Answer:
The margin of error is [tex]MOE = 9.68[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n= 16[/tex]
The standard deviation is [tex]\sigma = 15[/tex]
The confidence level is [tex]C = 99[/tex]%
Generally the level of significance is mathematically evaluated as
[tex]\alpha = 100 - C[/tex]
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1%[/tex]%
[tex]\alpha = 0.01[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] obtained from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
The reason obtaining the critical value of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because we are considering the two tails of the area normal distribution curve which is not inside the 99% confidence interval
Now the margin of error is evaluated as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 2.58 * \frac{15}{\sqrt{16} }[/tex]
[tex]MOE = 9.68[/tex]
What is the measure of
Answer:
x= 78
Step-by-step explanation:
Focus on the blue traingle:
∠BHI= 180° -47° -31° (∠sum of triangle)
∠BHI= 102°
x°= 180° -102° (adj. ∠s on a str. line)
x°= 78°
x= 78
Alternatively,
x°= 47° +31° (ext. ∠ of triangle)
x°= 78°
x= 78
Which of the following proves ABC DEF?
A.
SAS
B.
SSS
C.
SSA
D.
ASA
Option A is the correct answer.
Answer:
SAS
Step-by-step explanation:
According to the given information both the triangles are congruent by SAS postulate.
The given triangles are congruent by SAS rule.
What is congruency in triangles?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
Given are two triangles, ABC and DEF,
They have congruent parts, given;
AB ≅ DE
BC ≅ EF
∠ B ≅ ∠ E
The triangles have two congruent sides and one congruent angle between them.
The Side-Angle-Side theorem of congruency states that, if two sides and the angle formed by these two sides are equal to two sides and the included angle of another triangle, then these triangles are said to be congruent.
Hence, The given triangles are congruent by SAS rule.
For more reference on congruent triangles, click;
https://brainly.com/question/12413243
#SPJ2
-7(5-3x)=-35 what is the x in the problem
Answer:
x = 0
Step-by-step explanation:
-7(5-3x)=-35
Divide by -7
-7/-7(5-3x)=-35/-7
5 -3x = 5
Subtract 5 from each side
5-3x-5 = 5-5
-3x=0
Divide by -3
x=0
Answer: x = 0
Step-by-step explanation: Start by distributing the -7 through the parenthses on the left side of the equation.
-7(5) is -35 and -7(-3x) is 21x.
So we have -35 + 21x = -35.
Next, isolate the x term by adding 35 to both sides.
When we do this, we get 21x = 0.
Now divide both sides by 21 and x = 0.
i need these THREE questions ANSWERED please!!!! please i really need these done!!!
Step-by-step explanation:
8. As the name implies, a box-and-whisker plot looks like a box with two whiskers. The box is the middle 50%. The whiskers are the bottom 25% and the top 25%.
First, we need to sort the numbers from smallest to largest. Starting with Set A:
Set A = {56, 57, 62, 68, 71, 82, 84, 92, 97, 101, 103, 106}
Now we find the median of the set, or the middle number. Set A has 12 data points. Since 12 is an even number, the median will be the average of the 6th and 7th numbers.
M = (82 + 84) / 2 = 83
Next, we find the median of the lower half. There are 6 numbers in the lower half, so the median is the average of the 3rd and 4th numbers.
Ml = (62 + 68) / 2 = 65
Now we find the median of the upper half. Again, there are 6 numbers in the upper half, so the median will be the average of the 3rd and 4th numbers.
Mu = (97 + 101) / 2 = 99
So the left whisker is from 56 to 65.
The box is from 65 to 99.
The right whisker is from 99 to 106.
Don't forget to mark the median, 83.
Repeat for Set B.
Set B = {36, 37, 42, 46, 48, 56, 58, 63, 69, 72, 75, 78}
M = (56 + 58) / 2 = 57
Ml = (42 + 46) / 2 = 44
Mu = (69 + 72) / 2 = 70.5
So the left whisker is from 36 to 44.
