Answer: 1,7 and 1,5 on coefficient
Step-by-step explanation:
Equation at the end of step 1 :
(((5•(x4))+(x3))+3x2)-7
Step 2 :
Equation at the end of step 2 :
((5x4 + x3) + 3x2) - 7
Step 3 :
Checking for a perfect cube :
3.1 5x4+x3+3x2-7 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 5x4+x3+3x2-7
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 3x2-7
Group 2: 5x4+x3
Pull out from each group separately :
Group 1: (3x2-7) • (1)
Group 2: (5x+1) • (x3)
3.3 Find roots (zeroes) of : F(x) = 5x4+x3+3x2-7
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 5 and the Trailing Constant is -7.
The factor(s) are:
of the Leading Coefficient : 1,5
of the Trailing Constant : 1 ,7
The factor of the constant is [tex]\rm (x+1) (5x^3-4x^2+7x-7) =0\\\\[/tex].
Given
Expression; [tex]\rm 5x^4+x^3+3x^2-7[/tex]
What is the leading coefficient?The leading coefficient of the polynomial of the term has the highest degree of the polynomial.
The factors of the constant term;
[tex]\rm 5x^4+x^3+3x^2-7=0\\\\ 5x^4-4x^3+7x^2-7x+5x^3-4x^2+7x-7=0\\\\(x+1) (5x^3-4x^2+7x-7) =0\\\\[/tex]
Hence, the factor of the constant is [tex]\rm (x+1) (5x^3-4x^2+7x-7) =0\\\\[/tex].
To know more about the Leading coefficient click the link given below.
https://brainly.com/question/13577114
Adrian, Ben and Charlie share some sweets in the ratio of 8:5:10.
Charlie got 24 more sweets than Adrian.
Work out the total number of sweets.
Answer:
the answer is in the image attached
Hope this helps
find the perimeter of this figure
it is made up of semicircles and quarter circles
Answer:
16.84
Step-by-step explanation:
For perimeter, you are basically solving 2 different 1/2 circles
for the larger one, you do the equation: 3.14 x 4 = 12.56
For the smaller one, you do the equation: 3.14 x 2 = 6.28
12.56 + 6.28 = 18.84
and since I think you are putting em together you are supposed to remove 2 so the answer would be : 16.84
So, for the calculations (if doing area), you are gonna have to split the figures apart.
ok, for the first part, the 1/4 circles
Pi*2^2=12.566
12.566/4=3.1415
Since there is 2 of the same figure, you can do 1 of 2 ways
A. 3.1415x2 = 6.283
B. 12.566 / 2 = 6.283
Now for the 1/2 circle:
pi*1^2=3.142
3.142/2 = 1.571
Now to add:
1.571 + 6.283 = 7.854
What would x be?????
Answer:
12 cm
Step-by-step explanation:
The square of the length of the tangent segment is equal to the product of near and far distances to the circle from the point of intersection of the secant and tangent:
(8 cm)^2 = (4 cm)(4 cm +x)
16 cm = 4 cm +x . . . . . . divide by 4 cm
12 cm = x . . . . . . . . . . . . subtract 4 cm
A swimming pool in the shape of a right rectangular prism is filled with water. The pool is 25 yards long, 10 yards wide, and 2 feet deep. Water has an approximate density of 62.4 pounds per cubic foot. What is the weight of the water in the pool to the nearest pound? Enter the number only.
The weight of the water in the pool to the nearest pound is 280,800 pounds.
To find the weight of the water in the swimming pool, we need to calculate the volume of the pool in cubic feet and then use the density of water to determine the weight.
Convert dimensions to consistent units:
The depth of the pool is given in feet (2 feet), so we need to convert the length and width from yards to feet.
1 yard = 3 feet
Length = 25 yards × 3 feet/yard = 75 feet
Width = 10 yards × 3 feet/yard = 30 feet
Calculate the volume of the pool:
Volume = length × width × depth
Volume = 75 feet × 30 feet × 2 feet = 4,500 cubic feet
Calculate the weight of the water:
Weight of water = volume × density
Density of water = 62.4 pounds per cubic foot
Weight = 4,500 cubic feet × 62.4 pounds/cubic foot = 280,800 pounds
Your favorite breakfast cereal contains a toy dinosaur in each box. There are four different dinosaur toys in the complete collection, and each one has an equal chance of being in each box.
