The line of reflection is the y-axis
What is Reflection:Reflection is a geometric transformation that involves flipping an object over a line or a plane, creating a mirror image of the original object.
When a figure or polygon is reflected over the y-axis, it means that each point in the original figure is moved to a new point with the same y-coordinate but a negated x-coordinate.
Here we have
Triangle DEF has vertices at D(−3, 5), E(−10, 4), and F(−11, 8).
Triangle D′E′F′ is the image of triangle DEF after a reflection.
After reflection, the vertice E′ is located at (10, 4).
Here the x-coordinate of E, − 10 is changed to 10
As we know when the figure is reflected over the y-axis the sign of the x coordinate will be changes
Hence,
The line of reflection is the y-axis
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Sally bought a bag of candies and sorted them by color. She had 9 red candies, 43 orange candies, and 14 yellow candies. How many total candies were in the bag?
She had 9 red candies, 43 orange candies, and 14 yellow candies. Therefore, there are total 66 candies.
In mathematics, total is the addition of a series of arbitrary numbers called addition or addition; the result is their sum. In addition to numbers, other types of values can be added: functions, vectors, matrices, polynomials, and in general, elements of any type of mathematical object on which a "+" operation is defined. The sum of infinite sequence is called sequence. They involve the concept of limits and are not considered in this article.
Given that:
9 red candies
43 orange candies and 14 yellow candies.
Therefore, there are = 9 + 43 + 14
= 66 candies.
Therefore, there are total 66 candies.
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From a position 7 meters above the ground level in a building, an observer measures the angle of elevation of the top of a flagpole to be 50 degrees, and the angle of depression of the foot of the flag pole is 20degrees. How tall is the flagpole? (2 marks)
The flagpole is approximately 16.27 meters tall.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
We can solve these equations simultaneously to find h. First, we can rearrange the first equation to get:
x = h / tan(50)
Then, we can substitute this expression for x into the second equation and simplify:
tan(20) = h / (h / tan(50) + 7)
tan(20) = h / (h / 1.1918 + 7)
h(1 - 0.8393 tan(20)) = 7 tan(20)
h = 7 tan(20) / (1 - 0.8393 tan(20))
Using a calculator, we can evaluate this expression to get:
h ≈ 16.27 meters
Therefore, the flagpole is approximately 16.27 meters tall.
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how much would a new college graduate in business have to earn in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences (to the nearest whole number)?
A new college graduate in business would have to earn a starting salary of at least $85,095 to have a salary higher than 99% of all starting salaries of new college graduates in health sciences.
To solve this problem, we need to use the concept of z-scores, which measures the number of standard deviations away from the mean that a data point is.
First, we need to find the z-score that corresponds to the 99th percentile for the distribution of starting salaries in health sciences. We can use a standard normal distribution table or calculator to find that the z-score is approximately 2.33.
Next, we can use the formula for converting a z-score to an actual value:
z = (x - μ) / σ
where x is the actual value we want to find, μ is the mean, and σ is the standard deviation.
We can rearrange the formula to solve for x:
x = z * σ + μ
For business graduates, we want to find the salary that corresponds to a z-score of 2.33, using the standard deviation of $15,000 and mean of $53,901.
Plugging in the values, we get:
x = 2.33 * $15,000 + $53,901
x = $85,095
In summary, we used z-scores and the formula for converting z-scores to actual values to calculate the starting salary that corresponds to the 99th percentile for business graduates.
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Complete question is:
According to the National Association of Colleges and Employers, the average starting salary for new college graduates in health sciences is $51.541. The average starting salary for new college graduates in business is $53,901 (National Association of Colleges and Employers website, January , ). Assume that starting salaries are normally distributed and that the standard deviation for starting salaries for new college graduates in health sciences is $11,000. Assume that the standard deviation for starting salaries for new college graduates in business is $15,000.
How much would a new college graduate in business have to earn in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences (to the nearest whole number)?
the reliability of the source of information is one test to perform when assessing the reliability of group of answer choices premises. examples and illustrations. statistics. artifacts.
Artifacts are physical or digital objects which can be used to prove points.
Ultimately, determining the reliability of the source of information is essential to understanding the reliability of answer choices.
