Answer:
<abc
Step-by-step explanation:
Please simplify the following expression while performing the given operation.
(-3+1)+(-4-i)
Answer:
To simplify the expression (-3+1)+(-4-i), we can perform the addition operation within the parentheses first:
(-3+1)+(-4-i) = -2 + (-4-i)
Next, we can simplify the addition of -2 and -4 by adding their numerical values:
-2 + (-4-i) = -6 - i
Therefore, (-3+1)+(-4-i) simplifies to -6-i.
Step-by-step explanation:
You want to measure the height of an antenna on the top of a 125-foot building. From a point in front of the building, you measure the angle of elevation to the top of the building to be 68° and the angle of elevation to the top of the antenna to be 71°. How tall is the antenna, to the nearest tenth of a foot?
The antenna which is having an angle of elevation 71° from the front of the it is on is 19.67 feet tall to the nearest tenth of foot.
What is an angle of elevationThe angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.
To get the height of the antenna, we subtract the height of the building from the height from the bottom of the building to the top of the antenna.
we shall represent the distance from the point of observation to the building with x and the height from the bottom of the building to the top of the antenna with y. so that;
tan 68° = 125/x {opposite/adjacent}
x = 125/ tan 68° {cross multiplication}
x = 50.5033
tan 71° = y/50.5033
y = 50.5033 × tan 71°
y = 144.6722
height of the antenna = 144.6722 - 125
height of the antenna = 19.6722
Therefore, the antenna which is having an angle of elevation 71° from the front of the it is on is 19.67 feet tall to the nearest tenth of foot.
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Draw and label a rectangle with an area of 32 square units and a perimeter of 36 units
If the area of the rectangle is 32 square units and its perimeter is 36 units, then the length and width of the rectangle will be given as 16 units and 2 units respectively.
Area is defined as the measure of a specific region on ground which is enclosed by a closed polygon figure. The area of a rectangle is given as the product of its length (l) and its width (b) . Perimeter on the other hand is the sum of all four sides of a rectangle and is given by the formula as follows:
Perimeter of rectangle = 2 (length + width)
Now its is given that Area= length x width
32 = l*b ... 1
36 = 2(l+b) ... 2
Using equation 1, we get b = 32/l. Putting this value in equation 2, we get:
36 = 2 (32/l + l)
18 = 32/l + l
⇒ l^2 - 18l + 32 = 0
Solving this quadratic equation we get,
l = 16, 2
Thus the length and width of the rectangle will be equal to 16 units and 2 units respectively or vice versa.
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Refer to complete question below:
On a separate piece of paper, draw and label rectangle with an area of 32 sq. Unit and a perimeter of 36 units. Use numbers or words to show that you are correct.
g company xyz know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 17 years and a standard deviation of 1.7 years. find the probability that a randomly selected quartz time piece will have a replacement time less than 13.3 years?
The probability that a randomly selected quartz timepiece will have a replacement time less than 13.3 years is approximately 0.015 with a mean of 17 years and a standard deviation of 1.7 years.
What is Probability?To find the probability that a randomly selected quartz timepiece will have a replacement time of less than 13.3 years, we need to use the standard normal distribution formula which is as follows:
[tex]Z =\frac{X -μ }{σ}[/tex]
Where Z is the standard score
X is the variable value
μ is the mean
σ is the standard deviation
Given that the mean (μ) of the replacement times for the quartz timepieces is 17 years, the standard deviation (σ) is 1.7 years, and the variable value (X) we are looking for is 13.3 years.
Substitute the values into the standard normal distribution formula to get:
[tex]Z = \frac{13.3-17}{1.7} = -2.17[/tex]
Looking at the standard normal distribution table, we can find the probability of the standard score Z = -2.17 to be 0.015.
Therefore, the probability that a randomly selected quartz timepiece will have a replacement time less than 13.3 years is approximately 0.015.
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Ill give brainliest for the answer
Answer:
x = 20
Step-by-step explanation:
if a line is parallel to a side of a triangle and intersects the other two sides, it divides those sides proportionally.
