We have
probability of B occurs is 5/8
probability that event A occurs given B occurs is 5/8
We have the next formula, that is the conditional probability formula
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]where
P(A|B)= probability of A given B
P(B)= probability of B
P(A∩B)=probability of A and B
so we need to isolate the P(A∩B) in order to obtain the probability that events A and B both occur
[tex]P\mleft(A\cap B\mright)=P(A|B)\cdot P(B)=\frac{5}{8}\cdot\frac{5}{8}=\frac{25}{64}[/tex]Isotope: 239Pu
Half-life
(years): 24,100
Initial
Quantity:
Amount After
4000 Years:
3.7g
The mass of isotope 239-Pu left after 4000 years is approximately 3.3g
RadioactivityRadioactivity is the phenomenon of the spontaneous disintegration of unstable atomic nuclei to atomic nuclei to form more energetically stable atomic nuclei. Radioactive decay is a highly exoergic, statistically random, first-order process that occurs with a small amount of mass being converted to energy.
In solving the disintegration constant, we can use the half-life formula.
The half-life of a sample is given as;
[tex]T_\frac{1}{2} = \frac{ln2}{\lambda}[/tex]
Substituting the values into the equation;
[tex]T_\frac{1}{2} = \frac{ln2}{\lambda}\\24100 = \frac{ln2}{\lambda} \\\lambda = \frac{ln2}{24100} \\\lambda = 0.00002876years^-^1[/tex]
The formula of radioactivity is given as
[tex]N = N_oe^(^-^\lambda ^t)[/tex]
No = 3.7gt = 4000We can plug in the values and solve.
[tex]N = N_oe^(^-^\lambda ^t)\\N = 3.7e^-^(^0^.^0^0^0^0^2^8^7^6 ^*^4^0^0^0^)\\N = 3.297g\\N = 3.3g[/tex]
The amount left after 4000 years is 3.3g.
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You have $12 left to spend. Here are your options: $12 for 6 goodie bags for your guests or $12 for 4 goodie bags for your guests. We want to get the most for what our money can buy. Show your work in the space below. Which is the better deal?
For the first deal we get 6 goodie bags for $12, let's find how much each goodie bag cost in this case by dividing $12 by 6:
[tex]\frac{12}{6}=2[/tex]In the first deal, each goodie bag costs $2.
For the second deal, we get 4 goodie bags for $12, let's also find how much is 1 goodie bag in the scenario:
[tex]\frac{12}{4}=3[/tex]In the second deal, each goodie bag costs $3.
The better deal is the first one because each goodie bag is cheaper than in the second deal.
Answer: $12 for 6 goodie bags is the better deal
Find: f^-1(x)=2x/2+3x make sure it is 1-1, if so find the inverse and verify by composition in both directions
The function is one-one can be dtermined by using horizontal line test. If horizontal line on the graph of function intersect the function more than once then such function is not one-one. The graph of function is,
Since horizontal lines intersect the curve of function only once so function is one-one.
Determine the inverse of the function.
[tex]y=\frac{2x}{2+3x}[/tex]Interchange x with y and y with x and simplify the obtain equation for x.
[tex]\begin{gathered} y=\frac{2x}{2+3x} \\ y\cdot(2+3x)=2x \\ 2y+3xy=2x \\ 3xy-2x=-2y \\ x(3y-2)=-2y \\ x=-\frac{2y}{3y-2} \end{gathered}[/tex]Substitute y by x for the inverse of function.
[tex]f(x)=\frac{-2x}{3x-2}[/tex]So inverse of the function is -2x/(3x - 2).
So functions f and g are inverse of each other if,
[tex]f(g(x))=g(f(x))=x[/tex]Check the obtained inverse function by composition.
