The probability of winning the minimum award of $100 in the lottery is [tex]\frac{113}{140448}[/tex]
The probability of picking first winning number (out of 57 white balls) is [tex]\frac{1}{57}[/tex]
Now, out of the remaining 56 white balls, the probability of picking second winning number is [tex]\frac{1}{56}[/tex]
So total probability of the correctly matching two numbers drawn from the white balls is [tex]\frac{1}{57} + \frac{1}{56}[/tex]
Next, to match the winning number on the gold ball, probability of this event is [tex]\frac{1}{44}[/tex]
Thus overall probability of winning the minimum award is calculated by multiplying the individual probabilities of aforesaid two independent events as follows:
[tex](\frac{1}{44}) (\frac{1}{57}+\frac{1}{56})[/tex]
= [tex]\frac{113}{140448}[/tex]
Above value is the probability of winning the minimum award of $100.
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Consider the transformation shown.
6
8
Pre-image
Intro
10
3
5
Image
Use the drop-down menus to complete the sentence.
The transformation is
because the
preserved.
Done
The transformation is non rigid
What transformations ?Transformations involve the rotation, reflection, or translation of forms on a coordinate plane. Transformational geometry is a fresh viewpoint on geometry that Felix Klein suggested in the 19th century. The majority of geometric proofs rely on the transformations of objects. Any image in a coordinate plane can be changed using transformations. Applying the transformational laws will help you better understand the graphics in video games. Learn to recognize transformations, comprehend function transformation principles, and investigate the various forms of transformations.
What is non rigid transformations ?Non-Rigid Transformations actually alter the original object's structure. Scaling, for instance, allows us to make our object larger or smaller. Alternatively, shearing can be used to "push" it up or to the side. In essence, non-rigid transformations allow an object's size to change.
because the size became small as compare to pre image it is non rigid transformation
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Which is the set of integers greater than 9 and less than or equal to -6
The set of integers as described in the task content which are greater than 9 and less than or equal to -6 can be represented using interval notation as all integer values in the set ; (9, infinity) U (-infinity, -6].
How to find the set of integers?It follows from the task content that the set of integers greater than 9 and less than or equal to -6 is to be determined.
By considering each set of possible solutions for the integer in discuss; we have;
For greater than 9; (9, infinity).For less than or equal to -6; (-infinity, -6].Therefore, the required set of Integers includes integers in union of the two sets above and hence, we have;
x = (9, infinity) U (-infinity, -6].
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Match each phrase with its corresponding algebraic expression.
Answer/Step-by-step explanation:
Five more than a number = 5 + n
The sum of 3.6 and a number = n + 3.6
The difference of ten and a number = 10 - n
One-half less than a number = n - (1/2)
I hope this helps!
Answer:
The difference of 10 and a number: 10-n
Five more than a number: 5+n
The sum of 3.6 and a number: n+3.6
one-half less than a number: n-1/2
When a number is added to 20 and 5 is subtracted from the number, their product is 150. Find the two possible numbers
Answer:
--15 and --10 respectively
Step-by-step explanation:
Let the first no be a and second no be b
From the interpretation of the question
a + 20 (added) -- 5 (subtracted) = 0
a + 20 -- 5 = 0
a + 15 = 0
a = --15
Product = 150
a×b = 150
(--15) × b = 150
b = --150/15
b = --10
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Use a table of trigonometric values to find the angle θ in the right triangle in the following problem. Round to the nearest degree, if necessary.
sin θ = 0.7071 O = 5 H = ?
By applying sine trigonometry, the angle θ in this right angled triangle is approximately equal to 50 degrees.
What is the law of sines?In Trigonometry, the law of sines is also referred to as sine law or sine rule and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.
How to apply basic trigonometry?In order to determine the value of H, we would apply basic trigonometry. From the information provided about this right angled triangle, we can logically deduce the following parameters:
sinθ = 0.7071Opposite (Opp) = 5Hypotenuse (Hyp) = H.Therefore, we would use the sine trigonometry to determine the value of H as follows:
Sinθ = Opp/Hyp
0.7071 = 5/H
H = 5/0.7071
H = 7.0711.
Now, we can determine the angle θ in this right angled triangle as follows:
Sinθ = Opp/Hyp
Angle, θ = sin⁻¹(Opp/Hyp)
Angle, θ = sin⁻¹(5/7.0711)
Angle, θ = sin⁻¹(0.7071)
Angle, θ = 44.999 ≈ 50°.
Angle, θ = 50 degrees.
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can some one help meeeeee
Write an equation or inequality to model the situation:
The distance d to school is 1 1/2 miles more than the distance p to
the park.
