You are situated 300 feet from the base of Tower Glitz Plaza watching an external elevator descend down the side of the building. At a certain instant the elevator is 500 feet away from you, and its distance from you is decreasing at a rate of 16 ft/sec. How fast is the elevator descending at that instant?
Answer:
18.66 ft/s
Step-by-step explanation:
The distance between you and the elevator is given by:
[tex]h=\sqrt{x^2+y^2}[/tex]
The rate of change for the distance between you and the elevator is given by:
[tex]\frac{dh}{dt}=\frac{dh}{dy}*\frac{dy}{dt}[/tex]
[tex]-16=\frac{dh}{dy}*\frac{dy}{dt}[/tex]
[tex]\frac{dh}{dy}=\frac{d}{dy} (\sqrt{x^2+y^2})\\[/tex]
Applying the chain rule:
[tex]u=x^2+y^2\\\frac{dh}{dy}=\frac{d\sqrt u}{du} *\frac{du}{dy}\\\frac{dh}{dy}=\frac{1}{2\sqrt u} *2y\\\frac{dh}{dy}=\frac{y}{\sqrt {(x^2+y^2)}}[/tex]
Therefore, at x=300 and y = 500, dy/dt is:
[tex]-16=\frac{y}{\sqrt {(x^2+y^2)}}*\frac{dy}{dt}\\-16=\frac{500}{\sqrt {(300^2+500^2)}}*\frac{dy}{dt}\\\frac{dy}{dt}=-18.66\ ft/s[/tex]
The elevator is descending at 18.66 ft/s.
Exactly one pair of opposite sides is parallel
Answer:
Yeah btw is this a question?
Write the standard form of the line that passes through the given points. Inclide your work in the final answer. Type your answer in the box provided or use the upload option to submit your solution. (4,7) and (0,7)
Answer:
y=7
Step-by-step explanation:
Slope: 7-7/4-0=0
Point: (0,7)
pt/slope form:
y-7=(0)(x-0)
y=7
What is the point-slope form of a line with slope 3 that contains the point
(2, 1)?
Answer:
y-1 = 3(x-2)
Step-by-step explanation:
The point slope form of a line is
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on the line
y-1 = 3(x-2)
A tank contains 24 gallons of water when all of a sudden the water begins draining at a constant rate of 2 gallons per hour. Let t represent the number of hours since the water began draining and let v represent the volume of water in the tank.
Required:
a. Write a formula that expresses v in terms of t.
b. As t increases from 3 to 6, v varies from _________ to _________
Answer:
a) [tex]V(t) = 24 - 2t[/tex]
b) As t increases from 3 to 6, v varies from 18 gallons to 12 gallons.
Step-by-step explanation:
The volume of the tank in terms of the time can be described by the following equation:
[tex]V(t) = V(0) - at[/tex]
In which V(0) is the initial volume and a is the hourly decrease rate.
a. Write a formula that expresses v in terms of t.
The tank initially contains 24 gallons of water, which means that [tex]V(0) = 24[/tex]
Drains at a constant rate of 2 gallons per hour, so [tex]a = 2[/tex]
Then
[tex]V(t) = V(0) - at[/tex]
[tex]V(t) = 24 - 2t[/tex]
b. As t increases from 3 to 6, v varies from _________ to _________
[tex]V(t) = 24 - 2t[/tex]
[tex]V(3) = 24 - 2*3 = 18[/tex]
[tex]V(6) = 24 - 2*6 = 12[/tex]
So as t increases from 3 to 6, v varies from 18 gallons to 12 gallons.
Which one of the following is always true?a. The coefficient of variation measures variability in a positively skewed data set relative to the size of the median.b. None of the suggested answers are correctc. The coefficient of variation is a measure of relative dispersion that expresses the standard deviation as a percentage of the mean, for any data on a ratio scale and an interval scale.d. The interquartile range is very unique in the sense that it is a measure of central tendency as well as a measure of dispersion.e. The coefficient of variation should only be used to compare positive data on an interval scale.
Answer:
C. The coefficient of variation is a measure of relative dispersion that expresses the standard deviation as a percentage of the mean, for any data on a ratio scale and an interval scale
Step-by-step explanation:
Th Coefficient of Variance is a measure of dispersion that can be calculated using the formula:
[tex]CV = \frac{\sigma_{x} }{\mu_{x} } * 100%[/tex]
Where [tex]\sigma{x}[/tex] is the Standard Deviation
and [tex]\mu_{x}[/tex] is the sample mean
From the formula written above, it is shown that the Coefficient of Variation expresses the Standard Deviation as a percentage of the mean.
