The probability of exactly 3 items out of 15 being defective is 0.184 or approximately 18.4%.
What is Probability ?
Probability can be defined as ratio of number of favourable outcomes and total number outcomes.
To solve this problem, we can use the binomial distribution, which is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.
In this case, the probability of a single item being defective is 10%, or 0.1, and the probability of a single item being non-defective is 90%, or 0.9. We want to know the probability of getting exactly 3 defective items out of a sample of 15 items.
Using the binomial distribution formula, we can calculate this probability as follows:
P(X = 3) = (15 choose 3) * [tex]0.1^3[/tex] *[tex]0.9^12[/tex]
where (15 choose 3) is the number of ways to choose 3 items out of 15, which is given by the binomial coefficient:
(15 choose 3) = 15! / (3! * 12!) = 455
Substituting these values into the formula, we get:
P(X = 3) = 455 * [tex]0.1^3[/tex] *[tex]0.9^12[/tex]
Therefore, the probability of exactly 3 items out of 15 being defective is 0.184 or approximately 18.4%.
To learn more about Probability from given link.
brainly.com/question/30034780
#SPJ1
a random sample of 150 teachers in an inner-city school district found that 72% of them had volunteered time to a local charitable cause within the past 12 months. what is the standard error of the sample proportion?
The standard error for the sample proportion of 150 teachers in an inner-city school district is found to be 0.037.
The formula for the calculation of the standard error of a sample proportion is below,
SE = √((p × (1 - p)) / n)
Here,
SE is the standard error of the sample proportion
p is the sample proportion (in decimal form)
n is the sample size
In the mentioned case, the sample proportion is 0.72 (since 72% of 150 is 108), and the sample size is 150. Substituting these values into the formula, we will be getting,
SE = √((0.72 × (1 - 0.72)) / 150)
SE = √((0.2052) / 150)
SE = √(0.001367)
SE = 0.037
Therefore, the standard error of the sample proportion is 0.037.
Learn more about standard error :
https://brainly.com/question/5822616
#SPJ4
ON.4 Find missing angles in quadrilaterals 6V4
O
One angle of a parallelogram measures 70°. What are the measures of the other three angles
in the parallelogram?
Submit
T
Learn with an example
o, and
or Watch a video O
Work it out
Answer:
Hi There the answer for this one would be 20 and 90
Step-by-step explanation:
what is the value of f(40,20) and what does it represent? find an estimate for fv(40,20) and ft(40,20).
fv(40,20) ≈ (f(40.1,20) - f(40,20))/0.1 , ft(40,20) ≈ (f(40,20.05) - f(40,20))/0.05 are the required functional estimations of a given representations.
However, we can estimate the partial derivatives with respect to x (fv) and y (ft) at the point (40,20) using the definition of partial derivatives:
fv = ∂f/∂x ≈ (f(40+h,20) - f(40,20))/h
where h is a small increment in the x direction. Similarly,
ft = ∂f/∂y ≈ (f(40,20+k) - f(40,20))/k
where k is a small increment in the y direction.
To estimate fv(40,20) and ft(40,20), we need to choose small values of h and k and evaluate the function at the corresponding points. Let's say h = 0.1 and k = 0.05:
fv(40,20) ≈ (f(40.1,20) - f(40,20))/0.1
ft(40,20) ≈ (f(40,20.05) - f(40,20))/0.05
We can then use these estimates to approximate the value of f(40.1,20.05) using the first-order Taylor approximation:
f(40.1,20.05) ≈ f(40,20) + fv(40,20)0.1 + ft(40,20)0.05
Note that this is an approximation and may not be very accurate if the function is highly nonlinear or has discontinuities. However, it can give us a rough idea of the value of f(40,20) and how it changes with small variations in x and y.
To know more about first-order Taylor click here:
brainly.com/question/14787721
#SPJ4
50 Points
Janey paints a block of wood with gold glitter for an art project. The block measures
8 inches by 10 inches by 20 inches.
After she's done, she decides to make two blocks by cutting through the block on the
red line. She still wants each block to be covered with gold glitter.
What is the total area of the cut surfaces she still needs to paint?
Answer the questions to find out.
