Answer: BC ≈ 6.4 units
Step-by-step explanation: We can use trigonometry to find the length of line segment BC.
Since we know the length of AC and the measure of angle A, we can use the trigonometric function cosine (cos) to calculate BC.
Using the formula: cos(A) = Adjacent / Hypotenuse, we have
cos(34°) = BC / 9.
Solving for BC, we get BC ≈ 6.4 units (rounded to the nearest tenth).
Here is an article on trigonometry basics: https://byjus.com/maths/trigonometry/#:~:text=Trigonometry%20Basics,are%20based%20on%20these%20functions.
!!PLEASE HELPPPP MEEE!!
Answer:
Step-by-step explanation:
5989.87
a cylinder has a radius of 3 cm and a height of 8 cm. what is the longest segment, in centimeters, that would fit inside the cylinder?
The longest segment that would fit inside the cylinder is approximately 9.06 centimeters.
The longest segment that would fit inside the cylinder would be the diagonal of the cylinder's base, which is equal to the diameter of the base. The diameter of the base is equal to twice the radius, so it is 6 cm. Using the Pythagorean theorem, we can find the length of the diagonal:
[tex]diagonal^2 = radius^2 + height^2 \\diagonal^2 = 3^2 + 8^2 \\diagonal^2 = 9 + 64 \\diagonal^2 = 73 \\diagonal = sqrt(73)[/tex]
Therefore, the longest segment that would fit inside the cylinder is approximately 8.54 cm (rounded to the nearest hundredth).
To find the longest segment that would fit inside the cylinder, we need to calculate the length of the space diagonal of the cylinder. This is the distance between two opposite corners of the cylinder, passing through the center. We can use the Pythagorean theorem in 3D for this calculation.
The terms we'll use are:
- Radius (r): 3 cm
- Height (h): 8 cm
To find the space diagonal (d), we can use the following formula:
[tex]d = \sqrt{r^2 + r^2 + h^2}[/tex]
Plug in the values:
[tex]d = \sqrt{((3 cm)^2 + (3 cm)^2 + (8 cm)^2)} d = \sqrt{(9 cm^2 + 9 cm^2 + 64 cm^2)} d = \sqrt{(82 cm^2)}[/tex]
d ≈ 9.06 cm
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The longest segment that can fit inside the cylinder is. [tex]$\sqrt{73}$ cm[/tex].
The longest segment that can fit inside a cylinder is a diagonal that connects two opposite vertices of the cylinder.
The length of this diagonal by using the Pythagorean theorem.
Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.
It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation:[1]
[tex]{\displaystyle a^{2}+b^{2}=c^{2}.}[/tex]
The theorem is named for the Greek philosopher Pythagoras, born around 570 BC.
The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem.
The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.
Consider a right triangle with legs equal to the radius.
[tex]$r$[/tex] and the height [tex]$h$[/tex] of the cylinder, and with the diagonal as the hypotenuse.
Then, by the Pythagorean theorem, the length of the diagonal is:
[tex]$\sqrt{r^2 + h^2} = \sqrt{3^2 + 8^2} = \sqrt{73}$[/tex]
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write it as a fraction
Answer:
[tex] \frac{11}{13} \times \frac{1}{4} \times \frac{1}{3} = \frac{11}{156} [/tex]
So the volume of this rectangular prism is 11/156 of a cubic foot.
The answers are in the picture. I need help ASAP!
The perimeter and the area of the regular polygon are 20 inches and 27.53 square inches.
How to calculate the area and the perimeter of a regular polygon
The figure representing a regular polygon with five sides of same length, whose perimeter and area is well described by following formulas:
Perimeter
p = n · l
Area
A = (n · l · a) / 2
Where:
A - Area of the polygon, in square inches. n - Number of sides.l - Side length, in inches. a - Apothema, in inches. p - Perimeter, in inches.Where the apothema is:
a = 0.5 · l / tan (180° / n)
If we know that l = 4 in and n = 5, then the perimeter and the area of the polygon are:
Perimeter
p = 5 · (4 in)
p = 20 in
Area
a = 0.5 · (4 in) / tan (180° / 5)
a = 0.5 · (4 in) / tan 36°
a = 2.753 in
A = [5 · (4 in) · (2.753 in)] / 2
A = 27.53 in²
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If it is 15°c outside ang the temperature will drop by 16° in the next 8 hours,What is the temperature after 8 hours
Use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine, as in Example 4.
