The probability that the sample mean is greater than 105 is 0.0384.
What is meant by random sample?A simple random sample is a subset of persons chosen at random from a bigger collection. It is the process of randomly selecting a sample.
A simple random sample is a population subset chosen at random. Each member of the population has a precisely equal probability of being selected in this sampling approach, reducing the likelihood of selection bias.
Random sampling ensures that the results received from your sample are close to what would have been achieved if the full population had been measured.
The population mean is μ =100.
The population standard deviation is σ= 20.
n=50 is the sample size
Let [tex]\bar{x}[/tex] be the mean of the sample
The chance that the sample mean is greater than 105 is then given by :
P( [tex]\bar{x}[/tex]>105)=1-P( [tex]\bar{x}[/tex]≤105)
=1-P(( [tex]\bar{x}[/tex]-μ)/(σ/√n) ≤ (105-100)/(20/√50))
=1-P(z≤1.77)
=1-0.96164
=0.03836≈0.0384
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The complete question is:
"According to a survey, high school girls average 100 text messages daily (The Boston Globe, April 21, 2010). Assume the population standard deviation is 20 text messages. Suppose a random sample of 50 high school girls is taken. a. What is the probability that the sample mean is more than 105? (Round answer to 4 decimal places.)"
Brothers Bob and Tom Katz buy a tent that has a center pole 6.25 feet high. If the sides of the tent are supposed to make a 50° angle with the ground, how wide is the tent?
2.1 ft
10.5 ft
5.6 ft
18.4 ft
The width of the tent is twice the width of one side which is 10.5 feet.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
Given, Brothers Bob and Tom Katz buy a tent that has a center pole 6.25 feet high and the sides of the tent make a 50° angle with the ground.
Here the opposite is the height with the reference angle of 50° and we have to determine the adjacent which is the width of the tent.
∴ tan50° = Height of the pole/width.
1.19 = 6.25/width.
width = 6.25/1.19.
width = 5.25 feet.
But the total width of the tent will be twice as we have obtained only one side width.
∴ Total width is (2×5.25) = 10.5 feet.
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A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 150 nails and each large box has 400 nails. The contractor bought twice as many large boxes as small boxes, which altogether had 2850 nails. Determine the number of small boxes purchased and the number of large boxes purchased.
The total number of small boxes is 2.1 and the large boxes is 6.3.
Given;
To build a house, a contractor has to purchase nails. Both small and large boxes of nails are provided. There are 150 nails in each small box and 400 in each large box. The contractor purchased 3 more tiny boxes than large boxes. Totaling 2850 nails.
To calculate the proportion of small and large boxes that were bought,
Let's assume the small boxes as 's' and the big boxes as '3s'.
∴ s(150) + 3s(400) = 2850
150s + 1200s = 2850
1350s = 2850
s = 2850/1350
s = 2.1
∴ 3s = 2.1 * 3
= 6.3
Hence, the total number of small boxes is 2.1 and the number of large boxes is 6.3.
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Answer:
The number of small boxes purchased are 3 and the number of large boxes purchased are 6.
Step-by-step explanation:
Let the small boxes bought be x
Therefore the large boxes will be 2x
Total nails bought = 2850
Nails in x small boxes = 150x
Nails in 2x large boxes = 400. 2x = 800x
2850 = 150x + 800x
2850 = 950x
x= 2850/950 = 3
2x = 2x3= 6
If (3+2)+(2+ bi) = 5-4i, the value of b is
A. -2 B. 2 C. -6
D. 6
Answer:
[tex]b=\frac{-4i-2}{i}[/tex]
So the answer is...
A ) -2
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
Natasha is making a bookshelf she begin with 120  inches of oak boards she use 50.75 inches for shelves she bought 36 1/4 more inches 00 boards she didn’t use 40 1/2 inches for the top is 60.5 inches for the sides how many inches of oak boards does Natasha have left 
Natasha has left with 4.5 inches of oak boards.
What is a simplification?
The act of simplifying something such that it is simpler to carry out or understand, or the thing that is the product of this simplifying process: The group offers suggestions for streamlining trade processes.
Here, we have
120 inches of oak boards
50.75 inches for shelves, 36 1/4 more inches of oak boards, and she didn’t use 401/2 inches for the top and 60.5 inches for the sides.
We have to find how many inches of oak boards Natasha has left.
We use here simplification, we get
= 120 + 36 1/4 - 50.75 - 40 1/2 - 60.5
= 4.5 inches
Hence, Natasha has left with 4.5 inches of oak boards.
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Abe jogs 1. 8 miles on monday, 1. 3 miles on tuesday, and 1. 2 miles on wednesday. If beth jogs twice as far as abe, how many miles does beth jog?.
Abe jogs 1. 8 miles on Monday, 1. 3 miles on Tuesday, and 1. 2 miles on Wednesday.