1. What is the shape of each cut surface? what are its dimensions?
2. What is the area of each cut surface?
3. What is the total area Jenny needs to paint? Explain how you found your answer.
Answer:
The shape of each cut surface is a rectangle. The dimensions of the first cut surface are 8 inches by 10 inches, and the dimensions of the second cut surface are 10 inches by 20 inches.
The area of the first cut surface is 8 inches x 10 inches = 80 square inches. The area of the second cut surface is 10 inches x 20 inches = 200 square inches.
To find the total area Jenny needs to paint, we need to add the area of the first cut surface to the area of the second cut surface.
Total area = Area of first cut surface + Area of second cut surface
Total area = 80 square inches + 200 square inches
Total area = 280 square inches
Therefore, Jenny needs to paint a total area of 280 square inches.
Find the area and the circumference of a circle with radius 9km.
Write your answers in terms of π, and be sure to include the correct units in your answers.
Answer:
Area: 81*pi
Circumference: 18*pi
Step-by-step explanation:
Area: 9^2= 81
So it would be 81*pi
Circumference: 9*2= 18
So it would be 18*pi
If you want the full area then it's 81*pi= 254.34
If you want the full circumference it's 18*pi= 56.55
axel has figured out that his maximum heart rate (mhr) is 205. what is the range of his training zone?
The range of Axel's training zone, assuming a moderate exercise intensity, would be approximately 123 to 164 beats per minute (BPM).
To calculate this range, we use the Karvonen formula, which takes into account Axel's resting heart rate (RHR) and desired training intensity. Assuming a moderate-intensity workout, we can use a target heart rate range of 60% to 80% of his MHR.
Target Heart Rate = ((MHR - RHR) x %Intensity) + RHR
Assuming a resting heart rate of 65 BPM and moderate intensity of 60% to 80% of his MHR, Axel's target heart rate range would be approximately 123 to 164 BPM.
Therefore, the range of Axel's training zone would be approximately 123 to 164 BPM.
To know more about Karvonen formula, refer here:
https://brainly.com/question/30099221#
#SPJ11
A two-sided t-test for a population mean is conducted of the null hypothesis H0 : μ = 100. If a 90 percent t-interval constructed from the same sample data contains the value of 100, which of the following can be concluded about the test at a significance level of a = 0.10 ?A. The p-value is less than 0.10, and H0 should be rejected.B. The p-value is less than 0.10, and H0 should not be rejected.C. The p-value is greater than 0.10, and H0 should be rejected.D. The p-value is greater than 0.10, and H0 should not be rejected.
Option D is correct, the p-value is greater than 0.10, and H₀ should not be rejected.
What is Null hypothesis?The null hypothesis is denoted as H₀, is a statement or assumption that suggests there is no significant or meaningful relationship between two variables in a statistical hypothesis test.
If a 90 percent t-interval constructed from the sample data contains the value of 100, it means that the sample mean is within the confidence interval.
Since the null hypothesis H₀: μ = 100 is also assuming that the population mean is 100, this suggests that the sample data is consistent with the null hypothesis.
Given a significance level of α = 0.10, we compare the p-value with this significance level to make a conclusion.
If the 90 percent confidence interval contains the hypothesized value (100 in this case), it suggests that the p-value is likely to be greater than 0.10.
There is insufficient evidence to reject the null hypothesis at a significance level of 0.10.
Therefore, the p-value is greater than 0.10, and H₀ should not be rejected.
To learn more on Null hypothesis click:
https://brainly.com/question/30821298
#SPJ6
Given mn, find the value of x.
t
(7x-4)º
(3x+28)°
Hence, the value of variable in the given expression x is 8
What is Angle?An angle is formed when two straight lines meet at a common endpoint.
given:∠1 = 7x - 4
∠2 = 3x + 28
A secant line that crosses two parallel lines produces these angles. After that, these angles were congruent, which means that their measures are equal.
Then, equaling both given expressions and solving for x, we get:
Step1: subtract 3x both sides
7x - 4 = 3x + 28
Step2: add 4 both sides
7x - 3x - 4 = 28
Step2: simplify like terms
7x - 3x = 28 + 4
Step3: divide by 4 both sides
4x = 32
x = 32/4
x = 8
Hence, the value of x is 8.