The box is from 44 to 70.5.
The right whisker is from 70.5 to 78.
The median is 57.
By graphing both on the same number line, we can easily compare them.
9. To make a dot plot, draw a number line starting from the smallest number and ending at the largest number. For each number, draw a dot every time the number appears in the set. For example, the number 3 appears twice in Set A, so draw two dots on 3. You may find it helpful to sort the data first.
10. Draw a dot plot of the set to determine the shape.
Find (g/f)(x) for the given functions: f(x) = 5/x and g(x) = 3 + x/5
Step-by-step explanation:
just substitute the value of g(X) and f(X)
Joes employer will reimburse him $0.17 per mile driven. If Joe drives 107.78 miles on a business trip,
what is his mileage reimbursement?
Answer:
$18.3236
Step-by-step explanation:
If the employer reimburses $0.17 per mile driven, we just need to multiply $0.17 by the number of miles that Joe drives.
So, the mileage reimbursement for Joe is:
$0.17 * 107.78 = $18.3236
Please answer this correctly without making mistakes.Please simplify the correct answer
Answer:
19/70 of NASA shuttle missions were carried out by Discovery.
9/140 of NASA shuttle missions were carried out by Challenger.
17/70 of NASA shuttle missions were carried out by Endeavour.
Step-by-step explanation:
Adding the number of missions carried out by NASA gives us 140 in total.
Discovery's total amount of missions simplified is 19/70.
Challenger's total amount of missions is already in the simplest form.
Endeavour's total amount of missions simplified is 17/70.
Answer:
81/140
Step-by-step explanation:
Well to find the fraction we first need to total amount of NASA missions.
38 + 32 = 70
70 + 34 = 104
104 + 27 = 131
131 + 9 = 140
Now we need to find out the amount of Discovery, Challenger, and Endeavour missions.
38 + 9 + 34 = 81
Now we can make the following fraction,
81/140
This is already in simplest form.
Thus,
the answer is 81/140.
Hope this helps :)
The length l, width w, and height h of a box change with time. At a certain instant the dimensions are l = 3 m and w = h = 6 m, and l and w are increasing at a rate of 3 m/s while h is decreasing at a rate of 6 m/s. At that instant find the rates at which the following quantities are changing.
(a) The volume.
m3/s
(b) The surface area.
m2/s
(c) The length of a diagonal. (Round your answer to two decimal places.)
m/s
Answer:
a) The rate of change associated with the volume of the box is 54 cubic meters per second, b) The rate of change associated with the surface area of the box is 18 square meters per second, c) The rate of change of the length of the diagonal is -1 meters per second.
Step-by-step explanation:
a) Given that box is a parallelepiped, the volume of the parallelepiped, measured in cubic meters, is represented by this formula:
[tex]V = w \cdot h \cdot l[/tex]
Where:
[tex]w[/tex] - Width, measured in meters.
[tex]h[/tex] - Height, measured in meters.
[tex]l[/tex] - Length, measured in meters.
The rate of change in the volume of the box, measured in cubic meters per second, is deducted by deriving the volume function in terms of time:
[tex]\dot V = h\cdot l \cdot \dot w + w\cdot l \cdot \dot h + w\cdot h \cdot \dot l[/tex]
Where [tex]\dot w[/tex], [tex]\dot h[/tex] and [tex]\dot l[/tex] are the rates of change related to the width, height and length, measured in meters per second.
