Suppose that X has a lognormal distribution with parameters θ = 10 and ω2 = 16. Determine the following: (a) P(X 1500) (c) Value exceeded with probability 0.7.
Answers
the value exceeded with probability 0.7.
Given that X has a lognormal distribution with parameters θ = 10 and ω² = 16.Now, we have to determine the following:(a) P(X > 1500)(c) Value exceeded with probability 0.7.Solution:For the lognormal distribution, we have,X ~ logN(θ, ω²)Now, taking the logarithm of both sides, we have,log(X) ~ N(θ, ω²)So, we have log(X) ~ N(10, 4)Now, for normal distribution, we have, P(X > a) = 1 - P(X < a)Now, let Z = (X - θ)/ωThen, Z ~ N(0, 1)So, P(X > 1500) = P(Z > (log(1500) - 10)/2)P(Z > (log(1500) - 10)/2) = P(Z > (log(15) + 1)/2)Now, the value of P(Z > 1.407) is 0.0808 (rounded off up to four decimal places) from the standard normal distribution table.Hence, P(X > 1500) = P(Z > 1.407) = 0.0808. Therefore, P(X > 1500) = 0.0808.The value exceeded with probability 0.7 is given by the 0.7-quantile of the lognormal distribution which can be calculated as follows:z = qnorm(0.7) = 0.5244The 0.7-quantile of the normal distribution is (θ + ωz) = (10 + 4(0.5244)) = 12.0976.Now, since X is log-normally distributed, e^(12.0976) = 17567.75 is the value exceeded with probability 0.7.
To know more about,distribution, visit
https://brainly.com/question/29664127
#SPJ11
According to given information, P(X < 1500) ≈ 0.9996 and the value exceeded with probability 0.7 is about 179152.9.
X has a lognormal distribution with parameters θ = 10 and ω2 = 16.
(a) P(X < 1500)
To find the probability that X is less than 1500 we need to find the cumulative distribution function (CDF) first.
Cumulative distribution function is given as:
CDF of X = F(X)
= P(X ≤ x)
= Φ [(ln(x) - θ) / ω]
Here, θ = 10 and ω = √16 = 4.
Then, \(F(X) = P(X ≤ x) = Φ [(ln(x) - 10) / 4]\)
To find P(X < 1500), substitute x = 1500 in the above equation:
\(F(X) = Φ [(ln(1500) - 10) / 4] ≈ 0.9996\)
\(P(X < 1500) = F(X) ≈ 0.9996\)
So, \(P(X < 1500) ≈ 0.9996\).
(c) Value exceeded with probability 0.7.
To find the value exceeded with probability 0.7, we need to use the inverse of the CDF of X.
In other words, we need to find the value of x such that F(X) = P(X ≤ x) = 0.7.
To find the required value, we need to use the inverse function of the standard normal distribution, denoted as Zα, where α is the area under the standard normal curve to the left of Zα.
That is: Zα = Φ-1 (α)
From the given information, we can see that:
CDF of X = F(X) = Φ [(ln(x) - θ) / ω]
Here, θ = 10 and ω = √16 = 4.
So, \(F(X) = Φ [(ln(x) - 10) / 4]\)
\(F(X) = P(X ≤ x) = 0.7\)
Now, we want to find the value x such that \(F(X) = P(X ≤ x) = 0.7\).
That is, \(Φ [(ln(x) - 10) / 4] = 0.7\)
This means,\([(ln(x) - 10) / 4] = Φ-1 (0.7) = 0.5244\)
On solving this equation, we get:
\(ln(x) = 0.5244 x 4 + 10 ≈ 12.0976\)
\(x ≈ e12.0976 ≈ 179152.9\) (rounded to the nearest tenth)
So, the value exceeded with probability 0.7 is about 179152.9.
