Answer:
15 squares
Step-by-step explanation:
60/100 * 25 = 15
Find the area in the right tail more extreme than z=0.93 in standard normal distribution, rounded to three decimal places.
Answer:
17.62%
Step-by-step explanation:
z→ ρ
0.93 (L)0.82381 (R)0.17619
17.62% / 82.38%
The area in the right tail more extreme than z=0.93 in standard normal distribution is 17.62% rounded to three decimal places.
What is a normal distribution of data?A normal distribution of data occurs when the majority of data points are relatively similar and the data set has a small range of values.
We need to find the area in the right tail more extreme than z=0.93 in standard normal distribution.
Here, z=0.93
z→ ρ
The mean ( the population mean, at 0.93 standard deviation units, and it represents an area that is, 17.619% of the total area of the standard distribution).
In this normal distribution, every given score is a z-score. A z-score explain us the distance from the mean in standard deviation units.
A = 17.62% / 82.38%
Hence, The area in the right tail more extreme than z=0.93 in standard normal distribution is 17.62% rounded to three decimal places.
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help with 4b thank you.
First let's compute dx/dt
[tex]x = t - \frac{1}{t}\\\\x = t - t^{-1}\\\\\frac{dx}{dt} = \frac{d}{dt}\left(t - t^{-1}\right)\\\\\frac{dx}{dt} = 1-(-1)t^{-2}\\\\\frac{dx}{dt} = 1+\frac{1}{t^{2}}\\\\\frac{dx}{dt} = \frac{t^2}{t^{2}}+\frac{1}{t^{2}}\\\\\frac{dx}{dt} = \frac{t^2+1}{t^{2}}\\\\[/tex]
Now compute dy/dt
[tex]y = 2t + \frac{1}{t}\\\\y = 2t + t^{-1}\\\\\frac{dy}{dt} = \frac{d}{dt}\left(2t + t^{-1}\right)\\\\\frac{dy}{dt} = 2 - t^{-2}\\\\\frac{dy}{dt} = 2 - \frac{1}{t^2}\\\\\frac{dy}{dt} = \frac{2t^2}{t^2}-\frac{1}{t^2}\\\\\frac{dy}{dt} = \frac{2t^2-1}{t^2}\\\\[/tex]
From here, apply the chain rule to say
[tex]\frac{dy}{dx} = \frac{dy*dt}{dx*dt}\\\\\frac{dy}{dx} = \frac{dy}{dt} \times \frac{dt}{dx}\\\\\frac{dy}{dx} = \frac{dy}{dt} \div \frac{dx}{dt}\\\\\frac{dy}{dx} = \frac{2t^2-1}{t^2} \div \frac{t^2+1}{t^{2}}\\\\\frac{dy}{dx} = \frac{2t^2-1}{t^2} \times \frac{t^{2}}{t^2+1}\\\\\frac{dy}{dx} = \frac{2t^2-1}{t^2+1}\\\\[/tex]
We could use polynomial long division, or we could add 2 and subtract 2 from the numerator and do a bit of algebra like so
[tex]\frac{dy}{dx} = \frac{2t^2-1}{t^2+1}\\\\\frac{dy}{dx} = \frac{2t^2-1+2-2}{t^2+1}\\\\\frac{dy}{dx} = \frac{(2t^2+2)-1-2}{t^2+1}\\\\\frac{dy}{dx} = \frac{2(t^2+1)-3}{t^2+1}\\\\\frac{dy}{dx} = \frac{2(t^2+1)}{t^2+1}-\frac{3}{t^2+1}\\\\\frac{dy}{dx} = 2-\frac{3}{t^2+1}\\\\[/tex]
This concludes the first part of 4b
=======================================================
Now onto the second part.
Since t is nonzero, this means either t > 0 or t < 0.