Given that [tex]w = 6\,m[/tex], [tex]h = 6\,m[/tex], [tex]l = 3\,m[/tex], [tex]\dot w =3\,\frac{m}{s}[/tex], [tex]\dot h = -6\,\frac{m}{s}[/tex] and [tex]\dot l = 3\,\frac{m}{s}[/tex], the rate of change in the volume of the box is:
[tex]\dot V = (6\,m)\cdot (3\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot (3\,m)\cdot \left(-6\,\frac{m}{s} \right)+(6\,m)\cdot (6\,m)\cdot \left(3\,\frac{m}{s}\right)[/tex]
[tex]\dot V = 54\,\frac{m^{3}}{s}[/tex]
The rate of change associated with the volume of the box is 54 cubic meters per second.
b) The surface area of the parallelepiped, measured in square meters, is represented by this model:
[tex]A_{s} = 2\cdot (w\cdot l + l\cdot h + w\cdot h)[/tex]
The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time:
[tex]\dot A_{s} = 2\cdot (l+h)\cdot \dot w + 2\cdot (w+h)\cdot \dot l + 2\cdot (w+l)\cdot \dot h[/tex]
Given that [tex]w = 6\,m[/tex], [tex]h = 6\,m[/tex], [tex]l = 3\,m[/tex], [tex]\dot w =3\,\frac{m}{s}[/tex], [tex]\dot h = -6\,\frac{m}{s}[/tex] and [tex]\dot l = 3\,\frac{m}{s}[/tex], the rate of change in the surface area of the box is:
[tex]\dot A_{s} = 2\cdot (6\,m + 3\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m+6\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m + 3\,m)\cdot \left(-6\,\frac{m}{s} \right)[/tex]
[tex]\dot A_{s} = 18\,\frac{m^{2}}{s}[/tex]
The rate of change associated with the surface area of the box is 18 square meters per second.
c) The length of the diagonal, measured in meters, is represented by the following Pythagorean identity:
[tex]r^{2} = w^{2}+h^{2}+l^{2}[/tex]
The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time before simplification:
[tex]2\cdot r \cdot \dot r = 2\cdot w \cdot \dot w + 2\cdot h \cdot \dot h + 2\cdot l \cdot \dot l[/tex]
[tex]r\cdot \dot r = w\cdot \dot w + h\cdot \dot h + l\cdot \dot l[/tex]
[tex]\dot r = \frac{w\cdot \dot w + h \cdot \dot h + l \cdot \dot l}{\sqrt{w^{2}+h^{2}+l^{2}}}[/tex]
Given that [tex]w = 6\,m[/tex], [tex]h = 6\,m[/tex], [tex]l = 3\,m[/tex], [tex]\dot w =3\,\frac{m}{s}[/tex], [tex]\dot h = -6\,\frac{m}{s}[/tex] and [tex]\dot l = 3\,\frac{m}{s}[/tex], the rate of change in the length of the diagonal of the box is:
[tex]\dot r = \frac{(6\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot \left(-6\,\frac{m}{s} \right)+(3\,m)\cdot \left(3\,\frac{m}{s} \right)}{\sqrt{(6\,m)^{2}+(6\,m)^{2}+(3\,m)^{2}}}[/tex]
[tex]\dot r = -1\,\frac{m}{s}[/tex]
The rate of change of the length of the diagonal is -1 meters per second.
Find the value of x in the isosceles triangle shown below.
Answer:
the answer is x = sqrt 48
Step-by-step explanation:
Which group of plants were the first to adapt to life on land? flowering pine mosses conifers
Answer:
mosses
Step-by-step explanation:
use socratic
Mosses are also known as the amphibian of the plant kingdom. The mosses were the first plant that can even survive on the land.
Bryophytes:It is the group of small plants that complete its life cycle in both land and water. They were the first plants to adapt to live on the land.For example- mosses.Conifers, pines, and flowering plants developed much later after the evolution of bryophytes.
Therefore, the mosses were the first plant that can even survive on the land.
Learn more about Bryophytes:
https://brainly.com/question/841138
graph the function f(x)=3/2(x-4)^2+3
Answer:
its 23
Step-by-step explanation:
The equation of the graphed line is 2x – y = –6. A coordinate plane with a line passing through (negative 3, 0) and (0, 6). What is the x-intercept of the graph? –3 –2 2 6
Answer:
-3
Step-by-step explanation:
-3 is the answer
Answer:
-3
Step-by-step explanation:
What is the measure of x?