An equation or inequality to model the situation: The distance d to school is 1 1/2 miles more than the distance p to the park is d = p + 3/2
What is an equation ?a statement that the values of two mathematical expressions are equal indicated by the sign =, is known as equation.
What is inequality ?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions is known as inequality.
For this situation, we would assume that both the distances i.e 'd' and 'p' are in miles.
It is mentioned that the distance d is more than the distance p by 3/2 miles.
It means that if we add 3/2 miles to the distance 'p' the output will be distance 'd'
The equation for this is as follows :- d = p + 3/2
It also means that if we substract 3/2 miles from distance 'd', the output will be distance 'p'
The equation for this is as follows :- p = d - 3/2
But we are asked in the situation that distance d is more than than the distance 'p'.
Therefore , an equation or inequality to model the situation: The distance d to school is 1 1/2 miles more than the distance p to the park is d = p + 3/2.
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Please help I’ll mark you as brainliest if correct!!
A puzzle, defined as "anything which baffles or perplexes," refers to an enigma or a conundrum that requires creative thinking to solve.
The answer is A = 7.
How to find A?A puzzle, defined as "anything which puzzles or perplexes," refers to a riddle or issue that defies creativity to be solved.
Retaining mental quickness and short-term memory while working on a puzzle strengthens connections between brain cells.
Dopamine, a neurotransmitter that controls mood, memory, and focus, is produced more readily as a result of solving puzzles.
Every time we complete the puzzle, dopamine is produced.
Given the puzzle condition,
The sum of any 3 consecutive digits must be 17.
Given numbers 8, 2
So the third number would be 8 + 2 + A = 17
10 + A = 17
Therefore A is 17-10 = 7
A = 7
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Select all the equations that represent lines perpendicular to Y= 3x+4.A. Y= -1/3xB. 6x-2y=4C. 3y= -x+7D. X+3y=4E. y=3x-10
if two lines are perpendicular it is true that:
[tex]m1\cdot m2=-1[/tex]For the line:
[tex]\begin{gathered} y=3x+4 \\ m1=3 \end{gathered}[/tex]Let's check every line:
[tex]\begin{gathered} y=-\frac{1}{3}x \\ m2=-\frac{1}{3} \\ m1\cdot m2 \\ 3\cdot-\frac{1}{3}=-1=-1 \end{gathered}[/tex]So, A is a correct choice
[tex]\begin{gathered} 6x-2y=4 \\ y=3x-2 \\ m2=3 \\ m1\cdot m2 \\ 3\cdot3=9\ne-1 \end{gathered}[/tex]B is not a correct choice
[tex]\begin{gathered} 3y=-x+7 \\ y=-\frac{1}{3}x+\frac{7}{3} \\ m2=-\frac{1}{3} \\ m1\cdot m2 \\ 3\cdot-\frac{1}{3}=-1=-1 \end{gathered}[/tex]C is a correct choice
[tex]\begin{gathered} x+3y=4 \\ y=-\frac{1}{3}x+\frac{4}{3} \\ m2=-\frac{1}{3} \\ m1\cdot m2 \\ 3\cdot-\frac{1}{3}=-1=-1 \end{gathered}[/tex]D is a correct choice
[tex]\begin{gathered} y=3x-10 \\ m2=3 \\ m1\cdot m2 \\ 3\cdot3=9\ne-1 \end{gathered}[/tex]E is not a correct choice
Event A, Event B, and Event C are provided. Event A and Event B aremutually exclusive. Event A and Event C are not mutually exclusive.P(A) = 0.45P(B) = 0.30P(C) = 0.25What is the probability of the complement of Event A [Find P(A')] ?Be sure to show your work and/or explain your reasoning.
If two events are mutually exclusive this means they cannot occur at the same time and do not over lap
If two events are mutually inclusive this means they can occur at the same time and they over lap
Event A and Event B are mutually exclusive
Event A and event C are not mutually exclusive
To find the complement of event A (A'), which is the part of the universal set of events not in A
We use the formula
[tex]1\text{ - P(A)}=P(A^{\prime})[/tex]P(A) = 0.45
substituting this into the equation yields
[tex]\begin{gathered} 1-\text{ 0.45 = P(A')} \\ P(A^{\prime})\text{ = 0.55} \end{gathered}[/tex]P(A') = 0.55
what is the fraction to decimal of 2/13=
Answer:
0.1538461583
Step-by-step explanation:
2 divided by 13
can you help me please thankyou
Answer: 17
Step-by-step explanation:
15. The area of a triangle is given by
A = 1/2bh, where b is the base and h is the height of the triangle. In the triangle PQR above, PR=6, PQ=7, QR=12, and PH=3. If PH is perpendicular to QR, what is the area of the triangle PQR?