You want to figure out what the probability is that you will get more than one tyrannosaurus rex if you buy five boxes of cereal. Which experiment could be used to simulate this situation?
A) You flip a coin 5 times and record the number of times you get tails. You do 10 trials of the experiment, then calculate the percentage of trials that resulted in 2 or more tails.
B) You draw 5 cards from a deck of cards and record how many spades you get. You do 10 trials of the experiment, then calculate the percentage of trials that resulted in 2 or more spades.
C) You spin a 5-color spinner 4 times and record how many times you get a blue. You do 10 trials of the experiment, then calculate the percentage of trials that resulted in 2 or more blue spins.
D) You put 5 different colored marbles in a bag. You draw 4 marbles out and record how many are red. You do 10 trials of the experiment, then calculate the percentage of trials that resulted in 2 or more red marbles.
Answer:
The correct answer on USATestprep is B.
Step-by-step explanation:
Final answer:
To simulate the probability of obtaining more than one tyrannosaurus rex toy in five cereal boxes, we can use a deck of cards (Option B). Drawing five cards in 10 trials and counting the number of spades mirrors the conditions of the cereal box toy scenario. The law of large numbers ensures that this simulation's results will approach the actual probability with enough trials.
Explanation:
The question asks about the probability of obtaining more than one tyrannosaurus rex toy when buying five cereal boxes, each with an equal chance of containing one of four different dinosaur toys. To simulate this situation accurately, the experiment must mimic the conditions of the actual scenario by having four equally likely outcomes and a sample size of five.
Option B is the most suitable simulation for this situation because it replicates these conditions using a deck of cards. If we consider each dinosaur to be analogous to a suit in a standard deck of cards, then drawing five cards and recording the number of a particular suit (such as spades) simulates the probability of getting a particular dinosaur toy. We then repeat this simulation in multiple trials to estimate the probability based on the relative frequency of getting more than one spade, which would represent obtaining more than one tyrannosaurus rex toy.
Through simulations and the law of large numbers, we can acquire an empirical probability that approximates the theoretical probability. However, it's crucial to conduct a sufficient number of trials to ensure a sound approximation of the probability.
The equation of a line is y= -1/2x - 1 What is the equation of the line that is perpendicular to the first line and passes through the point (2, –5)?
Answer:
y=2x-9 or D
Step-by-step explanation:
To get the slope of the perpendicular line, you find the negative reciprocal. The negative reciprocal of -1/2 is 2.
Then, you need to find the y-intercept. Considering the line has to pass through the point (2,-5), you can use the slope to find that the y-intercept is -9.
Kay is a student in Mrs. Hudson’s class. Assuming you know nothing else about Kay, what is the probability that Kay’s birthday will fall on a weekday in any given year?
1. List the sample space for this problem.
2. Which outcome (or outcomes) of the sample space composes the event?
3. Express the probability of Kay’s birthday falling on a weekday as a fraction and as a decimal.
4. Describe the probability of Kay’s birthday falling on a weekday as impossible, unlikely, neither likely nor unlikely, likely or certain. Justify your response.
In a given week, there are seven possible outcomes for Kay's birthday falling on a particular day. Five of these outcomes are weekdays, so the probability of Kay's birthday falling on a weekday is 5/7 or 0.714, making the event likely.
Explanation:In this problem, we are dealing with the concept of probability in mathematics. Probability refers to the branch of mathematics that deals with the likelihood of occurrence of particular events.
1. List the sample space for this problem:
The sample space, which is the set of all possible outcomes, is all the days in a week. Therefore, the sample space in our case consists of these seven outcomes: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.
2. Which outcome (or outcomes) of the sample space composes the event?
The event in this case is Kay’s birthday falling on a weekday. Thus, the outcomes that compose the event are: Monday, Tuesday, Wednesday, Thursday and Friday.
3. Express the probability of Kay’s birthday falling on a weekday as a fraction and as a decimal:
The probability of an event is the ratio of the favorable outcomes to the total outcomes in the sample space. Here, the favorable outcomes are 5 (number of weekdays) and the total outcomes are 7 (total number of days in a week). As a fraction, the probability is 5/7. This can be expressed as a decimal by dividing 5 by 7, giving approximately 0.714.