Coefficient of variation can be used to compare positive as well as negative data on the ratio and interval scale, it is not only used for positive data.
The Interquartile Range is not a measure of central tendency, it is a measure of dispersion.
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
105.12 ft^2
Step-by-step explanation:
Area of a rectangle: bh
In this case 8*10.... so area of the rectangle is 80
Area of a circle: pir^2
Half it for a semicircle.
so 1/2 pi r^2
radius is 4 cuz its half of 8.
so 1/2(3.14)(4^2)=(0.5)(3.14)(16)=25.12
Now add up 80+25.12
Total is 105.12
Hope I helped :)
The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 258.7 and a standard deviation of 63.5. (All units are 1000 cells/muL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 68.2 and 449.2? b. What is the approximate percentage of women with platelet counts between 195.2 and 322.2?
Answer:
a) [tex]P( \mu -3\sigma <X< \mu +3\sigma)[/tex]
And from the empirical rule we know that this probability is 0.997 or 99.7%
b)[tex] P(195.2 <X<322.2)[/tex]
Using the z score we have:
[tex] z = \frac{322.2 -258.7}{63.5}= 1[/tex]
[tex] z = \frac{195.2 -258.7}{63.5}= -1[/tex]
And within one deviation from the mean we have 68% of the values
Step-by-step explanation:
For this case we defien the random variable of interest X as "blood platelet counts" and we know the following parameters:
[tex] \mu = 258.7, \sigma =63.5[/tex]
Part a
We can use the z score formula given by:
[tex] z =\frac{\bar X -\mu}{\sigma}[/tex]
And we want this probability:
[tex]P( \mu -3\sigma <X< \mu +3\sigma)[/tex]
And from the empirical rule we know that this probability is 0.997 or 99.7%
Part b
For this case we want this probability:
[tex] P(195.2 <X<322.2)[/tex]
Using the z score we have:
[tex] z = \frac{322.2 -258.7}{63.5}= 1[/tex]
[tex] z = \frac{195.2 -258.7}{63.5}= -1[/tex]
And within one deviation from the mean we have 68% of the values
What’s the correct answer for this question?
Answer:
A
Step-by-step explanation:
Volume of cone = (1/3) πr²h
Help asap giving branlist!!!
Answer:
D.
Step-by-step explanation:
So you know you have to have $62 as the base fee.
If you exceed 2 gigabytes, you subtract that by 2 because you want to find how many gigabytes you're going over. You then multiply it by 30 to find the cost.
You get C = 62 + 30(g - 2)
Answer:
anwser is d because it is write.
Step-by-step explanation:
Solve for x in the diagram below
Answer:
So the diagram couldn't come due to coronavirus?
Answer:
there is no diagram
Step-by-step explanation:
A small child has 6 more quarters than nickels. If the total amount of the coins is $3.00, find the number of nickels and quarters the child has.
Answer:
nickels- 5, quarters- 11
Step-by-step explanation:
nickel= 5 p, quarter= 25 p
5x+25(x+6)= 300
30x+150=300
30x=150
x=150/30
x=5 nickels
x+6= 11 quarters
Find the midpoint of (9,2) and (-7,-9)
Answer:
(1,-7/2)
Step-by-step explanation:
The midpoint of (9,2)(-7,-9) is (1,-7/2)
Please help me on this
Answer19/40=x/3.6
By cross multiplication
19*3.6=40*x
68.4 =40x
x=68.4/40
x=1.71
x=
Answer: C
Step-by-step explanation:
[tex]\frac{19}{40} = \frac{x}{3.6}[/tex] solve by cross product
40x = 68.4 Divide both sides by 40
x = 1.71
Find the range of the following data set.
11,5, 1, 11, 12
01
1.
017
Answer:
range 11
Step-by-step explanation:
The range is the largest number minus the smallest number
The largest number is 12 and the smallest number is 1
12 - 1 = 11
The value of m compared to the standard is
1/1000
1000
1/100
10
find the perimeter of of the shaded figure. ? units
Answer:
38 Units
Step-by-step explanation:
7 each down each side
10 each across top and bottom
2 more for each indent on bottom
7+7+10+10+2+2
14+20+4
38
Patricia can buy individual songs for $1.00 to download. Also, an entire album costs $10.00 to download. She can spend no more than a total of $80. She wants to buy no more than four albums, and at least 30 individual songs. The following system of inequalities represents this situation, where x is the number of individual songs and y is the number of albums.
Answer:
The system of inequalities is:
[tex]x\geq30\\\\y\leq4\\\\10x+1y\leq80[/tex]
Step-by-step explanation:
We will write each of the conditions stated in this problem
Patricia wants to buy at least 30 individual songs.
