Answer:
70,110,110
Step-by-step explanation:
angles in a parallelogram=360, opposite angles are equal, so two of the angles measure 70° each, 70+70=140, 360-140= 220, 220÷2= 110
solve for x using cross multiplication x+2/4=x+5/5
Answer:
There are no solutions
Step-by-step explanation:
x + 2/4 = x + 5/5
x + 1/2 = x + 1
1/2 = 1 or 0.5 = 1
or
x + 2/4 = x + 5/5
x + 1/2 = x + 1
0 = 1/2 or 0 = 0.5
How to graph -1/2x-2/3y=3/4
Answer:
To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = MX + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.
Step-by-step explanation:
Simplify all questions
√(3-√15)²-√(3+√15)²
3√c² if c≥0
√(x²+1)²=5
-5√y² if y>0
0.5√16a² if a<0
The given equations can be simplified as :
a. -2.√15
b. c ≥ 0
c. x = ±2√6
d. y < 0
e. a > 0
How to solve inequalities ?
When solving an inequality:
you can add the same quantity to each side you can subtract the same quantity from each side you can multiply or divide each side by the same positive quantity If you multiply or divide each side by a negative quantity, the inequality symbol must be reversed.a.
Given : √(3-√15)²-√(3+√15)²
√(3-√15)²-√(3+√15)² = (3-√15)-(3+√15)
√(3-√15)²-√(3+√15)² = 0 -2√15
√(3-√15)²-√(3+√15)² = -2.√15
b .
Given : 3√c² if c≥0
3√c² if c≥0
c ≥ 0
c.
Given: √(x²+1)²=5
√(x²+1)²=5
on Squaring both sides , we get
(x²+1) = 25
x² = 24
x = ±2√6
d.
Given : -5√y² if y>0
-5√y² if y>0
y < 0 [since , -5 < 0]
e.
Given : 0.5√16a² if a<0
0.5√16a² if a<0
a > 0
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At a busy street corner in a large city, right at the morning rush hour, a psychologist counted the number of people waiting for the light to change. A confederate dressed as a homeless man crossed the street against the light. The psychologist counted the number of people who followed him. Whern the next group collected to wait for the light to change, another confederate, dressed as a well-to-do businessman, crossed the street against the light, and the psychologist counted the number of people who followed him. Analyze the data, X2, Write the conclusions and answer the question below Followed Did Not Follow Homeless Man 3 15 Businessman 8 7 What can the psychologist say about the influence of appearance on whether or not a person takes risks?
Interpretation: At level of significance a = 0.05, the evidence is sufficient. A person's risk-taking behavior is influenced by their appearance.
What do hypotheses and null hypotheses mean?Using a statistical test, researchers compare the evidence supporting the null and alternative hypotheses, which are two conflicting claims: There is no population impact, or null hypothesis (H0). There is a population effect, or alternative hypothesis (Ha or H1).
Here,
Procedure for the Mega Stat Excel add-in:
The first step is to choose Add-Ins > Mega Stat > Chi-square/Crosstab > Contingency Table in EXCEL.
Step 2: Select the cell range A1:C3 in the input range box.
Step 3. Pick chi-square under Output Options. Click OK in Step 4.
Mega Stat output from the Excel add-in
Test for Independence Using a Chi-Square Contingency Table
Total Number of Followed Did Not Follow
Homeless Man 3 15 18
Businessman 8 7 15
Total 11 22 33
4.95 chi-square
1 df
.0261 p-value
Consequently, the p-value is 0.0261.
Decide on a significance threshold of 0.05.
The p-value in this instance, which is lower than the value of a = 0.05, is 0.0261. In other words, the p-value was (=0.0261) (=0.05).
Reject the null hypothesis in light of the rejection rule. [tex]H_{0}[/tex]
Interpretation: At level of significance a = 0.05, the evidence is sufficient. A person's risk-taking behavior is influenced by their appearance.
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Myra is taking her first hot-air balloon ride! The balloon was at an altitude of 288 meters until an air current caused it to rise another 36 meters.
What is the altitude of the balloon now?
