Answer:
Part A: To determine the exact value of cos 2θ, we can use the double-angle identity for cosine:
cos 2θ = 2 cos^2 θ - 1
We already know sin θ, so we can use the Pythagorean identity to find cos θ:
cos^2 θ = 1 - sin^2 θ
cos^2 θ = 1 - (2√2/5)^2
cos^2 θ = 1 - 8/25
cos^2 θ = 17/25
cos θ = ± √(17/25)
cos θ = ± (1/5) √17
Since θ is in the third quadrant (π/2 < θ < π), cos θ is negative, so we take the negative root:
cos θ = -(1/5) √17
Substituting into the double-angle identity:
cos 2θ = 2 cos^2 θ - 1
cos 2θ = 2 [-(1/5) √17]^2 - 1
cos 2θ = 2 (1/25) (17) - 1
cos 2θ = 34/25 - 1
cos 2θ = 9/25
Therefore, the exact value of cos 2θ is 9/25.
Part B: To determine the exact value of sin (θ/2), we can use the half-angle identity for sine:
sin (θ/2) = ± √[(1 - cos θ)/2]
We already know cos θ, so we can substitute it in:
cos θ = -(1/5) √17
sin (θ/2) = ± √[(1 - cos θ)/2]
sin (θ/2) = ± √[(1 - (-1/5) √17)/2]
sin (θ/2) = ± √[(5 + √17)/10]
sin (θ/2) = ± (1/2) √(5 + √17)
Since θ is in the third quadrant (π/2 < θ < π), sin θ is negative, so we take the negative root:
sin (θ/2) = -(1/2) √(5 + √17)
Therefore, the exact value of sin (θ/2) is -(1/2) √(5 + √17).
The exact values of the sine and cosine given are -(1/2) √(5 + √17) and 9/25.
What is the sine and the cosine of an angle?The sine of an angle in a right triangle is the ratio of the hypotenuse to the side opposite the angle.
The cosine of an angle in a right triangle is the ratio of the hypotenuse to the side adjacent the angle.
Part A: To determine the exact value of cos 2θ, we can use the double-angle identity for cosine:
cos 2θ = 2 cos² θ - 1
Using the Pythagorean identity to find cos θ:
cos² θ = 1 - sin² θ
cos² θ = 1 - (2√2/5)²
cos² θ = 1 - 8/25
cos² θ = 17/25
cos θ = ± √(17/25)
cos θ = ± (1/5) √17
Since θ is in the third quadrant (π/2 < θ < π), cos θ is negative, so we take the negative root:
cos θ = -(1/5) √17
Substituting into the double-angle identity:
cos 2θ = 2 cos² θ - 1
cos 2θ = 2 [-(1/5) √17]² - 1
cos 2θ = 2 (1/25) (17) - 1
cos 2θ = 34/25 - 1
cos 2θ = 9/25
Therefore, the exact value of cos 2θ is 9/25.
Part B: To determine the exact value of sin (θ/2), we can use the half-angle identity for sine:
sin (θ/2) = ± √[(1 - cos θ)/2]
We already know cos θ, so we can substitute it in:
cos θ = -(1/5) √17
sin (θ/2) = ± √[(1 - cos θ)/2]
sin (θ/2) = ± √[(1 - (-1/5) √17)/2]
sin (θ/2) = ± √[(5 + √17)/10]
sin (θ/2) = ± (1/2) √(5 + √17)
Since θ is in the third quadrant (π/2 < θ < π), sin θ is negative, so we take the negative root:
sin (θ/2) = -(1/2) √(5 + √17)
Therefore, the exact value of sin (θ/2) is -(1/2) √(5 + √17).
Hence, the exact values of the sine and cosine given are -(1/2) √(5 + √17) and 9/25.
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A financial advisor wants to show clients how their stock portfolio has changed over the last 12 months. The best type of chart to use is:
Group of answer choices
1. a line chart
2. a histogram
3. a pie chart
4. a bar chart
The best chart to represents changes in the stock portfolio over the last 12 months by financial advisor is shown by option 1. a line chart.
The best type of chart to use to show how a stock portfolio has changed over time is a line chart.
A line chart can show the trend in the portfolio's value over the 12-month period.
Which is useful for identifying patterns and changes in performance.
A histogram is used to show the distribution of a single variable.
While a pie chart is used to show the proportion of a whole made up by different parts.
A bar chart is useful for comparing different categories or groups.
