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.
4 students equally share 3/4 of a pizza. How much of the pizza does each student get?
To find out how much pizza each of 4 students gets when they equally share 3/4 of a pizza, we divide the amount of pizza (3/4) by the number of students (4). The result is 3/16, which means each student gets 3/16 of the pizza.
Explanation:The question asks how 4 students can equally share 3/4 of a pizza. In mathematics, to divide a quantity equally amongst a group, we perform division. So, in this scenario, we need to divide 3/4 (the pizza) by 4 (the students).
Step 1: Represent the given scenario as a division problem: 3/4 ÷ 4. Step 2: Convert the division into multiplication by the reciprocal. This changes our problem into a multiplication problem: 3/4 * 1/4. Step 3: Multiply the numerators together to get the numerator of the answer: 3 * 1 = 3. Step 4: Multiply the denominators together to get the denominator of the answer: 4 * 4 = 16.
So, the answer of 3/4 ÷ 4 is equal to 3/16. Therefore, each student gets 3/16 of the pizza.
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which algebraic expression represents the phase
A set of data with a mean of 45 and a standard deviation of 8.3 is normally distributed. Find the value that is +1 standard deviation away from the mean.
Answer:
53.3
Step-by-step explanation:
Add one standard deviation to the mean:
45 +1(8.3) = 53.3
Answer:
53.3
Step-by-step explanation:
+1 standard deviation away from the mean is 45+1(8.3)
Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) −1 s (s − 5)(s − 6)(s − 30)
John predicts the basketball team will score 68 points. If the basketball team actually scores 49 points, what is John's percent error? Round your answer to the nearest tenth of a percent.
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the second equation is substituted into the first equation.
2x – 7y = 4
3x + y = –17
Madison deposited a total of $5,000 between two saving accounts bearing simple interest. One of the accounts has an interest rate of 4% while the other rate is 5%. If the total interest earned after one year is $220, find the amount deposited into each of the accounts.
James wants to tile his floor using tiles in the shape of a trapezoid. To make the pattern a little more interesting he has decided to cut the tiles in half along the median. The top base of each tile is 15 inches in length and the bottom base is 21 inches. How long of a cut will John need to make so that he cuts the tiles along the median?
Answer:18 inches
Step-by-step explanation:
The answer would be 18 inches.
What is the median of a trapezoid?The median of a trapezoid is the segment that connects the midpoints of the non-parallel sides.
The length of the median is the average of the length of the bases.
The top base of each tile is 15 inches in length and the bottom base is 21 inches,
Add the top base and bottom base,
So, 15+21=36
Now, divide that by 2
⇒ 18
Hence, the answer would be 18 inches.
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A rectangle is 6 centimeters longer than is wide and has an area of 280 square centimeters if l represent the length,in centimeters of the rectangle solving which of the following formulas will give the correct value for l?
Calculus AB
lim x-->4 sqrt(x+5)-3 / 4-x
The answer is apparently -1/6
How do you solve this
2(8+h) simplify using distrubtive property
Find the work done by a force fâ =1.8i^+2.2j^n as it acts on an object moving from the origin to the point râ =56i^+31j^m.
The work done by the force is found by taking the dot product of the force vector and the position vector. This is achieved by multiplying corresponding components of the vectors and then adding the results together.
Explanation:To find the work done by the force, we use the formula Work = Force . Displacement, where the '.' signifies a dot product. In this case, the force vector is fâ = 1.8i^ + 2.2j^ and the position vector, râ = 56i^ +31j^. The dot product between force fâ and the displacement (position vector) râ is calculated by multiplying corresponding i and j components and then adding them together. Therefore, Work = (1.8i^.56i^) + (2.2j^.31j^). Perform the multiplication for both components and then add the results to get the total work done by the force.
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Which figure has the correct lines of symmetry drawn in?