4. Describe the probability of Kay’s birthday falling on a weekday as impossible, unlikely, neither likely nor unlikely, likely, or certain:
Given that the probability is 5/7 or 0.714, this event is likely to occur because the probability value is more than 0.5 or 50%.
Learn more about Probability here:https://brainly.com/question/32117953
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Find the slope of the line if its exists.
Answer:
5/4
Step-by-step explanation:
slope is rise/run, 5 is the amount rising or going up and is running straight
A diameter of a circle has endpoints p(-10,-2) and Q(4,6)
a find the center of the circle.
b. Find the radius radical form
c.write an equation for the circle
Answer:
a) center: (-3, 2)
b) radius: √65
c) equation: (x +3)² +(y -2)² = 65
Step-by-step explanation:
a) The center (point A) is the midpoint of the diameter, so its coordinates are the average of the endpoint coordinates:
A = (P +Q)/2 = ((-10, -2) +(4, 6))/2
= (-10+4, -2+6)/2 = (-6, 4)/2
A = (-3, 2)
__
b) The radius is the distance from the center to one end of the diameter. The distance formula can be used to find that.
r = √((x2 -x1)² +(y2 -y1)²) = √((4-(-3))² +(6 -2)²) = √(49+16)
r = √65
__
c) The circle centered at (h, k) with radius r has formula ...
(x -h)² +(y -k)² = r²
So the formula for this circle is ...
(x +3)² +(y -2)² = 65
What is the probability that 2 cards selected from a standard deck of 52 cards without replacement are both non-face cards?
A. 0.412
B. 0.588
C. 1.534
D. 0.408
Answer:
B. 0.588
Step-by-step explanation:
There are 40 non-face cards in the deck, so the probability of drawing the first one is 40/52. After doing that, the probability of drawing the second one is 39/51, since the number of non-face cards is 1 fewer, as is the size of the deck.
The joint probability is then ...
(40/52)·(39/51) ≈ 0.588
How many subsets can be made from a set of six elements, including the null set and the set itself?
84
64
32
Answer:
Each element is either included or not in a subset.
--> 2^6 = 64
Hope this helps you out!
64. 2 to the 6th power
Jack is 5 1/2 feet tall and casts a 9-ft shadow. At the same time, a basketball hoop casts a 24-foot Shadow. How tall is the basketball hoop?
ANSWER
The height of the basketball hoop is
[tex]14 \frac{2}{3} ft[/tex]
EXPLANATION
Let the height of the basketball hoop be x feet.
The shadow of the basketball hoop is 9 ft long.
The height of Jack is 5.5 feet.
Jack's shadow is 9 ft long.
By similar triangles,
[tex] \frac{x}{5.5} = \frac{24}{9} [/tex]
Multiply both sides by 5.5
This gives us,
[tex]x = \frac{24}{9} \times 5.5[/tex]
[tex]x = \frac{132}{9} [/tex]
[tex]x = 14 \frac{2}{3} [/tex]
The height of the basketball hoop is 14⅔ feet
If M is midpoint of UT, name a segment parallel to RU
The parallel line of RU would need to be the mid point S and midpoint M
Segment SM would be the parallel line.
Answer:
Though I'm not quite sure (as this is a bit of a trick Question) the only Parallel to Line/segment to RU would MS. Given the question they are asking MS are the only two points that run adjacent/parallel to RU. Hope this helps
Step-by-step explanation:
write a function to model the graph.
Answer:
[tex]f(x)=\left\{ \begin{array}{rcl}\dfrac{8}{3}x+4&\text{for}&x\le3\\\\-3(x-3)^2+12&\text{for}&x>3\end{array} \right.[/tex]
Step-by-step explanation:
The line to the left of x=3 goes up from 4 to 12 as x goes from 0 to 3. Thus, the slope of it is ...
slope = (12 -4)/(3 -0) = 8/3
It intersects the y-axis at y=4, so its equation is ...
y = (8/3)x +4
__
For x > 3, we observe that the curve falls 3 units (from 12 to 9) as x goes from 3 to 4, then falls 9 units (from 9 to 0) as x goes from 4 to 5. The slope of the curved portion at x=3 looks like it might be zero, suggesting a polynomial function instead of an exponential function.
