Answer:
Step-by-step explanation:
[tex]\int\limits^{\infty}_0 {A^2_1} (e^{-r/a})r^2dr= {A^2_1}\int\limits^{\infty}_0r^2(e^{-r/a})^2\, dr)[/tex]
[tex]=A_1^2\int\limits^{\infty}_0 r^2e^{-2r/a}\ dr[/tex]
[tex]=A_1^2[\frac{r^2e^{2r/a}}{-2/a} |_0^{\infty}-\int\limits^{\infty}_0 2r\frac{e^{-2r/a}}{-2/a} \ dr][/tex]
[tex]=A^2_1[0+\int\limits^{\infty}_0 a\ r\ e^{-2r/a}\ dr][/tex]
[tex]=A^2_1[\frac{a \ r \ e^{-2r/a}}{-2/a} |^{\infty}_0-\int\limits^{\infty}_0 \frac{a \ e^{-2r/a}}{-2/a} \ dr][/tex]
[tex]=A_0^2[0-0+\int\limits^{\infty}_0 \frac{a^2}{2} e^{-2r/a}\ dr\\\\=A_1^2\frac{a^2}{2} \int\limits^{\infty}_0 e^{-2r/a}\ dr\\\\=A_1^2\frac{a^2}{2} [\frac{e^{-2r/a}}{-2/a} ]^{\infty}_0[/tex]
[tex]=\frac{A_1^2a^2}{2} -\frac{a}{2} [ \lim_{r \to \infty} [e^{-2r/a} -e^0]\\\\=\frac{A_1^2a^2}{2} -(\frac{a}{2}) (0-1)[/tex]
[tex]=\frac{A_1^2a^3}{4}[/tex]
[tex]\therefore A_1^2\int\limits^{\infty}_0 r^2(e^{-r/a}) \ dr =\frac{A_1^2a^3}{4}[/tex]
Find the unique positive value of A1
[tex]=4\pi (\frac{A_1^2a^3}{4} )\\\\=A_1^2a^3\pi\\\\A_1^2=\frac{1}{a^3\pi} \\\\A_1=\sqrt{\frac{1}{a^3\pi} }[/tex]
Several surveys in the United States and Europe have asked people to rate their happiness on a scale of 3 = "very happy," 2 = "fairly happy," and 1 = "not too happy," and then tried to correlate the answer with the person's income. For those in one income group (making $25,000 to $55,000) it was found that their "happiness" was approximately given by y = 0.065x − 0.613, where x is in thousands of dollars.† Find the reported "happiness" of a person with the following incomes (rounding your answers to one decimal place).
Answer:
Step-by-step explanation:
We have to find the reported happiness of person of family income of $25,000, $35,000 and $45,000
Given that the formula for finding relation between a people happiness and his income is
y = 0.065x - 0.613
a) find the happiness of person of family income os $25,000
we put x = 25 as in the equation above
[tex]y=0.065(25)-0.613\\\\=1.625-0.613\\\\=1.02 \approx 1[/tex]
Hence, person happiness with with family income of $25,000 on a scale of 3 is y = 1
That means they come under catergory "not to happy"
b) Find the happiness of person of family income os $35,000
we put x = 35 as in the equation above
[tex]y=0.065(35)-0.613\\\\=1.667-0.613\\\\=1.667 \approx 1.7[/tex]
Hence, person happiness with with family income of $35,000 on a scale of 3 is y = 1.7
That means they come under catergory "not to happy" and "fairly happy"
c) Find the happiness of person of family income os $45,000
we put x = 45 as in the equation above
[tex]y=0.065(45)-0.613\\\\=2.925-0.613\\\\=2.312 \approx 2.3[/tex]
Hence, person happiness with with family income of $45,000 on a scale of 3 is y = 2.3
That means they come under catergory "fairly happy"
The scale would show the data as follows:
Happiness Scale at Income 25, 35, 45 & 55 thousand :
1.012 (Not too happy), 1.662 (Fairly Happy), 2.315 (Fairly Happy) , 2.965 (Very Happy)
Determine the scaleImportant Information :
Relationship between happiness scale 'y' and income in 1000s 'x' :y = 0.065x − 0.613, for people in income group between [tex]25000 & 55000[/tex]
Happiness scale : At level of income, between 25 and 55 thousands.