[tex]x\geq30[/tex]
She wants to buy 4 albums at most.
[tex]y\leq4[/tex]
The total expenditure has to be equal or less than $80, when each album cost $10 and each individual song cost $1.
[tex]10x+1y\leq80[/tex]
The system of inequalities is:
[tex]x\geq30\\\\y\leq4\\\\10x+1y\leq80[/tex]
A random sample of adult female reaction times has a sample mean of x¯=394.3 milliseconds and sample standard deviation of s=84.6 milliseconds. Use the Empirical Rule to determine the approximate percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds.
Answer:
The percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds is 99.7%.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 394.3 ms
Standard deviation = 84.6 ms
Use the Empirical Rule to determine the approximate percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds.
140.5 = 394.3 - 3*84.6
So 140.5 is 3 standard deviations below the mean.
648.1 = 394.3 + 3*84.6
So 648.1 is 3 standard deviations above the mean.
By the Empirical Rule,
The percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds is 99.7%.
plz answer this asap
Answer: 20
Step-by-step explanation: 5 times 4 is 20 times 2 is 40, but when you divide by 1/2 you drop down to 20.
Z=1.23 z=0.86 WHAT is the area of the shaded region between the two
Answer:
The area of the shaded region between [tex] \\ z = 1.23[/tex] and [tex] \\ z = 0.86[/tex] is [tex] \\ P(0.86 < z < 1.23) = 0.08554[/tex] or 8.554%.
Step-by-step explanation:
To solve this question, we need to find the corresponding probabilities for the standardized values (or z-scores) z = 1.23 and z = 0.86, and then subtract both to obtain the area of the shaded region between these two z-scores.
We need to having into account that a z-score is given by the following formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
Where
x is a raw score from the distribution that we want to standardize using [1].[tex] \\ \mu[/tex] is the mean of the normal distribution.[tex] \\ \sigma[/tex] is the standard deviation of the normal distribution.A z-score indicates the distance of x from the mean in standard deviations units, where a positive value "tell us" that x is above [tex] \\ \mu[/tex], and conversely, a negative that x is below [tex] \\ \mu[/tex].
The standard normal distribution is a normal distribution with [tex] \\ \mu = 0[/tex] and [tex] \\ \sigma = 1[/tex], and has probabilities for standardized values obtained using [1]. All these probabilities are tabulated in the standard normal table (available in any Statistical book or on the Internet).
Using the cumulative standard normal table, for [tex] \\ z = 1.23[/tex], the corresponding cumulative probability is:
[tex] \\ P(z<1.23) = 0.89065[/tex]
The steps are as follows:
Consult the cumulative standard table using z = 1.2 as an entry. Z-scores are in the first column of the mentioned table. In the first row of it we have +0.00, +0.01, +0.02 and, finally, +0.03. The probability is the point that result from the intersection of z = 1.2 and +0.03 in the table, which is [tex] \\ P(z<1.23) = 0.89065[/tex].Following the same procedure, the cumulative probability for [tex] \\ z = 0.86[/tex] is:
[tex] \\ P(z<0.86) = 0.80511[/tex]
Subtracting both probabilities (because we need to know the area between these two values) we finally obtain the corresponding area between them (two z-scores):
[tex] \\ P(0.86 < z < 1.23) = 0.89065 - 0.80511[/tex]
[tex] \\ P(0.86 < z < 1.23) = 0.08554[/tex]
Therefore, the area of the shaded region between [tex] \\ z = 1.23[/tex] and [tex] \\ z = 0.86[/tex] is [tex] \\ P(0.86 < z < 1.23) = 0.08554[/tex] or 8.554%.
We can see this resulting area (red shaded area) in the graph below for a standard normal distribution, [tex] \\ N(0, 1)[/tex], and [tex] \\ z = 0.86[/tex] and [tex] \\ z = 1.23[/tex].
Alex is planning to surround his pool ABCD with a single line of tiles. How many units of tile will he need to surround his pool? Round your answer to the nearest hundredth.
Answer:
19.82 units
Step-by-step explanation:
The number of units of tile simply refers to the perimeter.
So, we need to find all the sides of the rectangle.
Now, we have AB = 4.24 units and BD = 7.07 units.
So, we can find AD using pythagoras theorem.