To know more about variable, visit:
https://brainly.com/question/17344045
#SPJ1
HELP IS DUE TODAY!!!!!!!!!!!!!!!!!!
Using expressions,
4a. x= 0 is not possible.
4b. x= 1 is not possible.
5a. (9x-5)(9x+5)
5b. (x-3)(2x+1)
6. 1/(3x-7)
7a. x = (-5,∞)
7b. x = (∞,2]
7c. x = (-3,7]
What are expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
Let's examine the writing of expressions.
The other number is x, and a number is 6 greater than half of it.
As a mathematical expression, this proposition is denoted by the expression x/2 + 6.
Here the values of x has to be such that the denominator is not equal to zero.
So, x cannot be zero and x cannot be 1 as these two values in the respective questions will make the denominator zero.
a. 81x²-25
= 81x² + 45x-45x-25
=9x(9x+5)-5(9x+5)
= (9x-5)(9x+5)
b. 2x²-5x-3
= 2x² + x - 6x -3
= x(2x+1)-3(2x+1)
=(x-3)(2x+1)
Next, the intervals for x are as follows:
x = (-5,∞)
x = (∞,2]
x = (-3,7]
To know more about expression, visit:
https://brainly.com/question/14083225
#SPJ1
Help explain how to solve
The value of the angle U in the triangle is 92.10 degrees.
How to find the angle in a triangle?The angle U in the triangle can be found using cosine rule as follows:
Let's use cosine formula to find the angle U
c² = a² + b² - 2ab cos C
Hence,
Therefore,
a = 58.8
b = 38.4
c = 71.4
Hence,
71.4² = 58.8² + 38.4² - 2(58.8)(38.4) cos U
5097.96 = 3457.44 + 1474.56 - 4515.84 cos U
5097.96 - 4932 = - 4515.84 cos U
165.96 = - 4515.84 cos U
divide both sides by - 4515.84
cos U = 165.96 / - 4515.84
cos U = - 0.03675063775
U = cos⁻¹ - 0.03675063775
U = 92.1032274244
Therefore,
U = 92.10 degrees
learn more on triangle here: https://brainly.com/question/28855901
#SPJ1
If x represents the number of balls then write an expression for 4 less than 18 divided by the number of balls.
An international food festival charges for admission and for each sample of food. Admission and 4 samples cost $8. 75. Admission and 8 samples cost $12. 75. Write a linear function rule to model the cost y for any number of samples x
The linear function rule to model the cost y for any number of samples x is (y = x + 2.25) and this can be determined by forming the linear equation.
An international food festival charges for admission and for each sample of food.
Admission and 6 samples cost $8.25.
Admission and 8 samples cost $10.25.
The following steps can be used in order to determine the linear function rule to model the cost y for any number of samples x:
Step 1 - The linear equation is formed in order to determine the linear function.
Step 2 - The linear equation that represents the situation "admission and 6 samples cost $8.25" is:
8.25 - 6c = d --- (1)
Step 3 - The linear equation that represents the situation "admission and 8 samples cost $10.25" is:
10.25 = 8c + d --- (2)
Step 4 - Substitute the value of 'd' in equation (2).
10.25 = 8c + 8.25 - 6c
2 = 2c
c = 1
Step 5 - Substitute the value of 'c' in the equation (1).
d = 8.25 - 6
d = 2.25
Step 6 - So, the linear function rule to model the cost y for any number of samples x is:
y = x + 2.25.
To know more linear function about click here.
brainly.com/question/20286983
#SPJ4
miguel rode his bicycle 4 miles less than 5 times the number nathen rode. if Miguel rode his bicycle 6 miles, how many miles did nathan ride?
Answer:Hence, Nathan rode 2 miles
Step-by-step explanation:ask if you need any questions
profit = total income - total expenditure Calculate this company's a) total income. b) total expenditure. c) profit. Description Sales - Monday Wages - extra staff Stall hire fee Sales - Tuesday Supplies - stationery Sales - Wednesday Materials Online bulk order Money in £25.00 £20.00 £35.00 £100.00 Money out £110.00 £20.00 £6.00 £10.00
The company's total income, expenditure and profit is given respectively as follows:
a.) £180
b.) £146
C.) £34
How to calculate the profit of the company? seeTo calculate the profit of the company the formula such as given below is used.