The expression in terms of the first power of sine is 1 + 3[tex]sin^{4}[/tex]x - 3[tex]sin^{2}[/tex]x - [tex]sin^{6}[/tex]x. The solution has been obtained by using the trigonometric identities.
What are trigonometric identities?
All possible values of the variables in the equation must satisfy the equality condition known as a trigonometric identity. A triangle's side length and angle can be used to express a variety of unusual trigonometric identities.
We are given expression as [tex]cos^{6}[/tex] (x).
This can be written as a cosine function as [tex](cos^{2} x)^{3}[/tex].
We know that [tex]sin^{2}[/tex]x + [tex]cos^{2}[/tex]x = 1.
So, we get
⇒ (1 - [tex]sin^{2}[/tex]x[tex])^{3}[/tex]
⇒ 1 + 3[tex]sin^{4}[/tex]x - 3[tex]sin^{2}[/tex]x - [tex]sin^{6}[/tex]x
Hence, the required expression has been obtained.
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Maxine graphs the function m(x) which has a vertex of (-3,4) and passes through the point (-1,-8). Ricardo graphs p(x) = (x+3)² +4
Maxine thinks that both functions have the same axis of symmetry equation. Do you agree or disagree?
Both functions have the same axis of symmetry equation, which is x = -3.
Given that, Maxine graphs a function m(x) which has a vertex of (-3,4) and passes through the point (-1,-8).
Ricardo graphs p(x) = (x+3)² + 4
We need to check if both the function axis of symmetry equation.
So,
Both functions have a vertex of (-3,4), which means that the axis of symmetry must be a vertical line passing through x = -3.
Axis of symmetry = The axis of symmetry is an imaginary straight line that divides the shape into two identical parts or that makes the shape symmetrical.
For the function p(x) = (x+3)² +4, the axis of symmetry is indeed x = -3.
For the function m(x), since it has a vertex of (-3,4), the equation of the axis of symmetry is x = -3.
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A single marble tile measures 25 cm by 20 cm. How many tiles will be required to cover a floor with dimensions 2 meters by 3 meters?
A. 320 tiles
B. 240 tiles
C. 180 tiles
D. 120 tiles
(Please do step by step and the answer)
The number of tiles that will be required to cover a floor with dimensions 2 meters by 3 meters is given as follows:
D. 120 tiles.
How to obtain the area of a rectangle?To obtain the area of a rectangle, you need to multiply its length by its width. The formula for the area of a rectangle is:
Area = Length x Width
The area of the floor is given as follows:
2 x 3 = 6 m².
The area in m² of each tile is given as follows:
0.25 x 0.2 = 0.05.
Hence the number of tiles that will be required to cover the floor is given as follows:
6/0.05 = 120 tiles.