Beth will jog 8.6 miles, if she jogs twice as far as Abe.
The answer provided below has been developed in a clear step by step manner.
Step: 1
Given that,
Abe jogs 1.8 miles on Monday, 1.3 miles on Tuesday and 1.2 miles on Wednesday.
So,
Total miles jog by Abe =1.8+1.3+1.2
Step: 2
Adding, we get,
Total miles jog by Abe = 4.3 miles
To find :-
The number of miles Beth jogged.
Step: 3
Since Beth jogs twice as far as Abe, we have,
Number of miles Beth jog = 2×4.3 miles = 8.6 miles
Since Abe jog 4.3 miles in total, Beth will jog (2* 4.3) miles
Hence the answer is, Beth will jog 8.6 miles, if she jogs twice as far as Abe.
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Solve the inequality:
-5x + 18 < -12
Step-by-step explanation:
-5x + 18 < -12
subtract 18 from both sides:
-5x + 18 - 18 < -12 - 18
-5x < -30
divide both sides by -5: [remember, when dividing by a negative number you must FLIP the sign direction]
(-5x)/-5 > (-30)/-5
x > 6
or
(6 , ∞)
series with 12 terms,a1=3 and a12=25
The 12 terms of the series will be -
3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25
What is the formula to calculate the nth term of an Arithmetic Sequence ?The formula to calculate the nth term of an Arithmetic Sequence is -
a(n) = a + (n - 1)d
a - first term of A.P.
d - Common difference of A.P.
n - position of term
We have -
a[1] = 3
a[12] = 25
Then, using the formula to calculate the nth term, we get -
a(n) = a + (n - 1)d
a[1] = 3
AND
a(12) = 3 + 11 x d
25 = 3 + 11d
22 = 11d
d = 2
So, the terms of the series will be -
3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25
Hence, the 12 terms of the series will be -
3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25
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26.1.2 Exam: Semester Exam
Question 24 of 25
Which situation could be represented by -8?
OA. A distance of 8 meters above sea level
OB. A rise in temperature of 8 degrees
OC. A loss of 8 points
OD. A gain of
$8
SUBMIT
A loss of 8 points is the situation which is represented by integer -8.
What is Number system?A number system is defined as a system of writing to express numbers.
The situation that could be represented by -8 is option C, a loss of 8 points.
The negative sign indicates a decrease or loss in value.
A distance of 8 meters above sea level represents a positive number because the distance is above.
A rise in temperature of 8 degrees is also positive as it is increasing.
A gain of $8 is also represents the positive value.
-8 represents a loss of 8 points.
The negative sign denotes a decrease or loss in value.
Hence, a loss of 8 points is the situation which is represented by integer -8.
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Can you guys help me ??
a) Write an equation for a line in point-slope form that is parallel to the line y=2/3x-5 and passes through the point (3, 4).
b) Explain what would be different in part (a) if you were asked to write an equation for a line that is perpendicular instead of parallel.
Answer: a) y - 4 = 2/3(x) - 2
b) y - 4 = -3/2(x) -2
Step-by-step explanation:
equation of original line: y = 2/3x -5
point on a line parallel to original line: (3,4)
The slope of a line parallel to a given line has the same slope, so the equation of the parallel line (in point-slope form) is:
(y - y1) = 2/3(x - x1)
point (x1, y1) is (3, 4)
plug (3,4) into the equation:
y - 4 = 2/3(x - 3)
y - 4 = 2/3(x) - 2
rewrite in slope-intercept form: y = 2/3(x) + 2
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the first line: - 1/m
Therefore, the slope of the perpendicular line = -3/2
Equation for the perpendicular line is:
y - 4 = -3/2(x) -2
Which equation has no solution?
O
-3(x+5)= x - 15 - 2x
-3(x+5) = x - 15 - 4x
O c-3(x+5)= x − 10 - 4x
OD -3(x+5)= x −10+2x
Equation with option B and C has no solution.
What is equation?
When two expressions are connected with the equals sign, a formula known as an equation is created.
Main Body:
A) -3(x+5) = x-15 -2x
⇒ -3x -15 = x-15-2x
⇒ -3x = -x
⇒ -2x= 0
⇒ x = 0, this means it has a solution.
B) -3(x+5) = x- 15 -4x
⇒ -3x -15 = -3x -15
So this equation also has no solution.
as L.H.S cancels out R.H.S completely so this equation has no solution.
C) -3(x+5) = x-10 -4x
⇒ -3x -15 = -3x -10
⇒ -15 ≠ 10
hence the equation with no solution is option b and c.
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Write an expression for the following situation: A man earns a $5000 dividend from an investment and distributes it equally amongst his children.