Profit = total income - total expenditure
The total income = 25+20+35+100 = £180
The total expenditure = 110+20+6+10 = £146
Profit = 180-146 = £34
Learn more about profit here:
https://brainly.com/question/29785281
#SPJ1
Determine the value of X
Answer:
x = 26.
Step-by-step explanation:
Given: 2x + 3x + 50 = 180
First, write it down:
2x + 3x + 50 = 180
Then, collect like terms:
2x + 3x = 180 - 50
Then calculate:
5x = 130 (Divide both sides by 5)
x = 26
a reasonable abstraction for a car includes: group of answer choices an engine number of miles driven driving car color
Answer:
Of the given options, "an engine" is the most reasonable abstraction for a car.
An engine is a fundamental component of a car that powers its movement, and it is present in almost all cars. The number of miles driven and the driving car color are characteristics of a specific car rather than abstractions of a car itself. For example, a car can still be considered a car even if it has not been driven any miles yet or if it has no color at all.
Therefore, an engine is a more reasonable abstraction for a car as it captures an essential feature of a car that is present in all cars.
The solution is, D. Driving, a reasonable abstraction for a car includes. Driving is an action or behavior associated with a car, as it involves operating or using the car to travel from one place to another. It is an essential aspect of the car's purpose and function.
Here, we have,
we know that,
An engine is a machine designed to convert fuel into mechanical energy that can be used to power other machines or devices. In the context of automobiles, an engine is the primary source of power that drives the vehicle. It typically operates by burning fuel in a combustion chamber to generate high-pressure gases that drive a piston, which in turn rotates a crankshaft that ultimately powers the car's wheels.
Car color and number of miles driven are characteristics or properties of a car, while an engine is a component that helps to power the car. Driving, on the other hand, is an action or behavior associated with a car, as it refers to the act of operating or using the car to travel from one place to another.
Therefore, driving is a reasonable abstraction for a car, as it captures an essential aspect of the car's purpose and function.
To know more about car visit:
brainly.com/question/29509191
#SPJ2
2 + 4.8 + -11.4 = ?
Answer:
23 but not
Step-by-step explanation:
Complete the story problem so that it can be represented by the equation, and then solve. Aldo and Leola help their teacher, Ms. Krebs, put books on the bookshelves in her classroom. There are 2 times as many nonfiction books as fiction books. There are fiction books. They put the same number of books on each of the 7 bookshelves and put as many as they can on each shelf. Then, they put any remaining books on Ms. Krebs's desk. Aldo and Leola put books on each bookshelf. They put books on Ms. Krebs's desk
Aldo and Leola would put 9 fiction books and 18 nonfiction books on each of the 7 bookshelves, for a total of 189 books on the shelves. They would then put the remaining 7 books on Ms. Krebs's desk.
To represent the problem as an equation, we first need to define some variables. Let's let "f" represent the number of fiction books, and "n" represent the number of nonfiction books. We know from the problem that there are 2 times as many nonfiction books as fiction books, so we can write:
n = 2f
We also know that they put the same number of books on each of the 7 bookshelves and put as many as they can on each shelf. Let's call this number "s". We can then write an equation for the total number of books that can fit on the bookshelves:
7s = f + n
Since n = 2f, we can substitute 2f for n in the equation:
7s = f + 2f
Simplifying, we get:
7s = 3f
Finally, we know that any remaining books are put on Ms. Krebs's desk. Let's call this number "r". We can write an equation for the total number of books:
f + n = 7s + r
Substituting 2f for n, we get:
f + 2f = 7s + r
Simplifying, we get:
3f = 7s + r
Now we can solve for "f":
3f = 7s + r
f = (7s + r) / 3
We don't have enough information to solve for "s" or "r", but we can use this equation to find the number of fiction books. For example, if we know that there are a total of 70 books, we can write:
f + n = 70
f + 2f = 70
3f = 70
f = 23.33
Since we can't have a fractional number of books, we would round down to the nearest whole number and get:
f = 23
We could then use the equation f = (7s + r) / 3 to find the number of books on each shelf, assuming there are no books left over:
23 = (7s + 0) / 3
69 = 7s
s = 9.86
Since we can't have a fractional number of books on a shelf, we would round down to the nearest whole number and get:
s = 9
So Aldo and Leola would put 9 fiction books and 18 nonfiction books on each of the 7 bookshelves, for a total of 189 books on the shelves. They would then put the remaining 7 books on Ms. Krebs's desk.