QR is parallel to ST and intersects the other two sides of the triangle, then
[tex]\frac{PQ}{QS}[/tex] = [tex]\frac{PR}{RT}[/tex] ( substitute values )
[tex]\frac{x}{45-x}[/tex] = [tex]\frac{16}{30-16}[/tex]
[tex]\frac{x}{45-x}[/tex] = [tex]\frac{16}{20}[/tex] ( cross- multiply )
20x = 16(45 - x)
20x = 720 - 16x ( add 16x to both sides )
36x = 720 ( divide both sides by 36 )
x = 20
An amount of money is divided among A, B and C in the ratio 4: 7:9 A receives R500 less than C. Calculate the amount that is divided.
Answer:
We know that A receives R500 less than C, so we can write:
4x = 9x - 500
Solving for x, we get:
5x = 500
x = 100
Now we can calculate the amounts received by each person:
A = 4x = 4(100) = R400
B = 7x = 7(100) = R700
C = 9x = 9(100) = R900
To check our answer, we can verify that the ratios of the amounts received by A, B, and C are indeed 4:7:9:
A:B = 400:700 = 4:7
B:C = 700:900 = 7:9
Therefore, the total amount divided is:
400 + 700 + 900 = R2000
So the amount that is divided is R2000.
Step-by-step explanation:
The total amount of money divided is R2000.
What is the ratio?Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We are given that;
The ratio of A, B and C= 4:7:9
Now,
Let's start by assigning variables to the unknowns in the problem. Let's call the total amount of money "T". Then, if A receives 4x, B receives 7x, and C receives 9x, where "x" is some constant, we can write:
4x + 500 = C's share
We can also write an equation to represent the fact that the three shares add up to the total amount:
4x + 7x + 9x = T
Simplifying this equation, we get:
20x = T
Now we can substitute the first equation into the second equation and solve for x:
4x + 7x + (4x + 500) = 20x
15x + 500 = 20x
500 = 5x
x = 100
Now we can find the individual shares by multiplying x by the appropriate ratio factor:
A's share = 4x = 400
B's share = 7x = 700
C's share = 9x = 900
Finally, we can check that these add up to the total amount:
400 + 700 + 900 = 2000
Therefore, by the given ratio the answer will be R2000.
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I’m a bit stuck please help me out
On solving the question we can say that Therefore, the solutions to the inequality given inequality are: x < 4 or x > 6.
What is inequality?An inequality in mathematics is a relationship between two expressions or values that are not equal. Imbalance therefore leads to inequality. An inequality establishes a connection between two values that are not equal in mathematics. Equality is different from inequality. The inequality sign () is most commonly used when two values are not equal. Various inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be solved by changing both sides until only variables remain. But many things contribute to inequality.
two inequalities
4x - 6 < 10
4x < 16
x < 4
2x - 4 > 8
2x > 12
x > 6
Therefore, the solutions to the given inequality are:
x < 4 or x > 6.
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Your monthly take-home pay is $900. Your monthly credit card payments are about $135. What percent of your take-home pay is used for your credit card payments?
i came up with $765
Answer:15 percent
Step-by-step explanation:
5. There are 12 drinks in a pack. Sally Took 3/4 of these drinks for her party How many did she take?
Answer:
9
Step-by-step explanation:
To find the answer to this question, we have to find 3/4 of 12
To do this, we need to do 12 divide by 4, then that answer multiplied by 3...
12 ÷ 4 = 33 × 3 = 9This means that she took 9 drinks!
Hope this helps, have a lovely day! :)
Answer:
9
Step-by-step explanation:
[tex] multiply \: \\ = \frac{3}{4} \times 12[/tex]
[tex] = 9[/tex]
Therefore, sally took 9 drink for her party.
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2 reds and 18 blues
What is the ratio of red to blue squares in its simplest form?
Red Blue
Answer:
The ratio of red to blue squares in the given set of 2 reds and 18 blues can be written as:
Red:Blue = 2:18
To simplify the ratio, we can divide both the numerator and denominator by the greatest common factor (GCF) of 2 and 18, which is 2. Dividing both terms by 2, we get:
Red:Blue = 1:9
Therefore, the ratio of red to blue squares in its simplest form is 1:9.