[tex]\begin{gathered} f^{-1}(-\frac{2x}{3x-2})=\frac{2\cdot(-\frac{2x}{3x-2})}{2+3\cdot(-\frac{2x}{3x-2})} \\ =\frac{-\frac{4x}{3x-2}}{\frac{6x-4-6x}{3x-2}} \\ =-\frac{4x}{-4} \\ =x \end{gathered}[/tex][tex]undefined[/tex]For the square ABCD, it is known that | AB| = | AC| and |DA| = |DC| and corner ABC =
corner CDA. One of the corners of this square is 150 degrees. Find the sizes of the three remaining angles of the square ABCD.
Answer:
∠BAD = 150°∠ABC = 48°∠BCD = 114°∠ADC = 48°Step-by-step explanation:
Given quadrilateral ABCD with AB≅AC, DA≅DC, ∠ABC≅∠ADC, and one of the corner angles equal to 150°, you want the measures of all corner angles.
SetupThe given congruent angles and sides are marked in the attached diagram. If we let ∠ACB = x and ∠ACD = y, we can write some equations involving the sums of the various angles.
First of all, we note that both triangles are isosceles. That means ...
∠ABC≅∠ACB = x∠DAC≅∠DCA = yThe sum of angles in ∆ACD must be 180°, so we have ...
x + 2y = 180°
We know that the isosceles triangle base angles cannot exceed 90°, so the angles at corners B and D cannot be 150°. That leaves two possibilities:
(a) Corner angle C is 150° ⇒ x + y = 150°
(b) Corner angle A is 150° ⇒ (180°-2x) +y = 150°
Solution(a) Corner C is 150°
This makes the system of equations for x and y be ...
x +2y = 180°x +y = 150°Subtracting the second from the first gives y = 30°, and substituting that value for y gives x = 120°. We already know x is the base angle of an isosceles triangle, so cannot have that value. This possibility is eliminated.
(b) Corner D is 150°
This makes the system of equations for x and y be ...
x +2y = 180°(180° -2x) +y = 150°The second of these equations can be rearranged to ...
2x -y = 30°
Adding twice this to the first equation, we have ...
2(2x -y) +(x +2y) = 2(30°) +(180°)
5x = 240°
x = 48°
Substituting for x in the second equation gives ...
2(48°) -y = 30°
96° -30° = y = 66°
As we noted in the solution part (a), corner angle C is the sum of x and y:
∠BCD = x +y = 48° +66° = 114°
Corner anglesThen the corner angles are ...
∠BAD = 150°∠ABC = 48°∠BCD = 114°∠ADC = 48°The attached figure is drawn to scale.
Which equation in standard form has a graph that passes through the point (2,19) and has a slope of 11/2
Answer:
y=5.5x+8
Step-by-step explanation:
Replace x and y values so you get 19=5.5(2)+cMultiply 5.5 by 2 to get 19=11+cSubtract 11 from both sides to get 8=cSimplify to y=5.5x+8What ever I'm doing is making the circle equal 410 degrees.
Step 1
Redraw the cyclic quadrilateral
From the image;
[tex]\begin{gathered} mSTU=220 \\ \text{mSRU}=360\text{ -220=110(sum of angles at a point or in a circle is 3}60^o) \end{gathered}[/tex]Step 2
Find the measure of angle R
[tex]m\angle R=\frac{1}{2}mSTU[/tex][tex]m\angle R=\frac{1}{2}\times220=110[/tex]Find the measure of angle T
[tex]\begin{gathered} m\angle T=\frac{1}{2}mSRU \\ m\angle T=\frac{1}{2}\times140 \\ m\angle T=70 \end{gathered}[/tex]Find the measure of angle U
[tex]m\angle U=360-95-110-70=85\text{ ( sum of angles in quadrilateral)}[/tex]Find the measure of Arc SRU
[tex]\begin{gathered} \text{mSRU}=\text{ }360-\text{mSTU} \\ \text{mSRU}=360-220=140 \end{gathered}[/tex]Find the measure of Arc mRUT
[tex]\begin{gathered} \text{mRUT}=\text{ 2}\times m\angle S \\ \text{mRUT}=2\times95=190 \end{gathered}[/tex]Find the measure of mRST
[tex]\begin{gathered} \text{mRST}=2\times m\angle U \\ \text{mRST}=2\times85=170 \end{gathered}[/tex]There are 54 dogs in a pet store which is 90% of all pets. How many pets are in the pet store?