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An industrial/organizational psychologist has been consulting with a company that runs weekend job-seeking workshops for the unemployed. She collected data on several issues related to these workshops and, after conducting statistical tests, obtained statistically significant findings. She needs to find a way to evaluate effect size so that she can make recommendations to the company. One of the psychologist's findings is that 18 months after the workshop, a sample of 81 job seekers who received training on using the Internet to find job listings worked more than 30 hours per week an average of 8. 7 months in the last year, with a standard deviation of 4. 1. The typical job seeker works 7. 4 months. The psychologist finds that the estimated Cohen's d is _____, the t statistic is 2. 83, and r^2 is ______. Using Cohen's d and Cohen's guidelines for interpreting the effect size with the estimated Cohen's d, there is a ______ treatment effect. Using r^2 and the extension of Cohen's guidelines for interpreting the effect size using r^2, there is a ______ treatment effect. Another one of the psychologist's findings is that a sample of 81 job seekers who received training on interview skills scored an average of 8. 1 as measured on a 9-point job search motivation scale, with a standard deviation of. 8. The typical job seeker scores 7. 4 points. She finds that the estimated Cohen's d is _____, the t statistic is 7. 78, and r^2 is _____ Using Cohen's d and Cohen's guidelines for interpreting the effect size with the estimated Cohen's d, there is a treatment effect. Using r^2 and the extension of Cohen's guidelines for interpreting the effect size with r^2, there is a ___ treatment effect
The psychologist finds that the estimated Cohen's d is 0.32, the t statistic is 2. 83, and r² is 0.073. Using r² and the extension of Cohen's guidelines for interpreting the effect size using r², there is a small treatment effect. job seeker finds that the estimated Cohen's d is 0.88, the t statistic is 7. 78, and r² is 0.479.Using r² and the extension of Cohen's guidelines for interpreting the effect size with r², there is a large treatment effect
To calculate the estimated Cohen's d, we use the formula
d = (M - M0) / SD
where M is the mean of the treatment group (job seekers who received training on using the Internet to find job listings), M0 is the mean of the control group (typical job seeker), and SD is the pooled standard deviation of the two groups. Using the given values, we have
M = 8.7 months
M0 = 7.4 months
SD = 4.1 months
So, d = (8.7 - 7.4) / 4.1 = 0.32
Using Cohen's guidelines for interpreting effect size with Cohen's d, a value of 0.2 is considered a small effect, 0.5 a medium effect, and 0.8 a large effect. Therefore, with an estimated Cohen's d of 0.32, there is a small treatment effect.
To calculate r², we use the formula
r² = t² / (t² + df)
where t is the t statistic, df is the degrees of freedom (n-2 for a two-group design), and n is the sample size. Using the given values for the Internet training group, we have
t = 2.83
n = 81
df = 79
So, r² = 2.83² / (2.83² + 79) = 0.073
Using the extension of Cohen's guidelines for interpreting effect size with r², a value of 0.01 is considered a small effect, 0.09 a medium effect, and 0.25 a large effect. Therefore, with an r² of 0.073, there is a small treatment effect.
For the job seekers who received training on interview skills, we can calculate Cohen's d and r² in a similar way
d = (M - M0) / SD = (8.1 - 7.4) / 0.8 = 0.88
t = 7.78
n = 81
df = 79
r² = 7.78² / (7.78² + 79) = 0.479
Using Cohen's guidelines for interpreting effect size with Cohen's d, a value of 0.2 is considered a small effect, 0.5 a medium effect, and 0.8 a large effect. Therefore, with an estimated Cohen's d of 0.88, there is a large treatment effect.
Using the extension of Cohen's guidelines for interpreting effect size with r², a value of 0.01 is considered a small effect, 0.09 a medium effect, and 0.25 a large effect. Therefore, with an r² of 0.479, there is a medium to large treatment effect.
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Answer:.317
.091
Small to med
Med
.875
.431
Large
Large
Step-by-step explanation:
PLEASE HELP ME I BEEGGGG
Answer:miami is 43431.16 rounded to 43431 because you can't have .16 of a person.
washington dc is 4249.22 which is round to 4249 because you can't have .22 of a person.
and new york city is 27348.99 which is rounded to 27349 because you can't have .99 of a person.
Step-by-step explanation:
im smart and im really good at math
In art class students are mixing black and white paint to make gray paint. Hassan mixes 2 cups of black paint and 3 cups of white paint. Aaliyah mixes 4 cups of black paint and 5 cups of white paint. Use Hassan and Aaliyah’s proportions of black paint to determine whose gray paint will be darker.
Hassan black paint proportion (out of total) as fraction =
Aaliyah black paint proportion (out of total) as fraction =
Hassan’s gray paint will be darker.
Aaliyah’s gray paint will be darker.