The altitude of the balloon now is 324 meters
How to determine the altitude of the balloon now?From the question, we have the following parameters that can be used in our computation:
Initial altitude = 288 meters
Rise = 36 meters
The altitude of the balloon now is calculated as
Current altitude = Initial altitude + Rise in altitude
Substitute the known values in the above equation, so, we have the following representation
Current altitude = 288 + 36
Evaluate the sum
Current altitude = 324
Hence, the current altitude is 324 meters
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Part A: In two or more sentences, explain what a variable expense is and provide at least two examples.
Part B: In two or more sentences, explain what a fixed expense is and provide at least two examples.
An essential part of a business' operations is its fixed and variable expenses.
What is fixed expense?It is an expenditure that does not fluctuate, or rather, does not alter over time.
An illustration of a fixed expense is:
1. Mortgage,
2. Rent payments,
3. Utility bills etc
Let see about Variable expense:
It is a cost that typically varies based on how the business uses the goods or services.
Examples of variable costs are as follows:
1. Sales commissions
2. Direct labor costs
3. Cost of raw materials etc
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A store is having a sale on jelly beans and almonds. For 7 pounds of jelly beans and 9 pounds of almonds, the total cost is $46. For 5 pounds of jelly beans and 3 pounds of almonds, the total cost is $20. Find the cost for each pound of jelly beans and each pound of almonds.
Answer:
jelly beans: $1.75 per poundalmonds: $3.75 per poundStep-by-step explanation:
You want to know the prices of jelly beans and almonds when you can buy 7 pounds of jelly beans and 9 pounds of almonds for $46, or 5 pounds of jelly beans and 3 pounds of almonds for $20.
EquationsThe equations describing each purchase can be written as ...
7j +9a = 465j +3a = 20SolutionA graphing calculator plots these equations easily, and shows you the solution is (j, a) = (1.75, 3.75).
Jelly beans are $1.75 per pound; almonds are $3.75 per pound.
EliminationIf you like, you can solve these equations by elimination. We notice the coefficients of 'a' have a simple ratio, so we can eliminate 'a' easily.
3(5j +3a) -(7j +9a) = 3(20) -(46) . . . . . subtract the first from 3 times the second
8j = 14 . . . . . simplify
j = 1.75 . . . . . divide by 8
Substituting into the second equation, we get ...
5(1.75) +3a = 20
3a = 11.25 . . . . . . . . . subtract 8.75
a = 3.75 . . . . . . . . divide by 3
Jelly beans are $1.75 per pound; almonds are $3.75 per pound.
Which of the following is an equivalent expression of 14x² +18x + 5?
A 32x³ +5
B 14x²(18x + 5)
C 5(14x² + 18x)
D 18x + 14x² +5
Answer: the correct answer is D
Step-by-step explanation:
Graph the solution to the following system of inequalities.
y≤2x+3
y> -3x+5
The solution to the inequality is (0.4.3.8). The graph of the inequalities is attached with the answer.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given inequalities are.
y≤2x+3
y> -3x+5
When we plot the graph of the inequalities on the x-y axis the two lines intersect at the point (0.4,3.8). The graph is attached with the answer below.
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Can I have some days free because I really am struggling with math these days and I have no money
Please
God loves you
Camilla wants to attach a string of lights to the edges of her patio
for a party She does not want the string to go across the edge with
the steps. White a linear expression that represents the length of
string in feet she will need. Then find the length if x = 3. 7.EE1
4x-2
3r
The length of string in feet she will need for her patio is equal to : L{s} = 2(x + y).
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is Camilla who wants to attach a string of lights to the edges of her patio for a party. She does not want the string to go across the edge with the steps.
Assume the shape of the patio is a rectangle with the dimensions of [x] and [y] units long. The length of string in feet she will need will be equivalent to the perimeter of the rectangle. So, the length of string in feet she will need is equal to L{s} = 2(x + y).
Therefore, the length of string in feet she will need for her patio is equal to : L{s} = 2(x + y).
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186283 miles every second is how many feet per hour
Step-by-step explanation:
To convert 186283 miles per second to feet per hour, we need to first convert the distance from miles to feet. There are 5280 feet in a mile, so 186283 miles is equal to 186283 * 5280 = 9,839,784,000 feet.
We also need to convert the time from seconds to hours. There are 3600 seconds in an hour, so 186283 seconds is equal to 186283 / 3600 = 51.8 hours.