Let there are x pets in the store. So 90% of all pets means that 0.9x.
The equation for the dogs anf total pets in the store is,
[tex]0.9x=54[/tex]Simplify the equation to obtain the value of x.
[tex]\begin{gathered} 0.9x=54 \\ x=\frac{54}{0.9} \\ =60 \end{gathered}[/tex]So there are 60 pets in the pet store.
Every hour on the hour, Helen does jumping jacks. At 4:00 she does 4 jumping jacks. At 5:00 she does 5 jumping jacks, etc. How many jumping jacks will Helen do, in total, from the time prior to her final jumping jacks at 4:00 to the time prior to her first jumping jacks at 11:00 ?a) 46b) 56c) 57d) 60
We have to add the jumping jacks from 4:00 (not included) to 11:00.
So we have to add:
[tex]\sum ^{11}_{n\mathop=5}n=5+6+7+8+9+10+11=56[/tex]The answer is option b) 56.
what is the value of 10-¹
The value of
[tex]10^{-1}[/tex]which can be written as:
[tex]\frac{1}{10}[/tex]is
[tex]0.1[/tex]Quick
Check
Match the key aspect of a function's graph with its meaning.
f(x) <0
x-intercept
f(x) > 0
ching he Meaning of Key Features of a Graph
y-intercept
intervals of the domain where the
graph is below the x-axis
location on graph where output is
zero
location on graph where input is zero
intervals of the domain where the
graph is above the x-axis
Answer:
ramila ate four ninth of orange before lunch and two-ninths of orange after lunch.how much of the orange did she eat at All?
Can you help me Find x
Andy measures some pieces of yarn. He records the lengths in inches on the line plot.5, 4^1/2, 4^3/4, 4, 4^1/2, 3^3/4, 4^1/4, 4^1/2, 5what mistake does Andy make on the plot line A .Andy does not draw enough Xs at 4^3/4B Andy did not graph 3^3/4C .Andy measures 9 pieces of yarn but only graph 5 pieces D . Andy draws too many Xs for 4^1/2 inches and 5 inches
ANSWER
B. Andy did not graph 3 3/4
EXPLANATION
That measure, 3 3/4 in, is not graphed on the plot line.
If the first two terms of a fibonacci sequence are 5, 25 then what us the next term ?
30,60,90,
Step-by-step explanation:
Find the solution set to each inequality 6m + 2 < 5m - 4-3(x-7) > -278(p-6) - 4(p-4)
The inequality to solve is,
[tex]8(p-6)>4(p-4)[/tex]We will use the distributive property (shown below) to simplify the expression. Then, we will use algebra rules to solve the inequality.
Distributive Property
[tex]a(b-c)=ab-ac[/tex]The simplification process >>>
[tex]\begin{gathered} 8(p-6)>4(p-4) \\ 8(p)-8(6)>4(p)-4(4) \\ 8p-48>4p-16 \\ 8p-4p>-16+48 \\ 4p>32 \\ \frac{4p}{4}>\frac{32}{4} \\ p>8 \end{gathered}[/tex]Answerp > 8Estimate.45.86 + 54.14A.90B.99C.100D.110
We need to estimate the sum:
[tex]45.86+54.14[/tex]In order to do so, we first round each term to the nearest integer. Then we add them.
We have:
[tex]\begin{gathered} 45.86\cong46\text{ (because 0.86>0.50)} \\ \\ 54.14\cong54\text{ (because 0.14<0.50)} \end{gathered}[/tex]Then, we can estimate the sum to be:
[tex]45.86+54.14\cong46+54=100[/tex]Therefore, option C is correct.