Putting value of income 'x' to find scale of happiness i.e. 'y'
For income 'x' = 25 thousand : [tex]y = 0.065 (25) - 0.613 = 1.625 - 0.613 = 1.012[/tex] For income 'x' = 35 thousand : [tex]y = 0.065 (35) - 0.613 = 2.275 - 0.613 = 1.662[/tex]For income 'x' = 45 thousand : [tex]y = 0.065 (45) - 0.613 = 2.925 - 0.61 = 2.315[/tex] For income 'x' = 55 thousand :[tex]y = 0.065 (55) - 0.613 = 3.575 - 0.61 = 2.965[/tex]
Learn more about "Happiness Scale" here:
brainly.com/question/25609130
3. Match each staternent with an expression that could be used to find the price
p+ 0.3p
0.7p
e. 85% more than the original time
f 15% less time than the original
g. 85% time decrease
h, 15% time increase
17p
p-07p
I
4. Ronnie increased the amount of money in his piggy bank by 25%. Which expres
find the amount of money in his bank? Let "m" represent the original
Answer:
3a) 30% more than original price
b) 70% of the original price
c) 17times the original price
d) 70% less than original price
e) t + 0.85t
f) t - 0.15t
g) t - 0.85t
h) t + 0.15t
4. The expression that can be used to find the amount of money in his bank = m + 0.25m
Question:
3. Match each statement with an expression that could be used to find the price.
'The expressions for a to d were not stated in the question'.
a) p+ 0.3p
b) 0.7p
c) 17p
d) p-07p
'From e to h, we were not told what to determine'.
Write the expression in terms of time
e. 85% more than the original time
f. 15% less time than the original
g. 85% time decrease
h. 15% time increase
4. Ronnie increased the amount of money in his piggy bank by 25%. Which expression can be used to find the amount of money in his bank? Let "m" represent the original.
Step-by-step explanation:
let original price = p
a) p+ 0.3p = p + 30% of p
30% more than original price
b) 0.7p = 70% of p
= 70% of the original price
c) 17p = 17 × p
= 17times of the original price
d) p-0.7p = p - 70% of p
= 70% less than original price
Let original time = t
e) 85% more than the original time = t + 85%of t
= t + 0.85t
f) 15% less time than the original time = t - 15% of t
= t - 0.15t
g) 85% time decrease = t - 85% of t
= t - 0.85t
h) 15% time increase = t + 15% of t
= t + 0.15t
4. Since "m" represent the original amount in Hus piggy bank
An increase of 25% = original amount + 25% of original amount
= m + 25% of m
'Of' means multiplication
= m + 0.25 ×m
= m + 0.25m
= 1.25m
The expression that can be used to find the amount of money in his bank = m + 0.25m
Simplify the answer pls
Answer:
[tex]\frac{9}{8}[/tex]
Step-by-step explanation:
27 ÷ 9 = 3
3 * 3 = 9
9 ÷ 8 = [tex]\frac{9}{8}[/tex]
To solve a polynomial inequality, we factor the polynomial
into irreducible factors and find all the real_______polynomial. Then we find the intervals determined by the real__________sign of the polynomial on that interval. Let
$$P(x)=x(x+2)(x-1)$$
Fill in the diagram to find the intervals on which
$P(x) \geq 0$
we see that $P(x) \geq 0$ on the
intervals_______and________.
Answer:
To solve a polynomial inequality, we factor the polynomial into irreducible factors and find all the real _zeros_ polynomial. Then we find the intervals determined by the real _zeros and use test points in each interval to find the_ sign of the polynomial on that interval.
If P(x) = x(x+2)(x-1)
And P(x) ≥ 0
We see that P(x) ≥ 0 on the intervals (-2, 0) and (1, ∞).
Step-by-step explanation:
The complete question is attached to this solution
To solve inequality of a polynomial, we first obtain the solutions of the polynomial. The solutions of the polynomial are called the zeros of the polynomial.
If P(x) = x(x+2)(x-1)
The solutions of this polynomial, that is the zeros of this polynomial are 0, -2 and 1.