The two gray paints will be equally dark.
attempt 1 out of 2
Miracle Jackson
Which is more? (Fraction Comparison)
Apr 11, 8:08:47 AM
Watch help video
In art class students are mixing black and white paint to make gray paint. Hassan mixes 2 cups of black paint and 3 cups of white paint. Aaliyah mixes 4 cups of black paint and 5 cups of white paint. Use Hassan and Aaliyah’s proportions of black paint to determine whose gray paint will be darker.
$x$$y$$($$)$
$=$$\surd$$a^{2}$$a^{b}$
$7$$8$$9$$\div$
$4$
The correct answer is: Aaliyah’s gray paint will be darker.
What is proportion?
In mathematics, a proportion is an equation that states that two ratios are equal. A ratio is a comparison of two numbers or quantities that are usually written in the form of a fraction. For example, the ratio of apples to oranges in a basket could be written as 3/5, meaning that there are three apples for every five oranges.
Hassan mixed 2 cups of black paint and 3 cups of white paint, so the total amount of paint he mixed is 2 + 3 = 5 cups. The proportion of black paint in his mixture is 2/5.
Aaliyah mixed 4 cups of black paint and 5 cups of white paint, so the total amount of paint she mixed is 4 + 5 = 9 cups. The proportion of black paint in her mixture is 4/9.
Comparing the two proportions, we see that Aaliyah's proportion of black paint is greater than Hassan's proportion of black paint, so Aaliyah's gray paint will be darker.
Therefore, the correct answer is: Aaliyah’s gray paint will be darker.
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A bag of poker chips contains 4 purple, 6 red, 3 pink, and 2 black chips. What is the probability of pulling from the bag A black chip?
The answer of the given question based on the probability is , the probability of pulling a black chip from the bag is 2/15 or approximately 0.133 or 13.3%.
What is Probability?Probability is measure of likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event. For example, the probability of flipping a coin and getting heads is 0.5, or 50%, assuming a fair coin. Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes
The total number of poker chips in the bag is:
total = 4 + 6 + 3 + 2 = 15
The probability of pulling a black chip from the bag is the number of black chips divided by the total number of chips:
P(black) = number of black chips / total number of chips
P(black) = 2 / 15
Therefore, the probability of pulling a black chip from the bag is 2/15 or approximately 0.133 or 13.3%.
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PLEASE HELP!!!
The picture explains the problem
The inequality represented by the given number line is: -60 ≥ m.
Explain about the inequality on number line:We can see the values that an inequality represents by placing it on a number line.
On a number line, inequalities are represented by drawing a straight line and designating the end points as an open or closed circle.
An empty circle indicates that the value is not included.A closed circle indicates that the value is included.On a number line, inequality is represented as follows:
Choose the value or values that must be displayed on the number line.Determine if an > or < open circle or a ≥ or ≤closed circle is required; the situation either requires an open circle or a closed circle.Draw a straight line either to the number's left or right side or in between the circles to indicate the solution set.For the given number line,
-6 is shown with the closed circle, with lines extending towards +∞
Thus, the inequality represented by the given number line is: -60 ≥ m.
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9. Patricia has 5 cups of rice cereal. She
uses 3 cups of rice cereal to make
granola bars, then borrows 0.5 cup of
rice cereal from her friend. Her recipe
for cereal clusters calls for 3 cups of
rice cereal. Does Patricia have enough?
How much will she have left over, or
how much more will she need?
A Yes, she has 1/2cup left.
B No, she needs 1/2cup more.
C Yes, she 1/4 has cup left.
D No, she needs 1/4cup more.
Therefore, the correct answer is (B) No, she needs 1/2 cup more.
To determine if Patricia has enough rice cereal for her recipe, we need to calculate the total amount of rice cereal she has after all her actions and compare it to the 3 cups required for the cereal clusters.
Initially, Patricia had 5 cups of rice cereal. She used 3 cups to make granola bars, leaving her with 2 cups. She then borrowed 0.5 cup from her friend, which brings her total to 2.5 cups.
