The probability of selecting a marble at random is 10/21, or 5/10.
What is Probability?Probability is the likelihood or chance of something happening. It is a mathematical measure of how likely an event is to occur, expressed as a number between 0 and 1. Probability can be used to make predictions and decisions about the future and to explain the likelihood of various outcomes. Probability is an important concept in many fields, including mathematics, finance, statistics, and science.
This is because there are 10 marbles out of a total of 21 total objects (3 golf balls, 8 tennis balls, and 10 metal marbles).
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What are the solutions to the quadratic equation x2 - 10x + 18 = 0
Answer:
x = 5 + [tex]\sqrt{7}[/tex]
x = 5 - [tex]\sqrt{7}[/tex]
Step-by-step explanation:
The given quadratic equation is:
x^2 - 10x + 18 = 0
We can solve this equation using the quadratic formula, which states that for a quadratic equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 1, b = -10, and c = 18. Substituting these values into the quadratic formula, we get:
x = (-(-10) ± sqrt((-10)^2 - 4(1)(18))) / 2(1)
Simplifying the expression inside the square root, we get:
x = (10 ± sqrt(100 - 72)) / 2
x = (10 ± sqrt(28)) / 2
x = (10 ± 2sqrt(7)) / 2
Simplifying further, we get:
x = 5 ± [tex]\sqrt{7}[/tex]
Question content area top
Part 1
In a genetics experiment on peas, one sample of offspring contained 439 green peas and 30 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of
3
4 that was expected?
The result is not reasonably close to the value of 3/4 i.e. 0.75.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The probability of getting a green pea can be estimated by dividing the number of green peas by the total number of peas:
probability of green pea = number of green peas / total number of peas
In this case, the number of green peas is 439 and the total number of peas is the sum of the green and yellow peas, which is:
total number of peas = number of green peas + number of yellow peas
= 439 + 30 = 469
Therefore, the probability of getting a green pea is:
probability of green pea = 439 / 469 ≈ 0.935 or 93.5%
So, the estimated probability of getting an offspring pea that is green is approximately 93.5%.
The result is not reasonably close to the value of 3/4 i.e. 0.75.
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Evaluate the expression for w = 1 fith . 1 half w + 2 =
Therefore, when w = 1/2, the expression w + 1/2w + 2 evaluates to 17/4.
What structure should a math evaluation follow?You must replace each variable with a number and carry out the arithmetic procedures to evaluate an algebraic expression. Variable x in the preceding example is equivalent to 6, as 6 + 6 = 12. We can substitute our variables with their values before evaluating the expression if we are aware of their values.
To evaluate the expression for w = 1/2, we substitute w = 1/2 into the expression:
w + 1/2w + 2
= 1/2 + 1/2(1/2) + 2 (substitute w = 1/2)
= 1/2 + 1/4 + 2 (simplify multiplication)
= 9/4 + 2 (convert 1/2 to 2/4 and add fractions)
= 17/4 (add fractions)
Therefore, when w = 1/2, the expression w + 1/2w + 2 evaluates to 17/4.
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The volume of a cone whose height h and base radius is r is given by the formula of the volume of a cone,express r in terms of v,pie and h and find the value of h when the volume of the cone is 660cm raise to power 3,where r is 14cm(pie=22/7)
The formula for the volume of a cone is:
V = (1/3)πr^2h
Solving for r:
V = (1/3)πr^2h
3V = πr^2h
r^2 = (3V)/(πh)
r = sqrt[(3V)/(πh)]
Given that V = 660cm^3, h = 14cm and π = 22/7:
r = sqrt[(3 × 660)/(22/7 × 14)] ≈ 7 cm
So the radius is approximately 7 cm.
To find the value of h:
V = (1/3)πr^2h
660 = (1/3)(22/7)(7^2)h
660 = (22/3)(49/7)h
660 = (22/3)(7)h
h = 660 / [(22/3)(7)]
h = 9.45 cm (rounded to two decimal places)
Therefore, the value of h when the volume of the cone is 660 cm^3 is approximately 9.45 cm.
When rolling a 6-sided die twice, determine P(sum of 6).
12
36
7
36
LO
5
36
2|6
The probability of getting sum of 6 is C)5/36.
What is probability?
Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.
We know that,
Probability of event = number of favorable outcome/ Total outcome
When a 6 sided dice die twice then
Total number of outcome = 6*6=36
Favorable outcome is a sum of 6, Ways of obtaining a sum of 6
(1,5), (5,1), (2,4),(4,2) and (3,3). Thus, there are 5 ways in which 6 can be obtained using rolling dice twice, Then
=> P(sum of 6 )=5/36
Hence the correct option is C)5/36.