(A) 12
(B) 18
(C) 36
(D) 42
The answer is (B) 18.
In order to calculate the area of a triangle we must use the equation 1/2·base·height.
In this case, the base of the triangle would be QR, which is 12. The height would be PH, which is 3.
Using the formula above, we can do 1/2·12·3 which equals 18. This is the area of triangle PQR and our final answer.
Hope this helps.
What is the product of 18.5 0.31?
0.5735
5.730
5.735
57.35
Question 3 -
of 4 Step 1 of 1
A box contains 17 green marbles and 8 white marbles. If the first marble chosen was a white marble, what is the probability of choosing, without
replacement, a green marble? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
Step-by-step explanation:
17/25
A company is reviewing a batch of 26 products to determine if any are defective. On average, 3.6% of products are defective.What is the probability that the company will find 2 or fewer defective products in this batch?What is the probability that 4 or more defective products are found in this batch?If the company finds 5 defective products in this batch, should the company stop production?
The experiment has a binomial distribution just because the product could be or not defective. In this case you have n=26 the number of product that the company will check and you also know that the probability to get a defective one is 3.6%. Now we will proceed as follows, to find the probability of getting 2 or fewer defective products is exactly the same that
[tex]\begin{gathered} P(X\leq2)=P(X=0)+P(X=1)+P(X=2)\text{ } \\ \text{ where }X\text{ is a random variable that measures the number of defective products} \end{gathered}[/tex]We also should notice that
[tex]P(X=k)=(n;k)p^k(1-p)^{(n-k)};\text{ where }(n;k)=\frac{n!}{k!(n-k)!}[/tex]Now,
[tex]P(X=0)=(26;0)(0.036)^0(1-0.036)^{26-0}=(1-0.036)^{26}\approx0.3855[/tex][tex]P(X=1)=(26;1)(0.036)(1-0.036)^{26-1}=26(0.036)(1-0.036)^{25}\approx0.3743[/tex][tex]P(X=2)=(26;2)(0.036)²(1-0.036)^{26-2}=325(0.001296)(1-0.036)^{24}\approx0.1747[/tex]Then the probability that the company takes 2 or fewer defective products in this batch is
[tex]P(X\leq2)=P(X=0)+P(X=1)+P(X=2)=0.3855+0.3743+0.1747=0.9345[/tex]Now, to get the probability that the company find 4 or more defective products we proceed as follows. Since
[tex]P(X\ge4)+P(X<4)=1,\text{ }[/tex]then
[tex]P(X\ge4)=1-P(X<4)=1-(\text{ }P(X=0)+P(X=1)+P(X=2)+P(X=3)).[/tex]Notice that we only need to find one of these probabilities to get the answer.
[tex]P(X=3)=(26;3)(0.036)³(1-0.036)^{26-3}=\frac{23!(24)(25)(26)}{3!23!}(0.036)³(1-0.036)^{23}=0.05219[/tex]Then the probability to get more than 4 defective products is
[tex]\begin{gathered} P(X\ge4)=1-(P(X=0)+P(X=1)+P(X=2)+P(X=3))= \\ =1-(0.9345+0.05219)=0.01331 \\ \\ P(X\ge4)=0.01331 \end{gathered}[/tex]So if the company finds 5 defective products in this batch the company should stop the production because the probability to get more than 4 defective products is around 1.3%. It means that if you get 5 defective products even with this small probability then we could say that is really probable to get more defective products that those who were expected.
Find S7 of the sum of the geometric series. a1 = 729, a? = 1, r = 1
Let's write out the formula for the sum of geometric series,
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex][tex]\begin{gathered} \text{where a=first term=729} \\ r=\text{common ratio=}\frac{1}{-3} \\ S_7=?,\text{ where n= number of terms=7} \end{gathered}[/tex]Let's solve for the sum of seven geometric series,
[tex]\begin{gathered} S_7=\frac{729(1-(-\frac{1}{3})^7)}{1-(-\frac{1}{3})} \\ =\frac{729(1-(-\frac{1}{2187}))}{1+\frac{1}{3}} \\ =\frac{729(1+\frac{1}{2187})}{\frac{4}{3}} \end{gathered}[/tex][tex]\begin{gathered} S_7=\frac{729(1\frac{1}{2187})}{\frac{4}{3}} \\ =\frac{729(\frac{2188}{2187})}{\frac{4}{3}}=\frac{\frac{2188}{3}}{\frac{4}{3}} \\ =\frac{2188}{3}\frac{\text{.}}{.}\frac{4}{3} \\ =\frac{2188}{3}\times\frac{3}{4}=547 \end{gathered}[/tex]Hence,
[tex]S_7=547[/tex]Therefore, option 5 is the correct answer.