To know more about probability, visit:
https://brainly.com/question/31828911
#SPJ11
Related Questions
Write expressions that the cash register can use to determine the tax and the total for any item
Answers
The cash register can use the following expressions to determine the tax and total for any item
tax = p × t
total = p + tax
To determine the tax and total for any item, the cash register needs to know the item price and the tax rate.
Let's use "p" to represent the item price and "t" to represent the tax rate (as a decimal).
The expression for calculating the tax on an item would be:
tax = p × t
The expression for calculating the total cost of an item, including tax, would be:
total = p + tax
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ1
please help me !!!! trigonometric ratios !!!
Answers
Answer:
Step-by-step explanation:
If the questions is "What's x" then the answers is...
Use SOH CAH TOA to recall how the trig functions fit on a triangle
SOH: Sin(Ф)= Opp / Hyp
CAH: Cos(Ф)= Adj / Hyp
TOA: Tan(Ф) = Opp / Adj
use CAH
Cos(x) = 46/60
x = arcCos(46/60)
x = 39.9445 °
Answer:
\(\displaystyle 40°\)
Step-by-step explanation:
\(\displaystyle sec^{-1}\:1\frac{7}{23} = x; 39,94450519...° \\ \\ \boxed{40° \approx x}\)
OR
\(\displaystyle cos^{-1}\:\frac{23}{30} = x; 39,94450519...° \\ \\ \boxed{40° \approx x}\)
I am joyous to assist you at any time.
to determine the relative effectiveness of different study strategies for the sat, suppose three groups of students are randomly selected: one group took the sat without any prior studying; the second group took the sat after studying on their own from a common study booklet available in the bookstore; and the third group took the sat after completing a paid summer study session from a private test-prep company. the means and standard deviations of the resulting sat scores from this hypothetical study are summarized below: since we are comparing more than 2 groups, we will use anova to test whether the data provide evidence that sat score is related to study strategy. one of the conditions that allows us to use anova safely is that of equal (population) standard deviations. can we assume that this condition is met in this case?
Answers
We have to make a suspicion based on the given data. The standard deviations of the three bunches are not given within the address, so we cannot straightforwardly decide whether the condition of equal standard deviations is met. Be that as it may, ready to make a few taught surmises based on what we know almost each gather.
The primary gather, which did not think about, is likely to have a bigger change in scores than the other two bunches since understudies with shifting levels of arrangement and capacity took the test. Subsequently, we might anticipate the standard deviation of this group to be bigger than that of the other two bunches.
It is conceivable that the condition of rise to standard deviations isn't met. In case the condition of equal standard deviations isn't met, we may require to utilize an altered adaptation of ANOVA, such as Welch's ANOVA, which does not expect a rise in changes.
To learn about standard deviations visit:
https://brainly.com/question/13905583
#SPJ4
Nancy recorded eight movies on her DVR she watched five of the movies what percent of the movies did Nancy watch
Answers
Answer: Nany watched 62.5% of the movies
Step-by-step explanation:
5/8 as a percentage is 62.5%
Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week?
True or false?
Answers
The given statement "Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week" is true.
As given in the question,
If one amount is proportional to another, the two amounts increase and decrease at the same rate so there is always the same relationship between them
a:b = c:d
a ÷b = c ÷d
ad = bc
let Sal earns $480 per week and he works 40hours per week
480÷40 = 12
Lidia earn $300 per week and she works 25 hours per week
300÷25 = 12
Cross product of their salaries is
480×25=1200
300×40=1200
The ratio of their salaries and their product are equal.
Hence, The given statement "Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week" is true
Learn more about the proportional here:
brainly.com/question/8598338
#SPJ1
A company expects that the number N(x) of a product sold during a week is related to the amount spent on advertising by the function N(x)=-6x3+180x²+2250x + 13,000, where x (with 0 ≤x≤25) is the amount spent on advertising in thousands of dollars. What is the point of diminishing returns?
The point of diminishing returns is
(Simplify your answer. Type an ordered pair. Do not use commas in the individual coordinates.)