If t > 0, then,
[tex]t > 0\\\\t^2 > 0\\\\t^2+1 > 1\\\\\frac{1}{t^2+1} < 1 \ \text{ ... inequality sign flip}\\\\\frac{3}{t^2+1} < 3\\\\-\frac{3}{t^2+1} > -3 \ \text{ ... inequality sign flip}\\\\-\frac{3}{t^2+1}+2 > -3 + 2\\\\2-\frac{3}{t^2+1} > -1\\\\-1 < 2-\frac{3}{t^2+1}\\\\-1 < \frac{dy}{dx}\\\\[/tex]
note the inequality signs flipping when we apply the reciprocal to both sides, and when we multiply both sides by a negative value.
You should find that the same conclusion happens when we consider t < 0. Why? Because t < 0 becomes t^2 > 0 after we square both sides. The steps are the same as shown above.
So both t > 0 and t < 0 lead to [tex]-1 < \frac{dy}{dx}[/tex]
We can say that -1 is the lower bound of dy/dx. It never reaches -1 itself because t = 0 is not allowed.
We could say that
[tex]\displaystyle \lim_{t\to0}\left(2-\frac{3}{t^2+1}\right)=-1\\\\[/tex]
---------------------------------------
To establish the upper bound, we consider what happens when t approaches either infinity.
If t approaches positive infinity, then,
[tex]\displaystyle L = \lim_{t\to\infty}\left(2-\frac{3}{t^2+1}\right)\\\\\\\displaystyle L = \lim_{t\to\infty}\left(\frac{2t^2-1}{t^2+1}\right)\\\\\\\displaystyle L = \lim_{t\to\infty}\left(\frac{2-\frac{1}{t^2}}{1+\frac{1}{t^2}}\right)\\\\\\\displaystyle L = \frac{2-0}{1+0}\\\\\\\displaystyle L = 2\\\\[/tex]
As t approaches infinity, the dy/dx value approaches L = 2 from below.
The same applies when t approaches negative infinity.
So we see that [tex]\frac{dy}{dx} < 2[/tex]
---------------------------------------
Since [tex]-1 < \frac{dy}{dx} \text{ and } \frac{dy}{dx} < 2[/tex], those two inequalities combine into the compound inequality [tex]-1 < \frac{dy}{dx} < 2[/tex]
So dy/dx is bounded between -1 and 2, exclusive of either endpoint.
The correlation coefficient, r, between the prices of smartphones, x, and the number of sales of phones, y, equals −0.63.
Select the statement which best describes the relationship between the price and sales.
The value of r indicates that the number of sales decreases as the price decreases.
The value of r indicates that the number of sales decreases as the price stays the same.
The value of r indicates that the number of sales decreases as the price increases.
The value of r indicates that the number of sales is not related to the price.
I think its (C): The value of r indicates that the number of sales decreases as the price increases.
Answer:
(C) The value of r indicates that the number of sales decreases as the price increases.
ED2021.
The best statement, given the correlation coefficient of -0.63 is: value of r indicates that the number of sales decreases as the price increases.
What is a Negative Correlation Coefficient?A negative correlation coefficient has a negative sign, and implies a negative relationship between two variables.
This means that, as one variable decreases, the other variable increases.
Thus, a correlation coefficient of -0.63 shows a negative relationship between prices of smartphones and the number of sales.
Therefore, the best statement, given the correlation coefficient of -0.63 is: value of r indicates that the number of sales decreases as the price increases.
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Please help.........
Answer:
a
Step-by-step explanation:
Simone invests $2,000 in an account that compounds interest quarterly and earns 9%. How many years will it take for his money to double? (Round your answer to one decimal place.)
no te puedo contestarte yo no hablo inglés
The area of a rectangle is 44 m^2, and the length of the rectangle is 3 m less than twice the width. Find the dimensions of the rectangle.
length :
width :
Answer:
Length:8
Width:5.5
Step-by-step explanation:
We're given area = 44m^2, and the formula for the area of a rectangle is the length multiplied by the width. So,
A = L * w = 44
We're given that the length is 3m shorter than 2 times the width, which is 2w - 3. "2w" is the same as "2 times the width", and the 3 is subtracted because it says 3m shorter than 2 times the width. So L = 2w - 3, and we can substitute that into our equation above.