To now solve the inequality that arises when
P(x) ≥ 0
We redraw the table and examine the intervals
The intervals to be examined as obtained from the zeros include (-∞, -2), (-2, 0), (0, 1) and (1, ∞)
Sign of | x<-2 | -2<x<0 | 0<x<1 | x>1
x | -ve | -ve | +ve | +ve
(x + 2) | -ve | +ve | +ve | +ve
(x - 1) | -ve | -ve | -ve | +ve
x(x+2)(x-1) | -ve | +ve | -ve | +ve
The intervals that satisfy the polynomial inequality P(x) = x(x+2)(x-1) ≥ 0 include
(-2, 0) and (1, ∞)
Hope this Helps!!!
The top and bottom margins of a poster are each 15 cm and the side margins are each 10 cm. If the area of printed material on the poster is fixed at 2400 cm2, find the dimensions of the poster with the smallest area.
Answer:
the dimension of the poster = 90 cm length and 60 cm width i.e 90 cm by 60 cm.
Step-by-step explanation:
From the given question.
Let p be the length of the of the printed material
Let q be the width of the of the printed material
Therefore pq = 2400 cm ²
q = [tex]\dfrac{2400 \ cm^2}{p}[/tex]
To find the dimensions of the poster; we have:
the length of the poster to be p+30 and the width to be [tex]\dfrac{2400 \ cm^2}{p} + 20[/tex]
The area of the printed material can now be: [tex]A = (p+30)(\dfrac{2400 }{p} + 20)[/tex]
=[tex]2400 +20 p +\dfrac{72000}{p}+600[/tex]
Let differentiate with respect to p; we have
[tex]\dfrac{dA}{dp}= 20 - \dfrac{72000}{p^3}[/tex]
Also;
[tex]\dfrac{d^2A}{dp^2}= \dfrac{144000}{p^3}[/tex]
For the smallest area [tex]\dfrac{dA}{dp }=0[/tex]
[tex]20 - \dfrac{72000}{p^2}=0[/tex]
[tex]p^2 = \dfrac{72000}{20}[/tex]
p² = 3600
p =√3600
p = 60
Since p = 60 ; replace p = 60 in the expression q = [tex]\dfrac{2400 \ cm^2}{p}[/tex] to solve for q;
q = [tex]\dfrac{2400 \ cm^2}{p}[/tex]
q = [tex]\dfrac{2400 \ cm^2}{60}[/tex]
q = 40
Thus; the printed material has the length of 60 cm and the width of 40cm
the length of the poster = p+30 = 60 +30 = 90 cm
the width of the poster = [tex]\dfrac{2400 \ cm^2}{p} + 20[/tex] = [tex]\dfrac{2400 \ cm^2}{60} + 20[/tex] = 40 + 20 = 60
Hence; the dimension of the poster = 90 cm length and 60 cm width i.e 90 cm by 60 cm.
What is the final amount if 700 is increased by 4% followed by a further 3% increase
Answer:
8400
Step-by-step explanation:
Its too long and I answered it before
The amount of time, in minutes, that a woman must wait for a cab is uniformly distributed between zero and 12 minutes, inclusive. What is the probability that a person waits fewer than 11 minutes
Answer:
[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]
And using this formula we have this:
[tex] P(X<11) = \frac{11-0}{12-0}= 0.917[/tex]
Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917
Step-by-step explanation:
Let X the random variable of interest that a woman must wait for a cab"the amount of time in minutes " and we know that the distribution for this random variable is given by:
[tex] X \sim Unif (a=0, b =12)[/tex]
And we want to find the following probability:
[tex] P(X<11)[/tex]
And for this case we can use the cumulative distribution function given by:
[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]
And using this formula we have this:
[tex] P(X<11) = \frac{11-0}{12-0}= 0.917[/tex]
Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917
The function f determines the volume of the box (in cubic inches) given a cutout length (in inches). Use function notation to represent the volume of the box (in cubic inches) when the cutout length is 0.2 inches. Use function notation to represent the volume of the box (in cubic inches) when the cutout length is 1.3 inches. Use function notation to represent how much the volume of the box (in cubic inches) changes by if the cutout length increases from 0.2 inches to 1.3 inches. Use function notation to represent how much the volume of the box (in cubic inches) changes by if the cutout length increases from 5.5 inches to 5.6 inches.