To know more about fractional number click here:
brainly.com/question/29213412
#SPJ4
Find 7/8(3. 5) write your answer as a mixed number in the simplest form
to find 7/8 of 3.5, we multiplied 7/8 and 3.5 together to get 49/16, which we then converted to a mixed number in the simplest form, giving us the answer of 3 1/16.
To find 7/8 of 3.5, we can simply multiply 7/8 and 3.5 together.
7/8 x 3.5 = (7/8) x (7/2) = 49/16
So, the answer is 49/16. However, we need to write the answer as a mixed number in the simplest form.
To convert an improper fraction to a mixed number, we need to divide the numerator by the denominator. In this case, 49 divided by 16 is 3 with a remainder of 1.
So, the mixed number is 3 1/16.
To simplify the mixed number, we need to check if we can reduce the fraction part (1/16) further. 1 is not divisible by any number other than 1 itself, so it is already in its simplest form.
Therefore, the final answer is 3 1/16.
In summary, to find 7/8 of 3.5, we multiplied 7/8 and 3.5 together to get 49/16, which we then converted to a mixed number in the simplest form, giving us the answer of 3 1/16.
To know more about denominator. click here:
brainly.com/question/7067665
#SPJ4
What is the sum of A+C?  a.the matrices b -2,11,5,0,-2,1 c.12,3,1,-2,2,-1 d. -35,28,6,-1,0,12
Answer:on edge B)-2,11,5,0-2,1
The sum of the matrices A and C from the list of options is the matrix B
Calculating the sum of the matricesGiven the following matrices
Matrix A
| 0 6 2 |
| 1 5 -2 |
Matrix C
| -2 5 3 |
| -1 -7 3|
To find the sum of matrices A and C, we add the corresponding elements in each matrix:
So, we have: A + C
| 0 - 2 6 + 5 2 + 3 |
| 1 - 1 5 - 7 -2 + 3|
Evaluate the sum
| -2 11 5 |
| 0 -2 1 |
This represents option B
Therefore, the sum of matrices A and C is (B)
Read more about matrix at
https://brainly.com/question/2456804
#SPJ1
Complete question
What is the sum of A+C?
Matrix A
| 0 6 2 |
| 1 5 -2 |
Matrix C
| -2 5 3 |
| -1 -7 3|
a drug for the relief of asthma can be purchased from 10 different manufacturers in liquid, tablet, or capsule form, all of which come in regular and extra strength. how many different ways can a doctor prescribe the drug for a patient suffering from asthma?
So there are 200 different ways a doctor can prescribe the asthma drug to a patient, taking into account the various options for form, manufacturer, and strength.
This illustrates the importance of carefully considering all the available options and selecting the most appropriate prescription for each patient's unique needs.The number of different ways a doctor can prescribe the asthma drug to a patient depends on the number of options available for each of the three factors: form, manufacturer, and strength.
For each of the three factors, there are 10 different options. Therefore, the total number of different ways the doctor can prescribe the drug is the product of the number of options for each factor:
10 options for form x 10 options for manufacturer x 2 options for strength (regular or extra) = 200 total options.
Find out more about asthma drug
brainly.com/question/30610786
#SPJ4
The total number of cookies,y, contained in x packages can be represented by the equation y = 24x. Which of the following graphs best represents this situation?
The graph for the linear equation y=24x, will be a straight line having coordinate (1,24) i.e. B.
What is a linear equation, exactly?
A linear equation is a first-degree algebraic equation in which each term is either a constant or the product of a constant and a single variable (degree 1). A linear equation is stated as y = mx + b, where y is the dependent variable, x is the independent variable, m is the line's slope, and b= y-intercept .