We note that the change in the value of y=x^2 as x goes from 0 to 1 is 1, then as x goes from 1 to 2, it is 4-1 = 3 — 3 times the change in the first interval. This suggests a quadratic function that has been scaled by a vertical factor of -3, and had its vertex moved to (3, 12). Such a function is described by ...
y = -3(x -3)² +12
Then the graph is modeled by a piecewise function, defined as a line for x < 3, and as a quadratic curve for x > 3. Since the function is continuous at x=3, we can put "or equal to" signs on either or both of these boundaries. We choose to write it as ...
f(x) = (8/3)x +4, x ≤ 3; -3(x -3)² +12, x > 3.
____
The graph of our function is attached. It substantially matches the given graph.
The number of seats in each row of a theater forms an arithmetic sequence. The fifth row contains 22 seats. The tenth row contains 37 seats . How many seats are in the first row?
Let [tex]s_n[/tex] denote the number of seats in the [tex]n[/tex]-th row. [tex]s_n[/tex] is arithmetic, so
[tex]s_n=s_{n-1}+d[/tex]
for some constant [tex]d[/tex].
We're told [tex]s_5=22[/tex] and [tex]s_{10}=37[/tex], so that
[tex]s_{10}=s_9+d[/tex]
[tex]s_{10}=(s_8+d)+d=s_8+2d[/tex]
[tex]s_{10}=(s_7+d)+2d=s_7+3d[/tex]
and so on up to
[tex]s_{10}=s_5+5d\implies37=22+5d\implies5d=15\implies d=3[/tex]
The pattern continues:
[tex]s_5=s_4+3[/tex]
[tex]s_5=(s_3+3)+3=s_3+2\cdot3[/tex]
and so on up to
[tex]s_5=s_1+4\cdot3\implies22=s_1+12\implies\boxed{s_1=10}[/tex]
Answer:
8
Step-by-step explanation:
a board that is 2 5/8 feet long is cut from a larger board that is 7 1/3 feet long. How much of the board remains?
Answer:
[tex]4\frac{17}{24}[/tex] feet
Step-by-step explanation:
Total length of the board = [tex]7\frac{1}{3}=\frac{22}{3}[/tex] feet
Length of board that is removed from the larger board = [tex]2\frac{5}{8}=\frac{21}{8}[/tex]
When a smaller board is removed, the length of the remaining board can be calculated using subtraction as:
Remaining Length of board = Total Length - Length of smaller board
= [tex]\frac{22}{3}-\frac{21}{8}\\\\\text{Taking LCM, which is 24}\\\\ =\frac{8(22)-3(21)}{24}\\\\ =\frac{113}{24}\\\\ =4\frac{17}{24}[/tex]
This means [tex]4\frac{17}{24}[/tex] feet of board remains after removing the smaller board from it.
Each person in a group of students was identified by year asked
Answer:
0.184
Step-by-step explanation:
There are 38 seniors, of which 7 prefer evening classes.
7/38 ≈ 0.184
The question involves mathematical sampling techniques to generate categorical data from a high school population, which is shown in a pie chart and involves creating a stratified sample by selecting students from each year.
Explanation:The question pertains to a mathematical concept used in the selection of a sample from a population, which in this scenario, is a group of high school students. This involves using a random number generator to select two class years (freshman, sophomore, junior, or senior) and then including all students from those two years in the sample. The sampling process will result in categorical data, which can be represented in a pie chart as shown in Solution 1.10.
Moreover, organizing the students' names by classification and selecting 25 students from each (a, d) ensures a stratified sample of high school students across different academic stages.
In the context of the presented educational tasks, students might explore how their learning experiences have intersected with personal and global changes, engaging in an analysis of polymorphism, continuous variation, and clinal distribution based on surveyed traits among their peers (Conclusion).
Solve the Quadratic Equation.
x^2 = -4
Don't know where to start, would appreciate if someone would be able to explain the answer in detail!