When assessing the reliability of a group of answer choices, it is important to consider the source of the information. This can be done by analyzing the origin of the information and its credibility.
Examples and illustrations are useful forms of evidence that can be used to support an argument. Statistics are numerical data that can be used to demonstrate the validity of a point.
Artifacts are physical or digital objects which can be used to prove a point. By evaluating the source of the information, and considering examples, illustrations, statistics, and artifacts, one can assess the reliability of a group of answer choices.
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Which of the following equations represent(s) a line that goes through the
points (2,3) and (1,1)?
1) y = 2(x-2) + 3
II) y = 2x - 1
III) y = 2(x-1) + 1
O I, II & III
O III only
OI and III
OI only
O II only
Answer:
O I, II & III
Step-by-step explanation:
(2, 3) and (1, 1)
m = (3 - 1)/(2 - 1) = 2
y = 2x + b
1 = 2(1) + b
b = -1
The equation of the line is
y = 2x - 1
I) y = 2(x - 2) + 3 = 2x - 4 + 3 = 2x - 1 Yes
II) y = 2x - 1 Yes
III) y = 2(x - 1) + 1 = 2x - 2 + 1 = 2x - 1 Yes
Answer: O I, II & III
What is the pattern 6 1 8 4 2 7 answer i don’t understand this is sposed be for kindergarten and tell me how you know the answer
There is no specific number pattern for the sequence { 6, 1, 8,4, 2, 7} but to determine the next term of sequence we can use the following patterns
1) for even place terms pattern is
aₙ = aₙ₋₂ + 3.
2) for odd place terms pattern is first aₙ
= aₙ₋₂ + 2 and for next aₙ₊₂ = aₙ - 6, where n is odd number.
A pattern is a series or sequence of repetitions. A number pattern is a series of numbers that follow a specific order in mathematics. Patterns usually describe inverse relationships between numbers.
A sequence of numbers can also be called a pattern. The types of number patterns are classified as
arithmetic sequencegeometric sequenceWe need to write a pattern for 6, 1, 8, 4, 2, 7. Now the sequence is 6, 1, 8, 4, 2, 7,
First term = 6
Second term = 1
Break this sequence down into odd and even terms or enteries. The order of odd entries is 6,8,2,.. So the pattern here is 2 and -6, i.e. 7ᵗʰ entry = 2 + 2 = 4 and 9ᵗʰ entry = 4+ 6 = 10 and so on. Now for Evan's bit term, 1,4,7,.. The pattern here is aₙ = aₙ₋₂ + 3. where n is an even number. So the entire sequence has no pattern, but the odd and even elements can be determined by different patterns.
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WILL GIVE BRIANLIAT TO BEST ABWWER
The graph of an exponential of the form y = ab contains the points (2, 60) and (4, 960). What are the values of a and b
Answer:
(15/4)4^x
Step-by-step explanation:
Substituting the x and y values of the first point, we get:
y = ab
60 = ab^(2)
Substituting the x and y values of the second point, we get:
y = ab
960 = ab^(4)
Now we can solve for a and b by eliminating one of the variables. One way to do this is to divide the second equation by the first equation:
960/60 = (ab^(4))/(ab^(2))
16 = b^(2)
Taking the square root of both sides, we get:
b = ±4
Since an exponential function can only have positive values for b, we choose b = 4. Now we can solve for a by substituting b = 4 into one of the original equations:
60 = a(4^(2))
60 = 16a
a = 60/16
a = 15/4
Therefore, the values of a and b are a = 15/4 and b = 4, and the exponential function is y = (15/4)4^x.
∠A and ∠B are supplementary angles. If m∠A =(x−9)∘ and m∠B =(7x+21)∘, then find the measure of ∠B.
Answer: = 56
Step-by-step explanation:
rahquez and trinidad both leave the park at the same time, but in opposite directions. if trinidad travels 6 mph faster than rahquez and after 8 hours they are 288 miles apart, how fast is each traveling?
The propensity scoring method is a statistical technique used to adjust for differences in the characteristics of groups being compared in a study. In this case, we want to adjust for the fact that respondents aged 70 or older are underrepresented in an internet sample.
