The probability of selecting a number divisible by 1000 from the range of 1 to 6857 is approximately 0.0008763. The probability of selecting a number that is not divisible by 1000 is approximately 0.9991237.
Explanation:To find the probability of selecting a number divisible by 1000, we need to determine the total number of possible outcomes and the number of favorable outcomes. There are a total of 6857 possible outcomes since the company selects employee numbers ranging from 1 to 6857. For a number to be divisible by 1000, it must end with three zeros, so we need to find how many numbers satisfy this condition between 1 and 6857.
Since 1000 is the smallest number divisible by 1000, we can calculate the number of favorable outcomes by finding the largest integer that satisfies the condition. In this case, it is 6000. Therefore, there are 6 favorable outcomes.
The probability of selecting a number divisible by 1000 is calculated by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes = 6 / 6857 ≈ 0.0008763.
The probability of selecting a number that is not divisible by 1000 can be calculated as the complement of the probability of selecting a number divisible by 1000:
Probability(not divisible by 1000) = 1 - Probability(divisible by 1000) ≈ 1 - 0.0008763 ≈ 0.9991237.
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What is the next number?
3,4,6,9,13,18,24=
Below are grades in a course and how many students earned each grade:
5 students earned an A,
8 students earned a B,
10 students earned a C,
3 students earned a D
and 2 students earned a F.
What percent passed the course with a C or better? (Round your answer to one decimal place.)
The percentage of students who passed the class with a C or better is 82.1%. This is found by adding the number of students who earned A, B, or C grades, dividing by the total number of students, and multiplying by 100.
Explanation:The subject is Mathematics, specifically a problem in percentages. First, we need to find the total number of students in the class. We add the number of students that earned each grade: 5 (A) + 8 (B) + 10 (C) + 3 (D) + 2 (F) = 28 students in total.
Next, we need to identify the number of students who passed the class with a C or better. This includes the students who earned an A, B, or C. Adding these numbers together gets us 5 (A) + 8 (B) + 10 (C) = 23 students.
Then, to find the percentage of students who passed the class, we divide the number of students who passed (23) by the total number of students (28) and then multiply by 100 to convert the result to a percentage. So the calculation is as follows: (23/28)*100 = 82.14. Rounded to one decimal place, that is 82.1%. Therefore, 82.1% of students passed the class with a grade of C or better.
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The percent of students who passed the course with a C or better is: 82.14%
To find the percent of students who passed the course with a C or better, we need to divide the number of students who passed by the total number of students and multiply by 100%.
The number of students who passed is 5 + 8 + 10 = 23.
The total number of students is 5 + 8 + 10 + 3 + 2 = 28.
Therefore, the percent of students who passed the course with a C or better is:
(23 / 28) * 100% = 82.14%
Rounding to one decimal place, the answer is 82.1%.
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If I had 6 yellow fish and 7 blue fish, how many times can I make a pair?
If Kendra started working at 10:30 a.m.and left at 6:15, how many hours of work should she record for the day on her time card
The units digit of a perfect square is 6. What are the possible values of the tens digit?
Final answer:
The tens digit of a perfect square with a units digit of 6 could be any digit from 0 to 9. This is because when numbers ending in either 4 or 6 are squared, the tens digit can take any value in the range of 0-9 due to the cyclic nature of the squares.
Explanation:
The units digit of a perfect square can be 6, and this occurs when a number ending in either 4 or 6 is squared since 42 is 16 and 62 is 36. Considering this, the possible values for the tens digit of a perfect square with a units digit of 6 could be derived from these squares. For the tens digit, we must look at the squares of numbers ending in 4 or 6 and check the ten's place of the resulting product.
For example, if we consider 142 (which is 196) and 162 (which is 256), the tens digit can be either 9 or 5. Continuing with this pattern for numbers ending in 4 or 6 all the way to 942 and 962, we find that the tens digit is cyclic and can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. Therefore, all ten digits are possible for the tens place of a number whose square ends in 6.