So,
(AD)² + 4.24² = 7.07²
(AD)² + 17.978 = 49.985
(AD)² = 49.985 - 17.978
AD = √32.007
AD = 5.66 units
AD = BC = 5.66 units
Likewise, AB = DC = 4.24 units
Thus,
perimeter = 2(5.66) + 2(4.24) = 19.8 units
Closest answer among the options is approximately 19.82
Answer:
19.82 units
Step-by-step explanation:
just took test and got it right
Could someone please help me with the steps for this problem? Factor by grouping: w²+3w+w+3
Answer:
Please see steps below
Step-by-step explanation:
In order to factor by grouping, we divide the four terms given into two groups, and extract on each group any common factor we can.
In our example, we can select the terms: [tex]w^2[/tex] and [tex]w[/tex] as one of our groups, and [tex]3w[/tex] and 3 in the other group. Then we re-organize the expression as:
[tex](w^2+w)+(3x+3)[/tex]
Now we extract from the first binomial group, the factor [tex]w[/tex] as a common factor of both terms, and from the second group we extract the factor "3" as common factor of those two terms:
[tex](w^2+w)+(3x+3)\\w(w+1)+3(w+1)[/tex]
We notice now that after the extraction, we are left with two exactly equal binomial factors [tex](w+1)[/tex] that appeared in the first group and in the second group. We proceed then to extract it as common factor for the two groups:
[tex]w(w+1)+3(w+1)\\(w+1)(w+3)[/tex]
this last product of two binomials ([tex](w+1)\,(w+3)[/tex] is the result of factoring the original expression.
The perimeter of the rectangle is 28 units.
A rectangle with perimeter 28 units is shown. The length of the sides is w, and the length of the top and bottom sides are 2 w minus 1.
What is the value of w?
5 units
7 units
14 units
15 units
Answer:
5 units
Step-by-step explanation:
P=2(w)+2(2w-1)
28=2w+4w-2
30=6w
w=5
Answer:
5
Step-by-step explanation:
1)Twelve years ago Jane was five times as old as Anne. In three years time,Anne will be half Jane's age How old is each girl at the moment
Answer:
Step-by-step explanation:
Twelve years ago Jane was five times as old as Anne.
J-12=5(A-12)
In three years time, Anne will be half of Jane's age.
A+3=1/2(J+3)
Simplify and solve this system of equations:
J-12=5(A-12)
A+3=1/2(J+3)
Able, ben and cal each played a game.
able scored six times bens score.
cal scored a third of able's score. write down the ratio of able's score to ben;s score to cal's score
Answer:
Ratio of Able's score to Ben=6:1
Ratio of Ben's score to Cal's=1:2
Ratio of able's score to ben;s score to cal's score=6:1:2
Step-by-step explanation:
Let Ben's score =x
Able scored six times Ben's score
Able=6*x
=6x
Cal scored a third of Able's score
Cal=1/3 of 6x
=1/3(6x)
Ratio of Able's score to Ben
6x:x
=6:1
Ratio of Ben's score to Cal's score
x:1/3(6x)
=x:6x/3
=x:2x
=1:2
Ratio of able's score to ben;s score to cal's score=6:1:2
Based on her weight and pace, Kate burns 586 calories when she runs 5 miles. How many calories will she burn if she runs only 3 miles? How many miles (to the nearest mile) does she need to run each week if she wants to burn one pound (3500 calories) of body fat each week?
Answer:
Dear dandrexbox
Answer to your query is provided below
She will burn 351.6 calories if she run 3 miles.
She needs to run 4 miles (approx) per day for a week to burn one pound calories.
Step-by-step explanation:
Explanation for the same is attached in image
Two voting districts, C and M, were sampled to investigate voter opinion about tax spending. From a random sample of 100 voters in District C, 22 percent responded yes to the question "Are you in favor of an increase in state spending on the arts?" An independent random sample of 100 voters in District M resulted in 26 percent responding yes to the question. A 95 percent confidence interval for the difference
Answer:
Step-by-step explanation:
Confidence interval for the difference in the two proportions is written as
Difference in sample proportions ± margin of error
Sample proportion, p= x/n
Where x = number of success
n = number of samples
For district C,
x = 22
n1 = 100
p1 = 22/100 = 0.22
For district M,
x = 26
n2 = 100
p2 = 26/100 = 0.26
Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, the z score for the confidence level of 95% is 1.96
Margin of error = 1.96 × √[0.22(1 - 0.22)/100 + 0.26(1 - 0.26)/100]
= 1.96 × √0.00364
= 0.12
Confidence interval = (0.22 - 0.26) ± 0.12
= - 0.04 ± 0.12
The required 95 percent confidence interval for the difference is ( 0.8, 0.16).
Given that,
A random sample of 100 voters in District C, 22 percent responded yes to The question "Are you in favor of an increase in state spending on the arts?"