The pressure,p, of a gas varies inversely with its volume,v. Pressure is measured in units of pa. Suppose that a particular amount of a gas is initially at a pressure of 104 pa at a volume of 108 L. If the volume is expanded to 432 L, what will the new pressure be
If all of the diagonals are drawn from a vertex of a pentagon, how many triangles are formed?
A picture helps. There are 2 non-adjacent vertices, so two diagonals can be drawn, resulting in 3 triangles.
Drawing all diagonals from one vertex of a pentagon to the non-adjacent vertices creates three triangles within the pentagon.
When all the diagonals are drawn from one vertex of a pentagon, it divides the pentagon into several triangles.
A pentagon has five sides, and when selecting a single vertex, we can draw diagonals to the non-adjacent vertices. In this case, there are three non-adjacent vertices, which means we can draw three diagonals, thus creating three triangles inside the pentagon.
This is because each diagonal, combined with two sides of the pentagon, forms a triangle.
which property of congruence would prove that BD ≈ BD?
the reflexive property of congruence
the symmetric property of congruence
the transitive property of congruence
None of the choices are correct.
What is the value of of angle BAD:
30◦
5◦
15◦
20◦
The area of a rectangular patio is 5 5/8 square yards, and it's length is 1 1/2 yards. What is the patio's width in yards?
Two garden plots are to have the same area. One is square and one is rectangular. The rectangular plot is 2 meters wide and 18 meters long. How long is one side of the of the square garden plot in meters?
area of rectangle = l x w
area of rectangle = 2*18 = 36 square meters
area of square = S^2, or s = square root(area)
sqrt(36) = 6
length of side of square = 6 meters
The side length of the square garden plot with the same area as a rectangular plot of dimensions 2 meters by 18 meters is 6 meters.
The student is asking about finding the length of a side of a square garden plot that has the same area as a rectangular garden plot measuring 2 meters wide by 18 meters long. To find the area of the rectangular plot, we multiply the length by the width: 2 meters imes 18 meters = 36 square meters.
Since the area of the square plot must equal the area of the rectangular plot, we can use the formula for the area of a square, A = s2, where s is the side length of the square. Therefore, to find the side length of the square plot, we take the square root of the area of the rectangular plot:
√(36 square meters) = 6 meters
So, the side length of the square garden plot is 6 meters.
Find the area of the shaded region. The units are in millimeters.
Use 3.14 for π. Round your answer to two decimal places.
What is the difference of the polynomials?
(8r6s3 – 9r5s4 + 3r4s5) – (2r4s5 – 5r3s6 – 4r5s4)
Answer: The required difference is [tex]8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6.[/tex]
Step-by-step explanation: We are given to find the difference of the polynomials as follows :
[tex]DP=(8r^6s^3-9r^5s^4+3r^4s^5)-(2r^4s^5-5r^3s^6-4r^5s^4)~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the given difference, we need to choose the terms with same poers of the unknown variables r and s and then subtract their coefficients.
The difference (i) is as follows :
[tex]DP\\\\=(8r^6s^3-9r^5s^4+3r^4s^5)-(2r^4s^5-5r^3s^6-4r^5s^4)\\\\=8r^6s^3-9r^5s^4+3r^4s^5-2r^4s^5+5r^3s^6+4r^5s^4\\\\=8r^6s^3+(4-9)r^5s^4+(3-2)r^4s^5+5r^3s^6\\\\=8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6.[/tex]
Thus, the required difference is [tex]8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6.[/tex]
an actor gains 20pounds for a part and then losses 15 pounds during the filming of the movie to go along with the story.who do you write a addition expression to describe this situation
How to solve 7.86 x 4.6
Pick the correct description of the line 5x + 3y=15
Answer:
The correct description is [tex]y=5-\frac{5x}{3}[/tex]
Step-by-step explanation:
In this case, firts we have to organize the equation in the normal way, where y is alone in one side, this is:
[tex]5x+3y=15\\3y=15-5x\\y=\frac{15}{3}-\frac{5x}{3} \\y=5-\frac{5x}{3}[/tex]
The correct description is [tex]y=5-\frac{5x}{3}[/tex]
Now we can see that the slope of the equation is [tex]-\frac{5}{3}[/tex]
The formula can be used to find the velocity v in feet per second of an object that has fallen h feet. Find the velocity of an object that has fallen 23 feet. Round your answer to the nearest hundredth.