Cuál es el número que agregado a 3 suma 8,hacer una ecuacion
The length of a rectangle is 7 inches more than its width. The area of the rectangle is equal to 2 inches less than 5 times the perimeter . What is the length and width
Factor 2a^5b + 2a^4b^2 + 2a^3b^3.
A.)2a^2b(a^2+a
Choose if the following function is even, odd or neither. f(x) = x^3
Stacy is walking his dog on a path and his dog wiggled out of his collar. If the dog is 30 feet lower than the owner and the angle of elevation from the dog to the owner is 10 degrees, find the distance from the dog to the owner.
If gasoline costs
2.50
2.50 euros per liter, it will cost $
how much
to drive
220 kilometers
Which is true?
A
5.4793 < 5.4812
B
5.2189 = 5.219
C
5.0359 > 5.0923
D
5.0167 < 5.0121
If the constant c is chosen so that the curve given parametrically by ct, c 2 8 t 2 , 0 ≤ t ≤ 3 , is the arc of the parabola 8y = x 2 from (0, 0) to (4, 2), find the coordinates of the point p on this arc corresponding to t = 2.
By solving the given equations using the provided information, and assuming the constant c = 4/3, we can find the coordinates of the point P on the curve corresponding to t = 2 are (8/3, 32/9). There is a probable discrepancy in the question which causes two different solutions for c, therefore making the canonical form of the parabola ambiguous.
Explanation:The given parametric curve has its equations as x = ct and y = c/8 * t^2. We're given that it's the arc of the parabola 8y = x^2 from (0, 0) to (4, 2), meaning that we can set x = ct = 4 and y = c/8 * t^2 = 2 when t=3 (the upper limit of t) to find the value of the constant c. Solving these equations gives c=4/3 and c=48. Since c must be the same in both equations, there seems to be a discrepancy here, which could possibly originate from a mistake in the question. However, if we only use c from the first equation (x = ct), we get c = 4/3.
The question asks for the coordinates of the point on the curve corresponding to t = 2. Substituting t = 2 into x = ct and y = c/8 * t^2 gives x = 8/3 and y = 32/9, assuming c = 4/3. So, the coordinates of the point would be (8/3, 32/9).
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Question 1(Multiple Choice Worth 5 points) (04.03 MC) Because of the rainy season, the depth in a pond increases 3% each week. Before the rainy season started, the pond was 10 feet deep. What is the function that best represents the depth of the pond each week and how deep is the pond after 8 weeks? Round your answer to the nearest foot. Hint: Use the formula, f(x) = P(1 + r)x. f(x) = 10(0.03)x, 36 feet f(x) = 10(1.03)x, 14 feet f(x) = 10(1.3)x, 37 feet f(x) = 10(1.03)x, 13 feet
Eliminate the parameter t to find a cartesian equation for x=t^2 y=2+10t
To eliminate the parameter t in the equations x=t^2 and y=2+10t, solve [tex]t = \sqrt(x)[/tex] and substitute into the second equation to get [tex]y = 2 + 10\sqrt(x)[/tex]. This results in the cartesian equation [tex]y = 2 + 10\sqrt(x).[/tex]
To eliminate the parameter t and find the cartesian equation, follow these steps:
Start with the given parametric equations: x=t^2 and y=2+10t
Solve the first equation for t:
[tex]t = \sqrt(x)[/tex]
Substitute this expression for t into the second equation:
[tex]y = 2 + 10(\sqrt(x))[/tex]
Thus, the cartesian equation is [tex]y = 2 + 10 \sqrt(x).[/tex]
how do you solve this problem? I need help
Express the limit as a definite integral on the given interval. lim nââ n xi ln(1 + xi2) δx, [0, 3] i = 1
A video game sets the points needed to reach the next level based on the function g(x) = 7(3)^x − 1, where x is the current level. The hardest setting promises to multiply the points needed in each level according to the function h(x) = 4x. How many points will a player need on the hardest setting of level 4?
A player will need 2,264 points on the hardest setting of level 4 as calculated by evaluating g(4) using the function g(x) = 7(3)^x - 1 and then applying the function h(x) = 4x.