Answer:
9 in.
Step-by-step explanation:
Given that the 4 in and 10 in. lines are parallel, the two triangles are similar.
As such, the ratio of the sides would give the same results.
Hence,
4/6 = 10/(6 + x)
cross multiplying
4(6 + x) = 60
Dividing both sides by 4
6 + x = 15
collecting like terms
x = 15 - 6
= 9
Simplify the expression:
4w + 10(7w+1)
Answer:
74w+10
Step-by-step explanation:
That's the answer
Two friends are playing tic-tac-toe. If Amy wins 3/8 of the time, Lily wins 3/10 of the time, and they tie the rest of the time, then what fraction of the time do they tie?
Answer:
13/40
Step-by-step explanation:
The period they have played can be divided into 3 parts:
● The time Amy wins
● The time Lily wins
● The time they tie
So the sum of them is the total time of playing.
Let A be the time Amy wins, L the tile Lily wins and T the time they tie .
●●●●●●●●●●●●●●●●●●●●●●●
Since we have expressed the times using fractions then the total period of playing is 1 wich is 100%.
So:
A + P + T = 1
3/8 + 3/10 + T = 1
Multiply 8 by 10 and 10 by 8 so that you get a common denominator.
Cross multiply the numerators and the denominators.
(3*10+3*8)/80 + T = 1
(30 + 24)/80 + T =1
54/80 + T = 1
(27*2)/(40*2) + T = 1
Simplify by 2
27/40 + T = 1
T = 1 - 27/40
Multiply one by 40 to get a common denominator
T = (40-27)/40
T = 13/40
So they have tied 13/40 of the time
which graph represents a function? Please help!
Answer:
The last graph (to the far right).
Step-by-step explanation:
As long as each x-value has one y-value, it is a function. However, the last graph has an x-value at -1 where there are two y-values. So, it does not pass the Vertical Line Test, and it is a relation rather than a function.
Hope this helps!
Answer it pls option c
Answer:
[tex]x = \frac{1}{4}[/tex]
Step-by-step explanation:
[tex]\frac{x}{2} +\frac{3}{4} =\frac{7}{8}[/tex]
→ Find the LCM of the denominators (2,4 and 8)
LCM = 8
→ Multiply the whole equation by 8 to get rid of the fractions
4x + 6 = 7
→ Minus 6 from both sides to isolate 4x
4x = 1
→ Divide both sides by 4 to isolate x
[tex]x = \frac{1}{4}[/tex]
Answer:
[tex]x = \frac{1}{4} [/tex]Step-by-step explanation:
[tex] \frac{x}{2} + \frac{3}{4} = \frac{7}{8} [/tex]
Multiply both sides of the equation by 8
[tex] \frac{x}{2} \times 8 + \frac{3}{4} \times 8 = \frac{7}{8} [/tex]
[tex]4x + 6 = 7[/tex]
Move constant to R.H.S and change its sign
[tex]4x = 7 - 6[/tex]
Subtract the numbers
[tex]4x = 1[/tex]
Divide both sides of the equation by 4
[tex] \frac{4x}{4} = \frac{1}{4} [/tex]
Calculate
[tex]x = \frac{1}{4} [/tex]
hope this helps..
Best regards!!
Betty has $33 to buy plants for her greenhouse. Each plant costs $8. How
many plants can she buy? Do not include units in your answer.
Answer:
4 plants
Step-by-step explanation:
If betty has $33 dollars and each plant is $8, than 33/8 ≈ 4
(8 * 4 is 32)
She will have one dollar left but she can't buy another plant since that's not enough.
Answer:
4 plants
Step-by-step explanation:
Take the amount of money she has and divide by the cost per plant
33/8
The amount is 4 with 1 dollar left over
4 plants
Toni runs around her school's baseball diamond. Each side is 27 m long. Note: A baseball diamond is square. How far does Toni run?