Finally, she needs 3 cups of rice cereal for the cereal clusters recipe. Since she only has 2.5 cups, she does not have enough rice cereal and needs to get more. Therefore, the correct answer is B) No, she needs 1/2 cup more.
She then borrows 0.5 cup, so she now has 2 + 0.5 = 2.5 cups.
needs 3 - 2.5 = 0.5 cups more.
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Isabella was asked to solve the following trigonometric equation for 0 < x < 2π.
sin(x) = cos(2x) = 0
-
Isabella worked the problem the following way:
Line 1: sin(x) (1 - 2 sin²(x)) =
-
Line 2: sin(x) - 1+2 sin²(x) = 0
Line 3: 2 sin² (x) + sin(x) = 1
Line 4: sin(x) (2 sin(x) + 1) = 1
Line 5: sin(x) = 1,
Line 6: sin(x) = 1,
Line 7: x = 0, π
2 sin(x) + 1 = 1
sin(x) = 0
A. Isabella made a mistake in her work. In what line did the mistake occur? Justify your answer. (6
points)
B. What are the correct answers? Leave answers as exact values. WORK DOES NOT NEED TO BE
SHOWN. (6 points)
1. The equation she was supposed to solve was sin(x) = cos(2x), but she mistakenly added an extra "= 0" term.
2. The correct answers are x = π/6 and x = 5π/6.
How do we find the correct answers for the trigonometric equation?
To find the correct answers, we will solve the correct trigonometric equation sin(x) = cos(2x).
Since cos(2x) = 1 - 2sin²(x), the equation becomes:
sin(x) = 1 - 2sin²(x)
Now we can rewrite this equation as a quadratic equation in sin(x):
2sin²(x) + sin(x) - 1 = 0
This equation can be solved using the quadratic formula:
sin(x) = [-b ± sqrt(b² - 4ac)] / 2a
where a = 2, b = 1, and c = -1:
sin(x) = [-1 ± sqrt(1² - 42(-1))] / (2*2)
sin(x) = [-1 ± sqrt(9)] / 4
sin(x) = (-1 ± 3) / 4
There are two possible solutions for sin(x):
sin(x) = 1/2
sin(x) = -1
For sin(x) = 1/2, we have:
x = π/6, 5π/6
For sin(x) = -1, there is no solution in the interval 0 < x < 2π because the sine function does not reach -1 within this range.
So the correct answers are x = π/6 and x = 5π/6.
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1/2 x^4=8
Solve the equation
Answer:
x=2
Step-by-step explanation:
x^4=16
x=[tex]\sqrt[4]{16}[/tex]
x=[tex]2[/tex]
The diameter of a semicircle is 4 feet. What is the semicircle's perimeter?
IF YOU ANSWER CORRECTLY I WILL GIVE YOU BRAINLIEST***
Find the area of the shaded sector. Round to the nearest tenth.
167°
17. 8 yd
Area = [ ? ]yd? Enter
The area of the shaded sector is approximately 463.8 square yards.
To find the area of the shaded sector, we need to use the formula for the area of a sector, which is given by
Area of sector = (central angle / 360°) x πr²
where r is the radius of the sector, and the central angle is the angle between the two radii that form the sector.
In this case, we are given that the central angle of the shaded sector is 167°, and the radius is 17.8 yards. So, we can substitute these values into the formula as follows
Area of sector = (167° / 360°) x π(17.8)²
Simplifying this expression, we get:
Area of sector = 0.464 x 998.92
Multiplying these two numbers, we get
Area of sector = 463.8 square yards
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The given question is incomplete, the complete question is:
Find the area of the shaded sector. Round to the nearest tenth.
PLEASE HELP ME ITS DUE TODAY :(
I will give brainliest if you help me answer this!!!
Answer: it would be (b) because the number 64 7th graders hights are less than
65 inches tall
Step-by-step explanation:
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a password consists of four alphanumeric characters (case insensitive). a valid password must contain at least one digit and at least one letter. how many different passwords are there
There are 1,280,240 different passwords that meet the criteria of containing at least one letter and at least one digit, and consisting of four alphanumeric characters (case insensitive).
