The integral by interpreting it in terms of areas
[tex](1/2) \times \pi \times 49[/tex]
To evaluate the integral by interpreting it in terms of areas.
Let's solve the given integral:
[tex]\int [-7, 0] (4(49 - x^2)) dx[/tex]
Identify the geometric shape
The integrand, [tex]4(49 - x^2),[/tex] represents a semi-circle with radius 7 [tex](since 49 = 7^2)[/tex] and centered at the origin.
The integration limits are from -7 to 0, which means we are only considering the left half of the semi-circle.
Calculate the area of the entire semi-circle
The area of a circle is given by the formula [tex]A = \pi r^2.[/tex]
Since we're dealing with a semi-circle, we need to take half of that area:
[tex]A = (1/2) \times \pi \times (7^2) = (1/2) \times \pi \times 49[/tex]
Evaluate the integral
Now, we can evaluate the integral by interpreting it as the area of the left half of the semi-circle:
[tex]\int [-7, 0] (4(49 - x^2)) dx = (1/2) \times \pi \times 49[/tex]
So the integral evaluates to:
[tex](1/2) \times \pi \times 49[/tex].
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To evaluate the integral ∫−70(4 49−x2)dx, we can interpret it in terms of areas. We want to find the area under the curve between x = -7 and x = 0, and then subtract it from the area under the curve between x = 0 and x = 7. This gives us the total area enclosed by the curve.
Using the formula for the area of a semicircle (πr2/2), we can calculate the area of each half of the curve separately. The area under the curve between x = -7 and x = 0 is equal to (1/2)π(7^2)/2 = 24.5π, and the area under the curve between x = 0 and x = 7 is also equal to 24.5π. Therefore, the total area enclosed by the curve is 49π.
In summary, evaluating the integral by interpreting it in terms of areas involves visualizing the curve as a geometric shape and finding the areas that it encloses. By breaking down the curve into semicircles, we can use the formula for their areas to find the total area under the curve.
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if the price of an object with 13% vat is Rs 5650 find the net price of the object
Were the non-violent, civil disobedience tactics used by civil rights leaders like dr. king effective at creating change and ending injustice? why or why not
Yes, the non-violent, civil disobedience tactics used by civil right leaders were effective to a great extent at creating change and ending injustice.
How were the civil disobedience tactics effective?
Martin Luther King, Jr.'s and other civil right leaders' leadership and vision were shaped by their steadfast faith in the efficacy of nonviolence and civil disobedience. Although it permitted civil rights protesters to avoid harsher legal penalties, it also had a deeper significance. America only learned about the effectiveness of nonviolent protest as a result of the work of Martin Luther King, Jr. and his civil disobedience allies.
Civil Disobedience Tactics
The Civil Rights Act of 1964 and the Voting Rights Act of 1965 were primarily made possible thanks to King. The Civil Rights Act outlawed discrimination on the basis of "race, color, religion, or national origin" in the workplace and in public places. African Americans' right to vote is safeguarded by the Voting Rights Act.
Inspired by Gandhi, King and other non-violent leaders, utilized civil disobedience to pressure governments to change. It manifested as widespread, nonviolent defiance of official orders. Civil disobedience is the act of refusing to comply with governmental orders or demands and remaining unaffected by the arrest and punishment that may follow.
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PLEASE HELP ME AS SOON AS POSSIBLE
a) The linear function that models the population in t years after 2004 is: P(t) = -200t + 29600.
b) Using the function, the estimate for the population in 2020 is of 26,400.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The initial population in 2004, of 29600, is the y-intercept. In 12 years, the population decayed 2400, hence the slope is:
m = -2400/12 = -200.
Hence the equation is:
P(t) = -200t + 29600.
2020 is 16 years after 2004, hence the estimate is:
P(16) = -200(16) + 29600 = 26,400.
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Module 1: directions: respond to this question to demonstrate your understanding of the topic/content. be sure to provide adequate and relevant details learned in the module to support your response. pay close attention to organizing your response so it makes sense and uses correct grammar. your response should be at least 5-7 sentences at a minimum. question: given the two points (1,5) and (-2, -4), write a set of instructions for your younger cousin that determines the equation of the line in slope-intercept form (y=mx+b). be sure to write the equation.
The slope intercept form of the line whose points are (1,5) and (-2,-4) is y=3x+2.
Given two points of a line (1,5) and (-2,-4).