However, for tracking changes in a single variable over time, a line chart is the most appropriate choice.
Therefore, the best chart for financial advisor to show changes in stock portfolio over the last 12 months is given by option 1. a line chart.
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Find the zeros of the function. Then graph the function
y= (x+1)(x-2)(x-6)
Answer:
Step-by-step explanation:
To find the zeros of the function, we set y to zero and solve for x:
y = (x+1)(x-2)(x-6) = 0
Setting each factor equal to zero and solving for x gives us the zeros:
x+1 = 0 or x-2 = 0 or x-6 = 0
x = -1, x = 2, x = 6
So the zeros of the function are -1, 2, and 6.
To graph the function, we can use the zeros and the leading coefficient to sketch a rough graph. The leading coefficient is positive, so the graph will open upward. The zeros are -1, 2, and 6, so the graph will intersect the x-axis at those points. We can also find the y-intercept by plugging in x = 0:
y = (0+1)(0-2)(0-6) = 12
So the y-intercept is (0, 12).
Using this information, we can sketch the graph:
a friend has an 81% average before a final exam. The score includes everything but the final, which counts for 15% of the grade. What is the minimum to earn 75% for the course?
Answer:
57
Step-by-step explanation:
Okay, So we have this person That has 81% average before the quiz. For a course That score includes everything, but the final, which counts for 25% of the course grade, was the best course grade you your friend can earn. Okay, The best course grade given to me makes me. Mhm. 100. So we have .81 times. Actually we'll keep this as 81, times .75 right Plus 100 times. Excuse ME, Time 0.25. This is equivalent to 81 times 0.75. Mhm. This is equivalent to 81 times .75 plus 100 times 0.25, Which equals 85.75%. Now that's for part one. Report to we have what is the minimum score? Turn to 75%. So we have 75 equal to 81 times 0.75 Plus X. Times zero 25. So 81 times 0.75 equals 60.75 75- is value mhm. Is equal to 14.25. So we have 0.25 x. And if we divide 14.25 over 0.25, we isolate X. So the minimum score to get a 75 is a 57
Really Need help asap!
Step-by-step explanation:
h(-2) = 25
h(-1) = 5
h(0) = 1
h(1) = 1/5
h(2) = 1/25
I need the answer to this problem
Answer:
x = 4
Step-by-step explanation:
If we use A*B = C*D we get 2*6 = 3*x which is 12 = 3x. Dividing both sides by 3 you get 4 = x
Find the equation of the line with the slope 5 which goes through the point (8,5)
Answer:
y = 5x - 35
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
m = 5
The y-intercept is located at (0, -35)
So, the equation is y = 5x - 35
Answer: y=5x-35
Step-by-step explanation:
The formula I believe you are looking for would be y=mx+b. M is your slop and B is your y-intercept. Since the slope is already given, you would fill in the rest of the formula with that and the (x,y) you were provided, and it should look like this:
5=5(8)+b.
Then you solve that for b as follows:
5=5(8)+b
5=40+b
-35=b
Therefore the equation would be y=5x-35
Assume the weight of a randomly chosen American passenger car is a uniformly distributed random variable ranging from 1,557 pounds to 4,665 pounds.(e) What is the probability that a vehicle will weigh between 1,946 and 4,455 pounds? (Round your answer to 4 decimal places.)
The probability that a vehicle will weigh between 1,946 and 4,455 pounds is 0.8076.
To solve this problem, we need to find the probability that a randomly chosen car weighs between 1,946 and 4,455 pounds. Since weight is uniformly distributed, we know that the probability density function is constant over the entire range of possible values.
First, we need to find the total range of possible values:
Range = maximum weight - minimum weight
Range = 4,665 - 1,557
Range = 3,108
Next, we need to find the range of values that fall between 1,946 and 4,455:
Target range = 4,455 - 1,946
Target range = 2,509
Finally, we can calculate the probability of a randomly chosen car falling within this target range:
Probability = Target range / Range
Probability = 2,509 / 3,108
Probability = 0.8076 (rounded to 4 decimal places)
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Need Help!
A poster is to have a total area of 245 cm2. There is a margin round the edges of 6 cm at the top and 4 cm at the sides and bottom where nothing is printed.
What width should the poster be in order to have the largest printed area? **answer does not contain variables**
The largest printed area of the poster would be when the width and height of the poster are equal. To find the width of the poster, we need to subtract the total area of the margins from the total area of the poster.
