Answer:
The one with the better deal would be 30 ride tickets for $22.50 this is because you pay less money for more rides.
Step-by-step explanation:
First you divide 20 by 14. Doing this will give you the cost of a ride per ticket.
20/14 = 1.42
Then you do the same thing to 30 and 22.50.
30/22.50 = 1.30
Last you compare which deal has less money per ride.
1.42 > 1.30
simplify 2^3 ÷ 2^-3
leave your answer in the form 2^x, where x is an integer
these are the options for the answer
1
0
2^0
2^6
Answer:
[tex]2^{6}[/tex]
Step-by-step explanation:
[tex]2^3 \div 2^{-3}[/tex]
[tex]2^{3-(-3)}[/tex]
[tex]2^{3+3}[/tex]
[tex]2^{6}[/tex]
1. Use limit comparison test to determine whether the series converges or diverges:
Σ[infinity]_n=1 n^2 + 1 / 2n^3 - 1
2. Use limit comparison test to determine whether the series converges or diverges:
Σ[infinity]_n = 1 n / √n^5 + 5
3. Use direct comparison test to determine whether the series converges or diverges:
Σ[infinity]_n = 1 4 + 3^n / 2^n
Answer:
1. Diverges
2. Converges
3. Diverges
Step-by-step explanation:
Solution:-
Limit comparison test:
- Given, ∑[tex]a_n[/tex] and suppose ∑[tex]b_n[/tex] such that both series are positive for all values of ( n ). Then the following three conditions are applicable for the limit:
Lim ( n-> ∞ ) [tex][ \frac{a_n}{b_n} ][/tex] = c
Where,
1) If c is finite: 0 < c < 1, then both series ∑[tex]a_n[/tex] and ∑[tex]b_n[/tex] either converges or diverges.
2) If c = 0, then ∑[tex]a_n[/tex] converges only if ∑[tex]b_n[/tex] converges.
3) If c = ∞ or undefined, then ∑[tex]a_n[/tex] diverges only if ∑[tex]b_n[/tex] diverges.
a) The given series ∑[tex]a_n[/tex] is:
(n = 1) ∑^∞ [tex][ \frac{n^2+1}{2n^3-1} ][/tex]
- We will make an educated guess on the comparative series ∑[tex]b_n[/tex] by the following procedure.
(n = 1) ∑^∞ [tex][ \frac{n^2( 1 + \frac{1}{n^2} )}{n^3 ( 2 - \frac{1}{n^2} ) } ] = [ \frac{( 1 + \frac{1}{n^2} )}{n( 2 - \frac{1}{n^2} ) } ][/tex]
- Apply the limit ( n - > ∞ ):
(n = 1) ∑^∞ [tex][ \frac{1}{2n}][/tex] .... The comparative series ( ∑[tex]b_n[/tex] )
- Both series ∑[tex]a_n[/tex] and ∑[tex]b_n[/tex] are positive series. You can check by plugging various real number for ( n ) in both series.
- Compute the limit:
Lim ( n-> ∞ ) [tex][ \frac{n^2 + 1}{2n^3 - 1} * 2n ] = [ \frac{2n^3 + 2n}{2n^3 - 1} ][/tex]
Lim ( n-> ∞ ) [tex][ \frac{2n^3 ( 1 + \frac{1}{n^2} ) }{2n^3 ( 1 - \frac{1}{2n^3} ) } ] = [ \frac{ 1 + \frac{1}{n^2} }{ 1 - \frac{1}{2n^3} } ][/tex]
- Apply the limit ( n - > ∞ ):
Lim ( n-> ∞ ) [tex][ \frac{a_n}{b_n} ][/tex] = [tex][ \frac{1 + 0}{1 + 0} ][/tex] = 1 ... Finite
- So from first condition both series either converge or diverge.
- We check for ∑[tex]b_n[/tex] convergence or divergence.
- The ∑[tex]b_n[/tex] = ( 1 / 2n ) resembles harmonic series ∑ ( 1 / n ) which diverges by p-series test ∑ ( [tex]\frac{1}{n^p}[/tex] ) where p = 1 ≤ 1. Hence, ∑
- In combination of limit test and the divergence of ∑[tex]b_n[/tex], the series ∑[tex]a_n[/tex] given also diverges.
Answer: Diverges
b)
The given series ∑[tex]a_n[/tex] is:
(n = 1) ∑^∞ [tex][ \frac{n}{n^\frac{5}{2} +5} ][/tex]
- We will make an educated guess on the comparative series ∑[tex]b_n[/tex] by the following procedure.
(n = 1) ∑^∞ [tex][ \frac{n( 1 )}{n ( n^\frac{3}{2} + \frac{5}{n} ) } ] = [\frac{1}{( n^\frac{3}{2} + \frac{5}{n} )} ][/tex]
- Apply the limit ( n - > ∞ ) in the denominator for ( 5 / n ), only the dominant term n^(3/2) is left:
(n = 1) ∑^∞ [tex][ \frac{1}{n^\frac{3}{2} } ][/tex] .... The comparative series ( ∑[tex]b_n[/tex] )
- Both series ∑[tex]a_n[/tex] and ∑[tex]b_n[/tex] are positive series. You can check by plugging various real number for ( n ) in both series.
