(07.01 MC)Of the following sets, which numbers in {0, 1, 2, 3, 4} make the inequality 7x + 3 < 17 true? {0} {0, 1} {0, 1, 2} {2, 3, 4}

Answer:3

Step-by-step explanation:

Answer:

C.3

Step-by-step explanation:

[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]

Answer:

1/16 pound

Step-by-step explanation:

1/4 ÷ 4 = 1/4 x 1/4 = 1/16

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

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

Entonces 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:

Entonces 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

Si quieres aprender más, puedes leer:

https://brainly.com/question/18365407

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

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:

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

Answer:202.1

Step-by-step explanation:

7.5hrs +9.75hrs+6.25hrs=23.5

8.60 X 23.5 =202.1 pounds

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

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:

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

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

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

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

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.

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.

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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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

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

I hope This Helps❣ If U Nees Help Notify Me And I Will Post More❣

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]

Answer:

67

Step-by-step explanation:

Using triangle property

127+x=180

x=53

53+60+y=180

113+y=108

y=67

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.

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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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

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2.

.

I hope it helps you

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:

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].

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

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

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

Answer:

I need more explanation is there more to the question?

not an answer but is this what your doing?