Complete Question
A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides. However, the size of the paper is unknown!
Answer:
(a)[tex]f(0.2)=0.2(l-0.4)(w-0.4)[/tex]
(b)[tex]f(1.3)=1.3(l-2.6)(w-2.6)[/tex]
(c)f(1.3)-f(0.2)
(d) f(5.6)-f(5.5)
Step-by-step explanation:
Let the Length of the paper =l (in inches)
Let the Width of the paper =w (in inches)
Let the length of the cutout square = x (in inches)
Base Length of the Box = l-2xBase Width of the box =w-2xHeight of the box =xVolume of the box: [tex]f(x)=x(l-2x)(w-2x)[/tex]
(a)When the cutout length is 0.2 inches.
x=0.2
Volume of the box (in cubic inches) ,
[tex]f(0.2)=0.2(l-0.4)(w-0.4)[/tex]
(b)When the cutout length is 01.3 inches.
x=1.3
Volume of the box (in cubic inches) ,
[tex]f(1.3)=1.3(l-2.6)(w-2.6)[/tex]
(c)If the cutout length increases from 0.2 inches to 1.3 inches.
Change In volume (in cubic inches):
[tex]f(1.3)-f(0.2)\\=1.3(l-2.6)(w-2.6)-0.2(l-0.4)(w-0.4)[/tex]
(d)If the cutout length increases from 5.5 inches to 5.6 inches.
Change In volume (in cubic inches):
[tex]f(5.6)-f(5.5)\\=5.6(l-11.2)(w-11.2)-5.5(l-11)(w-11)[/tex]
Can You please help me cause I'm gangsta Simplify (5^-2)^4
Answer:
( 5 ^ -2)^4
= 5 ^ -8
= 1 /5^8
= 1 / 390,625
Maya is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Company A has no initial fee but charges 80 cents for every mile driven. Company B charges an initial fee of $65 and an additional cents for every mile driven. For what mileages will Company A charge more than Company B? Use m for the number of miles driven, and solve your inequality for m .
Answer:
m > 82.28
Step-by-step explanation:
Price to Pay (P)
distance (m)
Company A
Pa = 0.80m
Company B
Pb = 65 + 0.01m
Company A charge more than B is written like this
0.8m > 65 + 0.01m
then we can solve this inequality
(0.8 - 0.01)m > 65
0.79m > 65
m > 65/0.79
m > 82.28 miles
so if Maya will go more than 82.28 miles, I suggest Company B is cheaper
Write an equation in slope-intercept form for the line that passes through (0,1) and (1,3)
Answer:
y= 2x+1
Step-by-step explanation:
Points:
(0,1) and (1,3)Form of the line:
y=mx+b, m- the slope, b- y-interceptFinding the slope:
m= (y2-y1)/(x2-x1)m=(3-1)/(1-0)= 2/1= 2Line is now:
y= 2x+bUsing one of the given points to find out the value of b:
1=2*0+bb=1So the equation for the line is:
y= 2x+1Find the slope of the line: 3x-2y=6
Answer:
slope = 3/2
Step-by-step explanation:
3x-2y=6
Get this equation in the form y = mx+b where m is the slope and b is the y intercept
Subtract 3x from each side
3x-3x-2y=-3x+6
-2y = -3x+6
Divide each side by -2
-2y/-2 = -3x/-2 +6/-2
y = 3/2x -3
The slope is 3/2 and the y intercept is -3
Answer:
3/2
Step-by-step explanation:
I got this answer by putting it in the form y=mx+b
Step 1: Subtract 3x from each side
-2y = -3x+6
Step 2: Divide each side by -2
y = 3/2x -3
The slope is 3/2 and the y intercept is -3 because m is the slope and b is the y-intercept.
is the square root of 5/8 rational or irrational
Answer:
the answer is square root 5 over 2 square root 2
Step-by-step explanation:
In determining automobile-mileage ratings, it was found that the mpg (X) for a certain model is normally distributed, with a mean of 33 mpg and a standard deviation of 1.7 mpg. Find the following:__________.
a. P(X<30)
b. P(28
c. P(X>35)
d. P(X>31)
e. the mileage rating that the upper 5% of cars achieve.