Answers
The point of diminishing returns is (20.98, 21247.3).
The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.
Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.
The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:
0 = -18x² + 360x + 2250
Dividing by -18 simplifies the equation:
0 = x² - 20x - 125
Using the quadratic formula, we find the solutions to the equation:
x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)
x₁,₂ = 10 ± 5√5
Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.
To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:
N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8
N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8
From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.
To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).
Hence, the point of diminishing returns is approximately (20.98, 21247.3).
Learn more about diminishing returns
https://brainly.com/question/30766008
#SPJ11
I lost my notes for these and I am not good at remembering
Answers
Answer: 1, 4, and 5 are 125
2, 3, 6, 7 are 55
Step-by-step explanation:
1 and 8 are congruent by opposite exterior angles and I forgot how to explain 4 and 5 but you know 7 is 55 because a straight line is 180 degrees so is you subtract 125 (8) you get 55 (7)
A basketball player makes 95 out of 140 free throws. We should estimate the probability that the player makes the next free throw to be
Answers
Since the player makes 95 out of 140 free throws, the probability that he makes the next free throw is:
\(\frac{95}{140}\approx0.6786.\)Answer: 67.86%
propon
a. A recipe for 3 cups of snack mix calls for cup of pretzels. You can describe this
as 3 cups of snack mix for every cup of pretzels and as į cup of pretzels for every
3 cups of snack mix. Why?
Answers
Answer:
They are shown together to find units of 4 total
4 (j/ total + s/total )
= 4 (1/4 + 3/4)
= 4/4 + 12/4
= 4 cups total
Then show letters and work out for j + s
4(j/3 + 3/4) = 4
4j/3 + 12/4 = 4
4j/3 + 3 = 4
4j/3 = 4-3
4j/3= 1
j = 1/3 s = 3/4 * 4 = 3
You would rearrange 4 within the brackets to find total
3 (1/3 + 4t) = 4
1 + 12t = 4
12t = 4-1
12t = 3
t = 12/3 of the total
t = 4
Do the integral from (-2,2) of the function by Trapezoidal Rule
in Matlab.
1/((25+x^2))^3/2
Answers
Here's how you can use the Trapezoidal Rule to approximate the integral of the function \(f(x) = \frac{1}{{(25+x^2)}^{\frac{3}{2}}}\) from -2 to 2 in MATLAB:
```matlab
a = -2; % Lower limit
b = 2; % Upper limit
n = 1000; % Number of subintervals (increase for higher accuracy)
h = (b - a) / n; % Step size
x = a:h:b; % Generate evenly spaced x values
y = 1 ./ (25 + x.^2).^1.5; % Evaluate the function at x
approximation = h * (sum(y) - (y(1) + y(end)) / 2); % Trapezoidal Rule approximation
fprintf('Approximation: %.6f\n', approximation);
```
1. We define the lower limit `a` as -2, the upper limit `b` as 2, and the number of subintervals `n` as 1000 (you can adjust `n` for higher accuracy).
2. We calculate the step size `h` by dividing the range (`b - a`) by the number of subintervals (`n`).
3. We generate an array `x` of evenly spaced values from `a` to `b` using the step size `h`.
4. We evaluate the function `f(x)` at each point in `x` and store the results in the array `y`.
5. Finally, we use the Trapezoidal Rule formula to approximate the integral by summing the values in `y` and adjusting for the endpoints, multiplying by the step size `h`.
The Trapezoidal Rule approximation for the integral of the function \(f(x) = \frac{1}{{(25+x^2)}^{\frac{3}{2}}}\) from -2 to 2 is the value calculated using the MATLAB code above.
To know more about Trapezoidal Rule follow the link:
https://brainly.com/question/28592530
#SPJ11
express x and y in terms of trigonometric ratios of θ. (express your answer in terms of θ only.)
Answers
To express x and y in terms of trigonometric ratios of θ, we need to use the definitions of sine, cosine, and tangent ratios.