To do this, we can assign a propensity score to each individual in the sample based on their likelihood of being in the sample, given their age. We can then use this score to weight their responses to account for the underrepresentation of older individuals.
In this case, we know that respondents aged 70 or older are only one-third as likely to be in an internet sample as their actual incidence in the population. This means that we can assign a propensity score of 3 to each individual aged 70 or older in the sample, and a propensity score of 1 to everyone else.
Using these propensity scores, we can weight the responses of each individual in the sample. Responses from individuals with a propensity score of 3 would be weighted by a factor of 3, while responses from individuals with a propensity score of 1 would be weighted by a factor of 1.
By adjusting for the underrepresentation of older individuals in this way, we can obtain more accurate estimates of the characteristics of the population being studied, and reduce the potential for bias in our analysis.
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(e) find an expression that gives, as a function of time t, the rate at which thermal energy is produced in the resistor. (use the following as necessary: t. do not include units in your answer.)
The expression for the rate of thermal energy produced in the resistor as a function of time t is P(t) = V(t)²/R.
The thermal energy that is produced in a resistor can be determined by P = I²R, where P is the power, I is the current, and R is the resistance. The current is given by I = V/R where V is the voltage. Therefore, P = V²/R.
Using the Ohm's law, the voltage is V = IR, so P = I²R = (V/R)²R = V²/R.
Thus, the rate at which thermal energy is produced in the resistor as a function of time t can be expressed as: P(t) = V(t)²/R where P(t) represents the power or rate at which thermal energy is produced in the resistor, V(t) represents the voltage as a function of time t, and R represents the resistance of the resistor.
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if this paper gets finished by the end of today (i have 2 hours) then i might be able to stay in honors. can someone help? (2 attachments for 50 points)
Answer:
To solve for y, we need to isolate it on one side of the equation. Since there is only one term with y in it, we can begin by isolating that term:
7 + 4 + 25 + 6 = 42
42 + 5y - 2 = 40 + 5y
Subtracting 40 from both sides, we get:
2 + 5y = 5y
Subtracting 5y from both sides, we get:
2 = 0
This is a contradiction, which means that there is no value of y that satisfies the equation. Therefore, the equation has no solution.
Answer:
y= [tex]-\frac{12}{47}[/tex]
Step-by-step explanation:
second attachment
Sandy can saw three cords of wood and a standard workday, if the whole day is spent doing it. Sandy can split five cords of wood in a standard workday, if the whole day is spent doing it. In a standard workday, what is the largest number of cords of wood that Sandy can saw and split
Answer:
If Sandy spends the whole standard workday sawing, they can saw 3 cords of wood. If they spend the whole day splitting, they can split 5 cords of wood. However, Sandy cannot spend the whole day both sawing and splitting. Therefore, the largest number of cords of wood that Sandy can saw and split in a standard workday is less than or equal to 3 + 5 = 8.
To find the largest number of cords of wood that Sandy can saw and split, we need to find a way to divide the work between sawing and splitting. Let's assume that Sandy spends x fraction of the day sawing and (1-x) fraction of the day splitting. Then, the amount of wood that Sandy can saw in that time is 3x cords, and the amount of wood that Sandy can split in that time is 5(1-x) cords. The total amount of wood that Sandy can saw and split is the sum of these two amounts:
3x + 5(1-x) = 3x + 5 - 5x = 5 - 2x
To maximize this quantity, we need to choose the value of x that makes it as large as possible. Since 0 <= x <= 1, the maximum value of 5 - 2x occurs at x = 0 (Sandy spends the whole day splitting) or x = 1 (Sandy spends the whole day sawing). Therefore, the largest number of cords of wood that Sandy can saw and split in a standard workday is 5 cords, which Sandy can achieve by spending 2/5 of the day sawing and 3/5 of the day splitting.
I need help on this! Will give brainliest!
The solution (16, 2) is a feasible production plan that satisfies all the constraints of the problem.
What is inequality?Inequality is a mathematical statement that compares two values or expressions, indicating whether they are equal or not equal, greater than or less than, greater than or equal to or less than or equal to each other, using mathematical symbols such as "<", ">", "<=", ">=", and "≠".
According to question:The solution (16, 2) represents that Wanda can produce 16 small pairs of gloves and 2 large pairs of gloves, and this production plan satisfies all the given constraints.