How to calculate the total number of different passwords?To calculate the total number of different passwords, we can break the problem down into several steps:
Step 1: Calculate the number of possible characters for each position in the password. Since the password consists of four alphanumeric characters, there are 26 letters (A-Z) and 10 digits (0-9) for each position.
Therefore, there are 36 possible characters for each position.
Step 2: Calculate the total number of possible passwords without any restrictions.
Since there are 36 possible characters for each position and the password has four positions, the total number of possible passwords without any restrictions is:
36 x 36 x 36 x 36 = 1,679,616
Step 3: Calculate the number of passwords that do not contain at least one digit or at least one letter.
To do this, we can calculate the number of passwords that do not contain any digits and subtract it from the total number of possible passwords, and then do the same for passwords that do not contain any letters.
The number of passwords that do not contain any digits is:
26 x 26 x 26 x 26 = 456,976
The number of passwords that do not contain any letters is:
10 x 10 x 10 x 10 = 10,000
However, we have to be careful not to double-count the passwords that do not contain both letters and digits.
The number of passwords that do not contain both letters and digits is:
26 x 26 x 10 x 10 = 67,600
So the total number of passwords that do not contain at least one digit or at least one letter is:
456,976 + 10,000 - 67,600 = 399,376
Step 4: Subtract the number of invalid passwords from the total number of possible passwords:
1,679,616 - 399,376 = 1,280,240
Therefore, there are 1,280,240 different passwords that meet the criteria of containing at least one letter and at least one digit, and consisting of four alphanumeric characters (case insensitive).
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Rewrite the expression with rational exponents.
[tex]7^{(1/3)}[/tex] is the equivalent expression to ∛7 with rational exponents.
What are rational exponents?
Rational exponents are exponents that are expressed as fractions. Specifically, a rational exponent of the form m/n is equivalent to taking the nth root of a number and then raising it to the power of m.
When we talk about rational exponents, we are referring to exponents that are written as fractions. Specifically, a rational exponent of the form m/n is equivalent to taking the nth root of a number and then raising it to the power of m.
So, in the case of ∛7, we can rewrite the cube root symbol (∛) as a rational exponent with a denominator of 3. That is, ∛7 can be expressed as [tex]7^{(1/3)}[/tex] , where the 1/3 exponent means "take the cube root of 7".
Therefore, [tex]7^{(1/3)}[/tex] is the equivalent expression to ∛7 with rational exponents.
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please help me with all the blank ones hurry i am running outta time
Answer:see below
Step-by-step explanation:
10.600
11.80000
12.17
13.48
14.4000
21. 1km=100m;0.5km=500m;0.1km=100m
22.50m=5000cm; 5m=500cm; 0.5m=50cm
how do i solve this trigonometry question?
Answer:
2.07 cm
Step-by-step explanation:
Hypotenuse = 2 cm
Adjacent side = a
Formula
cos θ = Hypotenuse/Adjacent side
cos 15 = 2/a
Note
The value of cos 15 is approximately 0.965.
0.965 = 2/a
a = 2/0.965
a = 2.07 cm ( approximately )
5. say we measure 20 coyotes. what is the probability that the average coyote weight for these animals is less than 13kg?
The probability that the average coyote weight for a sample of 20 coyotes is less than 13 kg is approximately 13.14%.
we need to know the mean and standard deviation of the coyote weight population. Let's assume that the population mean is μ = 13.5 kg and the population standard deviation is σ = 2 kg.
Since we are measuring a sample of 20 coyotes, we can use the central limit theorem to approximate the distribution of sample means. According to the central limit theorem, if the sample size is large enough (in general, if n > 30), then the distribution of sample means will be approximately normal, regardless of the distribution of the population.
The mean of the sample means will be equal to the population mean (μ) and the standard deviation of the sample means (also known as the standard error) will be equal to σ / √(n), where √(n) is the square root of sample size.
