Suppose that, starting at a certain time, batteries coming off an assembly line are examined one by one to see whether they are defective (let D = defective and N = not defective). The chance experiment terminates as soon as a nondefective bettery is obtained.a. Give five possible outcomes for this chance experiment.b. What can be said about the number of outcomes in the sample space?c. What outcomes are in the event E, that the number of battery examined is an number?
Answer:
a. Possible outcomes for this chance experiment are:
NDNDDNDDDNDDDDN(Here, D means a defective battery, and N means a nondefective battery.)
b. The number of outcomes in the sample space is infinite, as the experiment could potentially continue indefinitely. However, in practice, we can define a maximum number of batteries that could be examined before the experiment is stopped.
c. The event E, that the number of batteries examined is a number, would include outcomes where the experiment stopped at a particular number of batteries. For example, if the experiment stopped after examining three batteries (i.e., the fourth battery was nondefective), then the outcome would be DDDN, and it would be included in event E. However, outcomes where the experiment continued indefinitely (e.g., DDDDD...) would not be included in event E.
Can two different angles have the same reference angle?
Please help with this question.
Mhanifa please help me if you are online thanks
Answer:
Step-by-step explanation:
Based on the symbols the two triangles there are the equal
Because its two base angles are equal
therefore sum of angle in a triangle is equal to 180°
62°+70°+∠c=180
∴∠c=180-70+62
∠c=180-132
∠c=48
Are M, N, and O collinear? If so, name the line on which they lie.
Answer: MO
Step-by-step explanation:
What are the solutions to lx + 2) = -13?
A. X=15 and 11
B. X=-15 and 11
C. X=-11 and 15
D. No solution
Answer:
B
Step-by-step explanation:
Because -15 + 2 = -13
elected at
pants?
D. 음
is divided
oun once,
will land
5.
To order a burrito from Teresa's Burrito Shop, Jim
always chooses 1 item from each column in the
table below.
Burrito Choices
Topping
beans sour cream
guacamole
Wrap Filling
plain
wheat beef
chicken
What is the total number of ways that Jim can
order a burrito at Teresa's Burrito Shop by
choosing 1 wrap, 1 filling, and 1 topping?
A. 6 B. 7 C. 10 D. 12
Answer: d.12
Step-by-step explanation:
A fisherman is 7 miles west and 3 miles north of the marina. To head directly back to the marina, what distance and direction must he travel? Include both angle value and how it is measured in the answer. Give both distance and direction to the nearest tenth.
SOLUTION
Let us represent this using a diagram
From the diagram above, h represents the Fisherman's distance back to the marina.
Now we can see that a right-angle triangle has been made. So to find h, which represents the hypotenuse of the right-angle above, we use Pytagoras theorem. we have
\(\begin{gathered} \text{hyp}^2=opp^2+adj^2 \\ h^2=3^2+7^2 \\ h^2=9+49 \\ h^2=58 \\ h=\sqrt[]{58} \\ h=7.615773 \\ h=7.6\text{ miles } \end{gathered}\)Hence his distance from the marina is 7.6 miles to the nearest tenth.
To find his direction, let us find the acute angle
From SOHCAHTOA, we have that
\(\begin{gathered} \tan \theta=\frac{opposite}{\text{adjacent}} \\ \tan \theta=\frac{3}{7} \\ \theta=\tan ^{-1}\frac{3}{7} \\ \theta=23.19859 \\ \theta=23.2\text{ } \end{gathered}\)So, from the diagram, his bearing is 90 degree + the angle theta. So we have
\(\begin{gathered} 90+23.2 \\ =113.2\degree \end{gathered}\)So his distance is 7.6 miles on a bearing of 113.2 degrees
You can also subtract 23.2 from 90 degree to get his direction in north-west, we have
\(\begin{gathered} 90-23.2=66.8\degree \\ =N66.8\degree W \end{gathered}\)So we can say his distance is 7.6 miles on a bearing of
\(N66.8\degree W\)A different car of the same type has an engine size of 2.5 litres.
(b) Estimate the distance travelled on one litre of petrol by this car.
=
kilometres
(2)
(3 marks)
How would I work this out please?
To estimate the distance traveled on one liter of petrol, you would need to know the fuel efficiency of the car, which is usually measured in kilometers per liter (km/L) or liters per 100 kilometers (L/100 km).