Let's assume that θ is an acute angle in a right triangle with hypotenuse of length 1. Then, we have:
sin θ = opposite/hypotenuse = y/1 = y
cos θ = adjacent/hypotenuse = x/1 = x
tan θ = opposite/adjacent = y/x
Therefore, we can express x and y in terms of trigonometric ratios of θ as follows:
x = cos θ
y = sin θ
Alternatively, if we are given the value of one trigonometric ratio and we need to find the others, we can use the Pythagorean identity:
sin^2 θ + cos^2 θ = 1
From this, we can derive:
cos^2 θ = 1 - sin^2 θ
sin^2 θ = 1 - cos^2 θ
And then use the definitions of tangent and cotangent ratios:
tan θ = sin θ/cos θ
cot θ = cos θ/sin θ = 1/tan θ
Hope this helps!
To express x and y in terms of trigonometric ratios of θ, we will use the basic trigonometric ratios: sine (sin), cosine (cos), and tangent (tan). In a right-angled triangle, we have:
1. sin(θ) = opposite side / hypotenuse
2. cos(θ) = adjacent side / hypotenuse
3. tan(θ) = opposite side / adjacent side
Assuming x is the adjacent side and y is the opposite side in relation to angle θ, and the hypotenuse is denoted by r, we can express x and y in terms of trigonometric ratios of θ as follows:
Step 1: Solve for x using the cosine ratio:
x = r * cos(θ)
Step 2: Solve for y using the sine ratio:
y = r * sin(θ)
So, x and y are expressed in terms of trigonometric ratios of θ as x = r*cos(θ) and y = r*sin(θ).
Learn more about trigonometric ratio here: brainly.in/question/54099968
#SPJ11
After a shift in the aggregate demand curve, which variable adjusts to restore general equilibrium? A.real interest rate B.investment spending C.consumption spending D.price level
Answers
In order to restore general equilibrium, price adjustments are undertaken. In the short run, prices increase, and when expectations rise above actual inflation, prices continue to climb until they do. answer is option (d). price level.
What is aggregate demand?The term "aggregate demand" in macroeconomics refers to the overall demand for locally produced commodities, including capital goods, consumer products, and services. Aggregate demand is calculated as the total of spending by consumers, corporate and governmental investment spending, and net imports and exports.
The overall demand of final products and services in an economy at any particular time is known as aggregate demand, often referred to as domestic final demand. Effective demand is a frequent word for it, however occasionally this phrase is used to distinguish between two things. This is the demand for a nation's gross domestic product.
To know more about time, visit:
https://brainly.com/question/26862717
#SPJ1
Define and distinguish among positive correlation, negative correlation, and no correlation. How do we determine the strength of a correlation?
Define positive correlation. Choose the correct answer below.
A. Positive correlation means that both variables tend to increase (or decrease) together.
B. Positive correlation means that there is a good relationship between the two variables.
C. Positive correlation means that two variables tend to change in opposite directions, with one increasing while the other decreases.
D. Positive correlation means that there is no apparent relationship between the two variables.
Define negative correlation. Choose the correct answer below.
A. Negative correlation means that there is no apparent relationship between the two variables.
B. Negative correlation means that two variables tend to change in opposite directions, with one increasing while the other decreases.
C. Negative correlation means that there is a bad relationship between the two variables.
D. Negative correlation means that both variables tend to increase (or decrease) together.
Define no correlation. Choose the correct answer below.
A. No correlation means that there is no apparent relationship between the two variables.
B. No correlation means that the two variables are always zero.
C. No correlation means that both variables tend to increase (or decrease) together.
D. No correlation means that two variables tend to change in opposite directions, with one increasing while the other decreases.
Answers
To determine the strength of a correlation, we can use a statistical measure called the correlation coefficient. This value ranges from -1 to 1, where -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 indicates no correlation.