Toastmasters International cites a report by Gallup Poll that 40% of Americans fear public speaking. A student believes that less than 40% of students at her school fear public speaking. She randomly surveys 361 schoolmates and finds that 137 report they fear public speaking. Conduct a hypothesis test at the 5% level to determine if the percent at her school is less than 40%. Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
-state the null hypothesis
-state the alternative hypothesis
- In words state what random variable P' represents
- State the distribution for the test: P'~
-what is the test statistics? z or t distribution
-What is the P value
- Explain what the P value means
- Sketch picture of the situation
- construct 95% construction interval for the true proportion
We can construct the 95% confidence interval for the true proportion. To do this, we need to calculate the margin of error, which is equal to the critical value (1.96) multiplied by the standard error (0.014). This equals 0.028.
The 95% confidence interval is then the sample proportion (0.38) plus or minus the margin of error (0.028). This is [tex](0.38 - 0.028, 0.38 + 0.028) = (0.352, 0.408).[/tex]
The test statistic in this case is the Z-statistic, as we are assuming that the underlying population is normally distributed. To conduct the hypothesis test, we must first state the null and alternative hypotheses.
Null Hypothesis (H0): The proportion of students at the school who fear public speaking is equal to or greater than 40%.
Alternative Hypothesis (H1): The proportion of students at the school who fear public speaking is less than 40%.
We must then calculate the test statistic, which is the Z-statistic in this case. To do this, we need to first calculate the sample proportion, which is the number of students who fear public speaking (137) divided by the total number of students surveyed (361). This equals 0.38. We then need to calculate the standard error of the sample proportion (SE), which is the square root of [tex](pq/n)[/tex], where p is the sample proportion (0.38) and q is the complement of the sample proportion (1-0.38 = 0.62). SE = [tex](0.38 x 0.62)/361 = 0.014.[/tex] The Z-statistic is then calculated as the difference between the sample proportion (0.38) and the population proportion (0.40) divided by the standard error [tex](0.014). Z = (0.38 – 0.40)/0.014 = -0.14.[/tex]
To conclude, we can use the Z-statistic and 95% confidence interval to test the hypothesis that the proportion of students at the school who fear public speaking is less than 40%. The Z-statistic of -0.14 falls within the critical region and the 95% confidence interval does not include 0.40, suggesting that the proportion of students at the school who fear public speaking is indeed less than 40%.
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Ty is a landscape architect. He needs to find the value of x in meters so that the sum of the areas of the patio, herb garden, and flower garden is 25% of the area of the entire rectangle. What in the area in square meters of the patio?
By using this value of x in the formula we previously discovered, we can get the patio's area Patio's size is equal to x2 + 4x + 4 = ((1 + 7)/3)2 + 4((1 + 7)/3) + 4 = 4.72 square meters.
What is a square's area?A square is a 2D shape with equal-sized sides on each side. The area would be length times width, which is equal to side side because all the sides are equal. As a result, a square's area is side square.
Let's first find the area of the entire rectangle:
A = lw = (3x + 6)(2x + 4) = 6x² + 30x + 24
Area of patio = (x + 2)² = x² + 4x + 4
Area of herb garden = (2x + 2)(x + 4) = 2x² + 10x + 8
Area of flower garden = (3x + 4)(x + 4) = 3x² + 16x + 16
Sum of areas = x² + 4x + 4 + 2x² + 10x + 8 + 3x² + 16x + 16
= 6x² + 30x + 28
0.25(6x² + 30x + 24) = 6x² + 30x + 28
Simplifying and solving for x, we get:
1.5x² - x - 1 = 0
Using the quadratic formula, we find that:
x = (1 ± √7)/3
x = (1 + √7)/3
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The area in square meters of the patio is 850 square meters.
What is a rectangle?
A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.
Let's start by calculating the total area of the rectangle:
Area of rectangle = length x width = 100m x 40m = 4000 square meters
Now, let's denote the width of the herb garden as x meters. Then, the length of the herb garden would be 10 meters.
The area of the herb garden would be:
Area of herb garden = length x width = 10m x x = 10x square meters
The area of the patio can be calculated as:
Area of patio = (100 - x) x (40 - 2x) square meters
(100 - x) is the length of the patio, and (40 - 2x) is the width of the patio, since the herb garden takes up x meters of the width.