- Compute the limit:
Lim ( n-> ∞ ) [tex][ \frac{n}{n^\frac{5}{2} +5} * n^\frac{3}{2} ] = [ \frac{n^\frac{5}{2}}{n^\frac{5}{2} +5} ][/tex]
Lim ( n-> ∞ ) [tex][ \frac{n^\frac{5}{2}}{n^\frac{5}{2} ( 1 + \frac{5}{n^\frac{5}{2}}) } ] = [ \frac{1}{1 + \frac{5}{n^\frac{5}{2}} } ][/tex]
- Apply the limit ( n - > ∞ ):
Lim ( n-> ∞ ) [tex][ \frac{a_n}{b_n} ][/tex] = [tex][\frac{1}{1 + 0}][/tex] = 1 ... Finite
- So from first condition both series either converge or diverge.
- We check for ∑[tex]b_n[/tex] convergence or divergence.
- The ∑[tex]b_n[/tex] = ( [tex][ \frac{1}{n^\frac{3}{2} } ][/tex] ) converges by p-series test ∑ ( [tex]\frac{1}{n^p}[/tex] ) where p = 3/2 > 1. Hence, ∑
- In combination of limit test and the divergence of ∑[tex]b_n[/tex], the series ∑[tex]a_n[/tex] given also converges.
Answer: converges
Comparison Test:-
- Given, ∑[tex]a_n[/tex] and suppose ∑[tex]b_n[/tex] such that both series are positive for all values of ( n ).
-Then the following conditions are applied:
1 ) If ( [tex]a_n[/tex] - [tex]b_n[/tex] ) < 0 , then ∑[tex]a_n[/tex] diverges only if ∑[tex]b_n[/tex] diverges
2 ) If ( [tex]a_n[/tex] - [tex]b_n[/tex] ) ≤ 0 , then ∑[tex]a_n[/tex] converges only if ∑[tex]b_n[/tex] converges
c) The given series ∑[tex]a_n[/tex] is:
(n = 1) ∑^∞ [tex][ \frac{4 + 3^2}{2^n} ][/tex]
- We will make an educated guess on the comparative series ∑[tex]b_n[/tex] by the following procedure.
(n = 1) ∑^∞ [tex][ \frac{3^n ( \frac{4}{3^n} + 1 )}{2^n} ][/tex]
- Apply the limit ( n - > ∞ ) in the numerator for ( 4 / 3^n ), only the dominant terms ( 3^n ) and ( 2^n ) are left:
(n = 1) ∑^∞ [tex][ \frac{3^n}{2^n} ][/tex] ... The comparative series ( ∑[tex]b_n[/tex] )
- Compute the difference between sequences ( [tex]a_n[/tex] - [tex]b_n[/tex] ):
[tex]a_n - b_n = \frac{4 + 3^n}{2^n} - [ \frac{3^n}{2^n} ] \\\\a_n - b_n = \frac{4 }{2^n} \geq 0[/tex], for all values of ( n )
- Check for divergence of the comparative series ( ∑[tex]b_n[/tex] ), using divergence test:
∑[tex]b_n[/tex] = (n = 1) ∑^∞ [tex][ \frac{3^n}{2^n} ][/tex] diverges
- The first condition is applied when ( [tex]a_n[/tex] - [tex]b_n[/tex] ) ≥ 0, then ∑diverges only if ∑[tex]b_n[/tex] diverges.
Answer: Diverges
In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of 10.25 hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.
a. Give a mathematical expression for the probability density function of battery life.
b. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?
c. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?
d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?
e. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?
Answer:
a. [tex]f_X(x) = \dfrac{1}{3.5}8.5<x<12[/tex]
b. the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%
c. the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %
d. the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%
e. 86 should have a battery life of at least 9 hours
Step-by-step explanation:
From the given information;
Let X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :
[tex]f_X(x) = \dfrac{1}{B-A}A<x<B[/tex]
where A and B are the two parameters of the uniform distribution
From the question;
Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours
So; Let A = 8,5 and B = 12
Therefore; the mathematical expression for the probability density function of battery life is :
[tex]f_X(x) = \dfrac{1}{12-8.5}8.5<x<12[/tex]
[tex]f_X(x) = \dfrac{1}{3.5}8.5<x<12[/tex]
b. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?
The probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:
F(x) = P(X ≤x)
[tex]F(x) = \dfrac{x-A}{B-A}[/tex]
[tex]F(10) = \dfrac{10-8.5}{12-8.5}[/tex]
F(10) = 0.4286
the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%
c. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?
