Four balls are selected at random without replacement from an urn containing three white balls and five blue balls. Find the probability of the given event. (Round your answer to three decimal places.)
All of the balls are blue
To find the probability of selecting all blue balls, we divide the number of ways to choose 4 blue balls out of 8 by the number of ways to choose 4 balls out of 8 blue balls and 3 white balls.
Explanation:To find the probability of selecting all blue balls, we need to consider the number of ways we can choose 4 blue balls out of the 8 blue balls in the urn, divided by the total number of ways we can choose 4 balls out of the 8 blue balls and 3 white balls in the urn.
The probability can be calculated as:
P(All blue balls) = (Number of ways to choose 4 blue balls out of 8) / (Number of ways to choose 4 balls out of 8 blue balls and 3 white balls)
Since the balls are selected without replacement, the number of ways to choose 4 blue balls out of 8 is 8 choose 4. The number of ways to choose 4 balls out of 8 blue balls and 3 white balls is 11 choose 4.
Therefore, the probability of selecting all blue balls is P(All blue balls) = (8 choose 4) / (11 choose 4).
An arrangement of marbles has 12 marbles in the first row and 10 rows in all. In each successive row one marble is added.
What is the explicit rule for this situation, and how many marbles will be in the 10th row?
Drag and drop the answers into the boxes to match the situation.
Explicit rule
Number of marbles in the 10th row
An = 11 + 11n, An = 12 + n, An = 11 + n, An = 12 + 10n, 19, 20, 21,
Explicit rule: An = 12 + n
Number of marbles in the 10th row: 22
The explicit rule for this situation is An = 12 + n, where "n" represents the row number.
To find the number of marbles in the 10th row, you can plug in n = 10 into the explicit rule:
A10 = 12 + 10
A10 = 22
So, there will be 22 marbles in the 10th row.
Matching the answers:
Explicit rule: An = 12 + n
Number of marbles in the 10th row: 22
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what do you call an object with one fixed endpoint that extends to infinity
Identifica la pendiente y el intercepto de y=2-5x
a rectangular park is 4 miles long and 2 miles wide. how long is pedestrian route that runs diagonally across the park
half of the sum of six and three then divided by seven
In order to find the answer, put six and three together to obtain nine, then divide nine in half to get 4.5, and then divide 4.5 by seven to get roughly 0.64.
Explanation:When translated into a mathematical operation, the phrase "half of the sum of six and three then divided by seven" looks like this: Find the value of the sum of 6 + 3 to get 9 first. Then divide by half, or 4.5, to get the answer. Divide this by seven, and you'll arrive at a result that is roughly 0.64 (rounded to two decimal places).
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Harper's house is 30 feet wide and 45 feet long. On a scale drawing, the house is 4 inches wide and 6 inches long, and Harper's bedroom is 1.2 inches wide and 1.6 inches long. What are the actual measurements of Harper's bedroom? Enter your answers in the boxes. Harper's bedroom is feet wide and feet long.
If the total labor cost is $865,000 and 12 percent is for concession staff, how much of the labor cost is for concession staff?
Sierra sawed 10 1/2 inches off the end of a board. the remaining board was 37 1/2 inches long. how long was the boared that sierra started with? please explain answer
In a shipment of 400 parts, 14 are found to be defective. How many defective parts should be expected in a shipment of 1,000? Really need this I'm giving you maximum points
Choose the correct simplification of the expression (−2x + 4y)(3x − 7y). −6x2 − 2xy − 28y2 6x2 + 26xy − 28y2 −6x2 + 26xy + 28y2 −6x2 + 26xy − 28y2
Answer:
[tex] - 6 {x}^{2} + 26xy - 28 {y}^{2} [/tex]
Step-by-step explanation:
The given expresion is:
(−2x + 4y)(3x − 7y)
We expand using the distributive property: (a+b)(c+d)=a(c+d)+b(c+d)
We apply this property to get:
[tex]( - 2x + 4y)(3x - 7y) = - 2x \times(3x - 7y) + 4y(3x - 7y)[/tex]
We expand further to obtain:
[tex] - 6 {x}^{2} + 14xy + 12xy - 28 {y}^{2} [/tex]
[tex] - 6 {x}^{2} + 26xy - 28{y}^{2} [/tex]
Answer:
[tex](-2x+ 4y)(3x - 7y)=-6x^2+26xy-28y^2[/tex]
Step-by-step explanation:
We multiply each term in the parentheses, by those of the other parenthesis:
[tex](-2x+ 4y)(3x - 7y)=(-2x)(3x)+(-2x)(-7y)+(4y)(3x)+(4y)(-7y)\\=-6x^2+14xy+12xy-28y^2[/tex]
Now, we simplify.
We have two terms that contain xy:
[tex]=-6x^2+26xy-28y^2[/tex]
Wich will be the correct simplification of the expressionn [tex](-2x+ 4y)(3x - 7y)[/tex]
Write the time another way 23 minutes after 4
My friend needs help with her homework. The problem she is on is: There is 11 sandwiches. 2 children shares each sandwich. How many children share the sandwiches?
convert 39/5 to a mixed number written in lowest terms
The Wilsons traveled 860 miles to New York City to attend a wedding. They took a different route on the way home to visit historical landmarks. The trip home was 920 miles. How many more miles did they travel on the way home?
The correct answer is actually 60 miles more !!
Simplify: (–5) • (7) – (6) • (–2)
The correct answer is -23.
To simplify the given expression, we need to perform the indicated operations and follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
Given expression: (–5) • (7) – (6) • (–2)
Step 1: Perform the multiplications inside the parentheses.
