A line passes through the point (6−6) and has a slope of 3/2 . Write an equation in point-slope form for this line.
A total of 804 tickets were sold for the school play. They were either adult tickets or student tickets. There were 54 more student tickets sold than adult tickets. How many adult tickets were sold?
On two investments totaling $10,500, Brian lost 6% on one and earned 8% on the other. If his net annual receipts were $497, how much was each investment?
Preston goes on a camel safari in Africa. They travel 5 km north, then 3km east and then 1 km north again. What distance did he cover? What was his displacement?
The total distance Preston covered on his camel safari is 9 km, and his displacement is 6.71 km toward the northeast.
Determining Distance and Displacement
To answer the student's question about Preston's journey during his camel safari, we need to consider the definitions of distance and displacement.
Distance is the total length of the path traveled regardless of direction. In Preston's case, he traveled 5 km north, then 3 km east, and then 1 km north again. Therefore, the total distance covered is the sum of these individual distances
Displacement, on the other hand, measures the change in position from the starting point to the final point and is direction-dependent. It is a vector quantity with both magnitude and direction. To find the displacement, we can represent Preston's movement on a coordinate system with north being the positive y-direction and east being the positive x-direction.
From the starting point, moving 5 km north and then 1 km north results in a total of 6 km in the positive y-direction.
The magnitude of the displacement can be calculated using the Pythagorean theorem:
√((6 km)² + (3 km)²) = √(36 km² + 9 km²) = √(45 km²) = 6.71 km (rounded to two decimal places)The direction of the displacement would be to the northeast. Therefore, Preston's displacement is 6.71 km toward the northeast.
Find the value of x, rounded to the nearest tenth. Please help me!!
The value of x for the circle is 25.8. The correct option from the following is (D).
Simple closed shapes include circles. It is the collection of all points in a plane that are a certain distance from the center. A segment is a section of a straight line that has every point on the line that lies in its middle and is enclosed by two clearly defined endpoints.
The products of two secant lines that cross one another outside of a circle are equal.
The value of x is:
5(x+5) = 7(15+7)
5x + 25 = 7 × 22
5x + 25 = 154
5x = 154 - 25
5x = 129
x = 129/5
x = 25.8
Hence, the value of x is 25.8.
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if f(x) = 3x - 2 then f (8) - f(-5)=
which is greater 2 or -13?
Assume the Poisson distribution applies. Use the given mean to find the indicated probability.
Find P(4) when μ = 8.
Using the Poisson distribution formula, substitute the given mean and the number of occurrences into the formula to find the probability. Hence P(4; 8)= e^-8 * 8^4 / 4!. The answer will be in decimal form, signifying the probability.
Explanation:The probability in a Poisson distribution that an event happens exactly k times when the mean occurrence rate (μ or Lambda) is given is determined using the following formula:
P(k; μ) = (e^-μ * μ^k) / k!
Where e is Euler's number (approximately equal to 2.71828), k is the number of occurrences (in this case, it is 4) and μ is the mean number of occurrences (in this case, it is 8).
Applying the values into the formula, we have:
P(4;8) = (e^-8 * 8^4) / 4!
You can calculate the above expression using a calculator to find the probability. Remember, the answer will be in decimal form, representing the probability of the event occurring 4 times when the average rate of occurrence is 8.
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The length of the hypotenuse is:
0.
1.
2.
4.
divide the base by the sin of the opposite angle
base = 2
opposite angle = 30 degrees
2/sin(30) = 4
x = 4
y=-x y=2x+3 graph the equation to solve the system
Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. suppose a sample of 100 major league players was taken. find the approximate probability that the mean salary of the 100 players exceeded $4.0 million.
Final answer:
The probability is approximately 0.267.
Explanation:
To find the approximate probability that the mean salary of the 100 players exceeded $4.0 million, we can use the Central Limit Theorem and the Z-score formula. The Z-score formula is:
Z = (x - μ) / (σ / sqrt(n))
where x is the value we want to find the probability for (in this case $4.0 million), μ is the mean of the population ($3.26 million), σ is the standard deviation of the population ($1.2 million), and n is the sample size (100).
We calculate the Z-score as follows:
Z = (4.0 - 3.26) / (1.2 / sqrt(100)) = 0.617
We then use a Z-table or a calculator to find the probability corresponding to a Z-score of 0.617. The probability is approximately 0.267.