A linear equation's graph is a straight line. The line's slope decides how steep it is, and the y-intercept indicates where the line crosses the y-axis. Linear equations are used to model relationships between variables that are directly proportional to each other, such as distance and time, or cost and quantity.
Now,
Given equation is y=24x
then for x, y is
1, 24
2, 48
3, 72
4, 96
Hence, the graph will be as represented in option 2.
To know about linear equations visit the link
brainly.com/question/29739212
#SPJ1
at the farmers market there is a large pile of small cauliflowers. the mean weight of these cauliflowers is 400 grams with a standard deviation of 20 grams. assume the weight of theses cauliflowers is normally distributed. which has a greater probability, the mean weight of an individual cauliflower being between 400 and 409 grams or the mean weight of a random sample of 36 of the cauliflowers being between 400 and 409 grams?
The mean weight of an individual cauliflower being between 400 and 409 grams has a greater probability.
Standard deviation of the given data is 20 grams. The mean weight of the cauliflower is 400 grams. Now, for calculating the probability, we need to standardize the given mean weight of cauliflower. It will be as follows. Z-score for the mean weight of cauliflower is given as:
z = (X - μ) / σwhere X = 400 grams (mean weight of cauliflower)
μ = 400 grams (mean weight of the population)
σ = 20 grams (standard deviation)z = (400 - 400) / 20 = 0
Now, the probability of the mean weight of an individual cauliflower being between 400 and 409 grams is as follows:
P(400 < X < 409) = P(0 < Z < 0.45)
Using the standard normal distribution table, the probability is 0.1745.
The mean weight of a random sample of 36 of the cauliflowers is between 400 and 409 grams. The mean weight of a random sample of 36 of the cauliflowers is given by:
(X-μ)/ (σ/√n)where μ = 400 grams (mean weight of cauliflower)
σ = 20 grams (standard deviation)
n = 36 (number of samples)
Now, we need to standardize the sample mean. It will be as follows:
z = (X - μ) / (σ/√n)z = (400 - 400) / (20 / √36)
z = 0
As the z-score is zero, the probability will be equal to 0.5. Hence, the mean weight of an individual cauliflower being between 400 and 409 grams has a greater probability than the mean weight of a random sample of 36 of the cauliflowers being between 400 and 409 grams.
To learn more about mean weight refer :
https://brainly.com/question/15904675
#SPJ11
Hey! I need help on this question and I would be so happy if you helped me!
Answer: Answer is below <3
Step-by-step explanation:
Which figure has the greater volume?A
Which figure has the greater surface area?B
Which figure has fewer edges?A
I hope this is correct, I'm sorry if its wrong :(
at 95% confidence, how large a sample should be taken to obtain a margin of error of 0.04 for the estimation of a population proportion? assume that past data are not available for developing a planning value for p*. (round your answer up to the nearest whole number.)
A sample size of at least 61 should be taken to obtain a margin of error of 0.04 for the estimation of a population proportion at a 95% confidence level.
Given data:
To determine the sample size required for estimating a population proportion with a given margin of error at a 95% confidence level, you can use the following formula:
[tex]n=\frac{Z^2 \cdot p(1-p)}{E^2}[/tex]
n is the required sample size.
Z is the Z-score corresponding to the desired confidence level. For a 95% confidence level, the Z-score is approximately 1.96.
p is an estimate of the population proportion (since you don't have prior data, you can use p =0.5 for maximum variability, which results in the largest sample size requirement).
E is the desired margin of error, which is 0.04 in this case.
Substitute the values into the formula:
[tex]n=\frac{1.96^2*0.5^2}{0.04^2}[/tex]
The value of n = 60.26
Since the sample size is a whole number, n = 61
Hence, a sample size of at least 61 should be taken for the estimation of a population proportion at a 95% confidence level.
To learn more about confidence interval, refer:
https://brainly.com/question/16807970
#SPJ12
PLS HELP ASAP .a vacuum cleaner costs the owner $220 to buy. They then mark up the cost to sell it by 30%. What as the amount of the mark up? What is the selling price?
The amount of the mark up is $66 and the selling price is $286.