If Eddy wants to have a party and invite all his friends, it is going to cost * 1 point him $150 to cater the party, plus $4 per person for drinks. If he only has $300 to spend, how many people can he invite to his party? Write and solve the equation for the above problem. What is the maximum number of people Eddy can invite?
The maximum number of people Eddy can invite is 37.
How to illustrate the equationThe equation is simply used to show the relationship between the variables given.
In this case, it is going to cost him $150 to cater the party, plus $4 per person for drinks and he only has $300 to spend.
Let the number of persons be represented by p
The equation will be:
150 + (4 × p) = 300
150 + 4p = 300
Collect like terms
4p = 300 - 150
4p = 150
Divide
p = 150 / 4
p = 37.5
The maximum number is 37.
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Can somebody solve this for me?
Thanks
Answer:
Rule SAS; side angle side
Step-by-step explanation:
Since they give that DM and CM are equal, and BM and AM are equal, you already have two sides. And since you have already marked vertical angles (correct because of intersection), you have 2 sides and 1 angle that are equal. This is enough to prove they are equal so it is the rule SAS or side, angle, side.
A bank account starts with a balance of £8000 and pays compound interest of 5% per year. Work out the balance of the account after 1 year and after 2 years.
The balance of the account after 1 year and after 2 years 16400 and 16820 is respectively.
A bank account starts with a balance, P = $8000
rate of interest = 5%
compound interest for 1 year is :
[tex]CI = P(1 + R/100)^n[/tex]
CI = 8000(1 + 5/100)
CI = 8000(1 + 1/20)
CI = 8000(21/20) = 8400
A = CI + P = 8000 + 8400 = 16400
compound interest for 1 year is :
[tex]CI = P(1 + R/100)^{2n}[/tex]
CI = 8000(1 + 5/100)^2
CI = 8000(1 + 1/20)^2
CI = 8000(21/20)^2 = 8820
A = CI + P = 8000 + 8820 = 16820
The balance of the account after 1 year and after 2 years 16400 and 16820 is respectively.
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14) WINDOWS This window is designed in the shape of a right trapezoid If the acute angle measures 52", what is the measure of the obtuse angle?
The measure of the obtuse angle is 128 degrees
How to determine the measure of the obtuse angle?From the question, we have the following statement that can be used in our computation:
Acute angle = 52 degrees
The measure of the obtuse angle is calculated as
Obtuse angle = 180 - Acute angle
Substitute the known values in the above equation So, we have the following equation
Obtuse angle = 180 - 52
Evaluate
Obtuse angle = 128
Hence, the angle is 128 degrees
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Martina spent a total of $60 at the grocery store. Of this amount, she spent $57 on fruit. What percentage of the total did she spend on fruit?
Answer:
95%
Step-by-step explanation:
The uniform rate of water flowing of a certain pipe is 75 litres per minute. Find the time taken in minute fill a tank having the capacity of 1.5m³
The time taken in minutes to fill a tank having a capacity or work of 1.5m³ is 1.2 minutes;
What are Time and Work?
According to fundamental mathematical concepts, time may be described as the amount of time that a specific activity occurs, whereas work can be described as the collection of actions carried out in order to attain a specific activity or outcome. It should go without saying that time is needed to accomplish a task. It implies that time and work have a certain relationship.
The task completed is calculated as the sum of the number of people participating in the work and the number of days it took to finish. The fundamental time and work equation is W = N X D.
W is the amount of work done.
N is the number of people.
D is the number of days or hours needed.
In the question, It is given that:
water flowing off a certain pipe is 75 liters per minute;
and;
the tank has a capacity of 1.5m³
First converting the Efficiency in liters per second,
So,
water flowing off a certain pipe is 75 liters per minute;
So, dividing it by 60 ;
Water flowing off the pipe = 1.25;
Now using the work-time relationship:
Efficiency × Time = work;
So,
1.25×Time = 1.5
⇒Time = 1.2
So, the time taken in minutes to fill a tank having a capacity of 1.5m³ is 1.2 minutes;
Hence,
the time taken in minutes to fill a tank having a capacity of 1.5m³ is 1.2 minutes;
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I NEED HELP ASAP RN
What fraction can not be simplified?
A. 9/15
B. 18/30
C. 8/12
D. 16/25
Answer: D. 16/25
Step-by-step explanation:
From 48 to 90
Increase or decrease?
Amout of change:
Calculate the percent change:
The percentage change from 48 to 90 is 87.5%.
What is percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, 48 to 90 represents a increase. The increase will be:
= 90 - 48
= 42
The percentage increase will be:
= Increase / Original number × 100
= 42 / 48 × 100
= 87.5%
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write the ratio 81:27 in its simplest form
Answer:
3:1
Step-by-step explanation:
bc the lcm is 3
Answer:
the ratio is 3/1
A bakery used 25% more butter this month than last month. If the bakery used 240 kilogrames of butter last month, how much did it use this month?