Write the system of equations associated with the given augmented matrix. Do not solve
The elements in the first 3 columns are the coefficients of system of equations.
The 4th column are the constants of the system of equations.
This is a system of 3 equations.
Let's write the system using the variables x, y, and z. Shown below:
[tex]\begin{gathered} 1x+1y+0z=3 \\ 0x+4y+1z=-5 \\ 1x+0y-1z=4 \end{gathered}[/tex]Let's simplify and write the equations:
[tex]\begin{gathered} x+y=3 \\ 4y+z=-5 \\ x-z=4 \end{gathered}[/tex]at 3:00 am the temperature was -8 degrees.By early evening, the temperature rose 25 degrees at late day the temperature dropped 5 degrees. What was the late day temperature?
According to the problem:
• At 3:00 am the temperature was -8°.
,• Then, it rose 25 degrees. ,This implies a sum.
,• At last, it dropped 5 degrees. ,This implies a subtraction.
Remember that "rising" shows a positive direction and "dropping" shows a negative direction. Following this rule, we can form the following expression
[tex]T=-8+25-5[/tex]There you can observe that the initial temperature (-8) increased (+)25, and then decreased (-)5.
Therefore, the temperature for the late day is
[tex]T=12[/tex]i need help with this problem
find the mode of the following list of points earned on a 16-point quiz given during a finance class 7, 7, 3, 2, 7, 16, 12, 16, 12
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
7, 7, 3, 2, 7, 16, 12, 16, 12
mode = ?
Step 02:
7, 7, 3, 2, 7, 16, 12, 16, 12
n = 9
2, 3, 7, 7, 7, 12, 12, 16, 16
The mode is the value that appears most frequently in a serie of data.
mode = 7
The answer is:
The mode is 7.
Solve the following system of equations.{x=2y−3 x−y=1Write your answer as an ordered pair in the form (x,y).
Solve the system of equations:
[tex]\begin{gathered} x=2y-3\ldots\ldots\ldots\text{.}(1) \\ x-y=1\ldots\ldots\ldots\text{.}(2) \end{gathered}[/tex]step 1: Substitute the value of 2y-3 for x in equation (2) and solve for y
[tex]\begin{gathered} x-y=1\ldots\ldots\ldots\text{.}(2) \\ (2y-3)-y=1 \\ 2y-3-y=1 \\ \text{ collect like terms} \\ 2y-y=1+3 \\ y=4 \end{gathered}[/tex]step 2: Solve for x by substituting 4 for y in equation (1)
[tex]\begin{gathered} x=2y-3\ldots\ldots\ldots\text{.}(1) \\ \text{put }y=4 \\ x=2(4)-3 \\ x=8-3 \\ x=5 \end{gathered}[/tex]Therefore, the solution to the system of equations in ordered pair is
[tex](x,y)=(5,4)[/tex]These two trangles are scaled copies of one another. the area of the smaller triangle is 9 square
units.
The area of the larger triangle will be equal to 36 square units.
Triangle may be defined as a closed figure of three sides and three interior angles. Scaling of image may be defined as a ratio that can be used to represent the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object. Dilation may be defined as the process for creating similar figures by changing the size. A graph can be defined as a pictorial representation or a diagram that represents data or values. According to question the area of smaller triangle is given as 9 square units. After scaling the length of scale copies become double and the area becomes four times. So, the area of bigger triangle is 4×9 = 36.
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Complete Question:
These two triangles are scaled copies of one another. The area of the smaller triangle is 9 square units. What is the area of the larger triangle? Explain or show how you know.
Given f(x)=-2x-1f(x)=−2x−1, solve for x when f(x)=-7f(x)=−7
The value of the function f(x) = 2x -1 when f(x) = 7 is 13.
Function:
A function is defined as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given,
Here we have the function f(x) = 2x - 1.
Now, we need to find the value of the function when f(7).
