Answer:
The 95% confidence interval for the population mean is between 17.9 and 20.3 years.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 9 - 1 = 8
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 8 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.306
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.306\frac{1.5}{\sqrt{9}} = 1.2[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 19.1 - 1.2 = 17.9 years.
The upper end of the interval is the sample mean added to M. So it is 19.1 + 1.2 = 20.3 years.
The 95% confidence interval for the population mean is between 17.9 and 20.3 years.
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
please answer quick i need to go to my friends to get my joy con fixed
The area is just the base times the height. In this case, the base is (x+4) and the height is (x+6), and then you just distribute to get x^2 +4x+6x+24 which is x^2+10x+24.
Please help!! Given the recursive formula shown, what are the first 4 terms of the sequence?
Answer:
C
Step-by-step explanation:
the fibrin definition tells us that the first term of the sequence a1 = 6
so, B is out.
and for every following term we always add 7 to every previous term to create the next one.
so, when I add 7 to 6, what is my second term in the sequence ? 7+6 = 13
not 42, not -7
therefore, only C is correct.
and 13+7 = 20
and 20+7 = 27
it all fits
tiếp tuyến của đồ thị hàm số x[tex]x^{3} -3x^{2} +2[/tex] tại điểm M(2,-2)
Answer:
what are you telling Id understand
Step-by-step explanation:
became
A survey asked 50 students if they play an instrument and if they are in band.
1.25 students play an instrument.
2. 20 students are in band.
3. 30 students are not in band.
Which table shows these data correctly entered in a two-way frequency?
C, just look at the "Total" for each single information.
the values in the inner grid combine multiple informations.
The table shows these data correctly entered in a two-way frequency is table C.
What is Two way Frequency?Two-way frequency tables show the potential connections between two sets of categorical data visually. The table's four (or more) inside cells contain the frequency (count) data, which is displayed above and to the left of the table's designated categories.
We have been the information 25 students play an instrument 20 are in a band 30 are not in a band.
So, the two way table is:
Band Not in Band Total
Play instrument 20 5 25
Do not play instrument 0 25 25
Total 20 30 50
So, Table C is Correct.
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A tank is filled at a constant rate. 10 minutes after filling is started, the tank contains 4.8L of water. After 35 minutes the tank contains 7.3L of water.
a. Find the rate at which the tank is being filled?
b. Find the initial volume of fluid in the tank and express it as a function in terms of V and t.
c. Find how long it takes to filled, if the tank has a maximum capacity of 60L?
Answer:
Part A)
0.1 liters per minute.
Part B)
There was initially 3.8 liters of water.
[tex]\displaystyle V(t) = 0.1(t - 10) + 4.8[/tex]
Part C)
562 minutes.
Step-by-step explanation:
A tank is filled at a constant rate. After 10 minutes, the tank contains 4.8 L of water and after 35 minutes, the tank contains 7.3 L of water.
Part A)
We can represent the current data with two points: (10, 4.8) and (35, 7.3). The x-coordinate is measured in minutes since the tank began to be filled and the y-coordinate is measured in how full the tank is in liters.
To find the rate at which the tank is being filled, find the slope between the two points:
[tex]\displaystyle m = \frac{\Delta y}{\Delta x} = \frac{(7.3)-(4.8)}{(35)-(10)} = \frac{2.5}{25} = 0.1[/tex]
In other words, the rate at which the tank is being filled is 0.1 liters per minute.
Part B)
To find the function of the volume of the tank, we can use the point-slope form to first find its equation:
[tex]\displaystyle y - y_1 = m( x - x_1)[/tex]
Where m is the slope/rate of change and (x₁, y₁) is a point.
We will substitute 0.1 for m and let (10, 4.8) be the point. Hence:
[tex]\displaystyle y - (4.8) = 0.1(x - 10)[/tex]
Simplify:
[tex]\displaystyle y = 0.1(x-10) + 4.8[/tex]
Since y represent how full the tank is and x represent the time in minutes since the tank began to be filled, we can substitute y for V(t) and x for t. Thus, our function is:
[tex]\displaystyle V(t) = 0.1(t - 10) + 4.8[/tex]
The initial volume is when t = 0. Evaluate:
[tex]\displaystyle V(0) = 0.1 ((0) - 10) + 4.8 = 3.8[/tex]
There was initially 3.8 liters of water.
Part C)
To find how long it will take for the tank to be completely filled given its maximum capacity of 60 liters, we can let V(t) = 60 and solve for t. Hence:
[tex]60 = 0.1(t - 10) + 4.8[/tex]
Subtract:
[tex]55.2 = 0.1(t - 10)[/tex]
Divide:
[tex]552 = t - 10[/tex]
Add. Therefore:
[tex]t = 562\text{ minutes}[/tex]
It will take 562 minutes for the tank to be completely filled.