Answer:
300kg
Step-by-step explanation:
125/100=x/240
30000=100x
x=300
The ratio of girls to boys in the school is 3 to 1. If there is a total of 400 students, how many are boys? The answer must be a whole number.
As per the given ratio, the number of boys in the school is 133.
Ratio:
Ratio refers the relationship between two things when it is expressed in numbers or amounts.
Given,
The ratio of girls to boys in the school is 3 to 1.
Here we need to find the number of boys in the school if the total number of students is 400.
Let x be the number of boys in the school.
So, the here we have the ratio from girls to boys and we have to convert it into boys into girls, then we get,
=> girls to boys ratio = 3:1
So, boys to girls ratio = 1:3
We know that the total number of students are 400
Therefore, the number of boys in the school is,
=> 1/3 x 400 = 133
So, the number of boys in the school is 133.
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Select the correct answer. Which equation has an extraneous solution? A. x 5 = - 2 B. x + 1 3 = 10 C. x = - 5 D. x − 5 4 = 3 Reset Next
An equation which has an extraneous solution is: C. √x = -5.
What is an extraneous solution?In Mathematics, an extraneous solution can be defined as a type of solution (root) to a squared equation or transformed equation that isn't a direct solution (root) of the original equation.
This ultimately implies that, extraneous solutions are numerical values that are obtained when we solve equations that aren't solutions to the original equation as shown below:
Taking the fifth root of both sides of the equation, we have:
[tex]\sqrt[5]{x} = -2\\\\(\sqrt[5]{x})^5 = -2^5\\\\[/tex]
x = -32.
Taking the cubic root of both sides of the equation, we have:
∛(x + 1) = 10
[∛(x + 1)]³ = 10³
x + 1 = 1000
x = 1000 - 1
x = 999.
Taking the fourth root of both sides of the equation, we have:
[tex]\sqrt[4]{x-5} =3\\\\(\sqrt[4]{x-5})^4 =3^4[/tex]
x - 5 = 81
x = 81 + 5
x = 86.
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2 lines are perpendicular. The slope of one line is -5/7. what is the slope of the other line?
Answer:
7/5
Step-by-step explanation:
trust me
33, 25, 42, 25, 31, 37, 46, 29, 38 what is the third quartile (upper quartile) of the data?.
The third quartile (upper quartile) of the data is 38
What is the Median?
The center value or middle value of a data set is the median.
What are the Upper Quartiles?
Upper quartile (Q3) is the center or middle data point of the second half of a data set.
The given data is 33, 25, 42, 25, 31, 37, 46, 29, 38
Order the data set given as:
25, 25, 29, 31, 33, 37, 38, 42, 46
Upper Quartile = 25, 25, 29, 31, 33, 37, 38, 42, 46 = 38
Therefore, the third quartile (upper quartile) of the data is 38
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find 4/5 -1/2
a.3/5
b.2/5
c.3/10
d.1/2
Answer:
3/10
Step-by-step explanation:
4/5 - ½
The l.c.m of the Denominator is 10
=8-5/10
=3/10
6.6 divided by 12 6.6 on top 12 on bottom
Answer:
Step-by-step explanation:
Step 1:
Start by setting it up with the divisor 12 on the left side and the dividend 6 on the right side like this:
12 ⟌ 6
Step 2:
The divisor (12) goes into the first digit of the dividend (6), 0 time(s). Therefore, put 0 on top:
0
12 ⟌ 6
Step 3:
Multiply the divisor by the result in the previous step (12 x 0 = 0) and write that answer below the dividend.
0
1 2 ⟌ 6
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (6 - 0 = 6) and write the answer below.
0
12 ⟌ 6
- 0
6
You are done.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 6 divided by 12 calculated using Long Division is:
0
6 Remainder
How many different 8-letter permutations can be formed from 6 identical h's and two identical t's?.
The required permutations are given as 168 letters will be formed.
Given that,
How many different 8-letter permutations can be formed from 6 identical h's and two identical t's is to be determined.
In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.
Here,
A total number of combinations = 8!
The number of repetitions, = 5!.2!
Permutation of letters = 8!/[5!.2!]
Thus, the required permutations are given as 168 letters will be formed.
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The required slope of the given line is 1 which is shown in the graph.
What is the slope of the line?The slope of the line is represented as the rise of the line.
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Grab two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
We take the two points (4, 10) and (9, 22)
Let
x₁ = 0, y₁ = 1
x₂ = 8, y₂ = 9
∵ Slope m = (y₂ - y₁)/(x₂ -x₁ )
Substitute values in the formula
m = (9 - 1) / (8 - 0)
m = (8)/(8)
m = 1
Thus, the required slope of the given line is 1 which is shown in the graph.
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