Find the surface area of a regular pentagonal prism with side length 8, altitude 20, and apothem approximately 5.5
The surface area of a regular pentagonal prism can be found by calculating the area of the pentagonal bases and the area of the rectangular sides and then summing those areas together.
Explanation:Calculating the Surface Area of a Regular Pentagonal Prism
To find the surface area of a regular pentagonal prism with given dimensions, we need to calculate the area of two components: the area of the pentagonal bases and the area of the rectangular sides (also called the lateral faces). We are given that the side length (s) of the pentagon is 8 units, the prism's altitude (h), or height, is 20 units, and the apothem (a) is approximately 5.5 units.
Firstly, the area of a pentagon (Apentagon) is calculated using the formula Apentagon = ½ * perimeter * apothem, where the perimeter (P) of a regular pentagon is the side length multiplied by 5. Thus, the area of one pentagonal base is ½ * 5 * 8 * 5.5. Next, to find the entire area of the two pentagonal bases, we multiply this result by 2.
The area of each of the rectangular sides can be found by multiplying the side length by the prism's altitude. Since there are 5 identical rectangular sides in a regular pentagonal prism, their total area is 5 * 8 * 20.
Adding these two results together gives us the total surface area of the prism. So, the formula for the surface area is Total Surface Area = (2 * ½ * 5 * 8 * 5.5) + (5 * 8 * 20).
Perform the indicated operation. (5 - 2i 2) 2
Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than or equal to y. Also, the sum of y and two-third of x is less than 4. Which graph represents the possible solutions?
Answer:
in other words b
Step-by-step explanation:
Pamela is 13 years older than Jiri. The sum of their ages is 53 what is Jiri's age?
The solution is: Jiri is 20 years old.
What is addition?Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
here, we have,
Pamela is 13 years older than Jiri so:
p=j+13
Then you are told that the sum of their ages is 53 so:
p+j=53
We already know from the first statement that p=j+13, this makes p+j=53 become:
(j+13)+j=53 so we combine the two j's on the left side
2j+13=53 subtract 13 from both sides
2j=40 divide both sides by 2
j=20
So Jiri is 20 years old.
Hence, The solution is: Jiri is 20 years old.
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6300 and 530
The value of 3 in ___is____times the value of 3 in ___.
Translate to an algebraic expression. 5 INCREASED BY y
there were 137 tickets purchased for a major league baseball game the lower box tickets cost $12.50 and the upper box tickets cost $10 the total amount of money spent was $1,502.50 how much of each kind of ticket
lower box = x
upper box = y
x+y=137
x=137-y
12.50x + 10y=1502.50
12.50(137-y) + 10y=1502.50
1712.5-12.50y+10y=1502.50
1712.5-2.50y=1502.50
-2.5y=-210
y=-210/-2.50 = 84
y = 84
x=137-84=53
53 lower box tickets
84 upper box tickets
Choose the polynomial written in standard form. (5 points)
xy2 + 4x4y + 10x2
x4y2 + 4x3y + 10x
x4y2 + 4x3y5 + 10x2
x6y2 + 4x3y8 + 10x
The polynomial in standard form from the given options is [tex]x^4y^2 + 4x^3y + 10x[/tex], as it orders the terms by degree in descending order, first by the degree of x and then y.
The term standard form in mathematics, especially in relation to polynomials, refers to a way of writing the polynomial so that the terms are ordered by their degree in descending order. More specifically, for a polynomial in two variables, x and y, the standard form would have the terms arranged first by the degree of x, then y, from highest to lowest.
Looking at the options provided in the question, the polynomial that is written in standard form would have the highest degree term first, and so on. The polynomial [tex]x^4y^2 + 4x^3y + 10x[/tex] follows this convention, with the terms ordered by decreasing powers of x first and y second. Therefore, this is the polynomial written in standard form.
Note that while the other options are all polynomials, they do not follow the standard form convention as closely as the correct option provided.
A fish is 5 feet below the surface of a lake. If its position can be recorded as −5 feet, what would the position of 0 represent?
A collection of quarters and nickels is worth $3.75. There are 27 coins in all. Find how many of each there are.