The total area of the margins is 6 cm x 4 cm + 4 cm x 6 cm = 88 cm2.
Therefore, 245 cm2 - 88 cm2 = 157 cm2.
We can then use the formula A = W x H, where A is the area and W and H are the width and height of the poster, respectively.
Therefore, 157 cm2 = W x W.
We can solve for W by taking the square root of both sides.
Therefore, W = √157 = 12.5 cm.
Therefore, the width of the poster should be 12.5 cm in order to have the largest printed area.
CAN SOMEONE HELP WITH THIS QUESTION?✨
Step-by-step explanation:
it was not clear if an average change rate would be sufficient, or if you needed an immediate change rate (as I also don't know if you covered derivatives already or not).
so, it would be helpful, if you could put a message to an answer that was not giving you what you need.
so, here now an answer for an immediate change rate (hopefully that is what you need) :
we have a right-angled triangle.
the direct line of sight (the direct distance between police and red car) is the Hypotenuse (the baseline opposite of the 90° angle).
the 50 ft and 180 ft are the legs.
Pythagoras gives us the length of the Hypotenuse :
Hypotenuse² = 50² + 180² = 2500 + 32400 = 34,900
Hypotenuse = sqrt(34900) = 186.8154169... ft
in general terms let's say x is the distance of the cop to the road, y is the distance on the road to the crossing point with the distance cop to road, and z is the line of sight distance between the red car and the cop (the Hypotenuse).
x² + y² = z²
now, the first derivative of distance is the change of distance = speed.
then dy/dt (= y') is how fast the car is traveling down the road. dx/dt (= x') is how fast the cop is traveling toward the road. and dz/dt (= z') is how fast the distance between the cop and the car is changing.
now, we take the derivative of our equation
x² + y² = z² with respect to time, variable by variable :
d(x² + y² = z²)/dt =
dx²/dx × dx/dt + dy²/dy × dy/dt = dz²/dz × dz/dt
that gives us the equation
2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)
x(dx/dt) + y(dy/dt) = z(dz/dt)
from the problem we know x (50 ft), y (180 ft), dz/dt (85 ft/s). we calculated z (the Hypotenuse = sqrt(34900), and since the cop is not moving, we know dx/dt = 0.
and we get
50ft×0ft/s + 180ft×(y') = sqrt(34900)ft×(85)ft/s
we solve for y' (the speed of the car on the road)
y' = sqrt(34900)×85/180 = 88.21839132... ft/s
≈ 88.22 ft/s
and now here the difference for an average change rate over the unrevealed of 1 second :
the radar measured the change of the distance (Hypotenuse) from 1 second ago to now.
so, 1 second ago, the distance was
186.8154169... + 85 = 271.8154169... ft
the 50 ft leg stays the same, but the 180 ft leg was (again via Pythagoras)
271.8154169...² = 50² + leg²
leg² = 271.8154169...² - 50² = 71,383.62088...
leg = 267.1771339... ft
so, the red car traveled
267.1771339... - 180 = 87.1771339... ft/s
as you can see, it is close, but there has to be a difference, as the average change rate is only an approximation to the immediate change rate.
If r and s are constants and r² +rx + 12 is equivalent to (x+3)(x + 5), what is the value of r?
F.:3
H. 7
J. 12
K. Cannot be determined from the given information
Answer:
H. 7
Step-by-step explanation:
Given x² + rx + 12 is equivalent to (x + 3)(x + s), equate the two expressions and expand the right side of the equation:
[tex]\begin{aligned}x^2+rx+12&=(x + 3)(x + s)\\ x^2+rx+12&=x^2 + sx + 3x + 3s\\x^2+rx+12&=x^2 + (s+3)x + 3s\end{aligned}[/tex]
To find the value of r, first find the value of s.
The constant term of the right-hand side must be equal to the constant term of the left-hand side. Therefore:
[tex]\implies 3s = 12[/tex]
Solve for s by dividing both sides of the equation by 3:
[tex]\implies s = 4[/tex]
Compare the coefficients of the terms in x:
[tex]\implies r = s + 3[/tex]
Substitute the value of s into the equation and solve for r:
[tex]\begin{aligned} \implies r &= s + 3\\&= 4 + 3\\&= 7\end{aligned}[/tex]
Therefore, the value of r is 7.
