A= -10140000 B= 3485800 C= 13414200
Step-by-step explanation: hope this helped!!!
Find an equation of a line with slope m = −25 that contains the point (10,−5). Write your answer in slope-intercept form
Answer:
-25
Step-by-step explanation:
You need at least $220 to do your Christmas shopping. You already have $70. You earn $7.00 dollars per hour at your after-school job. Write and solve an inequality to show how many hours you should work earn your Christmas money.
The unknown in an expression is called the__________________.
-Constant
-Exponent
-Variable
-Coefficient
Pls answer fast thank u!
Answer: The variable
Hope this helps :)
Step-by-step explanation:
A population of beetles are growing according to a linear growth model. The initial population (week 0) is
PO=4
, and the population after 8 weeks is
P8=52
Find an explicit formula for the beetle population after
n weeks
After how many weeks will the beetle population reach 184?
Thus, 18 weeks are needed for the population of beetles to reach 183. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will take place.
How does one determine probability?The number of possible outcomes is divided by the total of possible outcomes to determine probability. Odds are not the same as probability. Odds are calculated by dividing the chance of a given event but by probability that it won't.
How do probability and an example work?For instance, how many heads would appear if you throw a coin 100 times? Assuming a probability of 1/2, we can anticipate 50 heads. However, when we actually attempt it, we might just get 48 heads, 55 heads, or anything else, but most of the time it will be close to 50.
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Find the absolute extrema if they exist, as well as all values of x where they occur, for the function f(x)=(x²-64)^{1/11} on the domain [-8,9]
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. The absolute maximum is , which occurs at x= (Round the absolute maximum to two decimal places as needed. Type an exact answer for the value of x where the maximum occurs. Use a comma to separate answers as needed.)
B. There is no absolute maximum.
The absolute maximum is 1.29, which occurs at x= 9
What is absolute extrema?
An absolute extremum of a perform in an exceedingly given interval is that the purpose at that a most or minimum worth of the perform is obtained. Frequently, the interval given is that the function's domain, and therefore the absolute extremum is that the purpose admire the most or minimum worth of the complete perform.
Main body:
Given =
f(x) = [tex](x^{2} -64)^{1/11[/tex]
f' (x) = derivative of function f(x)
f'(x) = 1/11 . 2x[tex](x^{2} -64)^{-10/11[/tex]
= 2x/11[tex](x^{2} -64)^{-10/11[/tex]
putting f'(x) = 0
2x/11[tex](x^{2} -64)^{-10/11[/tex] = 0
[tex](x^{2} -64)^{-10/11[/tex] = 0
[tex]x^{2} -64[/tex] = 0
x² = 64
x = ±8
We are given interval [-8,9].
Hence, calculating f(x) at -8, 8, 9.
f(-8) = 0
f(8) = 0
f(9) = [tex]17^{1/11[/tex]
= 1.29
Hence, absolute maximum value is 1.29 at x=9.
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Write an equation of the graph.
The equation of the graph in slope intercept form is y = x + 2
How to find the equation of a graph?The equation of a graph can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptHence, let's find the slope using (1, 3) and (2, 4)
Therefore,
slope = 4 - 3 / 2 - 1
slope = 1 / 1
slope = 1
Let's find the y-intercept using (1, 3)
y = x + b
3 = 1 + b
b = 3 - 1
b = 2
Therefore, the equation is y = x + 2
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Suppose that you were trying to use the Putzer method to exponentiate the matrix A which has eigenvalues dı = 4 and A2 = 6, in that order. ao(t) is always the function et. Choose the correct equation for a1(t) da1О (а) 6a1 + e4t a1(0) = 1 O (b) dt da1 : 4a1 + e4t P (g) da1 a1(0) = 1 O (c) dt -4a1 + ett a1(0) = 0 da1 O (d) dt 4a1 + et a1(0) = 0 da1 O (e) : 6a1 + e4t a1(0) = 0 dt da1 O (f) dt — 4а, + e# a,(0) — 1
In that order. ao(t) is always the function is [tex]$$m_1=A-2 I $$[/tex].
What is function ?
A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.