To find the value of f(7), we have to replace the value of x with the value 7.
Then we get the equation like the following,
f(7) = 2(7) - 1
Now, we have to expand the terms in order to solve it,
f(7) = 14 - 1
When we subtract it, then we get the value of
f(7) = 13.
Therefore, the value of f(7) = 13.
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calculate the measure of SR
In the given figure
There is a triangle RST
∵ RU is perpendicular on ST and bisects it
∴ Triangle RST is an isosceles triangle
∴ RS = RT
∵ RS = 3x + 9 and RT = 7x + 17
Equate them
∵ 7x + 17 = 3x + 9
Subtract 3x from both sides
∴ 7x - 3x + 17 = 3x - 3x + 9
∴ 4x + 17 = 9
Subtract 17 from both sides
∵ 4x + 17 - 17 = 9 - 17
∴ 4x = -8
Divide both sides by 4 to find x
∴ x = -2
Now substitute x by -2 in the expression of RS to find its length
∵ RS = 3(-2) + 9
∴ RS = -6 + 9
∴ RS = 3
HELP ME PLEASE LIKE PLEASE I DONT UNDERSTAND THIS MATH
Given that:
- A race car game takes 6 points each time the player hits a cone.
- You must find the integer that represents the change in total points if the player hits 10 cones.
It is important to remember that the Set of Integers contains the negative numbers, the positive numbers, and zero.
Then, by analyzing the data given in the exercise, you can identify two integers that must be multiplied, in order to calculate the total points if the player hits 10 cones. These are:
[tex]\begin{gathered} 10\text{ } \\ -6 \end{gathered}[/tex]Since the game takes 6 points from the player each time this hits a cone, the integer that represents the points taken from the player must be negative.
In order to multiply the integers, you need to remember the Sign Rules for Multiplication:
[tex]\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ +\cdot-=- \\ -\cdot+=- \end{gathered}[/tex]Therefore, you get this result:
[tex](10)(-6)=-60[/tex]Hence, the answer is:
If cos(theta) = 5/0 and is in the 1st quadrant, find the following:
step 1
Find out sine
Remember the identity
[tex]cos^2\theta+sin^2\theta=1[/tex]substitute the given value of cosine
[tex]\begin{gathered} (\frac{5}{9})^2+s\imaginaryI n^2\theta=1 \\ \\ s\imaginaryI n^2\theta=1-\frac{25}{81} \\ \\ s\mathrm{i}n^2\theta=\frac{56}{81} \\ \\ sin\theta=\frac{\sqrt{56}}{9} \\ \\ sin\theta=\frac{2\sqrt{14}}{9} \end{gathered}[/tex]step 2
Find out cosecant
[tex]\begin{gathered} csc\theta=\frac{1}{sin\theta} \\ \\ csc\theta=\frac{9}{2\sqrt{14}}*\frac{\sqrt{14}}{\sqrt{14}}=\frac{9\sqrt{14}}{28} \\ \\ csc\theta=\frac{9\sqrt{14}}{28} \end{gathered}[/tex]step 3
Find out secant
[tex]\begin{gathered} sec\theta=\frac{1}{cos\theta} \\ \\ sec\theta=\frac{9}{5} \end{gathered}[/tex]step 4
Find out tangent
[tex]\begin{gathered} tan\theta=\frac{sin\theta}{cos\theta} \\ \\ tan\theta=\frac{\frac{2\sqrt{14}}{9}}{\frac{5}{9}}=\frac{2\sqrt{14}}{5} \end{gathered}[/tex]step 5
Find out cotangent
[tex]\begin{gathered} cot\theta=\frac{1}{tan\theta} \\ \\ cot\theta=\frac{5}{2\sqrt{14}}*\frac{\sqrt{14}}{\sqrt{14}}=\frac{5\sqrt{14}}{28} \\ \\ cot\theta=\frac{5\sqrt{14}}{28} \end{gathered}[/tex]372.2 is what percent of 642
Answer:
57.97507788%
Step-by-step explanation:
Write the problem as a mathematical expression.