Answer:
[tex]\large\boxed{\sf r = 7 }[/tex]
Step-by-step explanation:
Correct question:- If r and s are constants and r² +rx + 12 is equivalent to (x+3)(x + s), what is the value of r?
Here we are given that , the expression (x+3)(x+s) is equal to r² + rx + 12 .
Firstly, expand the expression (x+3)(x+s) as ,
[tex]\implies (x+3)(x+s) \\[/tex]
[tex]\implies x(x+s)+3(x+s) \\[/tex]
[tex]\implies x^2 + xs + 3x + 3s \\[/tex]
Take out x as common,
[tex]\implies x^2 + (3+s)x + 3s \\[/tex]
Now according to the question,
[tex]\implies x^2 + (3+s)x + 3s = r^2 + rx + 12\\[/tex]
On comparing the respective terms , we get,
[tex]\implies r = 3 + s \\[/tex]
[tex]\implies 3s = 12 \\[/tex]
Solve the second equation to find out the value of s , so that we can substitute that in equation 1 to find "r" .
[tex]\implies 3s = 12 \\[/tex]
[tex]\implies s =\dfrac{12}{3}=\boxed{4} \\[/tex]
Now substitute this value in equation (1) as ,
[tex]\implies r = 3 + s \\[/tex]
[tex]\implies r = 3 + 4 \\[/tex]
[tex]\implies \underline{\underline{ \red{ r = 7 }}} \\[/tex]
and we are done!
Which set of ordered pairs does not represent a function?
1. {(6,5), (3, 5), (−2, 8), (-9,4)}
2. {(-6, -1), (3, 1), (4, −4), (8, 1)}
3. {(-1,9), (-8, 5), (-1, 3), (-9, 1)}
4. {(5,9), (2,-5), (-1,-5), (0, 1)}
The set of ordered pairs does not represent a function is the one in the third option.
{(-1,9), (-8, 5), (-1, 3), (-9, 1)}
Which set of ordered pairs does not represent a function?A relation maps elements from one set, the domain, into elements of other set, the range.
Such that these mappings are of the form (x,y).
A function is a relation where each input is mapped into a single one output, then if you see a relation that has two points with the same value of x and different values of y, then that relation is not a function.
Particularly, if you look at the third option:
{(-1,9), (-8, 5), (-1, 3), (-9, 1)}
You can see that the first and second points have the same input and different outputs, then this is not a function, and that is the correct answer.
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PLEASE HELP ME ON THIS QUESTION
The frequency table is completed as follows
Number of books frequency
0 - 9 1
10 - 19 10
20 - 29 9
What is frequency table?
A frequency table is a way of organizing data in a table that shows the number of times each value or category appears in a dataset.
The table lists the unique values or categories in one column, and the frequency (or count) of occurrences of each value or category in the dataset in another column.
In the table attached, the solution is achieved by examining the tally column
Each item in the tally column is counted to get the numbers in place of l
A B C and D
Examining the table, we can say that
A = 1
B = 5 + 5 = 10
C = 5 + 4 = 9
D = 3
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Can someone please tell me what 5 divided by 1/3 is?
Answer:
15.
The trick to working out 5 divided by 1/3 is similar to the method we use to work out dividing a fraction by a whole number.All we need to do here is multiply the whole number by the numerator and make that number the new numerator. The old numerator then becomes the new denominator.
So, the answer to the question "what is 5 divided by 1/3?" is
15!
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Solve the equation 50/(1+e^-5r)=25
Does anyone know what x equals?
Answer:
X=18
Step-by-step explanation:
Answer:
x = 3.5 units (nearest tenth)
Step-by-step explanation:
The given triangle has a one right angle and two angles each measuring 45°. Therefore, it is a 45-45-90 triangle.
A 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : 1 : √2.
Therefore, the formula for the ratio of the sides is x : x : x√2 where:
x is each side opposite the 45 degree angles (legs).x√2 is the side opposite the right angle (hypotenuse).As the hypotenuse of the given right triangle is 5 units:
[tex]\implies x\sqrt{2} = 5[/tex]
To find the measure of x, solve for x:
[tex]\implies \dfrac{x\sqrt{2}}{\sqrt{2}} = \dfrac{5}{\sqrt{2}}[/tex]
[tex]\implies x = \dfrac{5}{\sqrt{2}}[/tex]
[tex]\implies x =3.5355339...[/tex]
[tex]\implies x=3.5\; \sf units\;(nearest\;tenth)[/tex]
Therefore, the length of side x to the nearest tenth is 3.5 units.