Option 5 is none of these are correct.
The world's population grew from approximately 2.6 to 5.2 billion between 1952 and 1987.
Assuming that the population growth during this time period followed an exponential model, calculate the
average annual population growth rate of the world between 1952 and 1987 as a percentage.
Answer:
R=100%
Step-by-step explanation:
Here
Increased population (Pt) = 5.2-2.6 = 2.6
Time = 1987-1952
Rate of increase=?
By formula
Pt = P(1-R/100)^t
2.6=2.6(1-R/100)^35
1=(1-R/100)^35
0^35 = (1-R/100)^35
0=1-R/100
0= 100-R
R=100%
so the average annual population growth rate of the world between 1952and1987 is 100%
i need help i doint think i did it right
Memory of the phones = 32 gigabytes
Now,
[tex]1\text{ gigabyte = }1073741824\text{ bytes}[/tex]Therefore ,
[tex]32\text{ gigabytes = }34359738368\text{ bytes}[/tex]Also ,
[tex]1\text{ byte = 8 bits}[/tex]Therefore,
[tex]34359738368\text{ bytes = }274877906944\text{ bits}[/tex]Thus the memory of the phone in bits is ,
[tex]274877906944\text{ bits}[/tex]There are 7 women and 5 men in a department.4 people are needed for a focus group how many ways can this group be formed if it must include at least 2 women
Scallops eject water from their shells to provide a thrust force. A 29 g scallop accelerates from rest straight up to escape a predator, reaching a
speed of 4.10 m/s in 0.15 s. What is the ratio of the net force to the weight of the scallop (Fnet/Weight) for this motion? (Hint: Remember that
grams are a measurement of mass, not force). Round to three decimal places and express in terms of SI units.
The ratio of the net force to the weight of the scallop (F net/Weight) for this motion exists 792.657 Newtons.
What is meant by net force?The net force exists the vector sum of all the forces that act upon an object. The total of all forces exerted on an object is known as the net force. A mass can accelerate due to net force. A body is subject to another force whether it is at rest or in motion. When there are a lot of forces acting on a system, the term "net force" is employed.
Given, mass = 29g, speed = 4.10 m/s , Time = 0.15 s
Acceleration (a ) = (final speed - initial speed)/time taken
= 4.10 - 0/ 0.15 = 27.333 m/s/s
F = m × a = 29 g × 27.33 m/s
= 792.657 Newtons
Therefore, the ratio of the net force to the weight of the scallop (F net/Weight) for this motion exists 792.657 Newtons.
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You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures:
61.3 56.2 63.9 49.2 57.6 30.1 69.7 62 58.8 55.5
Find the 98% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population.
98% C.I. =
Using the t-distribution, the 98% confidence interval for the mean temperature is of:
(47.335, 65.624).
What is a t-distribution confidence interval?The confidence interval is given as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the parameters are:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.Using a calculator, the parameters from this sample are given as follows:
[tex]\mu = 56.43, s = 10.198, n = 10[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 10 - 1 = 9 df, is t = 2.82.
The lower bound of the interval is:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 56.43 - 2.82\frac{10.198}{\sqrt{10}} = 47.335[/tex]
The upper bound of the interval is:
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 56.43 + 2.82\frac{10.198}{\sqrt{10}} = 65.524[/tex]
Hence the interval is:
(47.335, 65.624).
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I’ve been stuck on this one for awhile now, please help. Statement: Richard takes a hang gliding lesson. He lifts off at the top of a hill and glides downward for the first 5 minutes. Then he soars at a consistent elevation for 10 minutes. The last 3 minutes he glides upward until he lands on a smaller hill. Use the information about when Richard’s elevation is increasing, decreasing, or constant to choose the graph that beat approximates Richard’s gliding lesson over time.
Answer:
c
Step-by-step explanation:
6. Write an equation to represent the following: the product of the quantity
eight times a number x plus 4 and is equal to 17. I’ll give 60 points
Point M is the midpoint of AB¯¯¯¯¯. AM=2x+9, and AB=8x−50.
What is the length of AM¯¯¯¯¯¯?
Answer:
43
Step-by-step explanation:
→ Set up an equation
2x + 9 = 0.5 ( 8x - 50 )
→ Simplify
2x + 9 = 4x - 25
→ Minus 4x from both sides
-2x + 9 = -25
→ Minus 9 from both sides
-2x = - 34
→ Divide both sides by -2
x = 17
→ Substitute into AM
2 × 17 + 9 = 34 + 9 = 43
Hello I need help with this
The graph shows a quadratic function.