To calculate the number of points a player will need on the hardest setting of level 4, we need to consider the function h(x) = 4x provided in the context of the question. However, the question also mentions the function g(x) = 7(3)^x - 1, which indicates the points needed to reach the next level normally. Since we need to find the hardest setting value, we will use the function h(x) but before that, we need to evaluate g(4) to find out the base points at level 4.
To find g(4), we substitute x = 4 into g(x):
g(4) = 7(3)^4 - 1 = 7(81) - 1 = 567 - 1 = 566
Now we apply the function h(x) to this value to get the points on the hardest setting:
h(g(4)) = 4 × 566 = 2264
Therefore, a player will need 2,264 points on the hardest setting of level 4.
a plane takes 2hr to travel 1000mi with the wind. it can travel only 880mi against the wind in the same amount of time. find the speed of the wind and the speed of the plane in still air
A basketball is thrown with an initial upward velocity of 25 feet per second from a height of 8 feet above the ground. The equation h=-16t^2+25t+8 models the height in feet t seconds after it is thrown. After the ball passes its maximum height, it comes down and then goes into the hoop at a height of 10 feet above the ground. About how long after it was thrown does it go into the hoop?
Answer:
A quadratic equation is in the form of [tex]ax^2+bx+c =0[/tex]........[1], then the solution for this equation is given by:
[tex]x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
As per the statement:
The equation is given by:
[tex]h=-16t^2+25t+8[/tex]
where, h is the height in feet t seconds after it is thrown.
After the ball passes its maximum height, it comes down and then goes into the hoop at a height of 10 feet above the ground.
⇒h = 10 feet
then;
[tex]-16t^2+25t+8=10[/tex]
Subtract 10 from both sides we have;
[tex]16t^2-25t+2=0[/tex]
On comparing this equation with [1] we have;
a =16 , b =-25 and c =2
then;
[tex]t= \frac{25 \pm \sqrt{(-25)^2-4(16)(2)}}{2(16)}[/tex]
⇒[tex]t= \frac{25 \pm \sqrt{625-128}}{32}[/tex]
⇒[tex]t= \frac{25 \pm \sqrt{497}}{32}[/tex]
as we want the time when it was falling so ,
[tex]t= \frac{25 + \sqrt{497}}{32}[/tex]
Simplify:
[tex]t \approx 1.48[/tex] sec
Therefore, 1.48 sec long after it was thrown does it go into the hoop
Lateisha shaw deposits $12000 for 8 years in an account paying 5% compounded quarterly. She then leaves the money alone, with no further deposits, at 6% compounded annually for an additional 6 years. Approximate the total amount on deposit after the entire 14-year period.
Prove that if x is irrational, then 1/x is irrational
Proof by contradiction.
Let assume that when [tex]x[/tex] is an irrational number, then [tex]\dfrac{1}{x}[/tex] is a rational number.
If [tex]\dfrac{1}{x}[/tex] is a rational number, then it can be expressed as a fraction [tex]\dfrac{a}{b}[/tex] where [tex]a,b\in\mathbb{Z}[/tex].
[tex]\dfrac{1}{x}=\dfrac{a}{b} \Rightarrow x=\dfrac{b}{a}[/tex]
Since [tex]a,b\in\mathbb{Z}[/tex], the number [tex]x=\dfrac{b}{a}[/tex] is also a rational number. But this contardicts our initial assumption that [tex]x[/tex] is an irrational number. Therefore [tex]\dfrac{1}{x}[/tex] must be an irrational number.
Find the polar coordinates of the points with cartesian coordinates (−x, y).
Fill in the blanks to write the solutions to the quadratic equation. x2 + 2x + 10 = 0
How do you subtract an integer from another integer without using a number line or counters? Give an example.