The area of the flower garden can be calculated by subtracting the area of the rectangle, the herb garden, and the patio from each other:
Area of flower garden = 4000 - 10x - (100 - x) x (40 - 2x) square meters
Now, we need to find the value of x so that the sum of the areas of the patio, herb garden, and flower garden is 25% of the area of the entire rectangle. In other words:
Area of herb garden + Area of patio + Area of flower garden = 0.25 x Area of rectangle
10x + (100 - x) x (40 - 2x) + 4000 - 10x = 0.25 x 4000
Simplifying this equation, we get:
-2x^2 + 30x + 1000 = 1000
-2x^2 + 30x = 0
-2x(x - 15) = 0
Therefore, x = 0 or x = 15. Since x cannot be 0 (since the herb garden would have no width), the value of x must be 15 meters.
Now we can calculate the area of the patio:
Area of patio = (100 - x) x (40 - 2x) = (100 - 15) x (40 - 2(15)) = 850 square meters
Therefore, the area in square meters of the patio is 850 square meters.
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wind speeds, represented by random variable , in , have a lognormal distribution. in other words, is normal. if , and , what value of (the standard normal rv) is associated with a wind speed of ?
Wind speeds, represented by random variable X, have a lognormal distribution. The corresponding value of the standard normal random variable (Z) is associated with a wind speed of 14.35 is 25.5
Wind speeds represented by random variable X, in miles per hour, have a lognormal distribution. In other words, log(X) is normal.
If [tex]\mu = 4.8[/tex] and [tex]\sigma = 0.4[/tex], what value of Z (the standard normal rv) is associated with a wind speed of 15 miles per hour.
The value of Z (the standard normal rv) associated with a wind speed of 15 miles per hour.
The standard score (z) of a random variable X is calculated as follows:
[tex]z = \frac{(X - \mu)}{\sigma}[/tex]
Given: μ = 4.8, σ = 0.4
Let X be a wind speed 15 mph.
To find the standard normal rv Z associated with a wind speed of 15 miles per hour, we will use the formula for calculating the standard score (z):
[tex]z = (X - \mu) /\sigma \\z = (15 - 4.8) / 0.4\\z = 25.5[/tex]
Therefore, the value of Z (the standard normal rv) associated with a wind speed of 15 miles per hour is 25.5.
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Make a forecast for week 3, find the error for week 4, and make a final prediction for week 7.
Use the moving average method with k = 2
Rounding correctly will help ensure you get credit for this question. Please round to 2 decimal places.
Week Time Series Moving average Error 1 30 _____ _____
2 19 _____ 5.5
3 30 _____ -------- 4 16 24.5000 -----------
5 21 23.0000 -2.00
6 25 18.5000 6.5
7 Prediction -> _____ _____
The answers are 24.50, 8.50, 23.50 respectively.
Given that we are to forecast for week 3, find the error for week 4, and make a final prediction for week 7. We are to use the moving average method with k = 2.The calculation of the moving average is shown belowWeek Time Series Moving average Error 1 30 _____ _____ 2 19 _____ 5.5 3 30 24.50 -6.50 4 16 24.50 8.50 5 21 23.00 -2.00 6 25 18.50 6.50 7 Prediction -> 23.50 -2.50The forecast for week 3 is 24.50, error for week 4 is 8.50 and final prediction for week 7 is 23.50. Thus, the answers are 24.50, 8.50, 23.50 respectively.
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Please help and answer. Much appreciated
The correct answer is A. a-c+b-d=0. This is because when two sets of numbers are both negative, the result of subtracting the larger number from the smaller number will always be negative.
What is subtraction?Subtraction involves taking one number or value away from another. It is one of the four basic operations in mathematics, along with addition, multiplication, and division.
When subtracting a from c and b from d, the result of either subtraction will always be a negative number. When the two negative numbers are added together, the result will always be 0.
The other options are not always true. In option B, ac > bd, this is not always true because when a, b, c, and d are all negative, it is possible for the result of ac to be less than the result of bd. In option C, a+c>b+d, this is not always true because when both sets of numbers are negative, it is possible for the result of a+c to be less than b+d. Finally, in option D, a/d < b/c, this is not always true because when both sets of numbers are negative, it is possible for the result of a/d to be greater than b/c.
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The correct answer is A. a-c+b-d=0 because the expression is always true when a, b, c and d are all less than zero.
What is expression?Expression is a combination of symbols and operators that evaluate to a single value. It could be a mathematical equation, an arithmetic expression, a logical expression, or a combination of these.
This is because the expression is equivalent to (a-c)+(b-d)=0, which is always true when a, b, c and d are all less than zero.