(–5) • (7) = –35
(6) • (–2) = –12
Step 2: Perform the subtraction operation.
–35 – (–12) = –35 + 12 = –23
Therefore, the simplified expression is:
[tex](-5) \cdot (7) - (6) \cdot (-2) = -35 + (-12) = -23[/tex]
PLEASE HELP!!!!!
Give the piecewise function shown below select all of the statements that are true
A. f(4)=7
B. f(1)=0
C. f(-1)=2
D. f(-2)=0
how can 5% be written as a simplified ratio
Find the area of the circle with the given radius or diameter. Use pi = 3.14. r = 2
The football and soccer teams at Juans middle school are selling movie tickets. He wants to determine the average number of tickets sold at the school. First he surveyed eight random players on tge football team. Then he surveyed every third athlete on the football and soccer team. Which sampling technique should produce a more representative sample
Answer:
D is the answer.
"The second sampling method, surveying the both teams, is the most representative. "
Step-by-step explanation:
how could you use 1/8 cup measuring cup to measure the light corn syrup 9/12)
Final answer:
To measure 9/12 or 3/4 of a cup of syrup using a 1/8 cup, fill and level-off the 1/8 cup measuring cup six times. This uses basic fraction multiplication and measurement skills appropriate for middle school mathematics.
Explanation:
To measure light corn syrup using a 1/8 cup measuring cup, you first need to understand the fraction you're working with, which is 9/12 of a cup. Simplifying this fraction gives you 3/4 of a cup (since 9/12 reduces to 3/4 by dividing both the numerator and denominator by 3). Now, since there are 8 portions of 1/8 in a full cup, you need 6 portions of 1/8 (because 3/4 equals 6/8) to measure out 3/4 of a cup of light corn syrup.
To do this, you'll fill the 1/8 cup measuring cup six times and add each portion to your mixture to reach the desired amount of 9/12 or 3/4 of a cup of syrup. This is a simple example of using measurements and fractions to achieve the correct proportions in a recipe or any culinary preparation.
find the product of 80x^4/y^3 ×xy/5x^2
A rectangular prism has a length of 212 meters, a width of 4 meters, and a height of 214 meters.
What is the volume of the prism?
Enter your answer in the box as a simplified mixed number or a decimal.
m³
The volume of the rectangular prism is 22 1/2 m³
What is the volume of the rectangular prism?A rectangular prism is a three-dimensional object. It is made up of six faces, twelve sides and six vertices.
Volume = length x width x height
2 1/2 x 4 x 2 1/4
5/2 x 4 x 9/4 = 720 / 32 = 22 1/2 m³
Here is the complete question: A rectangular prism has a length of 21/2 meters, a width of 4 meters, and a height of 21/4 meters.
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Jessica grows two types of tomato plants in her garden. For each type, she records the heights, in inches, of five plants.
What can she infer about the heights of the plants?
Type 1: {42, 56, 44, 60, 48}
Type 2: {62, 59, 68, 55, 66}
Type 1 plants and Type 2 plants do not have similar height distributions.
Type 1 and Type 2 plants have similar height distributions.
Type 1 plants and Type 2 plants have identical height distributions.
Type 1 and Type 2 plants have somewhat similar height distributions.
The inference that can be made is that D. Type 1 and Type 2 plants have somewhat similar height distributions.
What is Inference?This refers to a statement or assertion that is made about something, which may or may not be true.
Hence, we can see that based on the height of the plants, there is a similarity in the heights of Type 1 and Type 2 plants, hence it can be inferred that Type 1 and Type 2 plants have somewhat similar height distributions.
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The product of 7 and a number, increased by 3, is equal to twice the number, subtracted from 39.
Find the number
10x - 4 = 2 ( ? ) is it a) 5x - 4 b) 5x - 2 c) 10x - 4 d ) 10x - 8
1 6 9 7 . 4
- 8 8 7 . 7 5
Two runners are to race one lap on a circular track, the radius to the inside circle is 50m.the radius on the outside lane is 51m. How much of a head start should the runner on the outside get?
Tmuch of a head start should the runner on the outside get would be = 2πm.
How to calculate the length of head start for the runner outside?
To calculate the length of head start for the runner outside against the inside runner, the following steps should be taken as follows:
The formula for circumferential of circle = 2πr
Circumference of inner circle;
= 2× π×50
= 100π
Circumference of outer circle;
= 2×π×51
= 102π
The length of head start for the runner outside = 102π-100π = 2πm
Complete the square to write y = 3x2 + 12x + 7 in vertex form, y = a(x - h)2 + k. y = 3(x2 + 4x) + 7 y = 3(x2 + 4x +4) + 7 -
Answer:
A. 12
B. 3
C. -2
D. -5
Step-by-step explanation:
Verified on edge, just finished it
The Vertex form is y= 3(x+ 2)² -5 and a= 3, h= -2, k= -12.
What is Vertex Form?The vertex form of a quadratic function is f(x) = a(x – h)² + k, where a, h, and k are constants.
Vertex form, one of the usual forms for quadratic functions, emphasises the coordinates of the vertex of the function's graph.
Given:
y = 3x² + 12x + 7
Now writing the equation in vertex form
y = 3x² + 12x + 7
y = 3x(x + 4) + 7
Adding and subtracting 12 on both side
y= 3(x²+ 4x) + 7 -12 + 12
y= 3(x² + 4x + 4) + 7- 12
y= 3(x+ 2)² -5
Now, Comparing it with y = a(x - h)² + k we get
a= 3
h= -2
and, k= -12
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Andy has 9 math books and 6 reading books if you wants to distribute them evenly among some bookshelves so that each has the same combination of books with none left over what is the greatest number of bookshelves Andy can use