The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.
given: [tex]$\quad d_1=4 \quad$[/tex] and [tex]$A_2=6$[/tex]
[tex]$$m_0=\Sigma=\left[\begin{array}{cc}1 & 0 \\0 & 1\end{array}\right]$$[/tex]
By putzes method
[tex]$$\text { matrix } m_1=A-N_1 p_0=A-d_1 m_0$$[/tex]
here [tex]$r_1=2, m_0=I$[/tex]
[tex]$$m_1=A-2 I $$[/tex]
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Vhich postulate or theorem proves A MNQ~A PNQ?
O AAS Congruence Theorem
O SAS Congruence Postulate
O SSS Congruence Postulate
ASA Congruence Postulate
Answer:
Rhs
Step-by-step explanation:
angle N (R)
pq=mq ( h)
Nq (s)
Please Help ASAP!!
100pts + Brainliest if correct!
1. If a polynomial function with rational coefficients has -4 and 8 as roots, it means we can factor this polynomial this way :
What is rational coefficients?
A coefficient is a number that is placed in front of a variable. A variable and a rational number are preceded by a rational coefficient, which may be an integer, decimal, or fraction.
(x - (-4))(x-8) = (x+4)(x-8) = x² - 8x + 4x - 32 = x² - 4x - 32
1x² - 4x - 32 is a polynomial function of least degree with rational coefficients that satisfices the given conditions. The leading coefficient here is 1, we call this a monic polynomial.
2. There may be something missing in the question here
3. We can use the factoring techniques to find the roots :
x^3 - 5x² + 9x - 45 let us group x^3 with -5x² and 9x with -45 :
(x^3 - 5x²) + (9x - 45) = x²(x - 5) + 9(x - 5)
We can notice now that there is a common factor : (x-5) this allows us to factor again by (x-5) :
Y = (x-5)(x²+9)
This is the maximum we can do on R, but on C the set of complex we can still factor again.
x² + 9 has a negative discriminant : Δ = b² - 4ac where b = 0 , a = 1, c = 9
Δ < 0, Δ = - 36
Applying the formulas for the roots x1 and x2 we get x1 = -3i, and x2 = + 3i
Y = (x-5)(x-3i)(x+3i)
So the solution is S = {5, 3i, -3i} the three roots of the function.
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Say that a woman and a man (who are unrelated) each has two children. We know that at least one of the woman's children is a boy and that the man's oldest child is a boy. Can you explain why the chances that the woman has two boys do not equal the chances that the man has two boys?My algebra teacher insists that the probability is greater that the man has two boys, but I think the chances may be the same. What do you think?
Therefore, the probability that a woman will give birth to two boys is only one in three, whereas the probability that a man will do so is one in two.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here,
The woman may have at least one boy in the three following ways: 1) older boy, younger girl; 2) older girl younger boy; 3) older boy, younger boy.
But the man's children may be distributed in only two ways: 1) older boy, younger girl; or 2) older boy, younger boy.
So the chances are only 1 out of 3 that the woman has two boys, but the chances are 1 out of 2 that the man has two boys.
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m/2 = 10x + 7
2
67°
Q. Solve for x.
e for x.
9
If ∠2=10x+7 and one angle is 67 degrees then value of x is 6.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given that the triangle has two equal sides which makes the triangle as isosceles.
In an isosceles triangle the two sides will be always equal and the angles will be also equal.
One angle of the triangle is 67 degrees
We need to find the ∠2.
As we know that the equal sides make equal angles.
∠2=67 degrees
and from given ∠2=10x+7
Now equation 67 with the 10x+7 to find the value of x.
So 67=10x+7
subtract 7 from both sides
67-7=10x+7-7
60=10x
Divide both sides by 10
x=60/10
x=6
Hence, the value of x is 6.
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Which expressions are equivalent to 8(-10x+ 3.5y - 7)? Select two options.
-80x+ 24.5y-56
-80x+28y-56
80x+28y+56
4(-20x+7y-14)
-4(-20x+ 7y-14
Answer:
-80x + 28y -56
4(-20x + 7y -14)
Step-by-step explanation:
The first answer is distributing the 8 through the whole expression. The second answer is when you factor out a 4.
Match the expression and its value to the value of x that gives the expression its value by filling in the box in the correct column.