The battery life for an iPad Mini will be at least 11 hours is calculated as follows:
[tex]P(X\geq11) = \int\limits^{12}_{11} {\dfrac{1}{3.5}} \, dx[/tex]
[tex]P(X\geq11) = {\dfrac{1}{3.5}} (x)^{12}_{11}[/tex]
[tex]P(X\geq11) = {\dfrac{1}{3.5}} (12-11)[/tex]
[tex]P(X\geq11) = {\dfrac{1}{3.5}} (1)[/tex]
[tex]P(X\geq11) = 0.2857[/tex]
the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %
d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?
[tex]P(9.5 \leq X\leq11.5) =\int\limits^{11.5}_{9.5} {\dfrac{1}{3.5}} \, dx[/tex]
[tex]P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} \, (x)^{11.5}_{9.5}[/tex]
[tex]P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (11.5-9.5)[/tex]
[tex]P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (2)[/tex]
[tex]P(9.5 \leq X\leq11.5) =0.2857* (2)[/tex]
[tex]P(9.5 \leq X\leq11.5) =0.5714[/tex]
Hence; the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%
e. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?
The probability that battery life of at least 9 hours is calculated as:
[tex]P(X \geq 9) = \int\limits^{12}_{9} {\dfrac{1}{3.5}} \, dx[/tex]
[tex]P(X \geq 9) = {\dfrac{1}{3.5}}(x)^{12}_{9}[/tex]
[tex]P(X \geq 9) = {\dfrac{1}{3.5}}(12-9)[/tex]
[tex]P(X \geq 9) = {\dfrac{1}{3.5}}(3)[/tex]
[tex]P(X \geq 9) = 0.2857*}(3)[/tex]
[tex]P(X \geq 9) = 0.8571[/tex]
NOW; The Number of iPad that should have a battery life of at least 9 hours is calculated as:
n = 100(0.8571)
n = 85.71
n ≅ 86
Thus , 86 should have a battery life of at least 9 hours
In monitoring lead in the air after the explosion at the battery factory, it is found that the amounts of lead over a 6 day period had a standard error of 1.93. Find the margin of error that corresponds to a 95% confidence interval. (Round to 2 decimal places) 4.56
Answer:
1.54
Margin of error M.E = 1.54
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
x+/-M.E
Where M.E = margin of error
M.E = zr/√n
Given that
Standard deviation r = 1.93
Number of samples n = 6
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
M.E = (1.96×1.93/√6) = 1.544321633166
M.E = 1.54 (to 2 decimal place)
Margin of error M.E = 1.54
Find the equation of the line through the points (-3,-3) and (2,-1) using point-slope form. Then rewrite the
equation in slope-intercept form.
Answer: See below
Step-by-step explanation:
The point-slope equation is y-y₁=m(x-x₁). Since we don't know our slope, we can use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] to find the slope. All we have to do is use the coordinate we were given and plug it into the formula.
[tex]m=\frac{-1-(-3)}{2-(-3)} =\frac{2}{5}[/tex]
Now that we have the slope, we can fill out the point-slope equation.
y-(-3)=2/5(x-(-3))
y+6=2/5(x+3)
This is the point-slope form.
Now, we can distribute and solve to get slope-intercept form.
y+6=2/5x+6/5
y=2/5x-24/5
a pail holds 3 1/2 gallons of water. How much is it in cups
Answer:
3 1/2 gallons of water is 56 cups
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
1 gallon=4cups
1/2 gallon=2cups
3*4=12
or 4cups+4cups+4cups=12
12+2=14
The amount of coffee that people drink per day is normally distributed with a mean of 17 ounces and a standard deviation of 4 ounces. 15 randomly selected people are surveyed. Round all answers to 4 decimal places where possible.
a) What is the distribution of XX? XX ~ N(,)
b) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
c) What is the probability that one randomly selected person drinks between 15.5 and 18 ounces of coffee per day?
d) For the 15 people, find the probability that the average coffee consumption is between 15.5 and 18 ounces of coffee per day.
e) For part d), is the assumption that the distribution is normal necessary? YesNo
f) Find the IQR for the average of 15 coffee drinkers.
Q1 = ounces
Q3 = ounces
IQR: ounces
Answer:
Step-by-step explanation:
(a)
The distribution of X is Normal Distribution with mean [tex]= \mu =17[/tex] and Variance [tex]= \sigma^{2} = 16 \ i.e., X \sim N (17, 16),[/tex]
(b)
The distribution of [tex]\bar{x}[/tex] is Normal Distribution with mean [tex]= \mu =17[/tex] and Variance = [tex]\sigma^{2}/n = 16/15= 1.0667[/tex].i.e., [tex]\bar{x}\sim N(17,1.0667)[/tex]
c)
To find P(15.5 < X < 18):
Case 1: For X from 15.5 to mid value:
Z = (15.5 - 17)/4 = - 0.375
Table of Area Under Standard Normal Curve gives area = 0.1480
Case 2: For X from mid value to 18:
Z = (18 - 17)/4 = 0.25
Table of Area Under Standard Normal Curve gives area = 0.0987
So,
P(15.5 < X< 18) = 0.1480 +0.0987 = 0.2467
So,
Answer is:
0.2467
(d)
[tex]SE = \sigma/\sqrt{n}\\\\= 4/\sqrt{15}[/tex]
= 1.0328
To find [tex]P(15.5 < \bar{x}< 18):[/tex]
Case 1: For [tex]\bar{x}[/tex] from 15.5 to mid value:
Z = (15.5 - 17)/1.0328 = - 1.4524
Table of Area Under Standard Normal Curve gives area = 0.4265
Case 2: For X from mid value to 18:
Z = (18 - 17)/1.0328 = 0.9682
Table of Area Under Standard Normal Curve gives area = 0.3340
So,
[tex]P(15.5 < \bar{x}< 18) = 0.4265 + 0.3340 = 0.7605[/tex]
So,
Answer is:
0.7605
(e)
Correct option:
No
because Population SD is provided.