Assuming that you have the fuel efficiency of the car, you can use the following formula to estimate the distance traveled on one liter of petrol:
distance per liter = fuel efficiency
For example, if the fuel efficiency of the car is 15 km/L, then the distance traveled on one liter of petrol would be:
distance per liter = 15 km/L = 15 kilometers
Therefore, the estimated distance traveled on one liter of petrol by the car with an engine size of 2.5 liters would depend on its fuel efficiency, which you would need to know in order to make an accurate estimate.
Which of the following is true?
Who ever answers correctly will get brainliest.
(Pls have atleast 1 or more sentences to support your answer. Tysm :D)
Answer:
C
Step-by-step explanation:
because if u add them together you get the answer
Answer:
The third one is correct
Step-by-step explanation:
what's the inverse of f(x)=(x+3)^5
Answer:
The inverse is,
\(f^{-1}(x) = \sqrt[5]{x} - 3\)
Step-by-step explanation:
f(x) = (x+3)^5
Finding the inverse,
\(f(x) = (x+3)^5\\or,\\y = (x+3)^5\)
We replace x with y and vice versa
so,
\(x = (y+3)^5\)
Solving for y,
the the 5th root,
\(\sqrt[5]{x} = y + 3\\y = \sqrt[5]{x} - 3\)
hence the inverse function is,
\(f^{-1}(x) = \sqrt[5]{x} - 3\)
Step-by-step explanation:
f(x)=(x+3)×5
Y=5X+15
now
interxchanging x and y we get,
x=5y+15
5y=x-15
y=x-15/5
therefor f~1(x)=x-15/5
A circle has an area of 12.251 x pi cm^2
Calculate:
a its diameter
b its circumference
Answer:
A) 3.94
B) 12.40
Step-by-step explanation:
Refer to the work image. You also need the radius to calculate A and B.
jim can solve 4 math problems in 7 minuts. At this rate, about how many math problems can he solve in 25 minuts?
Answer:
14.
JIm can solve 4/7 math problems in a minute. that is the unit rate. how did i get that? 7/7 = 1 and thats what we need for a unit rate, the number one. that means we have to divide 4 by 7 too. therefore, 4/7.
we aren't done. we multiply 4/7 * 25 to find out how many math problems jim can solve in 25 minutes.
about.. 14.29 and we need a whole number since you cant solve a decimal of a math problem so he can solve 14 math problems in 25 minutes.
Step-by-step explanation:
Answer:
43.57
Step-by-step explanation:
divide 4/4 and 7/4 to get the base amount of minutes per question then multiply 1.75 by 25 minutes
15)
136⁰
2
S
?
R
Find the measure of the arc or angle indicated
Answer:
224
Step-by-step explanation:
360.-136.
Twelve years from now a girl's age will be 7 times her present age. Find the girl's age now.
Answer: The girl is now 14.
Step-by-step explanation:
Let x represent the girl's age 12 years ago
x+12=7x
subtract x from both sides
12=6x
x=2
2+12=14
After 12 years the girl is 14.
BONJOUR AIDEZ MOI SIL VOUS PLAIT
The distance from the center of the Earth to the point where the net gravitational force is zero is one-ninth the distance from the Earth to the Moon.
Let's assume that the distance from the center of the Earth to this point is denoted as x.
Given:
Mass of the Moon (M\(_{moon}\)) = 1/81 × M\(_{earth}\)
Distance from Earth to Moon (d\(_{moon}\)) = distance on center
According to the principle of gravitational equilibrium, the gravitational force from the Earth and the gravitational force from the Moon acting on an object at that point must balance out. Mathematically, we can express this as:
F\(_{earth}\) = F\(_{moon}\)
The gravitational force between two objects can be calculated using Newton's law of universal gravitation:
F \(_{gravity}\)= G × (m₁ × m₂) / r²
Where:
G is the gravitational constant (approximately 6.67430 x 10⁻¹¹m²/kg/s²)
m₁ and m₂ are the masses of the two objects
r is the distance between the centers of the two objects
Considering the gravitational forces involved:
F\(_{gravity}\)\(_{earth}\) = G ₓ (M\(_{EARTH}\) ₓ m\(_{OBJECT}\)) / (d\(_{earth}\))²
F\(_{gravity}\) \(_{moon}\) = G ₓ (M \(_{moon}\) ₓ m\(_{object}\)) / (d \(_{moon}\))²
Since we are looking for the point where the net gravitational force is zero, we set these two forces equal to each other:
G × (M\(_{earth}\) × m\(_{object}\)) / (d\(_{earth}\))² = G × (M \(_{moon}\) × m\(_{object}\)) / (d \(_{moon}\))²
Canceling out the common factors of G and m\(_object}\), and substituting the given values:
(M\(_{earth}\) × 1) / (d\(_{earth}\))² = (M \(_{moon}\) × 1) / (d \(_{moon}\))²
Rearranging the equation:
(d\(_{earth}\))²/ (M\(_{earth}\)) = (d \(_{moon}\))² / (M \(_{moon}\))
Taking the square root of both sides:
d\(_{earth}\) / √(M \(_{moon}\))) = d_moon / √(M \(_{moon}\))
Substituting the given values:
d\(_{earth}\) /√(M\(_{earth}\)) = d\(_{moon}\) / √(1/81 × M\(_{earth}\))
Simplifying further:
d\(_{earth}\) / √(M\(_{earth}\)) =d\(_{moon}\) / (1/9 × √(M\(_{earth}\)))
Multiplying both sides by √(M\(_{earth}\)):
d\(_{earth}\) = (1/9) × d\(_{moon}\)
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-33+2x= -6(1 + 5x) +5x
Answer:
=1
Step-by-step explanation:
what is the area of this circle?