(2w - 3)(w) = 44
2w^2 - 3w - 44 = 0
Use the quadratic formula here.
x = {3 ± √(-3)^2 - 4(-44)(2)}/2(2)
= {3 ± √9 + 352}/4
= (3 ± 19)/4
You'll get two answers, but remember, we're measuring the length of the sides of shapes, so it has to be positive. It's impossible to have negative lengths, so we're going to stick with the (3 + 19)/4 answer, which is 22/4, which is 5.5. However, we are not finished yet. This is just the width. Now we need to plug it into the equation for length, which was 2w - 3
2(5.5) - 3 = 11 - 3 = 8
The length is 8m and the width is 5.5m.
5
13
The probabilities that three men win their respective races are 1/3,3/5and 3/4.what is theprobability that
a) all of them win their races)
b) only one of them win his race?
Answer:
a
Step-by-step explanation:
1/3 x 3/5 x 3/4 =7/12 so therefore that's what the answer isn't
ZA and ZB are vertical angles. If m A = (5x + 2)° and mZB = (6x – 12),
then find the value of x.
Answer:
x = 14
Step-by-step explanation:
Vertical angles are equal
5x+2 = 6x-12
Subtract 5x from each side
5x+2-5x = 6x-12-5x
2 = x-12
Add 12 to each side
2+12 = x-12+12
14 =x
Please help!!!
The figures to the right are similar. Compare the first figure to the second. Give the ratio of the perimeters and the ratio of the areas (integer or a simplified fraction)
Answer:
Perimeter: 3/4
Area: 9/16
Step-by-step explanation:
The ratio of the perimeters is equal to the ratio of the sides so:
18/24 = 3/4
Ratio of Area = (Ratio of Sides)^2
(3/4)^2 = 9/16
I wasn't sure about the answer so I used Gauthmath
180 °
X °
26 °
X = ? °
Answer:
X = 64
Step-by-step explanation:
All of the angles are right angles (because of the square at one of the angles shown above). This means each angle equals 90 degrees. If X + 26 = 90, then X = 64 because 90 - 26 = 64. I hope this helps!
Answer: X = 64
Step-by-step explanation:
If the cube root parent function is horizontally stretched by a factor of 4, then translated 5 units right and 3 units up, write an equation to represent the new function?
Answer:
The cube root parent function:
f(x) = [tex]\sqrt[3]{x}[/tex]Horizontally stretched by a factor of 4:
g(x) → f(1/4x) = [tex]\sqrt[3]{1/4x}[/tex]Translated 5 units right:
h(x) → g(x - 5) = [tex]\sqrt[3]{1/4x - 5}[/tex]Translated 3 units up:
k(x) → h(x) + 3 = [tex]\sqrt[3]{1/4x - 5} + 3[/tex]what is 98×63-32×69=
Answer: plz marl brainilist
3966
Step-by-step explanation:
(98 × 63 - 32 × 69
98 * 63) - (32 * 69)
The absolute value of the dilation factor is the ratio of each side length of the dilated quadrilateral to the corresponding side length of the preimage. How does the ratio of the perimeters in parts B and D compare with the ratio of corresponding side lengths
9514 1404 393
Answer:
perimeter ratio = dilation factor
Step-by-step explanation:
In general, all linear dimensions are scaled by the dilation factor. This includes lengths of sides, perimeter, circumference, diameter, radius, or any other 1-dimensional (length) measure of a figure.
The ratio of perimeters is equal to the ratio of side lengths.
Write the complies number z=3-3i in trigonometric form
Answer:
3*sqrt(2) and 3pi/4
Step-by-step explanation:
tan(theta)=y/x and r^2=y^+x^2.
tan(theta)=-3/3=-1, theta=3pi/4
r=sqrt(3^2+3^2)=3*sqrt(2)
Use the remainder term to find the minimum order of the Taylor polynomial, centered at 0, that is required to approximate the following quantity with an absolute error no greater than 10^-2.
√1.06.
n>= __________
Answer:
n ≥ 3
Step-by-step explanation:
Applying the remainder term in evaluating the minimum order of the Taylor polynomial
absolute error ≤ 10^-2
[tex]\sqrt{1.06}[/tex]
∴ n ≥ ?