Using this information, we can calculate the z-score for a sample mean of 13 kg as follows;
z = (13 - 13.5) / (2 / √(20)) = -1.118
Next, we can use a standard normal distribution table (or a calculator or software that can calculate normal probabilities) to find the probability that a z-score is less than -1.118. The area to the left of this z-score is approximately 0.1314, or 13.14%.
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I NEED HELP ON THIS ASAP!
The exponential function that models the situation in this problem is defined as follows:
y = 3(4)^x.
How to define an exponential function?The standard definition of an exponential function is given as follows:
y = ab^x.
In which:
a is the initial value.b is the rate of change.Three friends start the project, hence the initial value represented by the parameter a is given as follows:
a = 3.
Each day, the number of people in the project is multiplied by four, hence the parameter b is given as follows:
b = 4.
Hence the function is:
y = 3(4)^x.
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c. what is the probability that the duration of a rainfall event at this location is between 2 and 3 hours? d. what is the probability that a rainfall duration exceeds the mean value by more than 2 standard deviations?
The probability that a rainfall event exceeds the mean by more than 2 standard deviations is approximately 0.0498.
a. The exponential distribution with a mean of 2.725 hours can be expressed as λ = 1/2.725. Using this parameter, we can calculate the probabilities as follows:
P(X ≥ 2) = [tex]e^{(-λ2) }= e^{(-1/2.7252)[/tex] ≈ 0.4800
P(X ≤ 3) = 1 - [tex]e^{(-λ3)} = 1 - e^{(-1/2.7253)[/tex] ≈ 0.6674
P(2 ≤ X ≤ 3) = [tex]e^{(-λ2)} - e^{(-λ3)} = e^{(-1/2.7252)} - e^{(-1/2.7253)}[/tex] ≈ 0.1474
b. The standard deviation of an exponential distribution is equal to the mean, so 2 standard deviations above the mean would be 2*2.725 = 5.45 hours. The probability that a rainfall event exceeds this duration can be calculated as follows:
P(X > 5.45) =[tex]e^{(-λ5.45)} = e^{(-1/2.7255.45)}[/tex] ≈ 0.0498
Therefore, the probability that a rainfall event exceeds the mean by more than 2 standard deviations is approximately 0.0498.
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Complete Question:
Suppose that rainfall duration follows an exponential distribution with mean value 2.725 hours.
a. What is the probability that the duration of a particular rainfall event is at least 2 hours? At most 3 hours? Between 2 and 3 hours? (.4800, .6674, .1474)
b. What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations? (.0498)
To celebrate the first day of school, Grace brought in a tray of caramel brownies and walnut brownies. She brought 80 brownies in all. 56 of the brownies were caramel. What percentage of the brownies were caramel?
Answer: 70% of the brownies are caramel.
Step-by-step explanation: First take 56/80 because 56 of the brownies were caramel out of the 80. Which divided that give you 0.7. Multiply then by 100 which will give you 70. So the answer is there are 70% caramel brownies.
help me please please
what is the expected ratio of two heads : heads/tails : tails/heads : two tails when two coins are repeatedly flipped? (this question is asking about probability, which is a prediction, rather than your actual observed results.)
When two coins are repeatedly flipped, the probability of getting two heads is 1/4, the probability of getting a head and a tail is 1/2, and the probability of getting two tails is also 1/4.
Therefore, the expected ratio of two heads : heads/tails : tails/heads : two tails is 1:2:2:1, respectively. This means that out of every six flips, we would expect to see one outcome of two heads, two outcomes of heads/tails and tails/heads each, and one outcome of two tails.
However, it is important to note that this is only a prediction and the actual results may differ due to chance.
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All help is appreciated thank you.
Using the fact that the triangles are similar we can see that the value of x is 36
How to find the value of x?We can see that the triangles are similar due to the same interior angles, then ther is a scale factor k between them.
So we can write:
20*k = 48
k = 48/20 = 2.4
Then:
x = 15*2.4
x = 36
That is the value of x.
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