The closer the coefficient is to -1 or 1, the stronger the correlation, while values near 0 indicate a weak or no correlation. Positive correlation, negative correlation, and no correlation are types of relationships between two variables.
Positive correlation (A) means that both variables tend to increase (or decrease) together. When one variable increases, the other also increases, and when one decreases, the other also decreases.
Negative correlation (B) means that two variables tend to change in opposite directions, with one increasing while the other decreases. When one variable increases, the other tends to decrease, and vice versa.
No correlation (A) means that there is no apparent relationship between the two variables. The changes in one variable do not seem to consistently affect the changes in the other variable.
To know more about strength of a correlation visit:
https://brainly.com/question/30777155
#SPJ11
Can i pass 7th grade with 3 Fs?
Answers
Answer:
Depends on the state you’re from
Step-by-step explanation:
Answer:
Yes you can! Grades from middle school don't matter when you get to high school. But try to get those grades up!
Will mark brainly
ASAP
Answers
Solve the inequality. 6(b – 4) > 30 b > 34 b > 5 b 9
Answers
Answer:
b > 9
Step-by-step explanation:
6(b – 4) > 30
Divide each side by 6
6/6(b – 4) > 30/6
b-4 > 5
Add 4 to each side
b-4+4 > 5+4
b > 9
Answer:
\(\boxed{b > 9}\)
Step-by-step explanation:
\(6(b-4) > 30\)
Resolving Parenthesis
6b - 24 > 30
Adding 24 to both sides
6b > 30+24
6b > 54
Dividing both sides by 6
b > 9
Richard and Teo have a combined age of 39. Richard is 6 years older than twice Teo's age. How old are Richard and Teo?
Answers
Answer:
Teo is 11 years old
Richard is 28 years old
Step-by-step explanation
t=teo
Richard=2t+6
2t+6+t=39
3t=33
t=11
2*11+6=28
Answer: Richard is 28 and Theo is 11
Step-by-step explanation:
Because if theo was 11, 11 x 2 = 22 and since richard is 6 years older than double theos age, 22 + 6 = 28, so the combination of theos and richards age is 11+28 =39
at what points does the curve r(t) = ti (3t − t2)k intersect the paraboloid z = x2 y2? (if an answer does not exist, enter dne.)
Answers
To determine the points of intersection between the curve and the paraboloid, we need to find the values of t that satisfy the equations of both curves.
The curve is defined as r(t) = ti (3t - \(t^2\))k, and the paraboloid is defined as z = \(x^2\) \(y^2\). We can substitute the components of the curve into the equation of the paraboloid to find the points of intersection.
Substituting the values of x, y, and z from the curve into the equation of the paraboloid, we get \((ti)^2\)(3t - \(t^2\))\(^2\) = \((ti)^2\) (3\(t^2\) - 2\(t^3\)). Simplifying the equation, we have \((ti)^2\)(3t - \(t^2\) - 3\(t^2\) + 2\(t^3\)) = 0.
To find the values of t that satisfy this equation, we can set each term equal to zero. Thus, we have three possibilities: ti = 0, 3t -\(t^2\) = 0, and 3\(t^2\) - 2\(t^3\) = 0.
Solving these equations, we find that ti = 0 gives t = 0, 3t - \(t^2\) = 0 gives t = 0 or t = 3, and 3\(t^2\) - 2\(t^3\) = 0 gives t = 0 or t = 1/2. Therefore, the points of intersection between the curve and the paraboloid are (0, 0, 0), (0, 0, 0), (3, 3, 27), and (1/2, 1/2, 1/16).
Learn more about intersection here:
https://brainly.com/question/12089275
#SPJ11
PLEASE HELP WILL MARK BRAINLIEST
Answers
8 > 7- yes
7 = 7- no
12 > 7- yes
2 < 7- no
On a coordinate plane, a straight line with a positive slope begins at point (0, 50) and ends at point (5.5, 600).
Which scenario is most likely the one shown on the graph?