the solution set is
5r+20/10=3r-6/3
Answer:
r = -2
Step-by-step explanation:
5r + 20/10 = 3r -6/3
5r + 2 = 3r - 2
2r + 2 = -2
2r = -4
r = -2
Answer: r = -2
Step-by-step explanati
Which ordered pair maximizes the objective function p=3x+8y
(0,0)
(2,7)
(5,6)
(8,1)
Answer:
P(5,6) = 63
Step-by-step explanation:
Test each point to see which ordered pair maximizes the objective function:
(0,0): p = 3(0) + 8(0) = 0
(2,7): p = 3(2) + 8(7) = 6 + 56 = 62
(5,6): p = 3(5) + 8(6) = 15 + 48 = 63
(8,1): p = 3(8) + 8(1) = 24 + 8 = 32
Hence, (5,6) is the ordered pair that maximizes the objective function.
Standard Error of the Mean =
Confidence Interval Estimate for the Mean
Margin of Error E= Z
= Z. V
±Z
You want to rent a one-bedroom apartment near BCIT for next term. The mean
monthly rent for a random sample of 36 apartments advertised for rent on Craigslist is $1,235. Assume that the population standard deviation is $150.
(a) Give the point estimate of the true mean monthly rent for one-bedroom
apartments available for rent near BCIT.
Answer=$
(b) At the 95% confidence level, what is the margin of error on your estimate of
the true mean monthly rent for one-bedroom apartments available for rent near
BCIT.
Answer=$
(c) Construct a 95% confidence interval for the true mean monthly rent for one-
bedroom apartments.
Lower value=$
Upper value=$
Choose the correct statement to interpret the confidence interval.
1) I am totally confident that the population mean belongs to this confidence interval.
2) Clam 95% confident that the true population mean belongs to this confidence
interval.
(d) A friend claims the average monthly rent for a one-bedroom apartment available for rent near BCIT is at least $1,300. Based on your confidence interval do you agree?
• Yes
• No
(e) What is the z-score used to construct a 92% confidence interval?
Answer= (Enter a positive value in 2 decimal places)
The answers are a)the sample mean, which is $1,235. b) margin of error = $58.50. c)95% .d)the average monthly rent is at least $1,300.e)The z-score for a 92% confidence interval is 1.75.
How to calculate the sample mean and z-score ?a) The sample mean is the point estimate of the true mean monthly rent for one-bedroom apartments available for rent near BCIT, which is $1,235.
(b) At a 95% confidence level, the margin of error on the true mean monthly rent estimate is calculated as follows:
Margin of error = Z * (standard deviation / square root of sample size), where Z is the desired confidence level's z-score, which is 1.96 for a 95% confidence level.
Thus, the margin of error is equal to 1.96 * (150 / sqrt(36)) = $58.50.
(c) The 95% confidence interval for the true mean monthly rent is calculated as follows:
Lower value = point estimate minus margin of error = $1,235 minus $58.50 equals $1,176.50
Upper estimate + margin of error = $1,235 + $58.50 = $1,293.50.
(d) To see if the confidence interval supports the friend's claim that the average monthly rent for a one-bedroom apartment available for rent near BCIT is at least $1,300, we need to see if the lower limit of the confidence interval is greater than or equal to $1,300.
Given that the confidence interval is $1,176.50 $1,300, we can conclude that the confidence interval does not support the friend's claim that the
average monthly rent is at least $1,300. As a result, the answer is "No."
(e) A standard normal distribution table or calculator can be used to calculate the z-score corresponding to a 92% confidence interval.
A 92% confidence interval has a z-score of 1.75. (to two decimal places).
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please help with finding the answer
The answer of the given question based on the transformation from its parent function the explanation part is given below and The equation of the function is y = -2(x+3)².
What is Function?In mathematics, function is relation between set of inputs and set of possible outputs with property that each input is related to exactly one output. It is rule that assigns to each input value exactly one output value. Functions can be represented in various ways, like algebraic expressions, graphs, tables, and words. They are used to model relationships between variables, to describe how one quantity depends on another, and to make predictions about future values. Functions are important concept in many fields of mathematics, as well as in science, engineering, economics, and other areas where quantitative analysis is used.
a. The graph appears to be a reflection of the parent function f(x) = x² over the x-axis followed by a vertical stretch by a factor of 2 and a horizontal shift to the left by 3 units.
b. The equation of the function is y = -2(x+3)².