Therefore, 186283 miles per second is equal to 9,839,784,000 feet per 51.8 hours, or approximately 188,822,900 feet per hour. This is the final answer.
G(x) = 4x - 5, find g(3)
To find the value of g(3), we need to substitute the value 3 into the expression for G(x) in place of x and then evaluate the resulting expression. Since G(x) = 4x - 5, we can substitute 3 for x to get G(3) = 4 * 3 - 5 = 12 - 5 = 7. Therefore, g(3) = 7.
The temperature, t, in degrees Fahrenheit, can be found by counting the number of cricket chirps, c, heard in 14 seconds and then adding 40. The equation t = c + 40 models the relationship between the temperature and the number of cricket chirps. What is true about the graph that represents this real-world scenario? Select two options.
The graph is continuous.
All values of t must be positive.
A viable solution is (-2,38)
A viable solution is (0.5, 40.5)
A viable solution is (10,50)
The two true options are A and D
The two options that are true about the graph that represents this real-world scenario are;
All the t values must be positive, and a viable solution is (10, 50). Hence, the correct option for this question is A and D.
Plotting the data in the graph is advantageous because it gives a visual presentation of the data and makes it easy to observe and forecast the large data set in a short time.
In the case of this question, the temperature is directly reliant on the c number of cricket chirps heard in 14 seconds. Therefore, if all the c values must be positive integers, the values of t must also be positive numbers.
t = c + 40
Because 10 is a positive integer, it is a possible c value
If c = 10
t = 40 + 10
t = 50
A viable solution (10, 50) represents the values of c and t, respectively, to predict the data more accurately and with validity.
Therefore, the correct option for this question is A and D.
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A taxi service charges $1.50 plus $0.60 per mile for a trip to the airport. The total charge is $13.50. Determine how many miles it is to the airport.
Using the linear function y = 0.6x + 1.5, he drove 20 miles to be charged $13.50
Linear FunctionThe parent linear function is f(x) = x, which is a line passing through the origin. In general, a linear function equation is f(x) = mx + c
where m is the slope of the equation and c is the y - intercept.
To solve this problem, we have to write an equation that models y = mx + c
c = constant = service charge = 1.50m = slope = 0.60The linear function to model this is given as;
y = 0.6x + 1.5
Assuming a trip cost 13.50, the number of miles can be calculated as;
13.50 = 0.6x + 1.5
0.6x = 13.50 - 1.5
0.6x = 12
x = 12/0.6
x = 20
The drove 20 miles
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Use the Fundamental Theorem of Calculus to find an expression for the derivative of the given function defined on the given interval, if it exists.
F(x) = â«^x t+1/t-1 dt, [1,5]
The derivative of the function is not defined overall on the interval [1, 5]
What is the Fundamental Theorem of Calculus?The essential connection between areas under curves and function derivatives is the Fundamental Theorem of Calculus. The first fundamental theorem of calculus's first section asserts that an integral of a function f over an interval with a variable upper bound can be used to derive an antiderivative or indefinite integral of f. This implies that continuous functions have antiderivatives.The second fundamental theorem of calculus, on the other hand, asserts that the integral of a function f over a specified interval equals the change of any antiderivative F between the endpoints of the interval.Here ,[tex]F(x)=\int_{a}^{x}\frac{t +1}{t - 1} dt\\\\F^{'}(x) = \frac{x+1}{x-1}[/tex]
The derivative of the function is not defined overall on the interval [1, 5] as x = 1 makes the derivation infinite.To learn more about calculus, refer:
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. (PLEASE HELP!!!)
Write a rule that transforms ABC into A'B'C'
Answer:
(x - 5, y - 1)
Step-by-step explanation:
The x value tells how many units to move right or left. Right would be adding to x and left would be subtracting from x.
The figure is moved 5 spaces left that would be a rule of x -5.
The y value tells how many units to move up or down. Up would be addition and down would be subtraction. In this case, we are moving the figure down one unit so the rule would be y - 1
Estimate y when x = 8 from the best fitted straight line y = 13.06 + 0.6x.