What is the algebraic rule for a figure that is rotated 270 degrees clockwise
The algebraic rule for rotating a point [tex]\( 270^\circ \)[/tex] clockwise about the origin is:
[tex]\[ (x, y) \rightarrow (y, -x) \][/tex]
Rotations in the coordinate plane can be performed using rotation matrices or by following specific rules based on the degree of rotation and the direction (clockwise or counterclockwise). For a rotation of [tex]\( 270^\circ \) or \( -90^\circ \) (since \( 270^\circ \)[/tex] clockwise is equivalent to [tex]\( -90^\circ \)[/tex] counterclockwise), the rule can be derived as follows:
1.Starting Point:Consider a point [tex]\( (x, y) \)[/tex] in the coordinate plane.
2. 90° Rotation Counterclockwise (or 270° Clockwise):
When you rotate a point [tex]\( 90^\circ \)[/tex] counterclockwise about the origin, the new position is [tex]\( (-y, x) \)[/tex].
3. 80° Rotation (second 90° Counterclockwise):**
If you rotate [tex]\( (-y, x) \)[/tex] another [tex]\( 90^\circ \)[/tex] counterclockwise (making a total of 180°), the new position is [tex]\( (-x, -y) \)[/tex].
4.270° Rotation (third 90° Counterclockwise or 90° Clockwise):
Finally, rotating [tex]\( (-x, -y) \)[/tex] another [tex]\( 90^\circ \)[/tex] counterclockwise (or the original point [tex]\( (x, y) \) \( 90^\circ \)[/tex] clockwise), the new position is [tex]\( (y, -x) \).[/tex]
Therefore, the algebraic rule for rotating a point [tex]\( 270^\circ \)[/tex] clockwise about the origin is:
[tex]\[ (x, y) \rightarrow (y, -x) \][/tex]
This rule effectively swaps the x and y coordinates and negates the new x-coordinate, which corresponds to a [tex]\( 270^\circ \)[/tex] clockwise rotation.
Find the zeros of the function. f(x)=-3x^2+75
Brainliest to whoever is correct 30pts...!!!!!!!!!
Answer: y=(yx−16x)x+16
Step-by-step explanation:
Dots sells a total of 267 T-shirts ($2) and shorts ($3). In April, total sales were $633.
How many T-shirts and shorts did Dots sell?
A sample of 20 observations has a standard deviation of 4. the sum of the squared deviations from the sample mean is:
Answer: 304.
Step-by-step explanation:
The formula to calculate the sample standard deviation is given by :-
[tex]s=\sqrt{\dfrac{\sum(x-\overline{x})^2}{n-1}}[/tex]
, where x = sample element.
[tex]\overline{x}[/tex] = Sample mean
s=sample standard deviation.
n= Number of observations.
[tex]\sum(x-\overline{x})^2[/tex] = sum of the squared deviations from the sample mean
As per given , we have
s=4
n= 20
Substitute theses values in the above formula , we get
[tex]4=\sqrt{\dfrac{\sum(x-\overline{x})^2}{20-1}}[/tex]
[tex]4=\sqrt{\dfrac{\sum(x-\overline{x})^2}{19}}[/tex]
Square root on both sides , we get
[tex]\Righatrrow\ 16=\dfrac{\sum(x-\overline{x})^2}{19}\\\\\Righatrrow\ \sum(x-\overline{x})^2=16\times19=304[/tex]
Hence, the sum of the squared deviations from the sample mean is 304.
Sum of squared deviations: [tex]\( 16 \times (20 - 1) = 304 \),[/tex] given a standard deviation of 4 and sample size of 20.
To find the sum of the squared deviations from the sample mean, we'll use the formula for variance. Since the standard deviation is the square root of the variance, we'll square the standard deviation to get the variance. Then, we'll multiply by the sample size minus 1 to get the sum of the squared deviations.
Given:
Standard deviation (σ) = 4
Sample size (n) = 20
First, let's find the variance:
[tex]\[ \text{Variance} = \sigma^2 = 4^2 = 16 \][/tex]
Now, we'll use the formula for the sum of squared deviations:
[tex]\[ \text{Sum of squared deviations} = \text{Variance} \times (n - 1) \]\[ \text{Sum of squared deviations} = 16 \times (20 - 1) \]\[ \text{Sum of squared deviations} = 16 \times 19 = 304 \][/tex]
So, the sum of the squared deviations from the sample mean is 304.