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HELP ASAP, WILL GIVE BRAINLIEST, 53 POINTS!!!!
Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), D(4, 4) is dilated using a scale factor of three fourths to create polygon A′B′C′D′. Determine the vertices of polygon A′B′C′D′.
A′(−3, 4.5), B′(−1.5, 1.5), C′(3, −1.5), D′(3, 3)
A′(−12, 18), B′(−6, 6), C′(12, −6), D′(12, 12)
A′(3, −4.5), B′(1.5, −1.5), C′(−3, 1.5), D′(−3, −3)
A′(4.5, −3), B′(1.5, −1.5), C′(−1.5, 3), D′(3, 3)
Answer:
A′(−3, 4.5), B′(−1.5, 1.5), C′(3, −1.5), D′(3, 3)
Step-by-step explanation:
You would take three fourths of each coordinate to get the x and y values.
Answer:
A′(−3, 4.5), B′(−1.5, 1.5), C′(3, −1.5), D′(3, 3)
Step-by-step explanation:
You would take three fourths of each coordinate to get the x and y values.
A map is drawn on a coordinate plane. The school media center is located at (-20, 22). The school cafeteria is located at (-12,22). The school office is located at (-20,18). The three locations form a triangle. If one using on the cooridnate plane represents 100 feet, what is the distance, in feet, between the media center and the office
The distance between the media center and the office is 4 times 100, or 400 feet.
What is the distance formula?Distance Formula. ⇒ [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex] Using this formula in the equation, we get
Using the distance formula, we can find the distance between the media center and the office:
[tex]d = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]
where (x1, y1) are the coordinates of the media center (-20, 22) and (x2, y2) are the coordinates of the office (-20, 18).
[tex]d = \sqrt{((-20 - (-20))^2 + (18 - 22)^2)}\\= \sqrt{(0 + (-4)^2)}\\= \sqrt{(16)}\\= 4[/tex]
Since one unit on the coordinate plane represents 100 feet.
Hence, the distance between the media center and the office is 4 times 100, or 400 feet.
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I need help! Please include an explanation.
Measure of angle B is 40 degree
What is circle ?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, it has rotational symmetry around the centre for every angle.
From the figure,
As △ABC is inscribed in the circle, the points A , B and C lie on the circumference of the circle .
As O is the center of the circle.
Given , angle (BAC) is 50 degree
We know, a triangle drawn from two ends of a diameter of a circle makes an angle of 90° at the circumference.
so, angle (ACB) is 90 degree
Now, in triangle ABC
[tex]\angle ABC +\angle BCA +\angle BAC =180^0\\[/tex]
[tex]\angle B + 90^0 +50^0 = 180^0\\[/tex]
[tex]\angle B =40^0[/tex]
Hence, [tex]\angle B = 40^0[/tex]
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Complete the area model to describe how to divide 370 by 5.
Enter your answers in the boxes.
Answer: The first box in the model is 60. The box above it is 300. The box above 20 is 70. The answer is 74.
Step-by-step explanation: Self-explanatory.
Calculate the value 4-2(-5) =
answer is 14.
4-(2*-5)
4-(-10)
=4+10
=14.
Answer:
[tex]\bf 14[/tex]Step-by-step explanation:
[tex]\tt 4-2(-5)[/tex]
Follow the PEMDAS order of operations:-
P: Parentheses
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction
1) Multiply and/ or divide:-
[tex]\tt 2\left(-5\right)[/tex][tex]\tt -10[/tex][tex]\tt 4 -\left(-10\right)[/tex]
2) Addition/Subtraction:-
[tex]\tt 4-\left(-10\right)[/tex][tex]\tt 4+10[/tex][tex]\tt 14[/tex]_____________________
Hope this helps! :)
A clothing business finds there is a linear relationship between the number of shirts,n, it can sell and the
price,p, it can charge per shirt. In particular, historical data shows that 1000 shirts can be sold at a price
of $19, while 2000 shirts can be sold at a price of $16. Give a linear equation in the form p = mn + b
that gives the price p they can charge for n shirts.
A linear equation in the form p = mn + b that gives the price they can charge for n shirts is p = -0.003x + 22.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At data point (1000, 19), a linear function in standard form for this line can be calculated by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 19 = (16 - 19)/(2000 - 1000)(x - 1,000)
y - 19 = -0.003(x - 1,000)
y = -0.003x + 3 + 19
p = y = -0.003x + 22
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Keenan jumped 3 times every 18 minutes. At that rate, how many would he jump in 24 minutes?