An independent random sample of 100 voters in District M resulted in 26 percent responding yes to the question.
We have to determine,
A 95 percent confidence interval for the difference.
According to the question,
A random sample of 100 voters in District C, 22 percent responded yes to The question "Are you in favor of an increase in state spending on the arts?"
An independent random sample of 100 voters in District M resulted in 26 percent responding yes to the question.
Confidence interval for the difference in the two proportions is written as,
Difference in sample proportions ± margin of error
Sample proportion, p= x/n
Where x = number of success
n = number of samples
From a random sample of 100 voters in District C,
[tex]x = 22\\\\n_1= 100\\\\p_1 = \dfrac{22}{100} = 0.22[/tex]
From a random sample of 100 voters in District M,
[tex]x = 26\\\\n_1= 100\\\\p_1 = \dfrac{26}{100} = 0.26[/tex]
Therefore,
[tex]Margin \ of \ error = \sqrt{\dfrac{p_1(1-p_1}{n_1} + \dfrac{p_2(1-p_2)}{n_2}}[/tex]
To determine the z score, subtract the confidence level from 100% to get b
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since, the area in the middle, it becomes
1 - 0.025 = 0.975
The z-score corresponding to the area on the z table is 1.96. Thus, the z score for the confidence level of 95% is 1.96,
[tex]Margin \ of \ error = \sqrt{\dfrac{0.22(1-0.22)}{100} + \dfrac{0.26(1-0.26)}{100}}[/tex]
[tex]= \sqrt{\dfrac{0.22(0.78)}{100} +\dfrac{0.26(0.76)}{100}}\\\\= \sqrt{\dfrac{0.17}{100}+ \dfrac{0.19}{100}}\\\\= \sqrt{\dfrac{0.36}{100}}\\\\= \sqrt{0.0036}\\\\= 0.06[/tex]
Then, Confidence interval is given as;
[tex](0.22 - 0.26) \pm 0.12\\\\(-0.4) \pm 0.12\\\\(-0.4+0.12 , -0.4-0.12)\\\\(0.8, 0.16)[/tex]
Hence, The required 95 percent confidence interval for the difference is( 0.8, 0.16)
To know more about Confidence interval click the link given below.
https://brainly.com/question/15349022
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 1.25 minutes.
Answer:
P(greater than 1.25 minutes) = 0.8611 (Approx)
Step-by-step explanation:
Given:
Waiting time = 0 - 9 minutes
Find:
Probability that selected passenger has a waiting time greater than 1.25 minutes.
Computation:
⇒ The probability that a randomly selected passenger has a waiting time greater than 1.25 minutes =
⇒ P(greater than 1.25 minutes) = [9-1.25] / 9
⇒ P(greater than 1.25 minutes) = [7.75] / 9
⇒ P(greater than 1.25 minutes) = 0.8611 (Approx)
Write two trinomials that you can factor into two binomials. Factor each trinomial. Then write one trinomial that you cannot factor and explain why.
Answer:
- Trinomials that can be factored into two binomials are:
1. x² + 5x + 6
Factored to: (x + 3)(x + 2)
2. x² + x - 2
Factored to: (x - 1)(x + 2)
Example of a Trinomial that cannot be factored into two binomials:
x² + 5x + 1
Step-by-step explanation:
- A trinomial is a polynomial that consist of three terms. It is in the form:
ax² + bx + c.
- A binomial is a polynomial that consists of two terms. It is of the form:
bx + c.
A trinomial is said to be factorable if the can be written as a product of two binomials.
Example 1:
The expression: x² + 5x + 6
Can be rewritten as:
x² + 2x + 3x + 6
Grouping this, we have
(x² + 2x) + (3x + 6)
Which becomes
x(x + 2) + 3(x + 2)
Factoring (x + 2), we have
(x + 3)(x + 2)
Which is a product of two binomials as required.
Therefore, the expression is factorable.
Example 2:
The trinomial expression:
x² + x - 2
Can be written as:
x² + 2x - x - 2
= (x² + 2x) - (x + 2)
= x(x + 2) - (x + 2)
Factoring (x + 2), we have
(x - 1)(x + 2)
This a product of two binomials, hence, the tutorial is factorable.
Example 3:
Consider the trinomial:
x² + 5x + 1
This is not factorable, because the term 5x cannot be split into a sum or difference, in such a way that it has a common factor with x² and with 1.
Unlike in the case of Example 1.
x² + 5x + 6
5x was split into the sum of 2x and 3x
That is, x² + 5x + 6 = x² + 2x + 3x + 6
So that, 2x has a common factor, x with x², and 3x has a common factor, 3 with 6.