1.) the total amount of money in the cash register, y, containing $50 in change and small bills and x $100 bills
2.) the total number of puzzle pieces, y, in a brand new 50-piece puzzle, and x brand-new 100-piece puzzles
3.)the total weight of the barbell, y, where the bar weighs 50 pounds and x 100-pound weights are added to it
4.) the total number of calories, y, in a salad with vegetables containing 50 calories topped with x ounces of salad dressing at 100 calories per ounce
Answers
Answer:
The total number of calories, y, in a salad with vegetables containing 50 calories topped with x ounces of salad dressing at 100 calories per ounce.
Step-by-step explanation:
Answer:
D.
Step-by-step explanation:
Simplify to create an equivalent expression.
2 – 4(5p + 1)
Answers
Answer:
A. -20p - 2
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define
2 - 4(5p + 1)
Step 2: Simplify
Distribute -4: 2 - 20p - 4Combine like terms: -20p - 2Answer:
Step-by-step explanation:
Apply the distributive property
2-20p-4
Simplify expression
-20p-2
Answer choice A is correct
Amanda’s dog eats 12 1/2 pounds of dog food in 3 weeks. How much does Amanda's dog eat each day? Leave your answer as a fraction.
Answers
Work:
1. change the mixed number 12 1/2 to a fraction — 25/2
2. We can put 3 as a fraction by placing a 1 under it.
3. Now the equation looks like:
25/2 divided by 3/1
4. Remember when you divide fractions you change the sign to multiplication and flip your second term.
5. The equation now looks like:
25/2 x 1/3
6. Multiple across to get 25/6
7. The answer is 25/6 or you can write it as a mixed number 4 1/6
Seth bought a 15 ounce jar of peanut butter for $3.15. what is the unit price?
Answers
you can round that to 26 cents :) hope that helps!
The sampling distribution of differences between means approximates a normal curve whose _____is zero.
Answers
The sampling distribution of difference between means approximates a normal curve whose mean is zero.
The sampling distribution means the probability distribution based on the large number of samples of size n from the given population
Mean is the average of the given numbers and it is calculated by dividing the sum of observation by the number of observation. Here the term observation represents the given data.
Here they used the normal curve, sot its mean value is zero
To learn more about Sampling distribution here
https://brainly.com/question/13068170
#SPJ4
i truly need help with this
Answers
Write each number as a percent. 0.3056
Answers
To write the number 0.3056 as a percent, we multiply it by 100 and add the "%" symbol. 0.3056 * 100 = 30.56
To convert a decimal number to a percent, you multiply it by 100 and add the "%" symbol. Here's an explanation of the process:
Start with the decimal number: 0.3056
Multiply the decimal number by 100:
0.3056 * 100 = 30.56
Multiplying by 100 shifts the decimal point two places to the right, effectively converting the decimal into a whole number.
Add the "%" symbol:
30.56%
The "%" symbol represents "per hundred" or "out of 100" in percentage terms. By adding this symbol, we indicate that the number is being expressed as a proportion of 100.
So, when we write the decimal number 0.3056 as a percent, we get 30.56%. It means that 0.3056 is equivalent to 30.56 out of 100 or 30.56%.
Learn more about number from
https://brainly.com/question/27894163
#SPJ11
Write an equation, in slope/intercept form, for this graph. No spaces and
lower case letters only. Example: y=4x-8.
Answers
Answer:
y=3x-2
Step-by-step explanation:
y=mx+b
Slope = m = 3
b = y-intercept = -2
y=3x-2
Answer:
its is this
\(3x - 2\)
A sphere is inscribed in a cube, and the cube has a surface area of 24 square meters. A second cube is then inscribed within the sphere. What is the surface area in square meters of the inner cube
Answers
Check the picture below, I'll be referring to the material in the picture.
we know the outer cube has a surface area of 24, we also know is a cube, so it has 6 equal sides which are squares each, let's say the side of one of those squares in the cube is say of length "s", so the area of one square will just be s², and for 6 squares that'll be an area of 6s², that is the area of the outer cube, which we know is 24.