We have to form an equation in slop intercept form.
Equation is relationship between two or more variables which are expressed in equal to form.Equations of two variables looks like ax+by=c.
Point slope form of an equation is y=x+mc where m is slope of the line.
From two points the formula of equation is as under:
(y-[tex]y_{1}[/tex])=[tex](y_{2} -y_{1} )/(x_{2} -x_{1} )[/tex]*(x-[tex]x_{1}[/tex])
where [tex](x_{1} ,y_{1} ) and (x_{2} ,y_{2} )[/tex] are the points.
Putting the values of [tex]x_{1}[/tex]=1, [tex]x_{2}[/tex]=-2, [tex]y_{1}[/tex]=5 and [tex]y_{2}[/tex]=-4.
y-5=(-4-5/-2-1)*(x-1)
y-5=-9/-3*(x-1)
y-5=3(x-1)
y-5=3x-3
y=3x-3+5
y=3x+2
Hence the slope intercept form of the line having points (1,5)(-2,-4) is y=3x+2.
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Find the area of the polygon with the coordinates (1, 2), (3, 2), (3, 0), and (1, 0)
The area of the polygon is 4 square units
How to determine the area of the polygon?The vertices are given as:
(1, 2), (3, 2), (3, 0), and (1, 0)
The area is then calculated as:
A = 0.5 * |x1y2 - x2y1 +x2y3 - x3y2 + ....... |
So, we have:
A = 0.5 * |1 * 2 - 3 * 2 + 3 * 0 - 2 * 3 + 3 * 0 - 0 * 1 + 1 * 2 - 0 * 1|
Evaluate
A = 0.5 * |-8|
Remove the absolute bracket
A = 0.5 * 8
This gives
A = 4
Hence, the area of the polygon is 4 square units
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Circle U is shown. Chords R T and Q S intersect at a point forming 4 angles. The top left angle is angle 1, and the top right angle is angle 2. Arc R Q is 53 degrees and arc S T is 47 degrees. Angle 1 intersepts arc R Q. Angle 2 intersepts arc R S.
What are the measures of angles 1 and 2?
m∠1 =
°
m∠2 =
°
Answer:
∠1 = 50°∠2 = 130°Step-by-step explanation:
The relation between intercepted arcs and angles at crossing chords can be used to find the angles of interest. That relation tells you the angle where the chords cross is half the sum of the intercepted arcs.
Angle 1The arcs intercepted by the chords making angle 1 are given as 53° and 47°. Half their sum is the measure of angle 1:
∠1 = (53° +47°)/2 = 100°/2
∠1 = 50°
Angle 2Angles 1 and 2 form a linear pair, so angle 2 is the supplement of angle 1.
∠2 = 180° -∠1 = 180° -50°
∠2 = 130°
Based on the calculations, the measures of angles 1 and 2 are 50° and 135° respectively.
What is the theorem of intersecting chord?The theorem of intersecting chord states that when two (2) chords intersect inside a circle, the measure of the angle formed by these chords is equal to one-half (½) of the sum of the two (2) arcs it intercepts.
By applying the theorem of intersecting chord to circle U shown in the image attached below, we can infer and logically deduce that angle 1 will be given by this formula:
m∠1 = ½(53 + 47)
m∠1 = ½(100)
m∠1 = 50°.
Since angles 1 and 2 are linear pair, they are supplementary angles. Thus, we have:
m∠1 + m∠2 = 180°
m∠2 = 180 - m∠1
m∠2 = 180 - 50
m∠2 = 130°.
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Quick algebra 1 question for 15 points!
Only answer if you know the answer, quick shout-out to Yeony2202, tysm for the help!
The cost per person if number of students is 100 given the inverse variation is $46.75
Inverse variationCost per person = CNumber of students = nC = k / n
where,
k = constant of proportionalityIf n = 55 and C = $85
C = k / n
85 = k / 55
85 × 55 = k
4,675 = k
Find C if n = 100
C = k / n
= 4,675 / 100
C = $46.75
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Which is a function?
look at pic
Answer:
option 2 {(12, 3), (11,2), ...}
Step-by-step explanation:
For functions, multiple x-values can have the same y-value but each y-value must have a unique x-value. The second option matches this criterion.
Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 8% each week. The following function represents the weekly weed growth: f(x) = 86(1.08)x. Rewrite the function to show how quickly the weeds grow each day.
f(x) = 86(1.08)7x; grows approximately at a rate of 5.6% daily
f(x) = 86(1.087)x; grows approximately at a rate of 0.56% daily
f(x) = 86(1.01)x; grows approximately at a rate of 0.1% daily
f(x) = 86(1.01)7x; grows approximately at a rate of 1% daily
The function is f(x) = 86(1.01)^7x; grows approximately at a rate of 1% daily
How to rewrite the function?The function is given as:
f(x) = 86(1.08)^x
There are 7 days in a week.
This means that:
1 day = 1/7 week
So, x days is
x day = x/7 week
Substitute x/7 for x in
f(x) = 86(1.08)^(x/7)
Rewrite as:
f(x) = 86(1.08^1/7)^x
Evaluate
f(x) = 86(1.01)^x
In the above, we have:
r = 1.01 - 1
Evaluate
r = 0.01
Express as percentage
r = 1%
Hence, the function is f(x) = 86(1.01)^7x; grows approximately at a rate of 1% daily
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Answer: the answer is d
Step-by-step explanation:
For which pair of functions is the vertex of g(x) 2 units to the right of the vertex of f(x)?
For the following pair of functions, the vertex of g(x) 2 units to the right of f(x),
f(x) = x² and g(x) = (x - 2)²
What are functions?
Defining a relationship between an independent variable and a dependent variable using mathematical expressions, rules, or laws is known as a function. Mathematics is rife with functions, and the sciences depend on them for constructing physical relationships.
Determining the Correct Pair of Functions
For a given function f(x), its horizontal translation would be f(x + a). Here, a is the distance translated, owing to which f(x + a) is generated.
If a > 0, then it indicates a right translation of a units.
If a < 0, then it indicates a left translation of a units.
The required functions are to be such that the vertex of g(x) is 2 units to the right of the vertex of f(x).
Thus, if f(x) = x², then g(x) = (x - 2)²
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Using the quadratic formula, solve the
equation below to find the two possible
values of t.
6x^2-35=-11x
Give each value as a fraction in its
simplest form.
The two possible solutions to the given equation ( 6x^2-35 = -11x ) are x = 5/3 and x = -7/2
What are the two possible solution to the equation?
Given the equation; 6x² - 35 = -11x
The quadratic formula is expressed as;
x = [ -b±√( b² - 4(ac) ]/2a
First, we re-arrange our equation in the form of ax² + bx + c = 0
6x² + 11x - 35 = 0
a = 6b = 11c = -35We substitute into the formula.
x = [ -b±√( b² - 4(ac) ]/2a
x = [ -11±√( 11² - 4( 6 × -35 ) ]/2×6
x = [ -11±√( 121 + 840 ]/12
x = [ -11±√961 ]/12
x = [ -11 ± 31 ]/12
x = (-11 + 31)/12, (-11 + 31 )/12
x = 20/12, -42/12
x = 5/3, -7/2
Therefore, the two possible solutions to the given equation ( 6x^2-35 = -11x ) are x = 5/3 and x = -7/2
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Sa = 2(pi)(r)(h) + 2(pi)(r^2) v = (pi)(r^2)(h) find the surface area and the volume.
If Sa=2πrh+2π[tex]r^{2}[/tex]v=π[tex]r^{2}h[/tex] then the surface area is π[tex]r^{2} h[/tex] and volume is
(rh-2h)/2r.
Given Sa=2πrh+2π[tex]r^{2} v[/tex]=π[tex]r^{2}h[/tex].
We have to find surface area and volume from the given expression.
Volume is basically amount of substance a container can hold in its capacity.
First we will find the value of v from the expression. Because they are in equal to each other, we can easily find the value of v.
2πrh+2π[tex]r^{2}[/tex]v=π[tex]r^{2}[/tex]h
Keeping the term containing v at left side and take all other to right side.
2π[tex]r^{2}[/tex]v=π[tex]r^{2}h[/tex]-2πrh
v=(π[tex]r^{2}[/tex]h-2πrh)/2π[tex]r^{2}[/tex]
v=π[tex]r^{2} h[/tex]/2π[tex]r^{2}[/tex]-2πrh/2π[tex]r^{2}[/tex]
v=h/2-h/r
v=h(r-2)/2r
Put the value of v in Sa=2πrh+2π[tex]r^{2} v[/tex]
Sa=2πrh+2π[tex]r^{2}[/tex]*h(r-2)/2r
=2πrh+2πrh(r-2)/2
=2πrh+πrh(r-2)
=2πrh+π[tex]r^{2}[/tex]h-2πrh
=π[tex]r^{2}[/tex]h
Hence surface area is π[tex]r^{2}[/tex]h and volume is h(r-2)/2.