Evaluate the expression 4 n-5 r for n=-2 and r=3
(A) 23
(C) 7
(B) -7
(D) -23
The surface area for a rectangular prism with a square base is given the expression 2 s²+4 s h, where s is the side length of the square h is the height of the prism. What is the surface area in square feet rectangular prism when s=4 feet and h=6feet?
Part 1:- The answers are 12, 30, 56, 90
30, 35, 40, 45
2, 3, 4, 5
Part 2:-The correct answer is (D) -23
Part 3:-The surface area for the rectangular prism is 128 square feet.
What is a mathematical expression?
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
part 1:-
Solving expression 1:-
for x=2
[tex]4 {x}^{2} - 2x = 4 \times {2}^{2} - 2 \times 2[/tex]
=4×4 - 4
=16 - 4
=12
for x=3
[tex]4 {x}^{2} - 2x = 4 \times {3}^{2} - 2 \times 3[/tex]
= 4 × 9 - 6
= 36 - 6
= 30
for x=4
[tex]4 {x}^{2} - 2x = 4 \times {4}^{2} - 2 \times 4[/tex]
= 4 × 16 - 8
= 64 - 8
= 56
for x=5
[tex]4 {x}^{2} - 2x = 4 \times {5}^{2} - 2 \times 5[/tex]
= 4×25 - 10
= 100 - 10
= 90
solving expression 2:-
for x = 2
[tex]5x + 20 = 5 \times 2 + 20[/tex]
= 10 + 20
= 30
for x = 3
[tex]5x + 20 = 5 \times 3+ 20[/tex]
= 15 + 20
= 35
for x = 4
[tex]5x + 20 = 5 \times 4 + 20[/tex]
= 20 + 20
= 40
for x = 5
[tex]5x + 20 = 5 \times 5 + 20[/tex]
= 25 + 20
= 45
solving expression 3:-
for x=2
[tex] \frac{8x}{2} - 3x = \frac{8 \times 2}{2} - 3 \times 2[/tex]
= 8 - 6
= 2
for x=3
[tex] \frac{8x}{2} - 3x = \frac{8 \times 3}{2} - 3 \times 3[/tex]
= 12 - 9
= 3
for x=4
[tex] \frac{8x}{2} - 3x = \frac{8 \times 4}{2} - 3 \times 4[/tex]
= 16 - 12
= 4
for x= 5
[tex] \frac{8x}{2} - 3x = \frac{8 \times 5}{2} - 3 \times 5[/tex]
= 30 - 15
= 15
Hence the answers are, 12, 30, 56, 90
30 35, 40, 45
2, 3, 4, 5
part 2:-
Given,
4n - 5r;
for n=-2 and r=3
4n - 5r = 4 × (-2) - 5 × 3
= -8 - 15
= -23
Hence the answer is (D) -23
Part 3:-
Given,
The surface area for a rectangular prism with a square base is given the expression 2 s²+4 s h
s = 4 feet
h = 6 feet
then,
2 s²+4 s h = 2×4²+4×4×6
= 2×16+96
= 32+96
= 128
Hence the answer is 128 square feet.
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Determine each total cost, including a 20% tip,
$103.65
Answer:124.38
Step-by-step explanation:
103.65*.20=20.73 103.65+20.73=124.38
Let
U= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A= {1, 2, 4, 6}
B= {3, 7}
C= {1, 3, 6, 7, 8}
List all the members of the following set. (Enter your answers as a comma-separated list. Enter EMPTY or ∅ for the empty set.)
A ∩ (/B ∪ C)
I'm on my last attempt. I got 2,3,4,7,8 and it's wrong. Ughhhh
Please help me!!!