What is markup percentage?The amount by which a product's cost is raised to determine its selling price is known as the markup percentage. Usually, it is represented as a percentage of the item's price. Markup percentage is determined by the following equation:
Markup percentage = (Selling price - Cost price) / Cost price x 100%
Given that, the mark up is 30%.
Thus,
Mark up = 0.3 x $220 = $66
The selling price is:
Selling price = $220 + $66 = $286
Hence, the amount of the mark up is $66 and the selling price is $286.
Learn more about percentage here:
https://brainly.com/question/29763752
#SPJ1
A little help :) Appreciated - 30 points (Reupload)
Answer:
See below!
Step-by-step explanation:
a) 1, 2, 3, 4, 5
The possible outcomes are all the options that there are on the spinner
b) 2
There are only 2 even numbers!
c) [tex]\frac{2}{5}[/tex] or 0.4
There are 2 out of 5 numbers are even on the spinner so that must be the solution!
d) 1
The spinner has only one multiple of 3, so the possible outcome should also be 1.
e) [tex]\frac{1}{5}[/tex] or 0.2
There are only 1 out of 5 options which are multiples of 3, so that would be our solution
f) 4
There are 4 prime numbers in the spinner (1, 2, 3, 5), so that would be a possible outcome.
g) [tex]\frac{4}{5}[/tex] or 0.8
The spinner has 4 out of 5 prime numbers, so our answer would be that!
Hope this helps, have a lovely day! :)
find the value of x
The value of x in the given triangle is 1.82 cm using the angle bisector theorem.
What is a triangle?A triangle is a polygon with three edges and three vertices. It belongs to the basic geometric shapes. A triangle with the parts A, B, and C is referred to as triangle ABC. Any three points that are not collinear in Euclidean geometry result in a separate triangle and a distinct plane. A triangle is a type of polygon with three sides; the triangle's apex is the point where the two longest sides meet. Two sides are brought together at an angle.
What is angle bisector theorem?
The ratios of the two segments that a line that bisects the opposing angle splits a triangle's side into are the subject of the angle bisector theorem in mathematics. It contrasts their proportionate lengths with the other two triangle sides' proportional lengths.
In the given triangle,
5/6=x/4-x
20-5x=6x
20=11x
x=20/11= 1.82 cm
To know more about angle bisectors, visit
https://brainly.com/question/30234493
#SPJ1
The image shows the graph of the circle
Image of prob below:
Answer:
The line y = 2 - 5/20 can be simplified to y = 2 - 1/4 = 7/4.
Substituting y = 7/4 into the equation of the circle, we get:
(x - 5)² + (7/4 + 1)² = 25
(x - 5)² + (15/4)² = 25
(x - 5)² = 25 - (15/4)²
x - 5 = ±√(25 - (15/4)²)
x = 5 ± √(25 - (15/4)²)
Simplifying, we get:
x = 5 ± √(400/16 - 225/16)
x = 5 ± √(175/16)
x = 5 ± (√175)/4
Therefore, the two intersection points are:
Left point: (5 - (√175)/4, 7/4)
Right point: (5 + (√175)/4, 7/4)
what will happen to the solution if the objective function coefficient for variable 1 decreases by 20?
If the objective function coefficient for variable 1 decreases by 20, the solution will shift in the direction of the decrease in the objective function coefficient. It means that the optimal solution that was obtained previously will no longer remain optimal, and the new optimal solution will be found with the new objective function coefficient.
In linear programming, the objective function determines the maximum or minimum value that can be attained in the solution, subject to the constraints. The constraints in the problem can be either equalities or inequalities, which limit the range of values that the decision variables can take on.
The change in the objective function coefficient will change the direction of the optimal solution, and it may affect the feasibility of the solution. It means that some constraints may no longer be satisfied, or some variables may become infeasible.
In such cases, it will be necessary to revise the constraints or the variables to ensure the feasibility of the solution.
The solution can also be affected if the constraints of the problem change. The new constraints may limit the range of values that the variables can take on, or they may add new variables to the problem. These changes can affect the feasibility of the solution, and it may require the problem to be solved again to obtain the new optimal solution.
To know more about linear programming, refer here:
https://brainly.com/question/30763902#
#SPJ11