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James placed an online order for an item that costs US$75 via the Internet. Shipping and handling costs were charged at US$39. Given the exchange rate of US$1.00 to S$1.65, how much, in Singapore dollars, would James have to pay altogether?
James wοuld have tο pay a tοtal οf 188.10 Singapοre dοllars fοr the item and shipping and handling cοsts.
What is prοbability?Prοbability is a measure οf the likelihοοd οf an event οccurring. It is a numerical value between 0 and 1, where 0 means the event is impοssible and 1 means the event is certain tο οccur. Fοr example, the prοbability οf flipping a fair cοin and getting heads is 1/2 οr 0.5.
Tο calculate the tοtal cοst in Singapοre dοllars, we need tο cοnvert the US dοllars tο Singapοre dοllars using the given exchange rate, and then add the twο cοsts tοgether.
The cοst οf the item in Singapοre dοllars is:
75 USD * 1.65 SGD/USD = 123.75 SGD
The shipping and handling cοst in Singapοre dοllars is:
39 USD * 1.65 SGD/USD = 64.35 SGD
The tοtal cοst in Singapοre dοllars is the sum οf these twο cοsts:
Tοtal cοst = 123.75 SGD + 64.35 SGD = 188.10 SGD
Therefοre, James wοuld have tο pay a tοtal οf 188.10 Singapοre dοllars fοr the item and shipping and handling cοsts.
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(b) a dy integral that represents the surface area of the solid formed when c is rotated about the (x or y)-axis
The surface area of the surface generated by rotating the curve y = x² about the y-axis, and we found that the surface area is approximately 54.33 square units.
In this case, the curve we want to rotate is y = x², and we want to rotate it about the y-axis. To use the formula above, we need to express the equation of the curve in terms of x. Therefore, we need to rewrite y = x² as x = √y.
Next, we need to find the derivative of x = √y with respect to y, which is:
dx/dy = 1/2√y
Substituting this into the formula for the surface area, we get:
Surface Area = 2π ∫[0,4] √y √(1+(1/2√y)²) dy
Simplifying the expression inside the square root, we get:
Surface Area = 2π ∫[0,4] √(y+(1/4)) dy
We can evaluate this integral using the power rule of integration, which gives:
Surface Area = 2π [2/3(y+(1/4))^(3/2)]₀⁴
Simplifying further, we get:
Surface Area = 2π [2/3(17/4)^(3/2)]
Surface Area ≈ 54.33 square units
Therefore, the surface area of the surface generated by rotating the curve y = x² about the y-axis is approximately 54.33 square units.
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Complete Question:
How do you find the area of the surface generated by rotating the curve about the y-axis y = x^2 , 0 ≤ x ≤ 2 ?
Question 3 (2 points)
An article reports "attendance dropped 6% this year, to 300." What was the
attendance before the drop? (Round to the nearest person)
294
306
281
319
319 is the correct answer.
can someone help me please!
The median is the middle value of a data set when the values are arranged in order from lowest to highest (or highest to lowest). If there is an even number of values, then the median is the average of the two middle values. The median divides the data set into two halves, with half of the values being below the median and half of the values being above the median.
The first quartile, denoted as Q1, is the value that separates the lowest 25% of the data from the rest of the data. The second quartile, denoted as Q2, is the median of the data set. The third quartile, denoted as Q3, is the value that separates the lowest 75% of the data from the rest of the data.
The data-set has in this problem has two-halves of five elements, divided by the number 21, hence the median and the quartiles are given as follows:
The median of the data-set is of: 21 minutes.The lower quartile of the data-set is of 13 minutes. -> Median of the first five elements.The upper quartile of the data-set is of 27 minutes. -> Median of the last five elements.More can be learned about the median of a data-set at https://brainly.com/question/3514929
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Suppose a normal distribution has a mean of 48 and a standard deviation of 2. What is
the probability that a data value is between 46 and 47? Round your answer to the nearest
tenth of a percent.
VO A. 15.0%
О B. 13.0%
O C. 16.0%
D. 14.0%
15.0% is correct
The probability that a data value is between 46 and 47 in a normal distribution with mean 48 and standard deviation 2 is approximately A. 15.0%.
How to Calculate the Probability?To solve this problem, we need to first standardize the given values using the standard normal distribution formula:
z = (x - μ) / σ
where z is the standardized value, x is the data value, μ is the mean, and σ is the standard deviation.