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An ice cream store charges $3.00 per scoop,$2.00 per topping and $0.75 for each add syrup flavor
a) Write an algebraic expression to represent the cost of the ice cream.
b) Rafael orders 3 scoops of ice cream with added chocolate and marshmallows and peanut syrup and chocolate syrup Use the formula to solve for the cost of the ice cream. show your work
The algebraic expression for the ice cream is 3x + 2y + 0.75z.
The cost of Rafael ice cream is 12 dollars
How to find the algebraic expression that represent cost of the ice cream?The algebraic expression that represent the cost of an ice cream is as follows:
let
number of scoop = x
number of topping = y
number of added syrup = z
Hence,
cost of the ice cream = 3x + 2y + 0.75z
Therefore,
The cost of ice cream Rafael ordered is as follows:
cost of ice cream = 3(3) + 0.75(4)
cost of ice cream = 9 + 3
cost of the ice cream = 12
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Can u guys pls help me with this homework
The value of √(7 * 23 - 1)/8 is 4.47, the values of a, b and c are -14/11, -10/11 and 3, respectively and the area of the shape is 5√5 + 5 square meters
How to evaluate the radical expression?The question goes thus:
If √5 = 2.236, evaluate √(7 * 23 - 1)/8
We have:
√(7 * 23 - 1)/8
Evaluate the product of 7 and 23
√(7 * 23 - 1)/8 = √(161 - 1)/8
Evaluate the difference of 161 and 1
√(7 * 23 - 1)/8 = √160/8
Evaluate the quotient of 160 and 8
√(7 * 23 - 1)/8 = √20
Express 20 as the product 4 and 5
√(7 * 23 - 1)/8 = √(4 * 5)
Expand the product
√(7 * 23 - 1)/8 = √4 * √5
Express √4 as 2
√(7 * 23 - 1)/8 = 2 * √5
Substitute √5 = 2.236
√(7 * 23 - 1)/8 = 2 * 2.236
Evaluate the product
√(7 * 23 - 1)/8 = 4.472
Approximate
√(7 * 23 - 1)/8 = 4.47
Hence, the value of √(7 * 23 - 1)/8 is 4.47
How to simplify the radical expression?The expression is given as:
(3√2 + 5√6)/(3√2 - 5√6)
Rationalize the above expression
(3√2 + 5√6)/(3√2 - 5√6) * (3√2 + 5√6)/(3√2 + 5√6)
Evaluate the product
(3√2 + 5√6)²/((3√2)² - (5√6)²)
Simplify the denominator
(3√2 + 5√6)²/(18 - 150)
This gives
[(3√2)² + (5√6)² + 2 *(3√2) * (5√6)]/(-132)
Simplify the numerator
[168 + 120√3]/(-132)
Simplify the fraction
-14/11 - 10√3/11
Hence, the values of a, b and c are -14/11, -10/11 and 3, respectively
How to determine the area?The area is calculated as:
A = 1/2 * (Sum of parallel bases) * Height
So, we have:
A = 1/2 * (4 + 3√5 + 6 - √5) * √5
Evaluate the like terms
A = 1/2 * (10 + 2√5) * √5
Evaluate the product
A = (5 + √5) * √5
Evaluate the product
A = 5√5 + 5
Hence, the area of the shape is 5√5 + 5 square meters
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State the conditions required for a random variable x to follow a poisson process.
The conditions required for a random variable X to follow a Poisson process. The probability of success is the sme for aany two intervals of equal length. The probability of two or more successes in any sufficiently small subinterval is 0.
Is the time required to upload a file to the Internet discrete or continuous?Is the length of time it takes to download a file from the Internet a random variable, a continuous random variable, or not at all? A continuous random variable, that is.Is the a discrete random variable a continuous random variable or not a random variable?A variable whose value is determined by counting is referred to as a discrete variable. A continuous variable is one whose value may be determined through measurement. A random variable is a variable whose value is the resultant number of an unpredictable event. There are a countable number of potential values for the discrete random variable X.How do you determine whether the random variable is discrete or continuous?A discrete variable is one that is random. if the number of possible values is either countable or finite. Continuous refers to a variable that is random. if the range of possible values includes all conceivable numbers.