\(24=6s^2\implies \cfrac{24}{6}=s\implies 4=s^2\implies \sqrt{4}=s\implies 2=s\)
now, we know the sphere is inscribed in the outer cube, so it's touching its edges, like you see in the picture in blue, so if we get a cross-section of the whole lot, we'd get the picture to the right of blue cube in the picture, an outer cube with a side of 2, and therefore an sphere with a diameter of 2, and thus a radius of 1, as you can see in the red triangle.
Let's notice that the red triangle is a 45-45-90 triangle, and thus we can use the 45-45-90 rule to get its sides, as you can see in the picture on the far-right, which gives us half of one side of the inner cube to be 1/√2.
\(\stackrel{\textit{half a side}}{\cfrac{1}{\sqrt{2}}}\qquad \stackrel{\textit{a full side}}{\cfrac{1}{\sqrt{2}}+\cfrac{1}{\sqrt{2}}}\implies \cfrac{2}{\sqrt{2}}\implies \cfrac{2\sqrt{2}}{\sqrt{2}\sqrt{2}}\implies \cfrac{2\sqrt{2}}{2}\implies \sqrt{2}\)
now as you can see in the picture, the inner cube in orange, has 6 sides, each side is √2 long, so let's get the 6 squares area.
\(\stackrel{\textit{area of one square}}{\sqrt{2}\cdot \sqrt{2}\implies 2}\qquad \stackrel{\textit{area of all 6 sides of the inner cube}}{6\cdot 2\implies 12}\)
A ________ chart is a special type of scatter plot in which the data points in the scatter plot are connected with a line.
Answers
A line chart is a special type of scatter plot in which the data points in the scatter plot are connected with a line. A line chart is a graphical representation of data that is used to display information that changes over time. The line chart is also known as a line graph or a time-series graph. The data points are plotted on a grid where the x-axis represents time and the y-axis represents the value of the data.
The data points in the scatter plot are connected with a line to show the trend or pattern in the data. Line charts are commonly used to visualize data in business, economics, science, and engineering.Line charts are useful for displaying information that changes over time. They are particularly useful for tracking trends and changes in data. Line charts are often used to visualize stock prices,
sales figures, weather patterns, and other types of data that change over time. Line charts are also used to compare two or more sets of data. By plotting multiple lines on the same graph, you can easily compare the trends and patterns in the data.Overall, line charts are a useful tool for visualizing data and communicating information to others. They are easy to read, understand, and interpret, and can be used to display a wide range of data sets.
To know more about graphical visit:
https://brainly.com/question/14191900
#SPJ11
can anyone help me with this I tried to do it but i got to the wrong answer so i need help.
Answers
To use the quadratic formula, we need to identify the values of a, b, and c.
1. In this case, the equation is 4x² - 3x - 8 = 0, so a = 4, b = -3, and c = -8.
2. x = (-b ±√(b² - 4ac))/2a.
3. x = (3 ±√137)/8.
What is Quadratic Formula?The Quadratic Formula is a mathematical equation used to solve second-degree equations.
To use the quadratic formula, we need to identify the values of a, b, and c in the equation ax² + bx + c = 0.
In this case, the equation is
4x² - 3x - 8 = 0,
so a = 4, b = -3, and c = -8.
Once the values of a, b, and c are known, we can substitute them into the Quadratic Formula:
x = (-b ±√(b² - 4ac))/2a.
In this equation, a = 4, b = -3, and c = -8, so the equation becomes
x = (-(-3) ±√((-3)² - 4(4)(-8)))/2(4).
Simplifying, we get x = (3 ±√(9 + 128))/8.
Finally, solving for x yields x = (3 ±√137)/8.
Therefore, the solution to the equation is
x = (3 ±√137)/8.
For more questions related to equation
https://brainly.com/question/2228446
#SPJ1