(f)
(i)
Q1 is given by:
[tex]- 0.6745 = (\bar{x} - 17)/1.0328[/tex]
So,
X = 17 - (0.6745 * 1.0328) = 17 - 0.6966 = 16.3034
So,
Q1 = 16.3034
(ii)
Q3 is given by:
[tex]0.6745 = (\bar{x} - 17)/1.0328[/tex]
So,
X = 17 + (0.6745 * 1.0328) = 17 + 0.6966 = 17.6966
So,
Q3= 17.6966
(iii)
IQR = Q3 - Q1 = 17.6966 - 16.3034 = 1.3932
So
Answers are:
Q1 = 16.3034 ounces
Q3 = 17.6966 Ounces
IQR = 1.3932 Ounces
Liam needs a guitar case. It must be 1.18 m long. Select the case that is suitable? 11.8mm,118cm,1.8m ,11.18mm
Answer:
118 cm
Step-by-step explanation:
1 m = 100 cm
1 m = 1000 mm
1.18 m = 118 cm = 1180 mm
11.8 mm ----> too small
118 cm ----> just right
1.8 m ----> too big
11.18 mm ----> too small
Where the above dimensions are given, the suitable guitar case for Liam would be the one that is 1.8 m long.
How is this so?Since Liam's guitar case needs to be 1.18 m long, we need to select the option that is closest in length without exceeding it.
Among the given options, 11.8 mm and 11.18 mm are too small, and 118 cm is equal to 1.18 m, which exceeds the required length.
Hence , the only suitable option is 1.8 m, which matches Liam's requirement of a guitar case with a length of 1.18 m.
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Solve the following system of equations using the elimination method. 5x – 5y = 10 6x – 4y = 4
Answer:
x=-2,y=-4
Step-by-step explanation:
By dividing to lowest terms
5x – 5y = 10= x-y=2.......(1)
6x – 4y = 4=3x-2y=2........(2)
By elimination method
Multiply equation (1) by 3 so as to correspond with equation (2)
3(x-y)=3(2)
3x-3y=6..........(3)
Multiply equation (2) by 1 so as to correspond with equation (1)
1(3x-2y)=1(2)
3x-2y=2..........(4)
Then equation (3)-equation (4)
(3x-3y=6)
-
(3x-2y=2)
__________
-y=4
y=-4
Substitute y=-4 into equation(1)
x-(-4)=2
x+4=2
x=-2
Therefore x=-2,y=-4
Un prestigioso empresario decide repartir su herencia de S/ 176 000 entre sus tres hermanos Roberto, Luis y Armando, de manera DP al número de sus hijos e IP al monto de sus deudas. ¿Cuánto le corresponde a cada hermano?
Roberto :N° hijos 4,Monto de deudas (S/) : 2 000
Luis: N° hijos 3, Monto de deudas (S/): 6 000
Armando:N° hijos 5, Monto de deudas (S/): 8 000
Answer:
Amount received per brother based on number of children plus debt is given as
Roberto, S/ 55,333.33
Luis, S/ 46,000
Armando, S/ 74,666.67
Step-by-step explanation:
English Translation
A prestigious businessman decides to distribute his inheritance of S / 176,000 among his three brothers Roberto, Luis and Armando, DP to the number of his children and IP to the amount of his debts. How much corresponds to each brother?
Roberto: No of children 4, Amount of debts (S /): 2 000
Luis: No. of children 3, Amount of debts (S /): 6,000
Armando: No of children 5, Amount of debts (S /): 8,000
Solution
The man shares the inheritance according to the number of children per person and according to each brother's debts.
Assuming the debts are first settled,
The total debts = 2000 + 6000 + 8000 = S/ 16,000
We assume that each brother receives the respective debt amounts first, then the remaining cash is divided amongst the 3 brothers according to the number of their children.
Total amount available = S/ 176,000
total debt = S/ 16,000
Amount available less debts = 176,000 - 16,000 = S/ 160,000
There are 4, 3 and 5 children respectively for the 3 brothers.