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In the 1980’s, a clinical trial was conducted to determine if taking an aspirin daily reduced the incidence of heart attacks. Of 22,071 medical doctors participating in the study, 11,037 were randomly assigned to take aspirin and 11,034 were randomly assigned to the placebo group. Doctors in this group were given a sugar pill disguised to look like aspirin. After six months, the proportion of heart attacks in the two groups was compared. Only 104 doctors who took aspirin had a heart attack, whereas 189 who received the placebo had a heart attack. Can we conclude from this study that taking aspirin reduced the chance of having a heart attack? the purpose of this study was to determine whether taking an aspirin daily reduces the proportion of heart attacks.
There is enough evidence to conclude that taking aspirin cannot reduces the chance of cancer.
Given sample size of patients take aspirin 11037, sample size of patients who have assigned placebo group be 11034. 104 doctors who take aspirin had a heart attack, 189 doctors had placebo had heart attacks.
First we have to form hypothesis.
[tex]H_{0} :p{1} -p_{2} =0[/tex]
[tex]H_{1}:p_{1} -p_{2} < 0[/tex]
We have to find the respective probabilities.
[tex]p_{1}[/tex]=104/11037
=0.0094
[tex]p_{2}[/tex]=189/11034
=0.0171
Now their respective margin of errors.
[tex]s_{1}[/tex]=[tex]\sqrt{ {(0.0094*0.9906)/11037}[/tex]
=0.0009
[tex]s_{2}[/tex]=[tex]\sqrt{0.0171*0.9829}[/tex]
=0.0011
Hence the distribution of the differences,they are given by:
p=[tex]p_{1} -p_{2}[/tex]
=0.0094-0.0171
=-0.0077
S=[tex]\sqrt{s_{1} ^{2}+s_{2} ^{2} }[/tex]
=[tex]\sqrt{(0.0009)^{2} +(0.0011)^{2} }[/tex]
=0.00305
z=(p -f)/S (In which f=0 is the value tested at the null hypothesis)
=(-0.0077-0)/0.00305
=-2.52
p value will be 0.005.
p value of 0.05 significance level.
z=1.96.
1.96>0.005
So we will reject the null hypothesis which means it cannot reduce the whole chance of becomming a heart attack.
Hence there is enough evidence to conclude that taking aspirin cannot reduces the chance of cancer.
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If f(x) and ¹(x) are inverse functions of each other and f(x) = 2x+5, what is f¹ (8)?
-1
T MIN 700
3
8
23
Answer: 3/2
Step-by-step explanation:
[tex]f^{-1}(8)=k \implies f(k)=8\\\\\therefore 2k+5=8\\\\2k=3\\\\k=\frac{3}{2}[/tex]
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equations that have the same solution as the given equation are 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p
Writing equationsFrom the question, we are to determine the equations that have the same solution as the given equation
The given equation is
2.3p – 10.1 = 6.5p – 4 – 0.01p
Simplifying,
2.3p – 10.1 = 6.5p – 0.01p – 4
2.3p – 10.1 = 6.49p – 4
Thus, 2.3p – 10.1 = 6.49p – 4 is equivalent to the given equation
Also,
If we multiply both sides of the given equation by 100
That is,
100 × (2.3p – 10.1) = 100 × (6.5p – 4 – 0.01p)
230p – 1010 = 650p – 400 – p
∴ 230p – 1010 = 650p – 400 – p is equivalent to the given equation
Hence, the equations that have the same solution as the given equation are 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p
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35 POINTS please help asap
Type the correct answer in each box. Use numerals instead of words.
This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?
f(x) = _x(x - _)
f(x) = _(x − _)^2 + _
i know for sure the first four blanks are 2, 4, 2, and 2 but the last is NOT 8.
The quadratic equation given in the graph can be represented in these two following ways:
Factored: f(x) = 2x(x - 4).Vertex form: y = 2(x - 2)² - 8.What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
In this graph, the roots are [tex]x_1 = 0, x_2 = 4[/tex], hence the factored form of the polynomial is:
f(x) = ax(x - 4).
When x = 5, y = 10, hence the leading coefficient is found as follows:
10 = 5a(5 - 4)
5a = 10
a = 2.