This can be proven through a simple calculation.
Let us assume that the values of a, b, c and d are -1, -3, 8 and -4 respectively.
Substituting these values into the expression gives us
(-1-3)+(8-4)=0, which is clearly true.
Therefore, A. a-c+b-d=0 is the correct answer as the expression is always true when a, b, c and d are all less than zero.
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The random variable x is known to be uniformly distributed between 10 and 20. Show the graph of the probability density function: Compute P(x 15). Compute P(12 =x= 18). St Compute E(x). Compute Var(x).
Compute P(x ≤ 15) = (15-10)/(20-10) = 5/10 = 0.5.
Compute P(12 ≤ x ≤ 18) = (18-12)/(20-10) = 6/10 = 0.6.
Compute E(x): The expected value of x is: E(x) = (a+b)/2 = (10+20)/2 = 15
Compute Var(x):The variance of x is: Var(x) = (b - a)^2/12 = (20 - 10)^2/12 = 100/12 = 8.33.
The probability density function is as follows: As the random variable x is uniformly distributed between 10 and 20. Thus, f(x) = 1/(20-10) = 1/10 for 10 ≤ x ≤ 20.Compute P(x ≤ 15):Thus, P(x ≤ 15) = (15-10)/(20-10) = 5/10 = 0.5.Compute P(12 ≤ x ≤ 18):Thus, P(12 ≤ x ≤ 18) = (18-12)/(20-10) = 6/10 = 0.6.Compute E(x):The expected value of x is: E(x) = (a+b)/2 = (10+20)/2 = 15.Compute Var(x):The variance of x is: Var(x) = (b - a)^2/12 = (20 - 10)^2/12 = 100/12 = 8.33.
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Use the integration capabilities of a graphing utility to approximate to two decimal places the area of the surface formed by revolving the polar equation over the given interval about the polar axis. r = 7 cos(20), [0, Phi/4]
The approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis is 67.59 square units.
To solve the question, we can use the integration capabilities of a graphing utility to approximate to two decimal places the area of the surface formed by revolving the polar equation over the given interval about the polar axis. Polar curve is a type of curve that is made up of points that represent polar coordinates (r, θ) instead of Cartesian coordinates.
A polar curve can be represented in parametric form, but it is often more convenient to use the polar equation for a curve. According to the question, r = 7 cos(20), [0, Phi/4] is the polar equation and we need to find the approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis.
To solve the problem, follow these steps: Convert the polar equation to a rectangular equation. The polar equation r = 7 cos(20) is converted to a rectangular equation using the following formulas: x = r cos θ, y = r sin θx = 7 cos (20°) cos θ, y = 7 cos (20°) sin θx = 7 cos (θ - 20°) cos 20°, y = 7 cos (θ - 20°) sin 20°
Sketch the curve in the plane. We can sketch the curve of r = 7 cos(20) by plotting the points (r, θ) and then drawing the curve through these points. Use the polar equation to set up the integral for the volume of the solid of revolution.
The volume of the solid of revolution is given by the formula: V = ∫a b πf2(x) dx where f(x) = r, a = 0, and b = Φ/4.We can find the volume of the solid of revolution using the polar equation: r = 7 cos(20) => r2 = 49 cos2(20) => x2 + y2 = 49 cos2(20)Thus, f(x) = √(49 cos2(20) - x2) = 7 cos(20°) sin(θ - 20°)
So, V = ∫a b πf2(x) dx = ∫0 Φ/4 π(7 cos(20°) sin(θ - 20°))2 dθStep 4: Use a graphing utility to evaluate the integral to two decimal places. Using a graphing utility to evaluate the integral, we get V ≈ 67.59.
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What percent of light will pass through 10 panes?
Look at the simultaneous equations below.
(1) x-2y=10
(2) x-2=6y
a) Rearrange equation (2) to make x the subject.
b) Using your answer to part a), solve the simultaneous equations using substitution.