Answer:
113.1
Step-by-step explanation:
d= 2r
r = 6
area = \(\pi r^{2}\) = 36 x \(\pi\) = 113.09
Please help solve
-5<14-4x≤3
Answer:
Interval notation (-5,3]
Slope of (18,-5) ,(18, 20)
Answer:
y2-y1/x2-x1
20-(-5) = 25
18-18 = 0
slope is 25/0
Step-by-step explanation:
explain how utility could be used in a decision where performance is not measured by monetary value
The utility can be used to quantify and compare preferences in decision-making scenarios where performance is not measured by monetary value.
The utility can be used as a measure of preference or satisfaction in decision-making situations where performance is not directly measured by monetary value. Utility refers to the subjective value or desirability that an individual assigns to different outcomes or options.
In such cases, utility can be quantified using a utility function, which maps the outcomes or attributes of the decision problem to a numerical representation of the individual's preferences. This function allows for the comparison and evaluation of different options based on their utility values.
For example, consider a decision involving healthcare treatments. The performance of different treatments may not be easily measured in monetary terms, but individuals may have preferences based on factors such as effectiveness, side effects, or quality of life impact.
Utility can be used to capture these preferences and make a decision that maximizes the overall satisfaction or well-being of the individual.
To use utility in decision-making, it is necessary to understand and quantify individual preferences through techniques like surveys, interviews, or experimental methods. By assigning utility values to different outcomes or attributes, decision-makers can then compare options and select the one that maximizes utility.
However, it's important to note that utility is subjective and varies among individuals. Different people may have different utility functions and weigh attributes differently. Therefore, utility-based decision-making requires taking into account the preferences of the specific individual or group involved.
In summary, utility can be employed in decision-making scenarios where performance is not directly measured in monetary terms. It quantifies subjective preferences and allows for the comparison and selection of options based on the utility values assigned to different outcomes or attributes.
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one card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
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Please Help! Anyone know how to solve Rational Equations?
Answer:
The answer is D. x = 0 , 5
x equal to 0 and 5.
he two-way frequency table given shows the results from a survey of students who attend the afterschool program.
Takes Art Class Doesn't Take Art Class Total
Plays a Sport 45 120
Doesn't Play a Sport 45
Total 225
Does the data show an association between taking an art class and playing a sport?
There is a strong, positive association.
There is a strong, negative association.
There is a weak, positive association.
There is a weak, negative association.
The association between the variables art class and playing a sport is classified as follows:
There is a strong, negative association.
What is the association between the two variables?The association between variables can be classified either as positive or as negative, as follows:
Positive: both variables behave similarly, either both increases or both decreasing.Negative: the variables behave in an inversely manner, with one increasing and the other decreasing, or vice-versa.In the context of this problem, it is found that of the students that take art class, the majority do not play a sport, while among those who do not take art class, the majority play a sport, hence there is a strong and negative association between the two variables.
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You are given $893 in one, five, and ten dollar bills. There are 165 bills. There are twice as many five dollar bills as there are ones and tens combined. How many bills of each type are there?
Given:
You are given $893 in one, five, and ten dollar bills.
There are 165 bills.
There are twice as many five dollar bills as there are ones and tens combined.
To find:
How many bills of each type are there?
Solution:
Consider the number of bills of one dollars, five dollars and ten dollars are x, y and z respectively.