Hence the factored form of the polynomial is:
f(x) = 2x(x - 4).
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, the vertex is at point (2,-8), hence h = 2, k = -8 and:
y = a(x - 2)² - 8
When x = 5, y = 10, hence the leading coefficient is found as follows:
10 = a(5 - 2)² - 8
9a = 18
a = 2.
Hence the equation in vertex-form is:
y = 2(x - 2)² - 8
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Nine tiles are numbered $\color[rgb]{0.35,0.35,0.35}1, 2, 3, \ldots, 9$. Each of three players randomly selects and keeps three of the tiles, and sums those three values. Find the probability that all three players obtain an odd sum.
The probability that all three players obtain an odd sum is 3/14.
What is probability?The probability is the ratio of possible distributions to the total distributions.
I.e.,
Probability = (possible distributions)/(total distributions)
Calculation:Given that,
There are nine tiles - 1, 2, 3,...9, respectively.
A player must have an odd number of odd tiles to get an odd sum. That means he can either have three odd tiles, or two even tiles and an odd tile.
In the given nine tiles the number of odd tiles = 5 and the number of even tiles = 4.
The only possibility is that one player gets 3 odd tiles and the other two players get 2 even tiles and 1 odd tile.
So,
One player can be selected in [tex]^3C_1[/tex] ways.
The 3 odd tiles out of 5 can be selected in [tex]^5C_3[/tex] ways.
The remaining 2 odd tiles can be selected and distributed in [tex]^2C_1[/tex] ways.
The remaining 4 even tiles can be equally distributed in [tex]\frac{4 ! \cdot 2 !}{(2 !)^{2} \cdot 2 !}[/tex] ways.
So, the possible distributions = [tex]^3C_1[/tex] × [tex]^5C_3[/tex] × [tex]^2C_1[/tex] × [tex]\frac{4 ! \cdot 2 !}{(2 !)^{2} \cdot 2 !}[/tex]
⇒ 3 × 10 × 2 × 6 = 360
To find the total distributions,
The first player needs 3 tiles from the 9 tiles in [tex]^9C3=84[/tex] ways
The second player needs 3 tiles from the remaining 6 tiles in [tex]^6C_3=20[/tex] ways
The third player takes the remaining tiles in 1 way.
So, the total distributions = 84 × 20 × 1 = 1680
Therefore, the required probability = (possible distributions)/(total distributions)
⇒ Probability = 360/1680 = 3/14.
So, the required probability for the three players to obtain an odd sum is 3/14.
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PLEASE HELP IM SERIOUSLY STUCK
Answer: -1
Step-by-step explanation:
Remember to use the slope formula.
[tex]\frac{y2-y1}{x2-x1}[/tex]
Then plug in your points:
[tex]m=\frac{-1-(4)}{2-(3)}[/tex]
Simplify
[tex]m=\frac{-5}{5}[/tex]
Divide -5 by 5 and your Answer is:
[tex]m=-1[/tex]
Hopes this helps!
Answer:
-1
Step-by-step explanation:
As given in the picture you provided, the slope is defined as: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] and the reason for this, is because in subtracting y_1 from y_2, you're finding how much the y-value changed, or in other words, the rise. When subtracting x_1 from x_2 you're finding how much the x-value changed, or in other words the run. Another way of expressing the slope that you may have seen is: [tex]\frac{rise}{run}[/tex] which is essentially what this slope formula is doing.
One thing to note is that what I assign to (x_1, y_1) and (x_2, y_1) doesn't matter, as long as they're two different points on the linear line.
So let's just say that: [tex](x_1, y_1) = (-3, 4)[/tex] and that: [tex](x_2, y_2) = (2, -1)[/tex]
Now plugging these values into the equation we get: [tex]\frac{-1-4}{2-(-3)} = \frac{-5}{5} = -1[/tex]
So the slope is -1
Find x such that the matrix is singular. A = 3 x −6 −4 x =
The matrix A becomes singular when x is equal to ±√8 (positive or negative square root of 8).
We have,
Matrix A becomes singular (i.e., its determinant is zero).
The given matrix A is:
A = | 3x -6 |
| -4 x |
Using the determinant formula for a 2x2 matrix, we have:
det(A) = (3x * x) - (-6 * -4)
Simplifying the expression:
det(A) = 3x^2 - 24
To find the value of x for which det(A) = 0, we set the determinant equal to zero:
3x^2 - 24 = 0
Now, we can solve this quadratic equation for x:
3x^2 = 24
x^2 = 8
x = ±√8
Therefore,
The matrix A becomes singular when x is equal to ±√8 (positive or negative square root of 8).