The remainder term is the leftover term after computation ( dividing one polynomial with another )
attached below is the detailed solution
The minimum order of the Taylor polynomial, n≥3
What is Taylor polynomial?Taylor polynomial is a series of functions that has an infinite sum of terms that are expressed in terms of the function's derivatives.
[tex]\rm f(a)+\frac{f'(a)}{1!} (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +....,[/tex]
Applying the Taylor series polynomial, the minimum order of the Taylor polynomial, centered at 0
[tex]\rm f(0)+\frac{f'(0)}{1!} (x-0)+\frac{f''(0)}{2!} (x-0)^{2} +....,[/tex]
f(x) = [tex]\sqrt{x+1}[/tex]
[tex]f'(x)=\frac{1}{2}[/tex]
[tex]f''(x)=3/8[/tex]
substituting in the Taylors series
T(x) = [tex]1+\frac{x}{2} -\frac{x^{2} }{8} +\frac{x^{3} }{16}[/tex]......
T(0.06) = [tex]1+\frac{0.06}{2} -\frac{0.06^{2} }{8} +\frac{0.06^{3} }{16}...[/tex]
T(0.06) =1.03
f(0.06) =
[tex]\sqrt{0.06+1}\\= 1.03[/tex]
Therefore, the minimum order of the Taylor polynomial, n≥3
Learn more about Taylor polynomial;
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The ratio of red beads to blue beads on a necklace is 4:7. If there are 16 red beads, how many blue ones are there?
Answer:
There are 28 beads
Step-by-step explanation:
Total ratio:
[tex]{ \sf{ (4 + 7) = 11}}[/tex]
let total beads be x:
[tex]{ \sf{ \frac{4}{11} \times x = 16 }} \\ \\ { \sf{x = \frac{11 \times 16}{4} }} \\ x = 44 \: beads[/tex]
Blue beads:
[tex] = 44 - 16 \\ = 28 \: \: beads[/tex]
hawkville's population is 2500 people. next year the town clerk expects the population to grow by 1.2%, how many new residents will hawkville have next year?
Answer:
30 new residents
Step-by-step explanation:
Find how many new residents they will have by finding 1.2% of the current population.
2500(0.012)
= 30
So, Hawkville will have 30 new residents
The five number summary of a dataset is given as
0, 4, 12, 14, 20
An observation is considered an outlier if it is below _______
An observation is considered an outlier if it is above _______
The five number summary of a dataset is given as
2, 8, 14, 18, 20
An observation is considered an outlier if it is below _______
An observation is considered an outlier if it is above _______
.
.
Given:
The five number summary of two data sets are given as:
a) 0, 4, 12, 14, 20
b) 2, 8, 14, 18, 20
To find:
The range for the outliers.
Solution:
We know that,
An observation is considered an outlier if it is below [tex]Q_1-1.5(IQR)[/tex]
An observation is considered an outlier if it is above [tex]Q_3+1.5(IQR)[/tex]
Where, IQR is the interquartile range and [tex]IQR=Q_3-Q_1[/tex].
The five number summary of two data sets are given as:
0, 4, 12, 14, 20
Here, [tex]Q_1=4[/tex] and [tex]Q_3=14[/tex].
Now,
[tex]IQR=14-4[/tex]
[tex]IQR=10[/tex]
The range for the outliers is:
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-1.5(10),14+1.5(10)][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-15,14+15][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-11,29][/tex]
An observation is considered an outlier if it is below -11.
An observation is considered an outlier if it is above 29.
The five number summary of two data sets are given as:
2, 8, 14, 18, 20
Here, [tex]Q_1=8[/tex] and [tex]Q_3=18[/tex].
Now,
[tex]IQR=18-8[/tex]
[tex]IQR=10[/tex]
The range for the outliers is:
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-1.5(10),18+1.5(10)][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-15,18+15][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-7,33][/tex]
An observation is considered an outlier if it is below -7.
An observation is considered an outlier if it is above 33.
Use the order of operations to evaluate this expression (-2+1)
Answer:
12
Step-by-step explanation:
2²×3
I hope its correct
Answer:
4
[tex] {( - 2 + 1)}^{2} + 5(12 \div 3) - 9 \\ 2 + 1 + 5 \times 4 - 9 \\ 3 + 20 - 9 \\ 23 - 9 \\ 14[/tex]
help fast I'm dum
and I'm sorry if I keep spamming this.