Answer:
a) P(X < 30) = 0.0392.
b) P(28 < X < 32) = 0.2760
c) P(X > 35) = 0.1190
d) P(X > 31) = 0.8810
e) At least 35.7965 mpg
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 33, \sigma = 1.7[/tex]
a. P(X<30)
This is the pvalue of Z when X = 30. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30 - 33}{1.7}[/tex]
[tex]Z = -1.76[/tex]
[tex]Z = -1.76[/tex] has a pvalue of 0.0392.
Then
P(X < 30) = 0.0392.
b) P(28 < X < 32)
This is the pvalue of Z when X = 32 subtracted by the pvalue of Z when X = 28. So
X = 32
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{32 - 33}{1.7}[/tex]
[tex]Z = -0.59[/tex]
[tex]Z = -0.59[/tex] has a pvalue of 0.2776.
X = 28
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28 - 33}{1.7}[/tex]
[tex]Z = -2.94[/tex]
[tex]Z = -2.94[/tex] has a pvalue of 0.0016.
0.2776 - 0.0016 = 0.2760.
So
P(28 < X < 32) = 0.2760
c) P(X>35)
This is 1 subtracted by the pvalue of Z when X = 35. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35 - 33}{1.7}[/tex]
[tex]Z = 1.18[/tex]
[tex]Z = 1.18[/tex] has a pvalue of 0.8810.
1 - 0.8810 = 0.1190
So
P(X > 35) = 0.1190
d. P(X>31)
This is 1 subtracted by the pvalue of Z when X = 31. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{31 - 33}{1.7}[/tex]
[tex]Z = -1.18[/tex]
[tex]Z = -1.18[/tex] has a pvalue of 0.1190.
1 - 0.1190 = 0.8810
So
P(X > 31) = 0.8810
e. the mileage rating that the upper 5% of cars achieve.
At least the 95th percentile.
The 95th percentile is X when Z has a pvalue of 0.95. So it is X when Z = 1.645. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 33}{1.7}[/tex]
[tex]X - 33 = 1.645*1.7[/tex]
[tex]X = 35.7965[/tex]
At least 35.7965 mpg
The upper 5% of cars have a mileage rating of 35.805 mpg
What is z score?Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean) / standard deviation
Given; mean of 33 mpg and a standard deviation of 1.7
a) For < 30:
z = (30 - 33)/1.7 = -1.76
P(x < 30) = P(z < -1.76) = 1 - 0.8413 = 0.0392
b) For < 28:
z = (28 - 33)/1.7 = -2.94
P(x < 28) = P(z < -2.94) = 0.0016
c) For > 35:
z = (35 - 33)/1.7 = 1.18
P(x > 35) = P(z > 1.18) = 1 - P(z < 1.18) = 1 - 0.8810 = 0.119
d) For > 31:
z = (31 - 33)/1.7 = -1.18
P(x > 31) = P(z > -1.18) = 1 - P(z < -1.18) = 0.8810
e) The upper 5% of cars achieve have a z score of 1.65, hence:
1.65 = (x - 33)/1.7
x = 35.805 mpg
The upper 5% of cars have a mileage rating of 35.805 mpg
Find out more on z score at: https://brainly.com/question/25638875
3. In 28 days, a person saved $42. What was this person's
average daily savings?
Answer:
The average would be 42 / 28 = $1.50 / day.
Answer:
$1.50 per day
Step-by-step explanation:
Take the dollar amount and divide by the number of days
42 dollars / 28 days
1.50 dollars per day
$1.50 per day
The lifespan (in days) of the common housefly is best modeled using a normal curve having mean 22 days and standard deviation 5. Suppose a sample of 25 common houseflies are selected at random. Would it be unusual for this sample mean to be less than 19 days?