Answer:
a) To make x the subject of equation (2), we need to isolate x on one side of the equation. We can do this by adding 2 to both sides, and then dividing both sides by 6:
x - 2 = 6y
x = 6y + 2
b) We can now substitute the expression 6y + 2 for x in equation (1):
6y + 2 - 2y = 10
Simplifying the left-hand side, we get:
4y + 2 = 10
Subtracting 2 from both sides, we get:
4y = 8
Dividing both sides by 4, we get:
y = 2
Now we can substitute y = 2 back into either equation to find x. Let's use equation (2), since we have already rearranged it to make x the subject:
x = 6y + 2
x = 6(2) + 2
x = 14
Therefore, the solution to the simultaneous equations is x = 14 and y = 2.
Step-by-step explanation:
a business give 30% discount on everyting. If a radio costed 1610 Dollars how much did it cost before discount
Can someone help with the calculation of this.
Answer:
$2300
Step-by-step explanation:
$1610 is 7/10 the original cost. Multiplying by 10/7 reverses that, and we get the starting cost of $2300
Hope this helps!
In ΔKLM, l = 4.1 cm, m = 2.4 cm and ∠K=97°. Find the area of ΔKLM, to the nearest 10th of a square centimeter.
the area of the triangle KLM is 4.9 cm².
What is area?Area is the region bounded by a plane shape.
To calulate the area of the triangle, we use the formula below
Formula:
A = 1/2×absinCWhere:
A = Area of triangle ΔKLMa = Length of side lb = Lenth of side mC = Size of angle KFrom the question,
Given:
a = 4.1 cmb = 2.4 cmC = 97°Substitute these values into equation 1
A = 4.1×2.4×sin97°/2A = 4.9 cm²Hence, the area is 4.9 cm².
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a survey found that 10% of americans believe that they have seen a ufo. for a sample of 10 people, find each probability: a. that at least 2 people believe that they have seen a ufo b. that 2 or 3 people believe that they have seen a ufo c. that exactly 1 person believes that he or she has seen a ufo
The probability that at least 2 people believe that they have seen a ufo is 0.1937102445. The probability that exactly 1 person believes that he or she has seen a ufo is problem: P(X = 1) = 10C₁ (0.10) (0.90)⁹= 0.3874204890.
What is the probability?The probability that at least 2 people believe that they have seen a UFO would be 0.1937102445. For this we use the binomial distribution formula.
P(X ≥ 2) = 1 − P(X = 0) − P(X = 1)P(X = 0) = (9/10)¹⁰
P(X = 1) = 10C₁ (0.10) (0.90)⁹= 0.3874204890 (rounded to 10 decimal places)
P(X ≥ 2) = 1 − 0.3874204890 − 0.3486784401 = 0.1937102445 (rounded to 10 decimal places)
The probability that 2 or 3 people believe that they have seen a UFO would be 0.1937102445. Using the formula of binomial distribution again we can solve for the probability of this event.
P(2 ≤ X ≤ 3) = P(X = 2) + P(X = 3)P(X = 2) = 10C₂ (0.10)² (0.90)⁸= 0.1937102445 (rounded to 10 decimal places)
P(X = 3) = 10C₃ (0.10)³ (0.90)⁷= 0.0573956280 (rounded to 10 decimal places)
P(2 ≤ X ≤ 3) = 0.1937102445 + 0.0573956280 = 0.2511058725 (rounded to 10 decimal places)
The probability that exactly 1 person believes that he or she has seen a UFO would be 0.3874204890. Using the binomial distribution formula to solve this problem:
P(X = 1) = 10C₁ (0.10) (0.90)⁹= 0.3874204890 (rounded to 10 decimal places)
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D. On désire connaître la quantité de moulure dont on a besoin pour encadrer un tableau. Aire ou Périmètre
Answer:
Step-by-step explanation:
Perimeter
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Please help me and all my other questions imma fr fail 10th and I need help (Find the perimeter of a Regular Pentagon with consecutive vertices at (-3,4) and (2, 6)
Answer: 25
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
how is probability determined from a continuous distribution? why is this easy for the uniform distribution and not so easy for the normal distribution?
To determine the probability of a continuous distribution we use the integral to determine it and for the normal distribution the integral is not so simple, for that reason it is simpler to use range values from tables.
How is probability determined from a continuous distribution?Probability can be determined from a continuous distribution in the following way:To compute the probability of a given interval for a continuous random variable, the area under the curve over the interval is determined. Integrals are used to calculate this area under the curve, which can be done either numerically or analytically using probability density functions.
For some distributions, such as the uniform distribution, calculating the area under the curve is straightforward. However, for other distributions, such as the normal distribution, it can be more difficult to calculate the integral analytically.