Answer:
4 jumps in 24 minutes
Step-by-step explanation:
Rate: 1 jump every 6 minutes
24/6 = 4
what is the multiple of the unit fraction 3/8
The multiple of the unit fraction 3/8 is 15/40.
What is fraction ?
A fraction is a number that represents a part of a whole. It is a way of representing a quantity that is not a whole number. Fractions are written with two numbers, one above the other and separated by a horizontal line. The number above the line is called the numerator, and the number below the line is called the denominator.
To find the multiple of a fraction, you simply multiply the numerator and the denominator by the same number. For example, to find the multiple of 3/8, you can multiply both the numerator and the denominator by 2:
3/8 * 2/2 = 6/16
So the multiple of 3/8 by 2 is 6/16.
Similarly, you can find the multiple of 3/8 by any other number by multiplying both the numerator and denominator by that number. For instance, if you want to find the multiple of 3/8 by 5, you can multiply both the numerator and the denominator by 5:
3/8 * 5/5 = 15/40
Therefore, the multiple of the unit fraction 3/8 is 15/40.
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Area of compound figuresWhat is the area of this figure?
2 m
2 m
3 m
9 m
2 m
3 m
7 m
14 m
The compound figure has a 41 square metre surface area.
What do compound shapes mean?The combined shapes of one or more simple polygons and circles make up the area of the composite shapes. We can add the areas of all the fundamental shapes together to determine the area of the composite shapes. Simply calculate the area of each individual form to obtain the area of composite shapes.
The compound figure's area can be calculated by breaking it up into smaller shapes and adding the areas of each one.
Then, divide the figure into two rectangles:
The first rectangle is 2 m by 9 m in size and has a surface area of 18 m².
The surface area of the second rectangle, which is 3 m by 7 m in size, is 21 m².
Next, we may determine the areas of the two triangles:
Due to its 2 m base and 2 m height, the first triangle has an area of 1/2 x 2 m x 2 m, = 2 m².
The second triangle has a base of 3 m and a height of 2 m, and its area is 1/2 x 3 m x 2 m = 3 m².
The two rectangles' overlap can then be subtracted:
The overlap is a rectangle that is 2 m by 3 m in size, or 6 m2, and measures 2 m by 3 m.
The total area of the compound figure is calculated by adding the areas of the two rectangles, the two triangles, and then deducting the overlap between the rectangles.
Total area is (18 m² + 21 m²) + (2 m² + 3 m²) - 6 m².
Total area: 41 m².
Hence, the compound has a 41 square metre size.
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A principal is ordering pizzas for a school pizza party. He knows that 9 pizzas will feed 25 students. If there are 300 students in the school, how many pizzas will he need to order?
SHOW THE WORK AND HOW YOU GOT THIS ANSWER!!!!
The principal will need to order 108 pizzas to feed 300 students.
We may set up a proportion to determine how many pizzas are required to feed 300 students if 9 pizzas feed 25 students:
25 pupils × 9 pizzas = x pizzas / 300 students
where x is how many pizzas are required to feed 300 kids.
We can cross-multiply and simplify to find x's value:
300 kids times 9 pizzas equals 25 students (x pizzas)
2700 = 25x
x = 2700 / 25
x = 108
In order to serve 300 pupils, the principal will have to order 108 pizzas.
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I NEED HELPI NEED HELP I NEED HELP I NEED HELP I NEED HELP I NEED HELP I NEED HELP I NEED HELP I NEED HELP
Help plssss Quickkkk!!!!!
1. Patrick makes more per hour by $6.
2. Betthany makes more per hour by $5.25
3. Tommy makes more per hour by $ 1.25.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
The rate of Change of Critters and Co
Slope= Rise/ Run
= 15/2
= 7.5
So, the equation is y = 7.5x
and, rate of Change of Little Paws
= (52.50-35) / (6-4)
= 17.5 / 2
= 8.75
So, the equation is y = 8.5x + 5
and, rate of Change of The Waging Tail
= 8.25
1. Patrick makes more per hour by $6.
2. Betthany makes more per hour by $5.25
3. Tommy makes more per hour by $ 1.25.
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A right circular cylinder has the dimensions shown below.
r= 3 cm
h = 5 cm
Find the exact surface area of the cylinder.
Include correct units.
Show all your work.