Answer:
x = ± 2i
Step-by-step explanation:
The equation has no real roots, gut has complex roots
Given
x² = - 4 ( take the square root of both sides )
x = ± [tex]\sqrt{-4}[/tex]
= ± [tex]\sqrt{4(-1)}[/tex]
[ Note that [tex]\sqrt{-1}[/tex] = i ]
= ± [tex]\sqrt{4}[/tex] × [tex]\sqrt{-1}[/tex] = ± 2i
The jogging track is of a mile long. If Ashley jogged around it 4 times, how far did she run? A. B. C. D.
Ashley ran on the track for 4 miles. Option C is correct.
Solving word problems.
In the track event (joggling), the distance of the track is 1 mile (i.e. it represents a single mile).
It was noted that Ashley jogged for 4 times. Now, the length of the joggling time multiplied by the numbers of time Ashley jogged on this track will be how far Ashley ran on the track.
How far Ashley ran on the track = 1 × 4
How far Ashley ran on the track = 4 miles.
Thus, Ashley ran on the track for 4 miles.
The complete question.
The jogging track is of a mile long. If Ashley jogged around it 4 times, how far did she run? A.2 miles B. 1/2 miles C. 4 miles D. 5 miles.
Assume that you have a balance of $5000 on your Visa credit card and that you make no more charges. If your APR is 22% and each month you make only the minimum payment of 3% of your balance, then find a formula for the balance after t monthly payments.
A) 5000(0.952217)t
B) 5000(1.011117)t
C) 5000(0.987783)t
D) 5000(1.048883)t
Can someone explain to me how to solve this please
Answer:
C) 5000(0.987783)^t
Step-by-step explanation:
The monthly interest rate is the APR divided by 12, so is 22%/12 ≈ 0.018333.
Each month, the previous balance (B) has interest charges added to it, so the new balance is ...
balance with interest charges = B + (22%)/12×B = 1.018333×B
The minimum payment is 3% of this amount, so the new balance for the next month is ...
balance after payment = (1.018333B)(1 - 0.03) = 0.987783B
Since the balance is multiplied by 0.987783 each month, after t payments, the balance starting with 5000 will be ...
5000×0.987783^t . . . . . . . . . matches choice C
Need math help for this
Answer:
In the attachmentStep-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
We have the equation:
[tex]y-5=-\dfrac{2}{3}(x+9)\\\\y-5=-\dfrac{2}{3}(x-(-9))[/tex]
Therefore we have
the slope m = -2/3
and the point (-9, 5)
A slope
[tex]m=\dfrac{rise}{run}[/tex]
rise = -2
run = 3
From the point (-9, 5) ⇒ 2 units down and 3 units to the right.
(WILL GIVE BRAINLIEST)
Identify the domain of the exponential function shown in the following graph:
−5 ≤ x ≤ 5
0 ≤ x ≤ 5
All real numbers
All positive numbers
domain for a graph as shown (where the lines never stop) is always (Negative Infinity,Positive Infinity).
Answer:
Step-by-step explanation:
The domain of an exponential function is "the set of all real numbers."
[WILL MARK BRAINIEST] What is the amplitude of the function?
Answer:
B. 1
Step-by-step explanation:
The amplitude is the measure from the midline (0) to the peak (1). It is ...
1 - 0 = 1
Complete the identity
Answer:
sin(α+β)/sin(α-β) ==(tan α+tan β)/(tan α-tan β )
Step-by-step explanation:
We have to complete
sin(α+β)/sin(α-β) = ?
The identities that will be used:
sin(α+β)=sin α cos β+cos α sin β
and
sin(α-β)=sin α cos β-cos α sin β
Now:
= sin(α+β)/sin(α-β)
=(sin α cos β+cos α sin β)/(sin α cos β-cos α sin β)
In order to bring the equation in compact form we wil divide both numerator and denominator with cos α cos β
= (((sin α cos β+cos α sin β))/(cos α cos β ))/(((sin α cos β-cos α sin β))/(cos α cos β))
=((sin α cosβ)/(cos α cos β )+(cos α sin β)/(cos α cos β ))/((sin α cos β)/(cos α cos β )-(cos α sin β)/(cos α cos β))
=(sin α/cos α + sin β/cos β )/(sin α/cos β - sin β/cos β)
=(tan α+tan β)/(tan α-tan β )
So,
sin(α+β)/sin(α-β) ==(tan α+tan β)/(tan α-tan β)
find the measure of the angle indicated by the ?