Q +N =27
Q=27-N
0.25Q + 0.05N =3.75
0.25(27-N) + 0.05 =3.75
6.75-0.25N+0.05N=3.75
6.75-0.2N=3.75
-0.2N=-3
N=-3/-0.2 = 15
15 nickels
27-15 = 12
12 quarters
15x0.05 = 0.75
12 x 0.25 = 3.00
3.00 + 0.75 = 3.75
12 quarters & 15 nickels
Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.
A newspaper finds that the mean number of typographical errors per page is six. Find the probability that (a) exactly four typographical errors are found on a page, (b) at most four typographical errors are found on a page, and (c) more than four typographical errors are found on a page.
In this case, the Poisson distribution is the best one to use. The formula for Poisson distribution is given as:
P[x] = e^-m * m^x / x!
Where,
m = mean number of typographical errors = 6
x = sample value
A. The probability of exactly 4 errors are found on a page is:
P[4] = e^(-6) * 6^4/4!
P[4] = 0.1339
B. The probability that at most 4 errors will be the summation of x = 0 to 4:
P[0] = e^(-6) * 6^0/0! = 2.479 E -3
P[1] = e^(-6) * 6^1/1! = 0.01487
P[2] = e^(-6) * 6^2/2! = 0.04462
P[3] = e^(-6) * 6^3/3! = 0.08924
Therefore summing up all including the P[4] in A gives:
P[at most 4] = 0.2851
C. The probability that more than 4 would be the complement of answer in B.
P[more than 4] = 1 - P[at most 4]
P[more than 4] = 1 - 0.2851
P[more than 4] = 0.7149
A student was asked to use the formula for the perimeter of a rectangle, P = 2l + 2w, to solve for l. The student came up with an answer, P -2w=2l. What error did The student make? Explain. Then solve for l
The Sugar Sweet Company is going to transport its sugar to market. It will cost $6500 to rent trucks, and it will cost an additional $250 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S . Then use this equation to find the total cost to transport 19 tons of sugar.
Answer: Equation relating C to S : [tex]C=6500+250S[/tex]
The total cost to transport 19 tons of sugar is $11, 250.
Step-by-step explanation:
Given : It will cost $6500 to rent trucks, and it will cost an additional $250 for each ton of sugar transported.
Total cost = $6500 + $250 x (amount of sugar transported ( in tons))
Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported.
Then, the equation relating C to S would be : [tex]C=6500+250S[/tex]
When S= 19 , we get
[tex]C=6500+250(19)=6500+4750= 11250[/tex]
Hence, the total cost to transport 19 tons of sugar would be $11, 250.
An equation that relates Cost to the amount of sugar S
C = 6500 + 250S
The total cost is $1120
The total cost of transporting 19 tons of sugar at 250 eachC = total cost
C = 6500 + 250(19)
Total cost = 6500 + 4750
= 11250
Therefore the total cost of transporting the 19 tons of sugar is $11250
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Which expression is equivalent to the following complex fraction? (2/x)-(4/y)/(-5/y)+(3/x)
To find the equivalent expression, multiply the first fraction by y and the second fraction by x. Simplify the expression by combining like terms.
Explanation:To find the expression equivalent to the given complex fraction, we can simplify it step by step. First, multiply the numerator and denominator of the first fraction (2/x) by y, and multiply the numerator and denominator of the second fraction (-5/y) by x. This gives us (2y)/(xy) - (4x)/(-5x). Next, simplify the expression by combining like terms. The final equivalent expression is (2y - 4x)/(xy + 5x).
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You inherit one hundred thousand dollars. You invest it all in three accounts for one year. The first account pays 4% compounded annually, the second account pays 3% compounded annually, and the third account pays 2% compounded annually. After one year, you earn $3,650 in interest. If you invest five times the money in the account that pays 4% compared to 3%, how much did you invest in the 4% account?
what is 46 2/3 of 28
A triangle is cut out of a square whose side length is 8 feet. What will be the approximate area, in square feet, of the remaining board?
A cylinder has a base area of 169π cm2 . Its height is 4 cm more than the radius. Identify the volume of the cylinder. Round to the nearest tenth, if necessary.
Answer:
V = 9025.8 cm3
Step-by-step explanation:
Differentiate
1/√x^2-1