Curtis types 48 words in 1 minute how many words does Curtis type in 8 minutes? use the following equivalent rates to help solve the problem. how many words does Curtis type in 8 minutes?
Answer:
384
Step-by-step explanation:
Answer:
384 words
Step-by-step explanation:
Number of words typed in 1 minute = 48
So, number of words typed in 8 minutes
= Number of words typed in 1 minute × 8
= 48 × 8
= 384
So, Curtis types 384 words in 8 minutes.
7^300 chia 7 dư bao nhiêu
Answer:
dư 0... 7^300 chia 7 đc 7^299 mà
(y - .18) x .08 = needing help
Answer:
0.08y - 0.0144
Step-by-step explanation:
We need to solve the below expression i.e.
(y - .18) x .08
It can be done as follows :
Using distributive property to solve it.
(y - .18) x .08 = 0.08(y) - 0.18(0.08)
= 0.08y - 0.0144
So, the equivalent expression is 0.08y - 0.0144.
What is the slope of a relation with ordered pairs of (-5, 3) and (4.1).
9/2
2/9
-9/2
-2/9
2
-2
Three ducks and two ducklings weigh 32 kg. Four ducks and three ducklings weigh 44kg. All ducks weigh the same and all ducklings weigh the same. What is the weight of two ducks and one duckling?
Answer:
20kg
Step-by-step explanation:
Let the weight of one duck be x and the weight of one duckling be y
ATQ, 3x+2y=32 and 4x+3y=44, solving for x and y we get, weight of one duck is 8kg and one duckling is 4kg. The weight of two ducks and one duckling is 20kg
Each marble bag sold by Debra's Marble Company contains 8 yellow marbles for every 4 blue marbles. If a bag has 56 yellow marbles, how many blue marbles does it contain?
Answer:
28 blue marbles
Step-by-step explanation:
yellow: blue
8 4
To get to 56 yellow marbles multiply by 7
yellow: blue
8*7 4*7
56 28
There will be 28 blue marbles
What is the image of the point (-7, 4) after a rotation of 180° counterclockwise about the origin?
Answer: (7, -4)
Concept:
For each rotation angle, there is a specified rule that could be applied. Please refer to the attachment below for the list of rotation rules.
Solve:
Given point = (-7, 4)
Given rotation rule = (x , y) ⇒ (-x, -y)
(-7, 4) ⇒ (7, -4)
Hope this helps!! :)
Please let me know if you have any questions
LET R equal the rental fee for one locker write an equation that represents the situation
Answer:
R x 1= price of 1 locker
Step-by-step explanation:
it would continue the same way. Just multiply R and the number of lockers.
Is there a certain situation it was asking about?
Find the equation of the line passing through the point (-7,2)(−7,2) that is perpendicular to the line 4x - 3y = 104x−3y=10.
Answer:
Step-by-step explanation:
Slope of the given line: m=4/3
Slope of the perpendiclar : m'=-3/4 (the inverse of the opposed of m)
Equation of the perpendiclar line: (passing through (-7,2))
[tex]y-2=(x+7)*\dfrac{-3}{4} \ or\\\\ y=-\dfrac{3x}{4} -\dfrac{13}{4}[/tex]
(A) A small business ships homemade candies to anywhere in the world. Suppose a random sample of 16 orders is selected and each is weighed. The sample mean was found to be 410 grams and the sample standard deviation was 40 grams. Find the 90% confidence interval for the mean weight of shipped homemade candies. (Round your final answers to the nearest hundredth)
(B) When 500 college students are randomly selected and surveyed; it is found that 155 own a car. Find a 90% confidence interval for the true proportion of all college students who own a car.
(Round your final answers to the nearest hundredth)
(C) Interpret the results (the interval) you got in (A) and (B)
The correct answer to the given question is "[tex]\bold{392.47\ < \mu <\ 427.53}[/tex],[tex]\bold{0.28 \ < P <\ 0.34}[/tex], and for Interpret results go to the C part.