Answer:
y = 17.86
Step-by-step explanation:
y = 13.06 + .6x Substitute in 8 for x
y = 13.06 + .6(8)
y = 13.06 + 4.8
y = 17.86
One person from those who responded will be selected at random. Which of the following is closest to the probability that the person selected will be someone who responded no, given that the person selected is age 55 or older?
a. 0.350
b. 0.427
c. 0.462
d. 0.757
e. 0.818
Given that they are age 55 or older, it is discovered that there is a (E) 0.8181 = 81.81% probability that the person said no.
What is the probability?Simply put, probability refers to the likelihood that something will occur.
If we don't know how an event will turn out, one can discuss the probability or likelihood of several events.
Statistics is the study of occurrences that match a probability distribution.
So, as 36 out of 44 adults aged 55 or older chose not to answer the question, the probability is given by:
p = 36/44 = 0.8181
Therefore, given that they are age 55 or older, it is discovered that there is a (E) 0.8181 = 81.81% probability that the person said no.
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Solve for pressure #2 using Bernoullis equation
What is the definition of Bernoulli's principle?
In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy.
p+12ρ v2+ρgh=konstant Bernoulli equation(1)
Two states on a streamline are thus linked by the following equation:
p1+12ρv21+ρgh1=p2+12ρv22+ρgh2p1+12ρv21=p2+12ρv22p2=p1+12ρv21−12ρv2
Due to the constriction of the cross-section to only half the size, the flow speed is doubled. All known values can now be put in equation (5). Note that the pressure is to be used in the basic unit N/m² and the density in the unit kg/m³.
p2=p1+12ρv21−12ρv22p2=4⋅105Nm²+121000kgm³ (4ms)2–121000kgm³ (8ms)2=3.76⋅105Nm²p2=3.76 bar
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I NEED HELP ASAP!!! Martina and Sabrina created a number pattern that began with the number 0.
• Martina used the rule “Add 2.”
• Sabrina used the rule “Add 6.”
Which statement is true about each corresponding pair of numbers in the two patterns?
Responses
A Each number in Sabrina’s pattern is 4 more than the corresponding number in Martina’s pattern.Each number in Sabrina’s pattern is 4 more than the corresponding number in Martina’s pattern.
B Each number in Sabrina’s pattern is 3 times the corresponding number in Martina’s pattern. Each number in Sabrina’s pattern is 3 times the corresponding number in Martina’s pattern.
C Each number in Sabrina’s pattern is 4 times the corresponding number in Martina’s pattern. Each number in Sabrina’s pattern is 4 times the corresponding number in Martina’s pattern.
D Each number in Sabrina’s pattern is 4 less than the corresponding number in Martina’s pattern.
The correct statement is "each number in Sabrina’s pattern is 3 times the corresponding number in Martina’s pattern. Each number in Sabrina’s pattern is 3 times the corresponding number in Martina’s pattern."
What is a statement?
A statement in mathematics is a declarative utterance that can only be either true or false. A proposal is another name for a statement. It's important that there be no ambiguity. A sentence can only be true or untrue and not both for it to be a statement.
Given that:
Martina used the rule “Add 2.”
Sabrina used the rule “Add 6.”
The rule that Martina is follow is
M(n) = starting number + 2n
M(n) = 0 + 2n
M(n) = 2n
The rule that Sabrina is follow is
S(n) = starting number + 6n
S(n) = 0 + 6n
S(n) = 6n
S(n) = 3 × 2n
S(n) = 3 × S(n)
Thus Each number in Sabrina’s pattern is 3 times the corresponding number in Martina’s pattern. Each number in Sabrina’s pattern is 3 times the corresponding number in Martina’s pattern.
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Which can be represented by the expression 5+3(x-6)
O6 less than 3 times the sum of a number and 5
O the sum of 5 and 3 times the difference of a numbe
Othe cube of the sum of a number and 3 less than 5
the difference between 5 and the cube of the difference of a number and 6
Correct answer of the expression 5+3(x+6) is the sum of 5 and 3 times the difference of a number by 6
what is expression?A finite collection of symbols that are well-formed in mathematics according to context-dependent principles is called an expression or mathematical expression.
given
the expression 5+3(x+6)
it is concluded from the expression 5+3(x+6) that the sum of 5 and 3 times the difference of the number which is x by 6
so the correct answer of the expression 5+3(x+6) is the sum of 5 and 3 times the difference of a number by 6
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Solve 7x-6y=17 for y.