Answer:
Yes, it would be unusual.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
If [tex]Z \leq -2[/tex] or [tex]Z \geq 2[/tex], the outcome X is considered unusual.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 22, \sigma = 5, n = 25, s = \frac{5}{\sqrt{25}} = 1[/tex]
Would it be unusual for this sample mean to be less than 19 days?
We have to find Z when X = 19. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{19 - 22}{1}[/tex]
[tex]Z = -3[/tex]
[tex]Z = -3 \leq -2[/tex], so yes, the sample mean being less than 19 days would be considered an unusual outcome.
I need this question today. Pls help
[tex]answer \\ = 2 , 4 , 5 \\ additional \: information \\ let \: r \: be \: a \: relation \: a \: to \: b. \: then \: the \: set \\ of \: first \: components \: or \: the \: set \: of \: \\ elements \: of \: a \: are \: called \: domain \\ and \: the \: set \: of \: second \: components \\ or \: the \: set \: of \: elements \: of \: b \: are \: called \: the \: range. \\ hope \: it \: helps[/tex]
Please answer this correctly
Answer:
10 players
Step-by-step explanation:
If you count the x’s, there are 10.
Why ask this question? You could have just counted
Answer:
22 players
Step-by-step explanation:
It specifically says 'at least 3 runs' so you would have to count all the x's in the columns 3, 4, and 5.
There are 10 x's in the 3 column
There are 3 x's in the 4 column
There are 9 x's in the 5 column
Hope this helps!
Life tests performed on a sample of 13 batteries of a new model indicated: (1) an average life of 75 months, and (2) a standard deviation of 5 months. Other battery models, produced by similar processes, have normally distributed life spans. The 98% confidence interval for the population mean life of the new model is _________. Group of answer choices
Answer:
(71.28, 78.72)
Step-by-step explanation:
We have the following information from the statement:
mean (m) = 75
sample standard deviation (sd) = 5
Sample size (n) = 13
Significance level (alpha) = 1 - 0.98 = 0.02
Degrees of freedom for t-d (df) = n - 1 = 13 - 1 = 12
The critical value would be:
t (alpha / 2) / df = T (0.01) / 12 = 2,681 (this for the table)
Margin of error equals:
E = t (alpha / 2) / df * sd / n ^ (1/2), replacing:
E = 2,681 * 5/13 ^ (1/2)
E = 3.72
Therefore, the interval of 98% confidence interval would be:
75 + 3.72 = 78.72
75 - 3.72 = 71.28
(71.28, 78.72)
Florian ran 1.2 miles and walked 4.8 laps around the path at the park for a total distance of 3.6 miles. Which shows the correct equation and value of x, the distance of 1 lap around the path at the park? 3.6 x + 1.2 = 4.8; x = 1 mile 4.8 x + 1.2 = 3.6; x = 1 mile 3.6 x + 1.2 = 4.8; x = 0.5 mile 4.8 x + 1.2 = 3.6; x = 0.5 mile
Answer:
The correct answer would be D) 4.8x + 1.2 = 3.6; x = 0.5 mile
Step-by-step explanation:
This is because laps would be the dependent variable, so we know the number of them (4.8) would be multiplied by the variable (x). We also know that 1.2 is the constant. Now we can solve to make sure this is the right equation.
4.8x + 1.2 = 3.6
4.8x = 2.4
x = 0.5
Answer:
D) 4.8x + 1.2 = 3.6; x = 0.5 miles
What’s the correct answer for this?
Answer:
D
Step-by-step explanation:
Length × Width = Area
So we'll substitute the Area of the circle having formula, πr²
What is the formula to find the area of a triangle
Answer:
A= 1/2bh
Step-by-step explanation:
(how its supposed to be said: Area= one half base times height)
:)
Answer:
(1) As a simple definition, a triangle is a two-dimensional figure that has 3 sides (and 3 angles as well).
(2) A triangle as shown in attached picture has the area that is typical calculated by the multiplication of half of base and height.
A = (1/2) x Base x Height
Base can be a particular side of triangle
Height is the perpendicular line segment between the opposite vertex of selected base and that base.
Hope this helps!
:)
pleas guys can you answer this to me
Answer:
what is this boiii?