A 14 sided die is rolled find the possibility of rolling an even number the set of equally like outcomes is shown below 1,2,3,4,5,6,7,8,9,10,11,12,13,14
Answer:
50 % possibility or 1/2 chance
Step-by-step explanation:
2, 4, 6, 8, 10, 12, and 14 are all even and there are seven of them
Martina, Ryan, and Keith sent a total of 77 text messages during the weekend. Ryan sent 7 fewer messages than Martina. Keith sent 2 times as many messages as Martina. How many messages did they each send?
The number of messages are: Martina sent 21 messages, Ryan sent 14 messages, and Keith sent 42 messages.
Why are unknown values represented using variables when solving problems?We may build equations that link unknown values in a problem and describe those numbers using variables. We may modify these equations algebraically to get solutions for the unknowable numbers by employing variables. As a result, issue solving is more effective and we can come up with generic answers that may be used in a variety of situations. Moreover, employing variables enables us to see patterns and trends as well as better grasp the connections between various amounts in a situation.
Given that,
Ryan sent 7 fewer messages than Martina.
R = M - 7
Keith sent 2 times as many messages as Martina.
K = 2M
Martina, Ryan, and Keith sent a total of 77 text messages.
M + R + K = 77
Substitute the value of equation 1 and 2 in equation 3:
M + (M - 7) + 2M = 77
4M - 7 = 77
4M = 84
M = 21
Substitute the value of M in equation 1 and equation2:
R = M - 7 = 21 - 7 = 14
K = 2M = 2(21) = 42
Hence, the number of messages are: Martina sent 21 messages, Ryan sent 14 messages, and Keith sent 42 messages.
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I need help please anyone ?!!!!?
Answer:
b
Step-by-step explanation:
3 + 3 = 6 lol
6 how many apples
Given the definitions of f(x) and g(x) below, find the value of f(g(2)).
f(x) = 2x² + x - 13
g(x) = x - 6
Answer:
21 is the value of f(g(2)) in functions.
What is a function, exactly?
An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). Mathematics is rife with functions , and the sciences depend on them for constructing physical relationships.
f(x) = 2x² + x - 13
g(x) = x - 6
the value of f(g(2))
g(2) = 2 - 6
= -4
f(g(2)) = 2x² + x - 13
= 2(-4)² + 2 - 13
= 32 - 11
= 21
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PLEASE HELP ME ASAP
Therefore, the area of triangle XYZ is (1/2)bh = (1/2)(15)(15√3) = 225√3. Therefore, the area of triangle XYZ is 225√3.
What is Triangle?Triangle is a three-sided polygon that has three angles and three sides. It is one of the basic shapes in geometry and is a very important concept in mathematics. It is also used in various fields, such as physics and engineering. Triangles can be classified into different types, such as right triangles, isosceles triangles, acute triangles, obtuse triangles, and equilateral triangles. Triangles are also used to form polygons, such as quadrilaterals, pentagons, and hexagons.
To find the area of triangle XYZ, we must first calculate the length of each side of triangle XYZ. The length of each side can be determined by multiplying the length of each side of triangle ABC by five.
Since all three sides of triangle ABC are equal in length, then each side of triangle XYZ will be 5 times the length of triangle ABC. Therefore, the length of each side of triangle XYZ is 5 times the side length of triangle ABC, or 15.
The area of the triangle can be calculated using the Triangle Area formula, A = (1/2)bh, where b is the base of the triangle and h is the height of the triangle. Since we know the length of each side of triangle XYZ, we can use these values to calculate the base and height of the triangle. The base of the triangle is 15, and the height of the triangle is 15√3.
Therefore, the area of triangle XYZ is (1/2)bh = (1/2)(15)(15√3) = 225√3. Therefore, the area of triangle XYZ is 225√3.
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scatter plot, label each axis, and choose a
Over the last 8 snowstorms, Julian recorded the amount of
snowfall to the nearest inch and the amount of time it took him
to shovel his driveway. He recorded the data in the table.
Snowfall (in.)
2
5
8
18
10
6
12
14
Time Shoveling
1
2
2
5
3
2
4
4
Answer:
Have a good day and time and I6ykjjuu7ttggfszd to the 5tjyyv
Write the equation of a circle with a center (9,10) and containing the point on the circle (7,4).