To see why, let's substitute x=16 and y=2 in the two inequalities:
45x + 120y ≤ 960, becomes 45(16) + 120(2) ≤ 960, which simplifies to 720 ≤ 960. This inequality is true, meaning that Wanda can produce this number of gloves within the 16 hours she has available.2x + 4y ≤ 40, becomes 2(16) + 4(2) ≤ 40, which simplifies to 36 ≤ 40. This inequality is also true, meaning that the materials cost for this production plan is within the budget of $40.Therefore, the solution (16, 2) is a feasible production plan that satisfies all the constraints of the problem.
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A sphere has a radius of 9in. the sphere is cut in half. what is the volume of each hemisphere. use 3.14 for pi and round to the hundredths if needed. Show work. PLEASE ANSWER IT
no member of the green party voted for the tax cut. p2) mr jacobs did not vote for the tax cut. c) mr jacobs is a member of the green party.
Answer:
Mr Jacobs did not vote for the tax cut. C - Mr Jacob is a member of the Green Party. Invalid.
Step-by-step explanation:
(HELP PLS)
Milwaukee's average high temperature in the summer is four
degrees lower than other cities in its same latitude.
Which option best describes the reason for that change?
OSioux Falls is near mountains.
O Milwaukee is beside a lake.
OSioux Falls is closer to a desert.
O Milwaukee has more mountains.
We can claim that after answering the above question, the As a result, equation the correct answer is "Milwaukee is near a lake."
What is equation?In mathematics, an equation is a statement that states the equality of two expressions. An equation is made up of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" contends that the sentence "2x + 3" equals the value "9". The purpose of equation solving is to identify the value or values of the variable(s) that will make the equation true. Simple or complex equations, regular or nonlinear, with one or more factors are all possible. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are utilized in many areas of mathematics, including algebra, calculus, and geometry.
Milwaukee's average high temperature in the summer is four degrees lower than other cities in its latitude since it is located next to a lake. The lake (Lake Michigan) cools the surrounding areas, notably Milwaukee, which is located on the lake's western shore. This is referred to as the "lake breeze" effect, and it is a regular occurrence in cities located near major bodies of water. As a result, the correct answer is "Milwaukee is near a lake."
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someone says batman's iq is 192, and someone says lex luthor's iq is 225. assuming the average iq is 100 with a standard deviation of 15, how many sigma is batman's iq and luthor's iq?
Batman's IQ is 5.47 standard deviations above the mean, and Luthor's IQ is 8.33 standard deviations above the mean.
To find out how many standard deviations above the mean Batman's IQ of 192 and Luthor's IQ of 225 are, we first need to calculate the z-scores for each IQ.
The formula for the z-score is:
z = (x - μ) / σ
Where:
x is the value we want to standardize (Batman's or Luthor's IQ)
μ is the population mean IQ (100)
σ is the population standard deviation (15)
For Batman's IQ:
z = (192 - 100) / 15 = 5.47
For Luthor's IQ:
z = (225 - 100) / 15 = 8.33
Therefore, Batman's IQ is 5.47 standard deviations above the mean, and Luthor's IQ is 8.33 standard deviations above the mean.
Note that it is highly unlikely to have IQs this high in the general population, and these values are likely exaggerated for fictional characters.
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HELP!!!!!!!! For #19-20, solve for x. simplify all radicals.
Answer:
19. sqrt{305}
20. 3*sqrt{7}
Step-by-step explanation:
You use the Pythagorean theorem, which can be applied to right triangles. It states that x^2+y^2 = hypotenuse ^2, where x and y are the two sides other than the hypotenuse.
Step-by-step explanation:
hope this will gel help u
Select all expressions containing a coefficient of 4.
4xy
2x+4
4x+2y
4+x+y
All the given expressions containing a coefficient of 4 is 4x+2y and 4xy.
Explain about the coefficient of the number?A quantity or number that is combined with a variable is regarded as a coefficient. The variable is often multiplied by an integer, which is then typed next to it.