For x = 46:
z = (46 - 48) / 2 = -1
For x = 47:
z = (47 - 48) / 2 = -0.5
Next, we can use a standard normal distribution table or calculator to find the area under the standard normal curve between these two standardized values.
Using a calculator or table, we find that the area to the left of z = -1 is 0.1587 and the area to the left of z = -0.5 is 0.3085.
Therefore, the area between z = -1 and z = -0.5 is:
0.3085 - 0.1587 = 0.1498
Finally, we can convert this area back to a probability by rounding to the nearest tenth of a percent:
0.1498 ≈ 15.0%
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Help on #25 and #26 please
Answer:
Step-by-step explanation:
25.
[tex]cos 45=\frac{x}{18\sqrt{2} } \\\frac{1}{\sqrt{2}} =\frac{x}{18\sqrt{2} } \\x=\frac{18\sqrt{2}}{\sqrt{2}} \\x=18[/tex]
26.
sin30=30/x
[tex]\frac{1}{2} =\frac{30}{x} \\x=30 \times 2=60[/tex]
please help!!! i really need it
Step-by-step explanation:
Lisa started with $25 on her prepaid debit card. After her first purchase, she had $22.90 left. Therefore, she spent:
$25 - $22.90 = $2.10
We know that the price of the ribbon was 14 cents per yard. To find out how many yards Lisa bought, we can set up an equation:
$2.10 ÷ $0.14/yd = 15 yards
Therefore, Lisa bought 15 yards of ribbon with her prepaid debit card.
In a large study designed to compare the risk of cardiovascular disease (CVD) between smokers and nonsmokers, random samples from each group were selected. The sample proportion of people with CVD was calculated for each group, and a 95 percent confidence interval for the difference (smoker minus nonsmoker) was given as (-0.01, 0.04). Which of the following is the best interpretation of the interval? We are 95% confident that the difference in proportions for smokers and nonsmokers with CVD in the sample is between -0.01 and 0.04. We are 95% confident that the difference in proportions for smokers and nonsmokers with CVD in the population is between -0.01 and 0.04. We are 95% confident that the proportion of all smokers with CVD is greater than the proportion of all nonsmokers with CVD because the interval contains more positive values. The probability is 0.95 that for all random samples of the same size, the difference in the sample proportions for smokers and nonsmokers with CVD will be between -0.01 and 0.04. long Pa Docs The probability is 0.95 that there is no difference in the proportions of smokers and nonsmokers with CVD because o is included in the interval -0.01 and 0.04 D Submit hips..
The best interpretation of the confidence interval is We are 95% confident that the difference in proportions for smokers and nonsmokers with CVD in the population is between −0.01 and 0.04 that is option B.
Confidence interval is estimate of Parameter were parameter is difference in proportion of smokers and non smokers in population.
The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level. In other words, a limitless number of independent samples are used to calculate the confidence intervals at the specified degree of assurance. in order for the percentage of the range that includes the parameter's real value to be equal to the confidence level.
Most of the time, the confidence level is chosen before looking at the data. 95% confidence level is the standard degree of assurance. Nevertheless, additional confidence levels, such as the 90% and 99% confidence levels, are also applied.
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Sorry if photo is side ways or upside down
Which expressions are equivalent to 8(3/4y -2)+6(-1/2+4)+1
Answer: 6y + 6
Step-by-step explanation:
To simplify the expression 8(3/4y -2) + 6(-1/2+4) + 1, we can follow the order of operations (PEMDAS):
First, we simplify the expression within parentheses, working from the inside out:
6(-1/2+4) = 6(7/2) = 21
Next, we distribute the coefficient of 8 to the terms within the first set of parentheses:
8(3/4y -2) = 6y - 16
Finally, we combine the simplified terms:
8(3/4y -2) + 6(-1/2+4) + 1 = 6y - 16 + 21 + 1 = 6y + 6
Therefore, the expression 8(3/4y -2) + 6(-1/2+4) + 1 is equivalent to 6y + 6.
determine between which two whole numbers lies square root of 20
Answer:
The square root of 20 is approximately between 4 and 5.
To find this, you can estimate the square root of 20 by finding the square root of the closest perfect squares, which are 16 (4^2) and 25 (5^2):
√16 = 4
√25 = 5
Since 20 is closer to 25 than 16, we know that the square root of 20 must be closer to 5 than to 4. Therefore, the square root of 20 lies between 4 and 5.