A store, on average, has 500 customers per day.
a) what can be said about the probability that it will have at least 700 customers on a given day?
from now on, suppose in addition that the variance of the numbers of customers per day is 100.
b) what can be said about the probability that it will have at least 700 customers on a given day?
c) what can be said about the probability that there will be more than 475 and less than 525 customers on a given day?
Answer:
a) We can not estimate the probability.
b) Zero probability.
c) There is a probability between 95% and 99% that they have between 475 and 525 customers on a given day.
Step-by-step explanation:
a) We can not said nothing because we only know the average of customers per day. We need to know the probability distribution of the amount of customers per day to answer this question.
b) Now that we know that the variance is 100, although we do not know the exact distribution of the values, we can use the empirical rules to estimate the probability of having at least 700 customers on a given day.
If the variance is 100, the standard deviation is √100=10.
Applying the empirical rule (68-95-99.7 rule), we know that there is probability 0.15% of having at least 500+3*10=530 customers per day (more than 3 deviations from the mean).
Then, we can conclude that the probability of having at least 700 customers per day is zero.
c) To estimate this probability, we have to calculate how many deviations from the mean this values represent:
[tex]\Delta_1=475-500=-25=2.5\sigma\\\\\Delta_2=525-500=25=2.5\sigma[/tex]
We have an interval that have a width of ±2.5 deviations from the mean.
For 2 deviations from the mean, it is expected to have 95% of the data.
For 3 deviations from the mean, it is expected to have 99.7% of the data.
Then, for the interval 475 to 525, we can estimate a probability between 95% and 99%.
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
Answer:
–2(5 – 4x) < 6x – 4
<=>
-10 + 8x < 6x - 4
<=>
2x < 6
<=>
x < 3
Hope this helps!
:)
Answer:
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
A. x < –3
B. x > –3
C. x < 3
D. x > 3
Step-by-step explanation:
The correct answer here is C. x < 3
These tables of values represent continuous functions. For which function will the y-values be the greatest for very large values of x?
Answer:
C
Step-by-step explanation:
The function of table A can be written as ...
y = 100x -92
__
The function of table B can be written as ...
y = 10x +446
__
The function of table C can be written as ...
y = (5/3)·3^x
__
The function of table D can be written as ...
y = 2x +413
__
The exponential function of Table C will have the largest y-values for any value of x greater than 6.
_____
Comment on the functions
When trying to determine the nature of the function, it is often useful to look at the differences of the y-values for consecutive x-values. Here, the first-differences are constant for all tables except C. That means functions A, B, D are linear functions.
If the first differences are not constant, one can look at second differences and at ratios. For table C, we notice that each y-value is 3 times the previous one. That constant ratio means the function is exponential, hence will grow faster than any linear function.
Answer:
yes, what the other user is correct i just took the quiz
Step-by-step explanation:
Please solve the following inequality 2(3 - x) ≥ 14
Answer:
x ≤ -4
Step-by-step explanation:
2(3 - x) ≥ 14
Divide by 2
2/2(3 - x) ≥ 14/2
(3 - x) ≥ 7
Subtract 3 from each side
3-x-3 ≥ 7-3
- x ≥ 4
Divide each side by -1, remembering to flip the inequality
x ≤ -4
Answer:
-4
Step-by-step explanation:
6-2x≥14 (/expand )
-2x≥14-6=-2x≥8
x≤8/-2=-4
Michelle purchased a sofa that was on sale for $125 off. The original price of the sofa was $515. What was the sale price of the sofa?
Answer:
We know that:
The original price was $515
and
It was $125 off
so we need to find the price of the sofa after the discount.
$515 - $125 = $390
The sale price of the sofa after the discount was $390
hope This helps and pls mark me brainliest if it did :)
If f(x) = –8 – 5x, what is f(–4)?
Answer:
12
Step-by-step explanation:
f(-4) = -8-5(-4) = -8+20 = 12
Answer:
f(-4) = 12
Step-by-step explanation:
f(-4) = -8 - 5(-4)
= -8 + 20
= 12
which is a correct first step in solving the inequality-4(2x-1)>5-3x
Step-by-step explanation:
-8x + 4 > 5 - 3x
-8x + 3x > 5 - 4
-5x > 1
x > 1 / - 5