Following are the solution to the given parts:
A)
[tex]\to \bold{(n) = 16}[/tex]
[tex]\to \bold{(\bar{X}) = 410}[/tex]
[tex]\to \bold{(\sigma) = 40}[/tex]
In the given question, we calculate [tex]90\%[/tex] of the confidence interval for the mean weight of shipped homemade candies that can be calculated as follows:
[tex]\to \bold{\bar{X} \pm t_{\frac{\alpha}{2}} \times \frac{S}{\sqrt{n}}}[/tex]
[tex]\to \bold{C.I= 0.90}\\\\\to \bold{(\alpha) = 1 - 0.90 = 0.10}\\\\ \to \bold{\frac{\alpha}{2} = \frac{0.10}{2} = 0.05}\\\\ \to \bold{(df) = n-1 = 16-1 = 15}\\\\[/tex]
Using the t table we calculate [tex]t_{ \frac{\alpha}{2}} = 1.753[/tex] When [tex]90\%[/tex] of the confidence interval:
[tex]\to \bold{410 \pm 1.753 \times \frac{40}{\sqrt{16}}}\\\\ \to \bold{410 \pm 17.53\\\\ \to392.47 < \mu < 427.53}[/tex]
So [tex]90\%[/tex] confidence interval for the mean weight of shipped homemade candies is between [tex]392.47\ \ and\ \ 427.53[/tex].
B)
[tex]\to \bold{(n) = 500}[/tex]
[tex]\to \bold{(X) = 155}[/tex]
[tex]\to \bold{(p') = \frac{X}{n} = \frac{155}{500} = 0.31}[/tex]
Here we need to calculate [tex]90\%[/tex] confidence interval for the true proportion of all college students who own a car which can be calculated as
[tex]\to \bold{p' \pm Z_{\frac{\alpha}{2}} \times \sqrt{\frac{p'(1-p')}{n}}}[/tex]
[tex]\to \bold{C.I= 0.90}[/tex]
[tex]\to\bold{ (\alpha) = 0.10}[/tex]
[tex]\to\bold{ \frac{\alpha}{2} = 0.05}[/tex]
Using the Z-table we found [tex]\bold{Z_{\frac{\alpha}{2}} = 1.645}[/tex]
therefore [tex]90\%[/tex] the confidence interval for the genuine proportion of college students who possess a car is
[tex]\to \bold{0.31 \pm 1.645\times \sqrt{\frac{0.31\times (1-0.31)}{500}}}\\\\ \to \bold{0.31 \pm 0.034}\\\\ \to \bold{0.276 < p < 0.344}[/tex]
So [tex]90\%[/tex] the confidence interval for the genuine proportion of college students who possess a car is between [tex]0.28 \ and\ 0.34.[/tex]
C)
In question A, We are [tex]90\%[/tex] certain that the weight of supplied homemade candies is between 392.47 grams and 427.53 grams.In question B, We are [tex]90\%[/tex] positive that the true percentage of college students who possess a car is between 0.28 and 0.34.Learn more about confidence intervals:
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The grades in a statistics course for a particular semester were as follows:
Grade ABCDF f 14 18 32 20 16
Test the hypothesis, at the 0.05 level of significance, that the distribution of grades is uniform. (Test that each grade is equally likely) Round your solutions to 3 decimal places where necessary.
Test Statistic =
Critical Value =
Answer:
Test Statistic = 10
Critical Value = 9.488
Step-by-step explanation:
Given :
Grade A _ B _ C _ D _ F
_____14 _ 18 _32_ 20_16
H0 : distribution of grade is uniform
H1 : Distribution of grade is not uniform
Using the Chisquare statistic :
χ² = (observed - Expected)² / Expected
The expected value :
(14+18+32+20+16) / 5 = 20
χ² = (14-20)^2 / 20 + (18-20)^2 / 20 + (32-20)^2 / 20 + (20-20)^2 / 20 + (16-20)^2 / 20
χ² statistic = 10
The χ² critical at df = (n - 1) = 5 - 1 = 4
χ² Critical(10, 4) = 9.488