Total number of children = 4+3+5 = 12.
Amount corresponding based on a per child basis =( S/ 160,000/12) = S/ 13,333.33
Meaning that each brother receives the following amount based on their children's sake
Roberto, 4 × S/ 13,333 = S/ 53,333.33
Luis, 3 × S/ 13,333.33 = S/ 40,000
Armando, 5 × S/ 13,333 = S/ 66,666.67
Total amount each brother then receives when the amount received due to debts are added
Roberto, 53,333.33 + 2,000 = S/ 55,333.33
Luis, 40,000 + 6,000 = S/ 46,000
Armando, 66,666.67 + 8,000 = S/ 74,666.67
To check, 55,333.33 + 46,000 + 74,666.67 = 176,000 (total inheritance!)
Hope this Helps!!!
Queremos ver como se reparte una dada suma entre 3 hermanos, siendo que tenemos unas dadas restricciones, donde debemos trabajar con relaciones directamente proporcionales e inversamente proporcionales.
Veremos que:
Roberto recibe: $112,640
Luis recibe: $28,160
Armando recibe: $35,200
Sabemos que lo que se reparte es directamente proporcional al número de hijos de cada hermano, e inversamente proporcional a las deudas de cada hijo.
Entonces, definamos las variables:
R = lo que recibe Roberto.
L = Lo que recibe Luis
A = lo que recibe Armando.
Tendremos que:
R + L + A = $176,000
directamente proporcional significa: y = k*xInversamente proporcional significa: y = k/zEntonces como lo que recibe cada hermano es directamente proporcional al número de hijos (x) e inversamente proporcional a la deuda (z) lo que cada hermano recibe será:
R = k*4/2,000L = k*3/6,000A = k*5/8,000Entonces podemos escribir:
R + L + A = $176,000
k*4/2,000 + k*3/6,000 + k*5/8,000 = $176,000
k*(4/2,000 + 3/6,000 + 5/8,000) = $176,000
k*(0.003125) = $176,000
k = $176,000/(0.003125) = $56,320,000
Ahora que conocemos el valor de k, podemos calcular lo que cada hermano recibe:
R = $56,320,000*(4/2,000) = $112,640
L = $56,320,000*(3/6,000) = $28,160
A = $56,320,000*(5/8,000) = $35,200
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Solve 3(a + 3) – 6 = 21.
Answer:
a=6
Step-by-step explanation:
to find the value of a you need to simplify the equation first. so...
3(a+3)-6=21 (you remove the bracket first)
3a+9-6=21
3a+3=21 (you collect the like terms then)
3a=21-3
3a=18 (then you both divide both sides by 3 to find the value of a)
a=18/3
a=6
to check your answer substitute 3 instead of a
3(a+3)-6=21
3(6+3)-6=21
3(9)-6=21 (according to BODMAS since multiplication comes first you multiply 3 with 9 before subtracting it from 6.)
29-6=21
21=21
Answer:6
Step-by-step explanation:
3(a + 3) - 6 = 21
3(a + 3) = 21 + 6
3(a + 3) =27
a + 3. = 27 ÷ 3
a + 3. = 9
a. = 9 - 3
a. = 6
what is the solution set for the equation (2x-1)(x+5)=0
Answer:
x = 1/2 x=-5
Step-by-step explanation:
(2x-1)(x+5)=0
Using the zero product property
2x-1 =0 x+5 =0
2x= 1 x = -5
x = 1/2 x=-5
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Which graph represents the piecewise-defined function f(x) = -1.5x + 3.5, x < 2?
4 + x, x >2
Answer:
DID IT oN EDGEN UITY
Step-by-step explanation:
The first graph correctly represents our piecewise function f(x) = - 1.5x + 3.5 for x < 2 and 4 + x for x ≥ 2.
What is a piecewise function?A function that is piecewise-defined by numerous subfunctions, each of which has a separate domain interval for which it is applicable.
Piecewise definition is more of an expression of the function than it is a property of the function.
Given a piecewise function f(x) = - 1.5x + 3.5 for x < 2 and 4 + x for x ≥ 2.
Now, strictly less or greater than will be shown as an open circle in the graph and less than or greater than equal to will be shown by a closed circle on the graph.
If we observe the first graph when x = 0, y = 3.5, and the end is represented as an open circle which is < 2 and when x ≥ 2 it is 6 and represented with a closed circle.
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Blood types: The blood type o negative is called the "universal donor" type, because it is the only blood type that may safely be transfused into any person
Therefore, when someone needs a transfusion in an emergency and their blood type cannot be determined, they are given type o negative blood. For this
reason, donors with this blood type are crucial to blood banks. Unfortunately, this blood type is fairly rare; according to the Red Cross, only 7% of U.S.
residents have type o negative blood. Assume that a blood bank has recruited 18 donors. Round the answers to four decimal places
Part 1 of 3
(a) What is the probability that three or more of them have type o negative blood?