Answer:
108 m
Step-by-step explanation:
Tim and Jim are working on a school project together. If he had to work by himself, it would take
Tim 10 hours to complete the school project. If Jim worked alone, it would take him 15 hours.
Working together, how long will it take Tim and Jim to complete the school project together?
Answer: 6 hours
Step-by-step explanation:
Given, Tim and Jim are working on a school project together.
Tim takes 10 hours to complete the school project.
If Jim worked alone, it would take him 15 hours
Let t be the time they both take if they work together.
Then, [tex]\dfrac{1}{t}=\dfrac{1}{\text{Time taken by Tim}}+\dfrac{1}{\text{Time taken by jim}}[/tex]
[tex]\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{10}+\dfrac{1}{15}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{3+2}{30}=\dfrac{5}{30}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{1}{6}\\\\\Rightarrow t=6[/tex]
So, it will take 6 hours to complete the school project together .
Need help with this math problem
Answer:
4
Step-by-step explanation:
f(x) = 4 ^ ( x-2)
Let x=3
f(3) = 4 ^ ( 3-2)
= 4 ^ 1
= 4
Answer:
4
Step-by-step explanation:
4^(x - 2)
Plug x as 3.
4^(3 - 2)
Subtract.
4^(1)
4^1 = 4
There are 90 passengers on a commuter flight from SFO to LAX, of whom 27 are traveling on business. In a random sample of five passengers, use the binomial model to find the approximate hypergeometric probability that there is at least one business passenger. A).1681 B).3602 C).8319 D).3087
Answer:
C). 0.83193
Step-by-step explanation:
There are total of 90 passengers of which 27 are for business.
The probability of passengers for business = 27/90
The probability of passengers for business p = 0.3
The probability of passengers not for business q = 1-The probability of passengers for business
= 1-0.3
= 0.7
Random sample of 5 passenger, probability of at least one business passenger = 1 - probability of no business passenger
probability of no business passenger
= 5C0(0.3)^0 * (0.7)^5
= 1 *1*0.16807
= 0.16807
probability of at least one business passenger = 1 - probability of no business passenger
= 1-0.16807
=0.83193
You are hiking and are trying to determine how far away the nearest cabin is, which happens to be due north from your current position. Your friend walks 205 yards due west from your position and takes a bearing on the cabin of N 23.9°E. How far are you from the cabin? asap would be great also running out of points srry
Answer:
462.61 yards.
Step-by-step explanation:
To solve, you need to find the measurement of the angle that forms a 90 degree angle with the 23.9 degree angle.
90 - 23.9 = 66.1 degrees.
Now that you have the angle, you can use TOA to solve for x (TOA = Tangent; Opposite over Adjacent).
tan(66.1) = x / 205
x / 205 = tan(66.1)
x = tan(66.1) * 205
x = 2.256628263 * 205
x = 462.6087939
So, you are about 462.61 yards from the cabin.
Hope this helps!
A P E X!!!! URGENT :The annual interest rate of Belinda's savings account is 8.6% and simple interest is calculated quarterly. What is the periodic interest rate of Belinda's account?
Answer:
The answer is 2.15%
Step-by-step explanatio
A test was marked out of 80. Aboy scored
60% of the marks on the test. How many
marks did he score?
(A)20
(B)48
(C)60
(D)75
Answer:
B
Step-by-step explanation:
To solve this you do 80/100=.8
You than do .8×60= 48
Find the surface area of the triangular prism using its net (below).
Answer:
It is 96 square units
Step-by-step explanation:
A 5 hour conference booking is required fir an office party for 120 people which includes a buffet dinner hotel 5 has recently increased the Total chargers by 10% how much would thia Booking now cost from hotel 5
Answer:
Total cost = $4,873
Therefore, the booking cost of hotel 5 would be $4,873
Step-by-step explanation:
Please refer to the attached table.
The total cost includes the cost of the room and the cost of buffet dinner.