According to the question,
Number of bills : \(x+y+z=165\) ...(1)
Total amount : \(1x+5y+10z=893\) ...(2)
Condition : \(y=2(x+z)\) ...(3)
Equation (3) can be written as
\(\dfrac{y}{2}=x+z\) ...(4)
Substituting \(x+z=\dfrac{y}{2}\) in (1), we get
\(\dfrac{y}{2}+y=165\)
\(\dfrac{3y}{2}=165\)
\(3y=330\)
\(y=110\)
Substituting y=110 in (4), we get
\(x+z=\dfrac{165}{2}\)
\(x+z=55\)
\(x=55-z\) ...(5)
Substituting y=110 and x=55-z in (2), we get
\((55-z)+5(110)+10z=893\)
\(55-z+550+10z=893\)
\(9z+605=893\)
\(9z=893-605\)
\(9z=288\)
Dividing both sides by 9, we get
\(z=32\)
Substituting z=32 in (5), we get
\(x=55-32\)
\(x=23\)
Therefore,
One dollar bills = 23
Five dollars bills= 110
Ten dollars bills = 32
Whats the slope and y-intercept of y=-3x+4?
Answer:
slope= -3. y intercept is 4
Step-by-step explanation:
the x value is slope and the y value is y intercept.
REMEMBER THIS!!! ITS SUPPPER IMPORTANT
Answer:
\(\boxed {\sf m= -3}}\)
\(\boxed {\sf b= 4}\)
Step-by-step explanation:
The equation of the line is in slope intercept form or:
\(y=mx+b\)
where m is the slope and b is the y-intercept.
Essentially:
The coefficient to x, or number being multiplied is the slope The number added or subtracted from the x term is the y-interceptThe line given is:
\(y= -3x+4\)
-3 is the coefficient of x and 4 is being added to -3x.
The slope (m) is -3 and the y-intercept (b) is 4.
Select the correct answer.
The numbers of pages in the books in a library follow a normal distribution. If the mean number of pages is 180 and the standard deviation is 30
pages, what can you conclude?
OA About 60% of the books have fewer than 150 pages.
O B.
About 16% of the books have fewer than 150 pages.
OC.
About 95% of the books have more than 150 pages.
OD. About 16% of the books have more than 150 pages.
Answer:
B
About 16% of the books have fewer than 150 pages.
Step-by-step explanation:
Quizlet also said so
Which equation shows the same relationship as 1/2=3x1/6
Answer:
1 /2
Step-by-step explanation:
3×1 = 3
So it is 3 /6 = 1/2
3/6 ÷2 = 1/2
DUE IN A FEW MIN PLEASE HELP!!! SO CONFUSED! IM RUNNING OUT OF TIME AND DONT HAVE THE TIME TO TRY AND FIGURE IT OUT! PLEASE HELP!
QUESTION DOWN BELOW!
Answer:
This is a ssa situation, no triangle is possible.
Step-by-step explanation:
"SSA" means "Side, Side, Angle".
In an SSA triangle, we are given two sides and an angle that is not the angle between the given sides.
In triangle ABC:
A, B and C are the interior angles.a, b and c are the sides opposite the corresponding interior angles.Given:
m∠A = 44°side a = 12.6 cmside b = 19 cmThe angle that is between the sides a and b is angle C.
Therefore, as angle A is not the angle between the given sides, ΔABC is an SSA triangle.
Law of Sines
\(\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
To determine if any triangles are possible, substitute the given values into the Law of Sines to find angle B:
\(\implies \sf \dfrac{\sin 44^{\circ}}{12.6}=\dfrac{\sin B}{19}\)
\(\implies \sf \sin B=\dfrac{19\sin 44^{\circ}}{12.6}\)
\(\implies \sf \sin B=1.0475007...\)
As -1 ≤ sin B ≤ 1, there is no solution for angle B.
Therefore, although this is an SSA situation, no triangle is possible.
Picture of coordinates (5,4) (3,4)
On a Cartesian plan
Both the coordinate points are plotted on the graph. The cartesian graph is attached with the answer.
What are coordinates?Coordinates are numbers which determine the position of a point or a shape in a particular space (a map or a graph). In the cartesian coordinate system, the coordinates are of the form (x, y).Other coordinate systems are : cylindrical and spherical coordinate systemGiven are the two coordinates to be plotted on a Cartesian plan -
(5, 4) , (3, 4).
The two given coordinate points are (5, 4) , (3, 4).
Refer to the graph attached. It shows both the points plotted.
Therefore, both the coordinate points are plotted on the cartesian graph.
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