The set A ∩ (/B ∪ C) is given as { 1, 6 }
How to determine the elements of the setFrom the information given, we have the sets as;
U= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A= {1, 2, 4, 6}
B= {3, 7}
C= {1, 3, 6, 7, 8}
Note that;
U is the universal setSets A, B and C are subsets of the universal set∪ represents union of the set∩ represents intersection of setB∪C = { 1, 3, 6, 7, 8}
A ∩ (/B ∪ C) = { 1, 6 }
Hence, the set is { 1, 6 }
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Suppose a 3 X 3 real matrix A has only two (real) distinct eigenvalues. Suppose that tr(A) -2 and det(A) 96. Find the eigenvalues of with their algebraic multiplicities. smaller eigenvalue has mulitiplicity and larger eigenvalue has mulitiplicity
The smaller eigenvalue is -4 with multiplicity 2 and larger eigenvalue is 6 has multiplicity 1
If A is a square matrix of order n x n and v is a non-zero column vector of order n x 1 such that Av = λv , then the scalar (real number) λ is called an eigenvalue of the matrix A that corresponds to the eigenvector v.
According to the question,
We have a 3 x 3 matrix that has only two real distinct eigenvalues
Let two distinct eigen values be a and b
Its given that tr(A) = - 2
Det(A) = 96
If we add all the eigen values of a matrix it gives us trace of this and product of eigen values result to the determinant
Therefore , 2a + b = -2 --------(1)
a²b = 96 --------(2)
Using substitution method for solving these equations
=> b = -2 - 2a
Substituting the value of b in equation (2)
=> a²( -2 -2a) = 96
=> -2a² - 2a³ = 96
=> a²(1 + a) + 48 = 0
=> a³ + a² + 48 =0
Solving the cubic equation
a = -4 , 1.5-3i , 1.5+3i (but eigen values are only real)
therefore , a = -4
b = -2 -2(-4)
=> -2+8
=> 6
hence, the eigen values = -4 and 6
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Pls help I forgot how to do this
factor -2x-8x+20 pls
Answer:
10(-x + 1)
Step-by-step explanation:
-2x - 8x + 20
-10x + 20
10(-x + 1)
1. Consider the system described by the differential equation: d3y(t)/dt3 + 4d2y(t)/dt2 + 6dy(t)/dt + 8y(t) = 20u(t)
(i) Find the transfer function of the system.
(ii) Derive a state space representation for the system
2. A single input, single output system has the matrix equations:
x.(t)= [0 1 -3 -4] x(t) +[0 1]u(t) and y(t) = [3 0]x(t)
Determine the transfer function G(s) = Y(s)/U(s)
20 is the system's transfer function. A differential equation is a mathematical formula that includes one or more terms
What is a differential equation's formula?A differential equation is a mathematical formula that includes one or more terms as well as the derivatives of one variable (the dependant variable) with respect to another variable (i.e., independent variable) dy/dx = f (x) In this case, "x" is an independent variable and "y" is a dependent variable. For instance, dy/dx = 5x.The Laplace transform of the input variable divided by the Laplace transform of the output variable, with initial conditions of zero, is the definition of transfer functions.Explanation:
4 +2 + 6 + 8 = 20.
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. Suppose x is inversely proportional to y. if x is tripled, what happens to y?
Answer:
it also decreased by 3 times.
hope this work out.
Find the slope of the line that passes
through
The slopes of the linear equations are:
a) -1
b) 0
c) undefined, it is a vertical line.
How to find the slopes of the lines?
A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
a = (y2 - y1)/(x2 - x1)
1) The points are (3, 5) and (2, 6), so the first slope is:
a = (6 - 5)/(2 - 3) =1/-1 = -1
2) The points are (-3, 2) and (7, 2)
Notice that this is a horizontal line of the form y = 2, so the slope is zero.
3) The points are (6, 8) and (6, -2)
This is a vertical line of the form x = 6, so the slope is undefined.
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[tex]\large\boldsymbol{\rm{Slope}}[/tex]
[tex]\bf{Intro}[/tex]
To find the slope of a line, given that it passes through two points, use the slope formula:
[tex]\bf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
Substitute the known values and simplify:
[tex]\bf{m=\dfrac{6-5}{2-3}}[/tex]
[tex]\bf{m=\dfrac{1}{-1}}[/tex]
[tex]\bf{m=-1}[/tex] {slope}
[tex]\rule{250}{1}[/tex]
Substitute the known values and simplify:
[tex]\bf{m=\dfrac{2-2}{7-(-3)}}[/tex]
[tex]\bf{m=\dfrac{0}{7+3}}[/tex]
[tex]\bf{m=\dfrac{0}{10}}[/tex]
[tex]\bf{m=0}[/tex] {slope}
[tex]\rule{250}{1}[/tex]
Substitute the known values and simplify:
[tex]\bf{m=\dfrac{-2-8}{6-6}}[/tex]
[tex]\bf{m=\dfrac{-10}{0}}[/tex]
[tex]\bf{m=not\:de fined}[/tex]
✦ Therefore, the slopes are: -1, 0, not defined.