From the given table hotel 5,
The cost of the room for 120 people is found to be $166 per hour.
The conference will last for 5 hours so the total cost of the room is
Cost of room = 5*$166 = $830
From the given table hotel 5,
The cost of the buffet dinner per head is found to be $30.
Since there are total 120 people so the total cost of dinner is
Cost of dinner = 120*$30 = $3600
Total cost = $830 + $3600 = $4430
We are given that hotel 5 has recently increased the total chargers by 10%
Total cost = $4430*1.10
Total cost = $4,873
Therefore, the booking cost of hotel 5 would be $4,873.
What is the answer, plz help. 5(x-7) + 42 = 5x+7
Answer:
x is all real numbers
Step-by-step explanation:
5(x-7) + 42 = 5x+7
Distribute
5x - 35 +42 = 5x+7
Combine like terms
5x +7 = 5x+7
Subtract 5x from each side
7=7
This is always true, so x can be any number
Answer:
Hey there!
5(x-7)+42=5x+7
5x-35+42=5x+7
7=7
Infinite solutions.
Hope this helps :)
The geometric probability function is f (x) = (1-P) x-1 P. what is the approximate probability of rolling a standard die and getting the first 6 on the 3rd try?
Answer:
We know that for a standard dice the probability of obtain a 6 is:
[tex] P=\frac{1}{6}[/tex]
And for this case our value of x=3 and replacing we got:
[tex] f(x=3) = (1- \frac{1}{6})^{3-1} \frac{1}{6}[/tex]
[tex]f(x=3)=\frac{25}{36} \frac{1}{6}= \frac{25}{216}= 0.116[/tex]
Step-by-step explanation:
For this case we have the following function:
[tex] f(x) = (1-P)^{x-1} P[/tex]
We want to find the approximate probability of rolling a standard die and getting the first 6 on the 3rd try
We know that for a standard dice the probability of obtain a 6 is:
[tex] P=\frac{1}{6}[/tex]
And for this case our value of x=3 and replacing we got:
[tex] f(x=3) = (1- \frac{1}{6})^{3-1} \frac{1}{6}[/tex]
[tex]f(x=3)=\frac{25}{36} \frac{1}{6}= \frac{25}{216}= 0.116[/tex]
A movie theater has a seating capacity of 235. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1704, How many children, students, and adults attended?
Hey there! :)
Answer:
118 children
58 students
59 adults
Step-by-step explanation:
We can solve this problem by setting up a system of equations:
Let a = adults
2a = children (since double the # of adults were children), and
s = students
Set up the equations:
1704 = 5(2a) + 7s + 12(a)
1704 = 10a + 7s + 12a
235 = 2a + a + s
Simplify the equations:
1704 = 22a + 7s
235 = 3a + s
Subtract the bottom equation from the top by multiplying the bottom equation by 7 to eliminate the 's' variable:
1704 = 22a + 7s
7(235 = 3a + s)
1704 = 22a + 7s
1645 = 21a + 7s
---------------------- (Subtract)
59 = a
This is the number of adults. Substitute this number into an equation to solve for the number of students:
235 = 3(59) + s
235 = 177 + s
s = 58.
Since the number of children is equivalent to 2a, solve:
2(59) = 118 children.
Therefore, the values for each group are:
118 children
59 adults
58 students.
Answer:
adults: 59, students:58 and children 118
Step-by-step explanation:
let A for adults, and C = children and S for students
There are half as many adults as there are children=
A=C/2 , C=2A
A+C+S=235 or
A+2A+S=235 first equation
3A+S=235
12A+5C+7S =1704 or
12A+10A+7S=1704
22A + 7S=1704 second equation
3A+S=235 first
solve by addition and elimination
22A+7S=1704
21 A+7S=1645 subtract two equations
A=59 adults
C=2A=2(59)=118
substitute in :A+S+C=235
S=235-(118+59)=58
check: 5C+7S+12A=1704
5(118)+7(58)+12(59)=1704