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Which systems of equations have no real number solutions? Check all that apply.
Oy=x² + 4x + 7 and y = 2
□ y=x²-2 and y=x+5
-Oy=-x²-3 and y = 9 + 2x
y=-3x-6 and y = 2x² - 7x
y=x² and y = 10 - 8x
Answer + Step-by-step explanation:
Recall That the number of solution
of a quadratic equation ax² + bx + c = 0
depends on the discriminant b² - 4ac :
if b² - 4ac > 0 , the equation has two distinct solutions.
if b² - 4ac = 0 , the equation has only one solution.
if b² - 4ac < 0 , the equation has no solutions.
=======================================
System 1 :
y = x² + 4x + 7 and y = 2
⇔ x² + 4x + 7 = 2
⇔ x² + 4x + 5 = 0
→ b² - 4ac = 4² - 4×1×5 = 16 - 20 = -4 < 0
Then the quadratic equation has no solutions
Therefore the system has no solutions.
System 2 :
y = x² - 2 and y = x + 5
⇔ x² - 2 = x + 5
⇔ x² - x - 7 = 0
→ b² - 4ac = (-1)² + 4×7 = 29 > 0
Then the quadratic equation has two solutions
Therefore the system has two solutions.
System 3 :
y = -x² - 3 and y = 9 + 2x
⇔ -x² - 3 = 9 + 2x
⇔ -x² - 2x - 12 = 0
→ b² - 4ac = (-2)² - 4×(-1)×(-12) = 4 - 48 = -44 < 0
Then the quadratic equation has no solutions
Therefore the system has two solutions.
System 4 :
y = -3x - 6 and y = 2x² - 7x
⇔ -3x - 6 = 2x² - 7x
⇔ 2x² - 4x + 6 = 0
→ b² - 4ac = (-4)² - 4×(2)×(6) = 16 - 48 = -32 < 0
Then the quadratic equation has no solutions
Therefore the system has two solutions.
System 5 :
y = x² and y = 10 - 8x
⇔ x² = 10 - 8x
⇔ x² + 8x - 10 = 0
→ b² - 4ac = 8² - 4×1×(-10) = 64 + 40 = 104 > 0
Then the quadratic equation has two solutions
Therefore the system has two solutions.
can someone please help mee
Answer:
5/13
Step-by-step explanation:
sine=opposite/hypotenuse
cosine=adjacent/hypotenuse
opposite=-12 (I know that this is not possible)
hypotenuse=13
These are ratios, not real lengths
using the Pythagorean theorem, the other leg is 5
cos (theta)=5/13
PLS HELP FAST
Kryton -85 is a radioisotope of krypton that has a half-life of about 10.75years. This isotope is produced by the nuclear fission of uranium and plutonium in nuclear weapons and in nuclear reactors, as well as cosmic rays. An important goal of the Limited Nuclear Test Ban Treaty of 1963 was to eliminate the release of such radioisotopes into the atmosphere. At present, the activity of Krypton -85 in the atmosphere is about 135 mCi.
How much Krypton -85 will be present in the atmosphere after 12,532days?
Using an exponential function, it is found that 14.75 mCi of Krypton -85 will be present in the atmosphere after 12,532 days.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(0.5)^\frac{t}{h}[/tex]
In which:
A(0) is the initial value.h is the half life, in years.t is the time, in years.In this problem, the parameters are:
A(0) = 135, h = 10.75, t = 12532/365 = 34.334.
Hence the amount is:
[tex]A(t) = A(0)(0.5)^\frac{t}{h}[/tex]
[tex]A(t) = 135(0.5)^\frac{34.334}{10.75}[/tex]
A(t) = 14.75.
14.75 mCi of Krypton -85 will be present in the atmosphere after 12,532 days.
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what ac is equal to
Answer:
AC = 10
Step-by-step explanation:
Formula
(x + 1) + (x + 3) + 2x = 40 Remove the brackets
Solution
x + 1 + x + 3 + 2x = 40 Collect like terms
4x + 4 = 40 Subtract 4 from both sides
4x +4 -4 = 40 - 4 Combine
4x = 36 Divide both sides by 4
4x/4 = 36/4
x = 9
AC = x + 1
AC = 9 + 1
AC = 10
Select the correct answer.