Why is this easy for the uniform distribution and not so easy for the normal distribution?The normal distribution is a continuous probability distribution that is frequently used in statistics. It is defined by its probability density function, which is a bell-shaped curve with a mean and a standard deviation.
Calculating the area under the curve for the normal distribution requires the use of integrals. Integrals are difficult to solve analytically for the normal distribution because the probability density function is not simple. However, it is relatively simple to calculate the probability for a given range of values using standard statistical tables or computer software.
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Find the perimeter of each of the following
a] a square of side 4 cm
b] a rectangle of length 5 cm and breath 4 cm
c] a triangle with sides 11cm 7cm and 9 cm
a) The perimeter of square is 16 cm
b) The perimeter of rectangle is 18 cm
c) The perimeter of triangle is 27 cm
a) The perimeter of a square with side length 4 cm can be found by adding the length of all four sides. Since all sides of a square are equal, the perimeter is 4 times the length of a side. Therefore, the perimeter of a square of side 4 cm is:
Perimeter = 4 x 4 cm = 16 cm
b) The perimeter of a rectangle with length 5 cm and breadth 4 cm can be found by adding twice the length and twice the breadth of the rectangle. Therefore, the perimeter of a rectangle of length 5 cm and breadth 4 cm is:
Perimeter = 2 x (length + breadth)
Perimeter = 2 x (5 cm + 4 cm)
Perimeter = 2 x 9 cm
Perimeter = 18 cm
c) The perimeter of a triangle with sides 11 cm, 7 cm, and 9 cm can be found by adding the length of all three sides. Therefore, the perimeter of a triangle with sides 11 cm, 7 cm, and 9 cm is:
Perimeter = 11 cm + 7 cm + 9 cm
Perimeter = 27 cm
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Six friends play a carnival game in which a person throws darts at balloons. Each person throws the same number of darts and then records the portion of the balloons that pop. A piece of paper shows the portion of balloons that popped in a game of darts. The portions are, Whitney, 16 percent; Chen, start fraction 2 over 25 end fraction; Bjorn, 0. 06; Dustin, start fraction 1 over 50 end fraction; Philip, 0. 12; Maria, 0. 4. Find the mean, median, and MAD of the data. The mean is. The median is. The mean absolute deviation is
The mean, median, and mean absolute deviation MAD of the data are 15%, 10%, and 8%.
To find the mean, median, and mean absolute deviation (MAD) of the data, we need to first convert all the fractions to percentages:
Whitney: 16%
Chen: 8%
Bjorn: 6%
Dustin: 2%
Philip: 12%
Maria: 40%
a) Mean:
To find the mean, we add up all the percentages and divide by the total number of friends (6):
Mean = (16 + 8 + 6 + 2 + 12 + 40) / 6 = 15%
Therefore, the mean is 15%.
b) Median:
To find the median, we need to arrange the data in order from smallest to largest:
2%, 6%, 8%, 12%, 16%, 40%
Since there are six values, the median is the average of the two middle values: (8 + 12) / 2 = 10%
Therefore, the median is 10%.
c) Mean Absolute Deviation (MAD):
To find the MAD, we first need to find the absolute deviation of each value from the mean:
Whitney: |16 - 15| = 1%
Chen: |8 - 15| = 7%
Bjorn: |6 - 15| = 9%
Dustin: |2 - 15| = 13%
Philip: |12 - 15| = 3%
Maria: |40 - 15| = 25%
Next, we find the average of these absolute deviations:
MAD = (1 + 7 + 9 + 13 + 3 + 25) / 6 = 8%
Therefore, the mean absolute deviation is 8%.
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using the unit normal table, find the proportion under the standard normal curve that lies between the following values. (hint: draw a picture.) do not round your answer. (a) the mean and z
The standard normal distribution is a bell-shaped curve that has a mean of 0 and a standard deviation of 1.
What is standard deviations?Standard deviation is a measure of how spread out numbers are. It is a measure of the amount of variation or dispersion from the average. For a data set, it is calculated as the square root of the variance. It is calculated by taking the square root of the variance (the average of the squared differences from the mean). The standard deviation can tell you how much variation there is from the average (mean) value in a data set.