Answer: 50 degrees.
Step-by-step explanation:
The sum of the interior angles of a triangle is 180 degrees. Then, you can find the missing angle "x" of the larger triangle (Observe the figure attached):
[tex]53\°+45\°+x=180\°\\x=180\°-53\°-45\°\\x=82\°[/tex]
We know that:
[tex]x+y+68\°=180\°[/tex]
Then, "y" you need to substitute values and solve for "y":
[tex]y=180\°-68\°-82\°=30\°[/tex]
Then the angle ? is:
[tex]?=180\°-30\°-100\°\\?=50\°[/tex]
ANSWER
?=50°
EXPLANATION
From the diagram,
x+45+53=180
x+98=180
x=180-98
x=82°
Using angles on a straight line property,
x+68+y=180
82+68+y=180
150+y=180
y=180-150
y=30°
Using the sum of interior angles of the triangle,
?+y+100=180
?+30+100=180
?+130=180
?=180-130
?=50°
need help with this quick
Answer:
~24.4%
Step-by-step explanation:
A circle is 360 degrees, we all know this.
The angle representing Techno is 28° While Country has a 60°. Combine this and we get 88° of people total chose country or techno. 88° divided by 360° gives us 0.2444444... With percentages, we move the decimal two places to the right, giving us:
~24.4%
Jack has three coins C1, C2, and C3 with p1, p2, and p3 as their corresponding probabilitiesof landing heads. Jack flips coin C1 twice and then decides, based on the outcome, whetherto flip coin C2 or C3 next. In particular, if the two C1 flips come out the same, Jack flips coinC2 three times next. However, if the C1 flips come out different, he flips coin C3 three timesnext. Given the outcome of Jack’s last three flips, we want to know whether his first two flipscame out the same. Describe a Bayesian network and a corresponding query that solves thisproblem. What is the solution to this problem assuming that p1 = .4, p2 = .6, and p3 = .1and the last three flips came out as follows:(a) tails, heads, tails(b) tails, tails, tails
Let [tex]X[/tex] denote the event that the two [tex]C_1[/tex] flips yield the same faces (1 if the same faces occur, 0 if not), so that
[tex]P(X=x)=\begin{cases}2{p_1}^2-2p_1+1&\text{for }x=1\\2p_1-2{p_1}^2&\text{for }x=0\\0&\text{otherwise}\end{cases}[/tex]
For example,
[tex]P(X=1)=P(C_1=\mathrm{HH}\lor C_1=\mathrm{TT})=P(C_1=\mathrm{HH})+P(C_1=\mathrm{TT})={p_1}^2+(1-p_1)^2[/tex]
Let [tex]Y[/tex] denote the outcome (number of heads) of the next three flips of either [tex]C_2[/tex] or [tex]C_3[/tex]. By the law of total probability,
[tex]P(Y=y)=P(Y=y\land X=1)+P(Y=y\land X=0)[/tex]
[tex]P(Y=y)=P(Y=y\mid X=1)P(X=1)+P(Y=y\mid X=0)P(X=0)[/tex]
and in particular we have
[tex]P(Y=y\mid X=1)=\begin{cases}\dbinom3y{p_2}^y(1-p_2)^{3-y}&\text{for }y\in\{0,1,2,3\}\\\\0&\text{otherwise}\end{cases}[/tex]
[tex]P(Y=y\mid X=0)=\begin{cases}\dbinom3y{p_3}^y(1-p_3)^{3-y}&\text{for }y\in\{0,1,2,3\}\\\\0&\text{otherwise}\end{cases}[/tex]
Then
[tex]P(Y=y)=\begin{cases}\dbinom3y{p_2}^y(1-p_2)^{3-y}(2{p_1}^2-2p_1+1)+\dbinom3y{p_3}^y(1-p_3)^{3-y}(2p_1-2{p_1}^2)&\text{for }y\in\{0,1,2,3\}\\\\0&\text{otherwise}\end{cases}[/tex]
Jack wants to find [tex]P(X=1\mid Y=y)[/tex] for some given [tex]y[/tex].