the rate of electricity charge of 20 units is RS 3 per units and rs 6.50 per units from 21 to 30 unit. find the charge of consumption of 28 units with rs 50 service charge
electricity consumed:28 units
charge upto 20 units : 20 * Rs 3 : Rs 60
charge from (21 to 28) : 8 * Rs 6.50 : 52
total charge including service charge : Rs 60 + Rs 52 + Rs 50 : Rs 162
Samuel is folding his laundry. The table shows the proportional relationship between the number of shirts he folds and the time, in minutes, it takes him to fold them.
Number of Shirts 3 6 ?
Time (minutes) 0.25 0.50 2
How many shirts can Samuel fold in 2 minutes?
8 shirts
9 shirts
24 shirts
25 shirts
The number of shirts Samuel can fold in 2 minutes is 12
How to determine the number of shirts Samuel can fold in 2 minutes?From the question, we have the following parameters that can be used in our computation:
Number of Shirts 3 6 ?
Time (minutes) 0.25 0.50 2
Represent the missing value with x
So, we have the following representation
Number of Shirts 3 6 x
Time (minutes) 0.25 0.50 2
From the above table of values, we have the following equation
6 : x = 0.5 : 2
Multiply the second ratio by 12
So, we have
6 : x = 6 : 12
By comparison, we have
x = 12
Hence, the number of shirts is 12
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Which of the following statements best summarizes the pattern of causality captured by the graph above? Check all that apply.O a change in e causes a shift of the budget constraint. O a change in p causes O a change in s. the relationship between s and p is not a causal relationship. O a change in s causes a change in p.
The statements which best summarizes the pattern of causality captured by the graph attached are: A change in E causes a shift of the budget constraint; and, the relationship between S and P is not a causal relationship.
What is causality in linear regression?Causality means that there is a clear cause-effect relationship between two variables. By using a controlled study is the most effective way of establishing causality among variables. In a controlled study, the sample or population is split in two, with both groups being comparable in almost every way. Then, the two groups receive different treatments, and the outcomes of each group are assessed.
Although part of your question is missing, you might be referring to this full question: Which of the following statements best summarizes the pattern of causality captured by the graph above? Check all that apply. (Graph is attached.)
A change in E causes a shift of the budget constraint.A change in P causes a change in S.The relationship between S and P is not a causal relationship.A change in S causes a change in P.Learn more about causality at: https://brainly.com/question/14127087
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8 a What percentage of $680 is $490 ?
b A price is reduced from $680 to $490. What is the percentage decrease?
a) The percentage of $680 which is $490 is 72.06%.
b) When a price is reduced from $680 to $490, the percentage decrease is 27.94%.
What is the percentage?The percentage is the ratio of a value to another.
Percentages are depicted as fractional values expressed over 100.
To determine percentages, the smaller value is expressed as the numerator, while the more considerable value is described as the denominator.
The result is then multiplied by 100.
For instance:
$490 of $680 is 72.06% ($490/$680 x 100)
Price reduction from $680 to $490, the percentage decrease is computed as the difference between $680 and $490 divided by $680, multiplied by 100.
Thus, the percentage decrease in price from $680 to $490 is 27.94%, showing that the original price of the good or service has been reduced from 100% to 72.06%.
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Help ME! i really need help for this
Answer:
#4 is one, and #5 is two.
Step-by-step explanation:
At 5pm, Li rented bikes from Pearl's
Wheels. She returned the bike at 11pm, after
riding 38 miles: Li paid $26.00 for the
rentals
a. What was her average speed in miles per hour?
b. What was her cost per hour, to the nearest cent?
c. What was her cost per mile, to the nearest cent?
