
perimeter = 2(length + breadth)
60 = 2( l + b)
l + b = 30
We have to find the largest area, so when we will take the length and
breadth same then we get the largest area.
So length = breadth
2 length = 30
length = 15m
length = breadth = 15m
Therefore the dimensions are 15m and 15m.
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In circle Q, QR = 6 and the area of shaded sector=15. Find the length of RTS.
Express your answer as a fraction times .
S
77
The area of the shaded sector of the circle will be 12π units².
What is the Area of a Sector?Area of a sector of a circle = θ/360 × πr², where r is the radius of the circle and θ is the central angle.
In circle Q, QR = 6 and m∠RQS = 120°.
As per the given question given data:
θ = 120°
r = QR = 6
Substitute the values in the formula to get:
Area of sector of a circle = 120/360 × π(6)²
Area of sector of a circle = 1/3 × π(36)
Area of a sector of a circle = 12π units²
Thus, the area of the shaded sector of the circle is 12π units².
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The question seems to be incomplete the correct question would be:
In circle Q, QR = 6 and m∠RQS = 120°. Find the area of the shaded sector.
Express your answer as a fraction times pi.
What is a square Class 1?
A square Class 1 is a type of four-sided polygon. It is a regular polygon, meaning that all of its sides have the same length and all of its angles are equal.
There are only right angles in a square. Having the opposing sides parallel defines a square as a quadrilateral. Only one dimension, the side length, may be used to describe a square. Each angle is 90° in length and has an equal number of sides. To help you comprehend the topic better, let's talk more about square angles and work through a few instances. A square Class 1 is a type of four-sided polygon. It is a regular polygon, meaning that all of its sides have equal length and all of its angles are equal. The sides of a square Class 1 are all of the same length, and the angles between them are all 90 degrees. This type of polygon is also known as a regular square.
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evaluate 7 to the power of negative 2
-14
1/19
-49
-1/19
The value of the expression 7 to the power of negative 2 is 1/49.
Option B is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex]7^{-2}[/tex]
The value of this expression.
= 1/7²
= 1/49
Thus,
The value [tex]7^{-2}[/tex] is 1/49.
Option B is the correct answer.
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Can the distributive property be used to rewrite
2 x (7- 4)?
If yes, fill in the blanks below.
(? x ?) - ( ? x ?)
Yes the distributive property can be used to rewrite the equation 2 x (7- 4) to appear in the form
(2 * 7) - (2 * 4)What is the distributive property of multiplication?This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.
In other words, an equation of the type A (B + C) can be solved as
= A (B + C)
= AB + AC
in accordance with the distributive property.
As it relates to the problem, 2 x (7- 4)
A = 2
B = 7
C = 4
2 x (7- 4)
= 2 * 7 - 2 * 4
The distributive property is also applicable to subtraction as used in the problem,
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