a. With [tex]y=1[/tex], we have
[tex]P(X=1\mid Y=1)=\dfrac{P(X=1\land Y=1)}{P(Y=1)}[/tex]
[tex]P(X=1\mid Y=1)=\dfrac{P(Y=1\mid X=1)P(X=1)}{P(Y=1)}[/tex]
[tex]P(X=1\mid Y=1)=\dfrac{\binom31p_2(1-p_2)^2(2{p_1}^2-2p_1+1)}{\binom31p_2(1-p_2)^2(2{p_1}^2-2p_1+1)+\binom31p_3(1-p_3)^2(2p_1-2{p_1}^2)}[/tex]
[tex]P(X=1\mid Y=1)\approx\dfrac{0.1498}{0.2376}\approx0.6303[/tex]
b. With [tex]y=0[/tex], we'd get
[tex]P(X=1\mid Y=0)=\dfrac{P(X=1\land Y=0)}{P(Y=0)}[/tex]
[tex]P(X=1\mid Y=0)=\dfrac{P(Y=0\mid X=1)P(X=1)}{P(Y=0)}[/tex]
[tex]P(X=1\mid Y=0)\approx\dfrac{0.0333}{0.1128}\approx0.295[/tex]
You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $4000 per month. You have access to an account that pays an APR of 6.0% compounded monthly. This requires a nest egg of $620,827.46.
What monthly deposits are required to achieve the desired monthly yield at retirement? (Round your answer to the nearest cent.)
Answer:
$311.74
Step-by-step explanation:
A financial calculator computes the payment amount to be $311.74.
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Your graphing calculator may have the capability to do this. Certainly, such calculators are available in spreadsheet programs and on the web.
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The appropriate formula is the one for the sum of terms of a geometric series.
Sn = a1·((1+r)^n -1)/(r) . . . . . where r is the monthly interest rate (0.005) and n is the number of payments (480). Filling in the given numbers, you have ...
$620827.46 = a1·(1.005^480 -1)/.005 = 1991.4907·a1
Then ...
$620827.46/1991.4907 = a1 ≈ $311.74
To achieve a retirement income of $4000 per month with a 6% APR compounded monthly, a nest egg of $620,827.46, and a retirement plan spanning 40 years, one should deposit about $288.69 into the account each month.
Explanation:This question pertains to the concept of future value and annuities in finance. The purpose is to determine the monthly deposits required to achieve a specified future value, which in this case is the desired retirement income. Here, we use the future value of a series formula: FV = P * [((1 + r)^nt - 1) / r], where P is the monthly payment, r is the monthly interest rate, n is the number of times interest is compounded per year, and t is the time in years. Given that the future value FV is $620,827.46, the interest rate r is 0.06/12 (since it's compounded monthly), n is 12 (compounded twelve times a year), and t is 40 years. The aim is to solve for P, the monthly payment: P = FV / [((1 + r)^nt - 1) / r]. Plugging in the given values, the result is approximately $288.69. Thus, to receive a retirement income of $4000 per month, you should deposit about $288.69 into the account each month.
Learn more about Annuities here:https://brainly.com/question/39419397
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United States flags come in different sizes. Standard dimensions for a flag are a length to width ratio of 1 : 9 to 1. Flag 1 has a width of 1 foot and a length of 1.9 feet and Flag 2 has a width of 2.7 feet. What is the correct length of Flag 2?
Answer:
5.13 feet
Step-by-step explanation:
So, we have the full dimensions of flag #1, and we have the partial dimensions of flag #2, which should follow the same ratio as flag #1, since not indicated otherwise.
When you need to compare dimensions like that, the easiest way to proceed is to do a cross-multiplication. Let's say x is the length of flag #2 we're looking for. It's ratio over the width of flag #2 will be the same as the ratio of the length of flag #1 over its width, so:
[tex]\frac{x}{2.7} = \frac{1.9}{1}[/tex]
If we isolate x, we have x = (2.7 * 1.9) / 1 = 5.13 feet
Which makes sense since we know the result should be a bit less than 2.7 times 2.
is y=(x-4)(x+5) a quadratic formula
Answer:
yes
Step-by-step explanation:
It is the factored form of a 2nd-degree polynomial, so is a quadratic function.