The probability that three or more of them have type o negative blood is
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Part 2 of 3
(b) What is the probability that fewer than five of them have type o negative blood?
The probability that fewer than five of them have type o negative blood is
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Part 3 of
(©) Would it be unusual f none of the donors had type o negative blood?
be unusual if none of the donors had type o negative blood since the probability is
X
It choose one) Y
would
would not
Answer:
a) The probability that fewer than five of them have type o negative blood is 0.1275
b) The probability that fewer than five of them have type o negative blood is 0.9933
c) 0.2708 probability of no donors with type o negative blood. This probability is higher than 0.05, so it would not be unusual having none of the donors with type o negative blood.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they have type o negative blood, or they do not. The probability of a person having type o negative blood is independent of any other person. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
7% of U.S. residents have type o negative blood.
This means that [tex]p = 0.07[/tex]
18 donors.
This means that [tex]n = 18[/tex]
(a) What is the probability that three or more of them have type o negative blood?
Either less than three have, or at least three do. The sum of the probabilities of these events is 1. So
[tex]P(X < 3) + P(X \geq 3) = 1[/tex]
We want [tex]P(X \geq 3)[/tex]
So
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{18,0}.(0.07)^{0}.(0.93)^{18} = 0.2708[/tex]
[tex]P(X = 1) = C_{18,1}.(0.07)^{1}.(0.93)^{17} = 0.3669[/tex]
[tex]P(X = 2) = C_{18,2}.(0.07)^{2}.(0.93)^{16} = 0.2348[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2708 + 0.3669 + 0.2348 = 0.8725[/tex]
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.8725 = 0.1275[/tex]
The probability that fewer than five of them have type o negative blood is 0.1275
(b) What is the probability that fewer than five of them have type o negative blood?
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{18,0}.(0.07)^{0}.(0.93)^{18} = 0.2708[/tex]
[tex]P(X = 1) = C_{18,1}.(0.07)^{1}.(0.93)^{17} = 0.3669[/tex]
[tex]P(X = 2) = C_{18,2}.(0.07)^{2}.(0.93)^{16} = 0.2348[/tex]
[tex]P(X = 3) = C_{18,3}.(0.07)^{3}.(0.93)^{15} = 0.0942[/tex]
[tex]P(X = 4) = C_{18,4}.(0.07)^{4}.(0.93)^{14} = 0.0266[/tex]
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.2708 + 0.3669 + 0.2348 + 0.0942 + 0.0266 = 0.9933[/tex]
The probability that fewer than five of them have type o negative blood is 0.9933.
c) Would it be unusual f none of the donors had type o negative blood?
[tex]P(X = 0) = C_{18,0}.(0.07)^{0}.(0.93)^{18} = 0.2708[/tex]
0.2708 probability of no donors with type o negative blood. This probability is higher than 0.05, so it would not be unusual having none of the donors with type o negative blood.
describe the slope of the graph from 1 sec to 5.3 sec ( is the slope positive, negative, zero or non existent)
Answer:
[tex] m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]
Where x for this case represent the time and y the height waist off ground.
We have one point that can be extracted from the graph on this case:
[tex] x_1 = 1, y_1= 3[/tex]
Bout for the other point we have:
[tex] x_2 = 5.3 , y_2 = 9.6[/tex]
Is important to notice that 9.6 is an estimation since we don't have the scale to identify the real value. so then if we replace we got:
[tex] m =\frac{9.6-3}{5.3-1}= 1.535[/tex]
And for this case we can conclude that this slope is positive and around 1.5 and 1.6. And that means if we increase the time in one unit then the height off waist off ground would increae about 1.5 to 1.6 ft
Step-by-step explanation:
In order to calculate the slope we need to use the following formula:
[tex] m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]
Where x for this case represent the time and y the height waist off ground.
We have one point that can be extracted from the graph on this case:
[tex] x_1 = 1, y_1= 3[/tex]
Bout for the other point we have:
[tex] x_2 = 5.3 , y_2 = 9.6[/tex]
Is important to notice that 9.6 is an estimation since we don't have the scale to identify the real value. so then if we replace we got:
[tex] m =\frac{9.6-3}{5.3-1}= 1.535[/tex]
And for this case we can conclude that this slope is positive and around 1.5 and 1.6. And that means if we increase the time in one unit then the height off waist off ground would increae about 1.5 to 1.6 ft
What is the simplified value of the exponential expression 27 1/3?
1/3
1/9
3
9
Answer:3
Step-by-step explanation:
Answer:
C.3
Step-by-step explanation:
A=(-2,-7) B=(-6,4) C=(-2,7) D=(2,4) What is the perimeter?
[tex]\displaystyle\bf\\AB=\sqrt{\Big(-6-(-2)\Big)^2+\Big(4-(-7)\Big)^2}\\\\AB=\sqrt{\Big(-6+2\Big)^2+\Big(4+7\Big)^2}\\\\AB=\sqrt{\Big(-4\Big)^2+\Big(11\Big)^2}\\\\AB=\sqrt{16+121}\\\\\boxed{\bf AB=\sqrt{137}}[/tex]
.