It is assumed that the variables with no accompanying number have a coefficient of 1.A variable's coefficient is the quantity of any letter or number that the variable possesses. For instance, the coefficient for variable x in the formula 2x + 3y is 2, and thus the coefficient of variable y is 3 in the same formula.From the given equation:
4x+2y have the coefficient of 4 of variable 'x'.
4xy have the coefficient of 4 of variable 'x' and 'y' both.
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cylindrical container of paint is 3 cm across the top and about 7 cm high. how many cubic centimeters of paint can it hold?
The number of cubic centimeters of paint that will fit in the cylindrical container is:
66.36 cm³
How to find the volume of a cylindrical container?The volume of a cylinder can be determined by multiplying the area of the base by the height. It may be expressed using the formula:
V = πr²h
where π (pi) is approximately equal to 3.14, r is the radius, and h is the height.
You should also note that the radius of the cylinder is one-half of the diameter.
V = πr²h
Since the cylindrical container of paint has a diameter of 3 cm, its radius would be 1.5 cm. Furthermore, its height is around 7 cm. As a result, by substituting the given values into the formula, we may get the following result:
V = πr²hV = π(1.5)²(7)
V = 66.36 cm³
Therefore, the cylindrical container of paint can hold approximately 66.36 cubic centimeters of paint.
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Which expression is equivalent to (1/2[cos(Pi/5) + sin(Pi/5)])5 ?
A) 1/32 [cos(Pi/5)+i sin(Pi/5)]
B) 1/32[cos(Pi) + i sin(Pi)]
C) 1/10[cos(Pi/5) + i sin(Pi/5)]
D) 1/10[cos(Pi)+ i sin(Pi)]
the answer of given function is equivalent to option (C) 1/10[cos(Pi/5) + i sin(Pi/5)]
Define trigonometric functionTrigonometric functions are mathematical functions that relate angles and sides of triangles. There are six primary trigonometric functions: sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
We can simplify the expression (1/2[cos(π/5) + sin(π/5)])5 as follows:
([tex]\frac{1}{2}[/tex][cos(π/5) + sin(π/5)])5
= [tex]\frac{5}{2}[/tex][cos(π/5) + sin(π/5)]
Now, we can use Euler's formula:
e^ix = cos(x) + i sin(x)
to rewrite this expression in the form a + bi:
[tex]\frac{5}{2}[/tex][cos(π/5) + sin(π/5)]
= [tex]\frac{5}{2}[/tex][[e^(i(π/5) + (-π/2))]
=[tex]\frac{5}{2}[/tex][[e^(-iπ/2) e^(iπ/5)]
= [tex]\frac{5}{2}[/tex][[-i(cos(π/5) + i sin(π/5))]
=[tex]\frac{5}{2}[/tex][[-i cos(π/5) + 5/2 sin(π/5)]
Therefore, the equivalent expression in the form a + bi is:
-[tex]\frac{5}{2}[/tex][ cos(π/5) + (5/4) i sin(π/5)
And simplifying this expression, we get:
-[tex]\frac{5}{2}[/tex][ cos(π/5) + (5/4) i sin(π/5) = (1/10) [cos(π/5) + i sin(π/5)]
Therefore, the answer is option (C) 1/10[cos(π/5) + i sin(π/5)].
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2. The area of this trapezoid is 24.5 ft².
3 ft
4 ft
What is the height of the trapezoid? Write the formula first then SHOW YOUR WORK
Plsss help I really need the answer!!!
The height of the trapezoid is 7 ft.
How to find the height of the trapezoid?
The formula for the area of a trapezoid is:
A = 1/2 * (a + b)h
where A is the area, a and b are the lengths of the parallel sides, and h is the height (the perpendicular distance between the parallel sides).
Given A = 24.5 ft², a = 3 ft and b = 4 ft. We can solve for h. That is:
A = 1/2 * (a + b)h
24.5 = 1/2 * (3 + 4)h
24.5 = 1/2 * (7)h
24.5 = 3.5h
h = 24.5/3.5
h = 7 ft
Therefore, the height of the trapezoid is 7 ft.
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please answer asap!!
Answer:
y = csc(3x)
Step-by-step explanation:
You want an equation for a cosecant curve with vertical asymptotes at multiples of π/3.