Suppose that a particular artillery piece has a range r = 8320 yards . find its range in miles. use the facts that 1mile=5280ft and 3ft=1yard.
The range in miles is 4.72 mile
What do you mean by 1 mile?mile, any of various units of distance, such as the statute mile of 5,280 feet (1.609 km). It originated from the Roman mille passus, or “thousand paces,” which measured 5,000 Roman feet.
Given : range= 8320 yards
1 mile= 5280 feet
3 feet= 1 yard
Now,
8320yards X 3ft = 24,960
Now, divide that by 5,280ft in a mile
= 24960/5280
= 4.72 miles
Hence, range is 4.72 miles.
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Final answer:
To convert the artillery piece's range of 8320 yards to miles, you multiply by 3 to change yards to feet and then divide by 5280 to convert feet to miles, resulting in a range of approximately 4.727 miles.
Explanation:
To find the artillery piece's range in miles, starting with its range in yards, we need to use unit conversion factors. Knowing that 1 mile equals 5280 feet and 3 feet equals 1 yard, we can set up a conversion to calculate the distance in miles.
Steps to Convert Yards to Miles:
Convert the given distance from yards to feet by multiplying the number of yards by 3 (since there are 3 feet in a yard).Next, convert the distance from feet to miles by dividing the number of feet by 5280 (since there are 5280 feet in a mile).For an artillery range of 8320 yards:
8320 yards is equivalent to 8320 yards * 3 feet/yard = 24960 feetThen 24960 feet / 5280 feet/mile gives us the range in miles.When you divide 24960 by 5280, you get 4.727 miles (rounded to three decimal places).
The function g(x) = 3(x - 3)2 + 2 will translate 3 units to the right. True or False?
0.025 in scientific notation (step by step)
0.025 in scientific notation is 2.5 × 10⁻².
To express 0.025 in scientific notation, we need to convert the decimal form to a number multiplied by a power of 10.
Here's how you can do it step by step:
Start with the given decimal number: 0.025.
Identify the non-zero digit. In this case, it is 2.
Move the decimal point to the right until there is only one non-zero digit to the left of the decimal point. Count the number of places you moved the decimal point. In this case, we moved the decimal point two places to the right.
0.025 -> 2.5
Write the non-zero digit (2.5) as a decimal number.
Finally, express the power of 10 that represents the number of places you moved the decimal point. Since we moved the decimal point two places to the right, the power of 10 is -2.
Putting it all together, we have:
0.025 = 2.5 × 10⁻²
Therefore, 0.025 in scientific notation is 2.5 × 10⁻².
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What's the next value?
1 I 2 L 3 F 4
Davis Construction is building a new housing development. They begin by mapping the development out on a coordinate grid. They place one of the two swimming pools at coordinate (-16, -25) and the other at (18, 23). If they want the club house to be exactly halfway between the two pools, find the coordinate point for the clubhouse
To solve this problem, we can use the following ratio formulas to find for the coordinates of the club house:
x = [m / (m + n)] (x2 – x1) + x1
y = [m / (m + n)] (y2 – y1) + y1
Where,
m and n are the ratios (0.5 and 0.5 each since the club house are to be located exactly halfway)
x1 and y1 are the x and y coordinates of the 1st pool (-16, -25)
x2 and y2 are the x and y coordinates of the 2nd pool (18, 23)
Substituting:
x = [0.5 / (0.5 + 0.5)] (18 - -16) + -16
x = 1
y = [0.5 / (0.5 + 0.5)] (23 - -25) + -25
y = -1
Therefore the club house should be located at coordinates (1, -1).