[tex]\displaystyle\bf\\BC=\sqrt{\Big(-2-(-6)\Big)^2+\Big(7-4\Big)^2}\\\\BC=\sqrt{\Big(-2+6\Big)^2+\Big(7-4\Big)^2}\\\\BC=\sqrt{\Big(4\Big)^2+\Big(3\Big)^2}\\\\BC=\sqrt{16+9}\\\\BC=\sqrt{25}\\\\\boxed{\bf BC=5}[/tex]
.
[tex]\displaystyle\bf\\CD=\sqrt{\Big(2-(-2)\Big)^2+\Big(4-7\Big)^2}\\\\CD=\sqrt{\Big(2+2\Big)^2+\Big(4-7\Big)^2}\\\\CD=\sqrt{\Big(4\Big)^2+\Big(-3\Big)^2}\\\\CD=\sqrt{16+9}\\\\CD=\sqrt{25}\\\\\boxed{\bf CD=5}[/tex]
.
[tex]\displaystyle\bf\\AD=\sqrt{\Big(2-(-2)\Big)^2+\Big(4-(-7)\Big)^2}\\\\AD=\sqrt{\Big(2+2\Big)^2+\Big(4+7\Big)^2}\\\\AD=\sqrt{\Big(4\Big)^2+\Big(11\Big)^2}\\\\AD=\sqrt{16+121}\\\\\boxed{\bf AD=\sqrt{137}}[/tex]
.
[tex]\displaystyle\bf\\P=AB+BC+CD+AD=\sqrt{137}+5+5+\sqrt{137}\\\\\boxed{\bf P=10+2\sqrt{137}}[/tex]
Last weekend, Lena worked 7.5 hours on Friday, 9.75 hours on Saturday, and 6.25 hours on Sunday.
She earns £8.60 per hour. How much did she earn in total?
Answer:202.1
Step-by-step explanation:
7.5hrs +9.75hrs+6.25hrs=23.5
8.60 X 23.5 =202.1 pounds
Eli uses 1/4 pound of apples to make 4 servings of fruit salad. He uses the same amount of apples for each serving. What amount of apples does he use for each serving of fruit salad?
Answer:
1/16 pound
Step-by-step explanation:
1/4 ÷ 4 = 1/4 x 1/4 = 1/16
Y is directly proportional to 1/x. Write this in proportion notation.
2 points
d is proportional to e. When d is 10, e is 16. What is an equation connecting d and e
.
2.
.
I hope it helps you
I don’t know how to do this can someone help?
Answer:
67
Step-by-step explanation:
Using triangle property
127+x=180
x=53
53+60+y=180
113+y=108
y=67
Multiply 6.7 x 104 times 4.8 x 106 by using scientific notation. Round your answer to one decimal place in scientific notation with no spaces.
Answer:
3.216×[tex]10^{11}[/tex]
Step-by-step explanation:
I'm assuming 104 is [tex]10^{4}[/tex] and 106 is [tex]10^{6}[/tex].
6.7×[tex]10^{4}[/tex]×4.8×[tex]10^{6}[/tex]=
32.16×[tex]10^{10}[/tex]=
3.216×[tex]10^{11}[/tex]
Our answer is 3.216×[tex]10^{11}[/tex].
A bicycle ramp used for competitions is a triangle prism. The volume of the ramp is 313.2 cubic feet. Write and solve an equation to find the the width of the ramp.
Answer:
8.7 ft
Step-by-step explanation:
The diagram of the ramp is attached below.
Volume of a Triangular Prism = Base Area X Width
From the diagram:
Base of the triangle = 6 ft
Height of the Triangle = 12 ft
Therefore:
Base Area of the Prism [tex]=\frac{1}{2}X 12X6=36$ ft^2[/tex]
From the diagram, Width of the ramp =x
Given that the volume of the ramp is 313.2 cubic feet.
Therefore, substituting into the formula for Volume of a Triangular Prism
[tex]313.2=36 X x\\x= 313.2 \div 36\\$Width of the ramp, x=8.7 ft[/tex]
Answer:
8.7
Step-by-step explanation:
9.2 An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has an average life of 780 hours, find a 96% confidence interval for the population mean of all bulbs produced by this firm.
Answer:
765,795 = 96%
Step-by-step explanation:
confidence interval = 0.04
The Za/2 theorem = 1/2 = 0.04/2 = 0.02= /x = 720z
If ; 0.02 = 2.05 then the interval is 780-2.05 x 40/√30 x 780+2.05 x 30/√30 = 765,795 = 96%
We see 40/ √30 which is found in equation of finding the sample mean at point /x = 720z
σ 40/ n√30 = 7.3029674334 and is simply a fraction of /x 720z
By normal distribution we find
The 96% confidence interval for the population mean of all bulbs = 765,795
As 765, x 1.04 = 795 = 765, 795
To find Sampling mean.