The value of y in the linear equation 7x - 6y = 17 is y = -(17 + 7x)/6
Linear EquationLinear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable.
In this problem, we are to solve for y.
7x - 6y = 17
Step 1
Take 7x to the right hand side of the equation
-6y = 17 - 7x
Step 2
Divide both sides by the coefficient of y
-6y / -6 = (17 - 7x) / - 6
y = - (17 + 7x) / 6
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Jocelyn and her children went into a movie theater and she bought $75.50 worth of candies and pretzels. Each candy costs $4.75 and each pretzel costs $3.50. She bought a total of 18 candies and pretzels altogether. Determine the number of candies and the number of pretzels that Jocelyn bought.
Jocelyn buys 41 candies and 25 pretzels by solving system equation using elimination method.
What is a linear equation?
The equations with one, zero, or an infinite number of solutions are known as linear equations with two variables. Each of the two variables in these equations has the largest exponent order of 1. A two-variable linear equation has the conventional form axe + by + c = 0, where x and y are the two variables. The answers can also be expressed as ordered pairs, such as (x, y).
Given that the cost of 1 candy is $4.75 and 1 pretzel is $3.50.
Jocelyn buys 18 candies and pretzels altogether with cost $75.50.
Assume that she buys x candies and y pretzels
Therefore,
x + y = 18 ......(i)
The cost of x candies and y pretzels is 4.75x + 3.50y.
4.75x + 3.50y = 75.50 .....(ii)
Solving equation (i) and (ii) by using elimination method.
Multiply equation (i) by 4.75
4.75x + 4.75y = 85.5 ....(iii)
Subtract equation (ii) from (iii)
4.75x + 4.75y = 85.5
4.75x + 3.50y = 75.50
(-) (-) (-)
________________
1.25 y = 10
y = 8
Putting y = 8 in equation (i)
x + 8 = 18
x = 10
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It is given that Cos(A) = 1/4 and Sin(B) = 1/2
Where A is in the 3rd quadrant and B is in the 2nd quadrant
a) Find value of Sin(A)
b) Find Value of Cos(A)
c) Find value of cos(A + B) and cos (A - B)
d) Find Value of Sin(A + B) and sin (A - B)
e) What is the quadrant of A + B and A - B
f) Find the value of Sin(2A + 2B)
The answers for the following trigonometric functions are:
a) Sin(A)=√15/4
b) Cos(A)=1/4
c) Cos(A+B)=(√3-√15)/8
Cos (A- B)=(√3+15)/8
d) Sin(A+ B) =(3√5+1)/8
Sin (A- B)==(3√5-1)/8
e) The quadrant of A+B and A-B is 4th quadrant
f) Sin(2A + 2B)= (√15-6√5+4√3)/8
What are trigonometric functions?The trigonometric functions in mathematics are real functions that link the angle of a right-angled triangle to the ratios of two side lengths. They are also known as circular functions, angle functions, or goniometric functions. They are widely employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many more. Because they are some of the most basic periodic functions, Fourier analysis is frequently employed to examine periodic events.
The sine, cosine, and tangent are the trigonometric functions that are most frequently utilized in contemporary mathematics.
Given,
Cos(A) = 1/4 and Sin(B) = 1/2
4=√1+x²
1+x²=16
x²=15
x=√15
4=1+x²
x²=3
x=√3
a) Sin(A)=√15/4
Sin(B)=1/2
b) Cos(A)=1/4
Cos(B)=√3/2
c) Cos(A+B)=CosACosB-SinASinB
=(1/4)(1/2)-(√15/4)(1/2)
=(√3-√15)/8
Cos(A-B)=CosACosB+SinASinB
=(1/4)(√3/2)+(√15/4)(1/2)
=(√3+15)/8
d) Sin(A+B)+SinACosB+CosASinB
=(√15/4)(√3/2)+(1/4)(1/2)
=(3√5+1)/8
Sin(A-B)=SinACosB-SinBCosA
=(√15/4)(√3/2)-(1/4)(1/2)
=(3√5-1)/8
e) The quadrant of A+B and A -B is 4th quadrant.
f) Sin(2A+2B)=Sin2ACos2B+Cos2ASin2B
=(√15/8)(1-√3)+((4-√15)/4)(√3/2)
=(√15-3√5+4√3-3√5)/8
=(√15-6√5+4√3)/8
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If x)=x+7 and 9(x)=x-13.