The unit normal table is a statistical tool used to calculate probabilities related to the standard normal distribution. The standard normal distribution is a bell-shaped curve that has a mean of 0 and a standard deviation of 1. This table provides the probability of a given score falling within a certain range of the mean of the normal distribution.
For example, in part (a) the question is asking for the proportion between the mean and z = 1.96. Using the unit normal table, we can find this proportion to be 0.975. This means that 97.5% of the scores fall between the mean and z = 1.96.
In part (b), the question is asking for the proportion between the mean and z = 0. Since z = 0 is the mean, this proportion is 0.500, meaning that 50% of the scores fall between the mean and z = 0.
In part (c), the question is asking for the proportion between z = −1.90 and z = 1.90. This proportion can be found in the unit normal table to be 0.954. This means that 95.4% of the scores fall between z = −1.90 and z = 1.90.
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Complete questions as follows-
Using the unit normal table, find the proportion under the standard normal curve that lies between the following values. (Round your answers to four decimal places.)
(a) the mean and
z = 1.96
1
(b) the mean and
z = 0
2
(c)
z = −1.90 and z = 1.90
3
(d)
z = −0.40 and z = −0.30
4
(e)
z = 1.00 and z = 2.00
5
In Problems 47 through 56, use the method of variation of parameters to find a particular solution of the given differential equation. 47.y′′+3y′+2y=4ex48.y′′−2y′−8y=3e−2x
Eventually, the differential equation's general solution is:
y = y_h + y_p
y = c1e^(-2x) + c2e^(-x) - (1/6)e^(-x) + (2/3)
What is homogeneous solution?In the context of differential equations, the homogeneous solution of a differential equation is a solution that satisfies the equation when the right-hand side is equal to zero.
According to question:To find the particular solution of y'' + 3y' + 2y = 4e^x using the variation of parameters method, we first find the homogeneous solution of the differential equation by setting the right-hand side to zero:
y'' + 3y' + 2y = 0
The characteristic equation is r^2 + 3r + 2 = 0, which factors as (r + 2)(r + 1) = 0. Therefore, the solutions are y_h = c1e^(-2x) + c2e^(-x), where c1 and c2 are constants.
Next, we find the Wronskian of the homogeneous solution:
W(y1, y2) = |e^(-2x) e^(-x) | = e^(-3x)
To find the particular solution, we assume that it has the form y_p = u1(x)e^(-2x) + u2(x)e^(-x), where u1(x) and u2(x) are unknown functions to be determined.
We then find y_p' and y_p'':
[tex]y_p' = u1'(x)e^(-2x) + u2'(x)e^(-x) - 2u1(x)e^(-2x) - u2(x)e^(-x)y_p'' = u1''(x)e^(-2x) + u2''(x)e^(-x) - 4u1'(x)e^(-2x) - 2u2'(x)e^(-x) + 4u1(x)e^(-2x) + u2(x)e^(-x)u1''(x)e^(-2x) + u2''(x)e^(-x) + u1'(x)e^(-2x) + u2'(x)e^(-x) - 4u1'(x)e^(-2x) - 2u2'(x)e^(-x) + 4u1(x)e^(-2x) + u2(x)e^(-x) = 4e^x[/tex]
Simplifying and grouping terms, we get:
[tex]u1''(x)e^(-2x) - 3u1'(x)e^(-2x) + u2''(x)e^(-x) - u2'(x)e^(-x) = 4e^x[/tex]
To solve for u1(x) and u2(x), we use the method of undetermined coefficients and assume that they are both linear combinations of the exponential function and its derivative:
u1(x) = A(x)e^x
u2(x) = B(x)e^(2x)
Substituting these expressions into the previous equation and solving for A(x) and B(x), we get:
A(x) = -e^x/6
B(x) = 2e^x/3
Therefore, the particular solution is:
[tex]y_p = (-e^x/6)e^(-2x) + (2e^x/3)e^(-x)y_p = (-1/6)e^(-x) + (2/3)[/tex]
Eventually, the differential equation's general solution is:
y = y_h + y_p
y = c1e^(-2x) + c2e^(-x) - (1/6)e^(-x) + (2/3)
Therefore, the particular solution of the given differential equation y′′+3y′+2y=4ex is
[tex]y(x)=c_1e^{-x} + c_2e^{-2x} - 4 + 2e^{x}.[/tex]
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