372.2
642
Multiply by 100 to convert to a percentage.
372.2
642 * 100
Simplify
372.2.
642. * 100 = 57.97507788%
There are same number of packets of sweets and biscuits. There are 5 sweets
in a packet. There are 3 biscuits in a packet. Faizal counted 120 sweets and
biscuits altogether. How many packets of biscuits are there?
Y.
Answer:
There are 45 packets of biscuits
Step-by-step explanation:
Ratio Actual
5 Sweets
3 Biscuits
8 120 Total
Make a proportion:
[tex]\frac{Bicuit}{total}[/tex] = [tex]\frac{biscuits}{total}[/tex] ratio on the left and actual on the right
[tex]\frac{3}{8}[/tex] = [tex]\frac{x}{120}[/tex] x equals the unknown actual biscuit count.
8 x 15 =120, so solve for x by multiplying 3 by 15
x = 45
Answer:
15
Step-by-step explanation:
equation=
[tex]5x+3x=120\\equals..\\8x=120\\x= 15[/tex]
There are 15 packets each of both sweets and biscuits.
Check!
[tex]5(15)=75[/tex] sweets
[tex]3(15)=45[/tex] biscuits
[tex]75+45=120[/tex] sweets and biscuits altogether
Hence, there are 15 packets of biscuits.
i need help can anyone help me please??
Hence the second option, [tex]y=\frac{2}{3}x +\frac{11}{3}[/tex] is the correct option.
What is slope interception form?
Y=mx+b, where m is the slope and b is the y-intercept, is the slope intercept form. The graph of the linear equation can be drawn on the x-y coordinate plane using this form of the equation.
For the given question we are given,
slope (m) = 2/3
and we are also given the point that the line passes through to be,
(-1,3).
that is
(x,y)=(-1,3)
x=-1
y=3
we, know that slope interception form is of the form,
y=mx+c
substituting the value of m (slope) and the point (-1,3) we get
3=(2/3)*(-1)+b
= 3= -2/3 +b
= 3+2/3=b
= (9+2)/3=b
= 11/3=b
from this we get b=11/3
now substituting this again in
y=mx+b
we get
y=(2/3)x+(11/3)
Hence the second option [tex]y=\frac{2}{3}x +\frac{11}{3}[/tex] is correct.
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Chewbacca is standing from atop a plateau 500 feet in the air looking down ata Jedi Trainee. If the Jedi Trainee is 150 feet away from the base of theplateau, what is the angle of depression from Chewbacca to the Jedi Trainee ifChewbacca's eye height is 7.25 feet?Show your work here and explain how you arrive at your answer.
In the given situation the angle of depression is θ. To find it, use the trigonometric ratio of tangent of angle θ in a right triangle (the ratio of tangent is the relation between the two legs of a right traingle):
[tex]\tan \theta=\frac{opposite\text{ leg}}{adjacent\text{ leg}}[/tex]In the given situation the opposite leg to the angle of depresion is the distance between the base of the plateau and the Jedi Trainee and the adjacent leg is the sum of 500ft in the air and Chewbacca's eye height:
[tex]\begin{gathered} \tan \theta=\frac{150ft}{500ft+7.25ft} \\ \\ \tan \theta=\frac{150}{507.25} \\ \\ \tan ^{-1}(\tan \theta)=\tan ^{-1}(\frac{150}{507.25}) \\ \\ \theta=\tan ^{-1}(\frac{150}{507.25}) \\ \\ \theta\approx16.47 \end{gathered}[/tex]Then, the angle of depression from Chewbacca to the Jedi Trainee is approximately 16.47°A wise man once said 200 reduce twice my age is 32.
what is his age?
Answer:84
Step-by-step explanation:
200 - 2x = 32-2x = -168x = 84
Answer:
His age is 84