Horizontal compressionThe vertical asymptotes of the parent cosecant function are at multiples of π. Putting them at multiples of π/3 means compressing the graph horizontally by a factor of 3.
That compression means x will be replaced by 3x in the equation. You want ...
y = csc(3x)
What is 3 - 5 written as a decimal (not a negative number)
Example: 1 - 5 = 0.2
I WILL GIVE BRAINIEST PLEASE HELP THIS IS SO CONFUSING!!!!!
Step-by-step explanation:
3/5 as a decimal is 0.6(explanation is given in your another question please check)
What is 4.8 x 0.1 ?
Question :
4.8 x 0.1 =
Answer: 0.48
Step-by-step explanation:
× 0.1 = ÷10
÷ 0.1 = ×10
× 0.01 = ÷100
÷ 0.01 = ×100
So, we do=
4.8 x 0.1 = 4.8 ÷ 10
= 0.48
So our answer is 0.48
how do i know if the cost is proportional
Proportionality describes a relationship between values that have the same ratio.
Direct Proportionality
The are 2 types of proportionality; the first is directly proportional. If a relationship is directly proportional, both values will increase or decrease together at the same rate. Directly proportional relationships are described by the equation:
y = kxIn this equation, y and x are variables while k represents the constant of proportionality. In a directly proportional relationship, both the y and x value grow at the same rate. For example, take this set of values:
y = {20, 40, 80}x = {2, 4, 8}These values are directly proportional because they both double each time, meaning they grow at the same rate. Additionally, the ratio between terms remains the same. Take the ratios 20:2 and 40:4, when simplified these are both 10:1 (for proportionality it's easier to write ratios as y:x). Since the ratio is the same, they are proportional. Additionally, the ratio tells us that the constant of proportionality is 10. So the equation to represent this situation is
y = 10xIndirectly Proportional
Indirect proportionality is similar to direct, but instead of increasing or decreasing together, one value increases while the other decreases. Indirect proportionality is described by the equation:
[tex]y=\frac{k}{x}[/tex]We can represent this with another set of x and y values.
x = {1, 2, 5}y = {10, 5, 2}Unlike directly proportional relationships, the growth rate is not constant. Still, we can represent this relationship as
[tex]y=\frac{10}{x}[/tex].So, k still equals 10, but the relationship is indirectly proportional. As x increases, y decreases, and vice versa.
The greenville park rangers want to know the number of visitors who arrive by bus
The correct option is B. The best number of people who will arrive by car is 90.
Bus: 185+175 = 359
Car: 38+43 = 81
Total: 359+81= 440
So, the proportion of arriving by car is [tex]\frac{81}{440 } = \frac{81}{440 }*500 = 90[/tex]
Regard frequency as probability
Probability is a branch of mathematics that deals with the study of random events. It is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1. An event with probability 0 means it will never occur, while an event with probability 1 means it will always occur.
The calculation of probability involves analyzing the possible outcomes of an event and assigning a probability to each outcome based on its likelihood of occurring. The probability of an event is determined by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in various fields, such as statistics, finance, engineering, and science, to make predictions and informed decisions.
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Complete Question:
The Greenville Park rangers want to know the number of visitors who arrive by bus and the number who arrive by car. Park officials record the method of transportation for a random selection of park visitors over two weeks.
Methods of Transportation:
Week Bus Car
1 185 38
2 174 43
if 500 people visit the park in week 3, which is the best number of people who will arrive by car.
A). 40
B). 90
C). 130
D). 200
exercise 1.2.21 a boy finds $1.05 in dimes, nickels, and pennies. if there are 17 coins in all, how many coins of each type can he have?
The boy can have 9 dimes, 0 nickels, and 8 pennies.
We have,
a boy finds $1.05 in dimes, nickels, and pennies.
Let's assume that the boy has x number of dimes, y number of nickels, and z number of pennies.
We know that the total value of these coins is $1.05, and there are 17 coins in total.
Now, let's convert the values into cents.
We have 10 cents for each dime, 5 cents for each nickel, and 1 cent for each penny.
Therefore, the equation we can set up is:
10x + 5y + z = 105
(since $1.05 is equal to 105 cents)
We also know that the total number of coins is 17, so:
x + y + z = 17
Now, we have a system of equations.