The answer is that, save from 13, all real numbers fall into the domain of (fog)(x).
So, {x|x≠13} option 4 is correct.
What is meant by domain?A function's domain is the collection of all potential inputs. For instance, all real numbers are in the domain of f(x)=x², and all real numbers are in the domain of g(x)=1/x, with the exception of x=0.
Let y = f(x) be a function where x and y are the independent and dependent variables. If a function f offers a means of successfully generating a single value y while using a value for x to that end, then that selected x-value is said to belong to the domain of f.
The result of multiplying the expression for f(x) by the expression for g(x) is (x + 7)(1/x-13).
This can be expressed much more clearly as (x + 7) (x – 13)
All real numbers, with the exception of 13, can be used to replace x in the expression in this condensed form. This is due to the fact that if we substitute 13 for x, our denominator will be equal to 0, making our formula illogical.
The answer is that, save from 13, all real numbers fall into the domain of (fog)(x).
So, {x|x≠13}
Therefore, option 4 is correct.
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help pls will give branliiest if you explain
Answer:
slope = - 2
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (11, - 17) and (x₂, y₂ ) = (2, 1) ← 2 ordered pairs from the table
m = [tex]\frac{1-(-17)}{2-11}[/tex] = [tex]\frac{1+17}{-9}[/tex] = [tex]\frac{18}{-9}[/tex] = - 2
A cactus casts a shadow 33 feet long. At the same time of day,Liam,who is 6 feet tall,casts a shadow 9 feet long,as shown. how tall is the cactus
If x = 2, y = 6, and z = 4, which expression is equivalent to 4? à 54+0-3+2=4. D Xtra 4 ... A tree is 12 feet tall and casts a shadow 9 feet long. A building nearby.
If five standard (six-sided) dice are tossed onto the table, what is the probability that
a. all of them will show an odd number on top?
b. no aces or deuces (that means ones or twos) will show on top?
C. the five dice will show five different values on top?
If Five standard (six-sided) dice are rolled, one at a time. What is the probability that
a. the first two dice show aces, and the next three do not?
b. two of the five dice show aces, and the other three do not?
The probability of getting a specific number on the first roll of the die is 1/6. The probability of getting that same number on five successive rolls is (1/6)^5 = 1/7776. Because there are six different ways to get the same number on five rolls, multiply by 6 to get the probability of the same number on five successive rolls to be 6/7776 =1/1296.
Determining the probability that all five rolls will be different starts with asking how many ways can you choose 5 numbers from six with replacement and without repetition where order does not matter, then dividing that number by the total number of outcomes in five rolls of the die.
The total number of possible rolls is easy. There are six possible outcomes for each of the five rolls, so the total number of possible combinations after 5 rolls is 6^5 = 7776.
Now if each roll has to be a different number, consider that there are six acceptable outcomes on the first roll of the die. There are only five acceptable outcomes on the second roll, four on the third, three on the fourth, and two on the fifth. Multiplying all these together gives 6x5x4x3x2 = 6! = 720 ways to get a different number on five successive rolls of the die. This probability is 720/7776 ( 0.0926 or 9.26% or 120 times greater than getting the same number on each of five rolls.
Consider a game in which six true dice are rolled. What is the probability of obtaining exactly one ace, at least one ace and exactly two aces?
Exactly 1 ace(one) =6C1 * 5^5 = 18750 / 6^6 = 0.401877572
At Least 1 ace(one) =6C1 *5^5 +6C2 * 5^4 + 6C3 * 5^3......6C6 * 5^0= 31031/6^6 = 0.6651020233
Exactly 2 aces(ones) =6C2 * 5^4 = 9375 / 6^6 = 0.200938786
If you require two specific times(e.g. first time and second time) to be 5(probability 1/6), others to be non-5(probability 1−1/6=5/6). The probabiliy is (1/6)2(5/6)3, you have C52=10 different ways to roll two 5. Therefore the answer is 10(1/6)2(5/6)3, which is approximately 0.1608.
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