Darren is going to the state fair. Each ride costs $6 to ride, and each exhibit costs $3 to view. Darren can spend at most $84 at the fair.
The inequality and graph that represent this situation are shown, with x representing the number of rides Darren can ride and y representing
the number of exhibits he can view
6x+3y< 84
-10
A (9,10)
B (85.11)
C (11.2)
D. (-3,15)
The solution to the inequality 6x + 3y ≤ 84 is the dark region shown and the point (9, 10) satisfies this inequality.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the number of rides Darren can ride and y represent the number of exhibits he can view. Hence:
6x + 3y ≤ 84
The solution to the inequality 6x + 3y ≤ 84 is the dark region shown and the point (9, 10) satisfies this inequality.
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It was A! I got it right on the Edmentum/Plato test!! YW!!!
Half of a set of the parts are manufactured by machine A and half by machine B. Eight percent of all the parts are defective. Two percent of the parts manufactured on machine A are defective. Find the probability that a part was manufactured on machine A, given that the part is defective. (Round your answer to 4 decimal places.)
The probability that a part was manufactured on machine A, given that the part is defective is P ( A | D ) = 0.024.
What is probability?Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true. The probability of an event is a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty.To find the probability that a part was manufactured on machine A, given that the part is defective:
The probability that a part was manufactured on machine A given that part is defective:
P ( A | D )
P ( A | D ) = [P (A) * P ( D | A )]/ P ( D )
Where: P (A) is the probability that the part is manufactured in machine A which is 0.2 (half of the parts are manufactured in machine A)
P (D/A) is the probability of a defective part given that the part was manufactured in machine A which is 2% or 0.02
And finally, the probability of defective part in the production is 8% or 0.08 hence :
P ( A | D ) = [ ( 0.2 ) * 0.02 ] / 0.08
P ( A | D ) = 0.024
Therefore, the probability that a part was manufactured on machine A, given that the part is defective is P ( A | D ) = 0.024.
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Which terms could be used as the first term of the expression below to create a polynomial written in standard form? Select five options.
+ 8r2s4 – 3r3s3
Which statement is true about the polynomial
5s6t2 + 6st9 – 8s6t2 – 6t7 after it has been fully simplified?
It has 3 terms and a degree of 9.
It has 3 terms and a degree of 10.
It has 4 terms and a degree of 9.
It has 4 terms and a degree of 10.
The polynomial + 8r²s⁴ – 3r³s³ can have a possible first term of -rs⁵
The polynomial 5s⁶t² + 6st⁹ – 8s⁶t² – 6t⁷ has three terms with a degree of 10.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the polynomial + 8r²s⁴ – 3r³s³. The polynomial is of degree 6, hence the possible first term could be -rs⁵
Also, the polynomial 5s⁶t² + 6st⁹ – 8s⁶t² – 6t⁷
= 6st⁹ - 3s⁶t² - 6t⁷
It has three terms with a degree of 10.
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Dad is 4 times as old as his son Jim is now. In 10 years, Dad's age will be 20 years more than twice Jim's age. If D = dad's age now and J = Jim's age now, how old is Jim?
Answer:
Jim is 5
Step-by-step explanation:
word problems can be sort of like translation questions
'times' means multiply
'as old as' means equal or =
'will be' means equal or =
'more than' means plus or +
when I saw
"Dad is 4 times as old as his son Jim is now"
I knew needed to make
Jim = x &
Dad = 4x
when I saw
"In 10 years, Dad's age will be 20 years more than twice Jim's age"
I knew
'Dad's age' means 4x
'In 10 years' means 10 +
'will be' means equal sign or =
'20 years more than' means 20 +
'twice Jim's age' means 2x
sentence can be re written
4x+10=20+2x
'if D = dad's age now' means 4x=D (Dad)
'J = Jim's age now' means x = J (Jim)
I solved for x
4x+10=20+2x
2x=10
x=5
then I checked the math
today
x = Jim = J = 5
4x = Dad = D = 20
'in 10 years'
Dad is 20 + 10 = 30
means
does 30 = 20 years more than twice Jim's age?
does 30 = 20 + 2x ?
does 30 = 20 + 2(5)?
does 30 = 20 + 10?
does 30 = 30?
yes!
it checks out!