The Sampling Distribution of the Sample Mean. If repeated random samples of a given size n are taken from a population of values for a quantitative variable, where the population mean is μ (mu) and the population standard deviation is σ (sigma) then the mean of all sample means (x-bars) is population mean μ (mu).
Confidence Level z*-value
80% 1.28
90% 1.645 (by convention)
95% 1.96
96% 2.05
98% 2.33
99% 2.58
A group of professors investigated first-year college students' knowledge of astronomy. One concept of interest was the Big Bang theory of the creation of the universe. In a sample of 149149 freshmen students, 3232 believed that the Big Bang theory accurately described the creation of planetary systems. Based on this information, is it correct at the alphaαequals=0.100.10 level of significance to state that more than 20% of all freshmen college students believe the Big Bang theory describes the creation of planetary systems? State the null and alternative hypotheses. Choos
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
A group of professors investigated first-year college students' knowledge of astronomy. One concept of interest was the Big Bang theory of the creation of the universe. In a sample of 149 freshmen students, 32 believed that the Big Bang theory accurately described the creation of planetary systems. Based on this information, is it correct at the alpha = 0.01 level of significance to state that more than 20% of all freshmen college students believe the Big Bang theory describes the creation of planetary systems? State the null and alternative hypotheses. Choose the correct answer below. H_0: p = 0.20 H_a: p not equal to 0.20 H_0: p not equal to 0.20 H_a: p = 0.20 H_0: p = 0.20 H_a: p 0.20 If alpha = 0.05, find the rejection region for the test. Choose the correct answer below. z > 1.645 z > 1.96 z
Solution:
We would set up the null and alternative hypothesis. The correct options are
For null hypothesis,
p ≥ 0.2
For alternative hypothesis,
p < 0.2
This is a left tailed test.
Considering the population proportion, probability of success, p = 0.2
q = probability of failure = 1 - p
q = 1 - 0.2 = 0.8
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 32
n = number of samples = 149
P = 32/149 = 0.21
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.21 - 0.2)/√(0.2 × 0.8)/149 = 0.31
The calculated test statistic is 0.31 for the right tail and - 0.31 for the left tail
Since α = 0.05, the critical value is determined from the normal distribution table.
For the left, α/2 = 0.05/2 = 0.025
The z score for an area to the left of 0.025 is - 1.96
For the right, α/2 = 1 - 0.025 = 0.975
The z score for an area to the right of 0.975 is 1.96
In order to reject the null hypothesis, the test statistic must be smaller than - 1.96 or greater than 1.96
Therefore, the rejection region is z > 1.96
3/11 ÷ 3/11
and
9/10 ÷ 3/5
PLZ HELP ME
Answer:
3/11 divided by 3/11 is 1
9/10 divided by 3/5 is 1 1/2 (1.5)
Step-by-step explanation:
Answer:
1
1.5
Step-by-step explanation:
3/11 ÷ 3/11 = 1
9/10 ÷ 3/5 = 3/2 ≈ 1.5
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. Listed below are the jersey numbers of 11 players randomly selected from the roster of a championship sports team. What do the results tell us? 24 72 41 76 15 29 64 93 74 38 99
Answer:
a) 56.82
b) 64
c) there is no mode
d) 57
e) the jersey numbers are nominal data and they do not measure or count anything, so the resulting statistic are meaningless
Step-by-step explanation:
The first thing is to organize the data from least to greatest:
15 24 29 38 41 64 72 74 76 93 99
a) the mean would be the average of the data, thus:
m = (15 + 24 + 29 + 38 + 41 + 64 + 72 + 74 + 76 + 93 + 99) / 11
m = 56.82
b) the median is the data of half, when the data is organized, in this case the value of half would be the sixth data that is 64.
c) the mode is the value that is most repeated, therefore as none is repeated there is no mode.
d) the midrange is the average between the minimum value and the maximum value:
mr = (15 + 99) / 2
mr = 57
e) the jersey numbers are nominal data and they do not measure or count anything, so the resulting statistic are meaningless
if you flip three fair coins, what is the probability that you’ll get a head on the first flip, a tail on the second flip and another head on the third flip?
Answer: The probability if getting a head on the first flip is 1/2 or 50 percent,the probability of getting a tail on the second flip is also 1/2 and the probability of getting another head on the third flip is 1/2.
Step-by-step explanation:
Answer:
3/8
Step-by-step explanation:
On a coordinate plane, triangle A B C is shifted 4 units up and 3 units to the left to form triangle A prime B prime C prime. Triangle ABC is reflected over the line y = 1. What are the coordinates of B’? (–2, 3) (–2, 5) (2, –3) (4, –3)
Answer:
(–2, 5)
Step-by-step explanation:
I know its late now but here is the answer.
Answer:
The answer is a
Step-by-step explanation:
the price of a CD that sells for 21% more than
the amount (m) needed to manufacture the CD
Answer:
I need more explanation is there more to the question?
not an answer but is this what your doing?