Answer: The equation of a circle with center (a,b) and radius r is given by:
(x - a)^2 + (y - b)^2 = r^2
In this case, the center is (9,10) and the point on the circle is (7,4). To find the radius, we can use the distance formula between the center and the point on the circle:
r = sqrt((7 - 9)^2 + (4 - 10)^2) = sqrt((-2)^2 + (-6)^2) = sqrt(40)
So, the equation of the circle is:
(x - 9)^2 + (y - 10)^2 = 40
Alternatively, we can also expand the equation to get:
x^2 - 18x + 81 + y^2 - 20y + 100 = 40
Simplifying and rearranging, we get:
x^2 + y^2 - 18x - 20y + 41 = 0
Therefore, the equation of the circle is either (x - 9)^2 + (y - 10)^2 = 40 or x^2 + y^2 - 18x - 20y + 41 = 0.
Step-by-step explanation:
select all of the expressions that are equivalent to 3²/3-²
Answer:
3 to the power of -4 and -81Step-by-step explanation:
Intensive care units (ICUs) generally treat the sickest patients in a hospital. ICUs are often the most expensive department in a hospital because of the specialized equipment and extensive training required to be an ICU doctor or nurse. Therefore, it is important to use ICUs as efficiently as possible in a hospital. Suppose that a large-scale study of elderly ICU patients shows that the average length of stay in the ICU is 3.3 days. Assume that this length of stay in the ICU has an exponential distribution. (Round your answers to four decimal places.)
By answering the above question, we may infer that Hence, the probability likelihood is 0.2752. (rounded to four decimal places).
What is probability?Calculating the chance that an event will occur or a statement will be true is the subject of probability theory, a branch of mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and a probability of about 0 denotes the likelihood that an event will occur. The likelihood that an event will take place is mathematically expressed as probability. Probabilities can also be expressed as percentages ranging from 0% to 100% or as integers between 0 and 1. the proportion of equally plausible possibilities that actually happen in relation to all possible outcomes when a certain event occurs.
We may utilize the complement of the CDF to respond to this query.
For x 0, the complement of the CDF is defined as 1 - F(x) = e(-x).
Thus, the likelihood that an old ICU patient will be there for more than five days is as follows:
[tex]1 - F(5) = e^(-0.3030 * 5) = 0.2052[/tex]
Hence, the likelihood is 0.2052. (rounded to four decimal places).
We may utilize the difference between the CDF at two distinct values to get an answer to this query.
The likelihood that an old ICU patient will be there for two to four days is as follows:
[tex]F(4) - F(2) = (1 - e^(-0.3030 * 4)) - (1 - e^(-0.3030 * 2)) = e^(-0.3030 * 2) - e^(-0.3030 * 4) = 0.2752[/tex]
Hence, the likelihood is 0.2752. (rounded to four decimal places).
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Calculate the rate of power drainage per hour if the capacity of the cell phone is 3600 mAh
calculate the rate of power drainage per hour if the capacity of the cell phone is 3600 mAh
EASY MATH POINTS! Answer from the screenshot :)
The function that is non-linear is function D.
Which of the functions is non-linear?A function is linear if its graph is represented by a straight line, and that line is usually written as:
ax + by = c
Where x is the horizontal variable and y the vertical variable.
For example, here we can see that A, B, and C are represented by straight lines, thus, these are linear functions.
But if you look at graph D, you can see that it is not linear, it's shape is like an "M", so that is the non-linear function.
The correct option is D.
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The number of books borrowed from a library each week follows a normal distribution. When a sample is taken for several weeks, the mean is found to be 190
There is a 2.28% chance that more than 250 books were borrowed in a week.
Describe Probability?Probability can also be calculated using other methods, such as counting techniques and probability distributions. Probability distributions provide a way to model the behavior of random events and describe the likelihood of different outcomes occurring.
Probability has many applications in fields such as statistics, finance, engineering, and science. It is used to make predictions, analyze data, and make decisions based on uncertain information. Understanding probability is an important skill for many professions, as it allows individuals to make informed decisions and assess risk.
To solve this problem, we need to use the standard normal distribution and calculate the z-score.
First, we find the z-score:
z = (x - μ) / σ
z = (250 - 190) / 30
z = 2
We can then use a standard normal distribution table or calculator to find the probability of getting a z-score of 2 or higher.
Using a standard normal distribution table, we find that the probability of getting a z-score of 2 or higher is approximately 0.0228.
To convert this to a percentage, we multiply by 100:
0.0228 x 100 = 2.28%
Therefore, there is a 2.28% chance that more than 250 books were borrowed in a week.
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The complete question is:
The number of books borrowed from a library each week follows a normal distribution. When a sample is taken for several weeks, the mean is found to be 190 and the standard deviation is 30. There is a % chance that more than 250 books were borrowed in a week.