The quadratic function has been shifted downwards by 2 units and to the left by 3 units.
The rules that show the translation above are given to be:
1) f (x) − b shifts the function b units downward.
2) f (x + b) shifts the function b units to the left.
Therefore, the transformation for h(x) is given to be:
[tex]h(x)\to h(x+3)-2[/tex]A pound of potatoes costs $0.95. The total cost varies directly with the pounds of potatoes purchased. Write an equation that relates the total cost, c, and the number of pounds of potatoes purchased, p.
Responses
c=p+0.95c is equal to p plus 0 point 9 5
c=0.95pc is equal to 0 point 9 5 p
p=0.95cp is equal to 0 point 9 5 c
c=p0.95c is equal to p over 0 point 9 5
Answer:
c = 0.95*p
Step-by-step explanation:
With p representing the number of pounds purchased, and each pound costing 0.95, the total cost c can be found by multiplying the cost per pound by the total number of pounds. Simply put, total cost = 0.95 * total pounds.
HOPE THIS HELPS!!
At a track and field meet, the longest shot-put throw by a boy is 25 feet 8 inches. The longest shot-put throw by a girl is 19 feet 3 inches. How many times greater is the longest shot-put throw by the boy than by the girl? If you can, may I have the answer as a mixed number please?
Answer:
difference = 6 feet 5 inches
Step-by-step explanation:
The longest shot put throw by a boy is given as 25 feet 8 inches . The longest shot put throw by a girl is given as 19 feet and 3 inches. The number of times the longest shot put throw by a boy is greater than by a girl can be computed as follow.
The question asked us to find the difference between the throw. The difference between the throw is the boy throw minus the girls throw. Mathematically,
The longest boys throw = 25 feet 8 inches
The longest girls throw = 19 feet 3 inches
difference = The longest boy throw - The longest girl throw
difference = 25 feet 8 inches - 19 feet 3 inches
difference = 6 feet 5 inches
Jerry made 8,700 mL of tomato soup. He packed 1.6 L of the soup for his kids' lunches. He then froze half of the remaining soup.How many milliliters of soup did Jerry freeze? Jerry froze ______mL of soup
7100 mL
Explanationto solve this we need to do a subtraction, note the unit must be the same, so
Step 1
convert 1.6 Liters into mL
to do this we need to use the equivalence:
[tex]\begin{gathered} 1000\text{ mL= 1 L} \\ so \\ \frac{1000\text{ mL}}{1\text{ L}} \end{gathered}[/tex]so,
a) convert 1.6 Liters into mm
[tex]\begin{gathered} 1.6\text{ L*\lparen}\frac{1000\text{ mL}}{1\text{ L}}\text{\rparen=1600 mL} \\ 1600\text{ mL} \end{gathered}[/tex]Step 2
b)now, we can do the subtraction:
so
soup she froze = total soup made - soup she packed
so, replace
[tex]\begin{gathered} frozen\text{ soup=8700 mL -1600 mL} \\ frozen\text{ soup=7100 mL} \end{gathered}[/tex]therefore, the answer is
7100 mL
I hope this helps you
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
For the given question,
Figure A and D are the cases of reflection over y and x axis respectively.
What is termed as Translation?In mathematics, a translation is the movement of a shape to the left or right and/or upward or downward. The translated shapes appear to be the same size as that of the original shape, and thus the shapes are congruent. They were simply shifted in one or even more directions.For the given question,
Figure B and C are the cases of translation 3 right and 4 down respectively.
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It's a chess set lol there's 16 of black: 8 pawns, 2 knights, 2 rooks, 2 bishops, 1 queen, and one king. (It's the same for white as well).
You choose one piece at random, do not replace it, then choose a second piece at random. Find the probability that you choose a king, then a pawn. Express your answer as a fraction in simplest form.
HELP I NEED TO GET THESE DONE FAST TYSMMM
The total probability that a king and pawn are selected without replacement is 1 / 31 .
The area of mathematics known as probability primarily deals with numerical(fractions or decimals) 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.
Sample space = 32 (16 black and 16 white pieces)
number of kings in the set = 2
Probability that a king is selected first
P(king) = 2 ÷ 32 = 1 / 16
Now the total number of pieces left = 32 - 1 = 31
number of pawns = 8+8 =16
Probability that a pawn is selected = 16 ÷ 31
P(pawn) = 16/31
Now the total probability that a king and pawn are selected without replacement = P(king) × P(pawn) = 1/16 × 16/31 = 1 / 31
Therefore the required probability is 1 / 31 .
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