Let's solve it using a method called substitution.
From the second equation, we can express z in terms of x and y:
z = 17 - x - y
Substituting this value of z into the first equation, we get:
10x + 5y + (17 - x - y) = 105
Simplifying this equation, we get:
9x + 4y = 88
Now we have a new equation to work with.
We can rearrange it to solve for x:
x = (88 - 4y) / 9
To find the possible values for x and y, we can try different values of y and calculate the corresponding values for x.
Since the number of coins cannot be negative, we can start by setting y to 0 and calculate x:
x = (88 - 4(0)) / 9
x = 88 / 9
x ≈ 9.78
Since the number of coins must be a whole number, we can round x down to the nearest whole number, which gives us x = 9.
Now, let's substitute this value of x back into our second equation:
9 + y + z = 17
Simplifying this equation, we get:
y + z = 8
We can now try different values of y and calculate the corresponding values of z that satisfy this equation.
Let's start with y = 0:
0 + z = 8
z = 8
So, one possible solution is x = 9, y = 0, and z = 8.
This means the boy can have 9 dimes, 0 nickels, and 8 pennies.
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After forming a system of equations according to the given information
We find that the boy can have 5 pennies, 13 dimes, and 2 nickles.
Given that,
The boy finds a total of $1.05 in dimes, nickels, and pennies.
There are 17 coins in total.
Number of pennies = 5
Let "d" represent the number of dimes.
Let "n" represent the number of nickels.
Let "p" represent the number of pennies = 5
We know that,
1 $ = 100 cent
1 cent = 0.01$
According to the given information:
The system of equations be:
0.10d + 0.05n + 0.01 x 5 = 1.05 ......(i)
d + n + 2 = 17 .....(ii)
Proceeding with equation (i):
After simplifying:
0.10d + 0.05n = 1
Multiply 10 both sides
10d + 5n = 10 ....(iii)
Proceeding with equation (i):
After simplifying:
d + n = 15 .
Multiply 5 on both sides,
5d + 5n = 75 ....(iv)
Subtract (iii) from (iv):
5d = 65
d = 13
So, there are 13 dimes.
Now substitute this value of d into (iv),
n = 2
So, there are 2 nickels.
Hence.
We find that the boy can have 5 pennies, 13 dimes, and 2 nickles.
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The complete question is attached below:
A boy finds $1.05 in dimes, nickels, and pennies.
Dimes are 10 cents coins, Nickle is 5 cents coins and pennies are 1 cent coins. If there are 17 coins and the number of pennies is 5 in all.
How many coins of each type can he have?
an arch top window is being built whose bottom is a rectangle and the top is a semicircle. if there is 12 meters of framing amterials what is the width of the window that lets in the most light?
An arch top window is a window with a bottom in the form of a rectangle and the top in the form of a semicircle. The width of the window that lets in the most light is 6 meters.
The width of the window that lets in the most light is determined by the length of the base of the rectangle, which is equal to the diameter of the semicircle. The total length of the framing materials is 12 meters, so the base length of the rectangle should be 6 meters. Thus, the width of the window is 6 meters.
To explain further, the width of an arch top window is determined by the base of the rectangle that forms the bottom part of the window, and the top is a semicircle. To determine the width of the window that lets in the most light, the length of the base should be equal to the diameter of the semicircle. Since the total length of the framing materials is 12 meters, the base length of the rectangle should be 6 meters, and the width of the window should also be 6 meters.
This means that the width of the window that lets in the most light is 6 meters, as the length of the base of the rectangle is equal to the diameter of the semicircle.
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according to studies, what percentage of deaths among 16 to 19 year-olds is related to motor vehicles?
Approximately 38% of deaths among 16 to 19 year-olds are related to motor vehicles.
According to the Centers for Disease Control and Prevention (CDC), motor vehicle crashes are the leading cause of death for teenagers in the United States.
In 2019, a total of 2,375 teenagers aged 16-19 years died in motor vehicle crashes, and an additional 258,000 were treated in emergency departments for injuries sustained in motor vehicle crashes.
These deaths accounted for 62% of all deaths among teenagers aged 16-19 years.
Therefore, around 38% of fatalities among individuals aged 16 to 19 are connected to automobiles.
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