Answer:
(a) 6.33 miles per hour
(b) $4.33 per hour
(c) $0.68 per mile
Step-by-step explanation:
Li drove 6 hours (5pm - 11pm) for a total of 38 miles
[tex]\textrm{(a) Her average speed is determined by the formula}\\\\\dfrac{\textrm{Distance Travelled}}{\textrm{Time taken for travel}}[/tex]
[tex]\textrm{So average speed }=$\dfrac{38}{6} = 6.33$ \;\textrm{miles per hour}}\\\\[/tex]
(b) She paid $26 for 6 hours of usage
[tex]\textrm{So cost per hour } = \dfrac{26}{6} = \$4.33\;\textrm{per hour}\\\\[/tex]
(c) Cost per mile, c, can be computed as follows
[tex]c = \dfrac{\textrm{Total Cost}}{\textrm{Miles Traveled}}[/tex]
[tex]\longrightarrow \dfrac{26}{38} = \$0.68\; \textrm{per mile}[/tex]
Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases.
The curve for the vector equation r(t) = <t, -t, 2t>, is |r(t)| = (√6)t.
Find the curve in the attachment
What is a vector?A vector is a physical quantity that has both magnitude and direction
What is a vector equation?A vector equation is a linear combination of vector quantities
What is a curve?A curve is a path which an object follows.
How to sketch the curve of the given vector?Since we are given the vector equation r(t) = <t, -t, 2t>, to sketch the curve of the vector equation, we need to know the magnitude of the vector.
What is the magnitude of a vector?The magnitude of a vector r = <a, b, c> is |r| = √(a² + b² + c²)
So, to sketch the vector equation, since r(t) = <t, -t, 2t>, comapring bothnequations,
a = t, b = -t and c = 2tSo, the magnitude of r(t) = √(a² + b² + c²)
= √(t² + (-t)² + (2t)²)
= √(t² + t² + 4t²)
= √(6t²)
= (√6)t
Since |r(t)| = (√6)t, we sketch the curve for this equation
Find the curve in the attachment
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Critical Thinking Consider a family with three children . Assume the prob- ability that one child is a boy is 0.5 and the probability that one child is a girl is also 0.5 and that the events "boy" and "girl" are independent . ( a ) List the equally likely events for the gender of the three children , from oldest to youngest (b) What is the probability that all three children are male ? Notice that the complement of the event " all three children are male " is "at least one of the children is female ." Use this information to compute the probability that at least one child is female .
The equally likely events are
Boy, Boy, BoyBoy, Boy, GirlBoy, Girl, BoyBoy, Girl, GirlGirl, Boy, BoyGirl, Boy, GirlGirl, Girl, BoyGirl, Girl, GirlThe probability that all three children are male
0.875.
the probability that at least one child is female.
0.875.
What are the probabilities?(a) The equally likely events for the gender of the three children, from oldest to youngest, are:
Boy, Boy, BoyBoy, Boy, GirlBoy, Girl, BoyBoy, Girl, GirlGirl, Boy, BoyGirl, Boy, GirlGirl, Girl, BoyGirl, Girl, Girl(b) The probability that all three children are male is (0.5)^3 = 0.125.
The probability that at least one child is female is the complement of the event "all three children are male," which means it is 1 - 0.125 = 0.875.
In conclusion, The probability that at least one child is female is 1 - (0.5)^3 = 0.875.
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The game is played on a square court divided into four smaller squares that meet at the center. If a line is drawn diagonally from one corner to another corner, then a right triangle QTS is formed, where _QTS is 45°. Using a trigonometric function, find the length of the
diagonal for a 15-foot square court.The length of the diagonal is about how many feet. (round to nearest tenth)
The length of the diagonal of the right triangle is 21.2 units.
How to find the side of a right triangle?The game is played on a square court divided into four smaller squares that meet at the centre.
A right triangle QTS is formed, where QTS is 45°. Using trigonometric function, the length of the diagonal can be found as follows:
Therefore,
sin 45 = opposite / hypotenuse
opposite side = 15 feet
hypotenuse side = 15 feet
The hypotenuse side is the diagonal.
Hence,
sin 45° = 15 / h
cross multiply
h = 15 / sin 45
h = 15 / 0.70710678118
h = 21.2132034356
h = 21.2 units
Therefore,
length of diagonal = 21.2 units
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