How much wrapping is needed to cover a cubed gift box that is 9 inches high? (Include the bow which takes 115 sq. inches.)
Answer:
601 in²
Step-by-step explanation:
To obtain the amount of wrapping needed to cover the cube shaped gift box, including the bow
Area of bow = 115 in²
Surface area of cube shaped box = 6a²
a = side length of cube = 9
Hence,
Surface area of gift box = 6 * 9²
Surface area = 6 * 81 = 486 in²
Total wrapping required = area of gift box + area of bow = (486 in² + 115 in²) = 601 in²
8 A test rocket is fired and follows a path described by y = 0.1x(200 – x). The height is y metres above
ground and x is the horizontal distance in metres.
How far does the rocket travel horizontally?
b How high does the rocket reach mid-flight?
Answer:
a) The rocket travels 200 meters horizontally.
b) The height of the rocket mid-flight is of 1000 meters.
Step-by-step explanation:
Height of the rocket:
The height of the rocket, in meters, after an horizontal distance of x, is given by:
[tex]y = 0.1x(200 - x)[/tex]
a) How far does the rocket travel horizontally?
This is x when [tex]y = 0[/tex]. So
[tex]0.1x(200 - x) = 0[/tex]
Then
[tex]0.1x = 0[/tex]
[tex]x = 0[/tex]
And
[tex]200 - x = 0[/tex]
[tex]x = 200[/tex]
So
The rocket travels 200 meters horizontally.
b How high does the rocket reach mid-flight?
This it the height y when x = 0, so:
[tex]y = 20*100 - 0.1*100^2 = 1000[/tex]
The height of the rocket mid-flight is of 1000 meters.
the length of a building is 720 in. Use dimensional analysis to convert this quantity to yards.
Answer:
20 yards
Step-by-step explanation:
First, we have to know how to get from inches to yards. 12 inches = 1 foot, and 3 feet = 1 yard.
Next, we have
[tex]\frac{720 in}{1}[/tex]
as a given. We want to multiply this by our conversions to get the end amount in yards.
We can first multiply our expression by 12 inches = 1 foot. To do this, we can set one number as the divisor and one as the dividend, e.g. 12 inches / 1 foot. However, to figure out which number should be the numerator/denominator, we first must examine our original expression. We want to multiply it by a value that cancels something out in conversion. To do this, we can have the same unit of something in the numerator in one and the denominator in the other in terms of what we're multiplying. Here, we can see that [tex]\frac{720 in}{1}[/tex] has inches on the top, so we want inches on the bottom in 12 inches = 1 foot. Therefore, we have
[tex]\frac{720 in}{1} * \frac{1 foot}{12 inches}[/tex]
= [tex]\frac{720feet}{12}[/tex]
= 60 feet
= [tex]\frac{60 feet }{1}[/tex]
We have feet as the numerator, so we want feet in the denominator in what we're multiplying this by. In 3 feet = 1 yard, we can multiply this to get
[tex]\frac{60 feet }{1} * \frac{1 yard}{3 feet} \\= \frac{60 yards}{3}[/tex]
= 20 yards
There are 6 people named A,B,C,D,E,F. The people named A,B, and C are all over the age of 40. The people named D,E,F are all under the age of 40. How many different orders are there for the people to sit on a bench, if both ends of the bench must be occupied by someone over the age of 40?
If sam runs 63,756 feet in 70 min what's his miles per hour
Answer:
10.35 miles per hr
Step-by-step explanation:
first convert ft into mi
then calculate the distance traveled in one min
multiply the answer by 60
then you get the answer
Which of the following questions are equivalent to the answer below x 3/5
Answer:
[tex]x^\frac{3}{5} = (x^3 )^\frac{1}{5}[/tex]
[tex]x^\frac{3}{5} = \sqrt[5]{x^3}[/tex]
[tex]x^\frac{3}{5} = (\sqrt[5]{x})^3[/tex]
Step-by-step explanation:
Given
[tex]x^\frac{3}{5}[/tex]
Required
The equivalent expressions
We have:
[tex]x^\frac{3}{5}[/tex]
Expand the exponent
[tex]x^\frac{3}{5} = x^{ 3 * \frac{1}{5}}[/tex]
So, we have:
[tex]x^\frac{3}{5} = (x^3 )^\frac{1}{5}[/tex] ----- this is equivalent
Express 1/5 as roots (law of indices)
[tex]x^\frac{3}{5} = \sqrt[5]{x^3}[/tex] ------ this is equivalent
The above can be rewritten as:
[tex]x^\frac{3}{5} = (\sqrt[5]{x})^3[/tex] ------ this is equivalent
White colour is painted in 2 ft wide which lies inside from both sides in the basketball court of length 78 ft and breadth 46 ft . find the area of the painted part.
Answer:
L1=78
W1=46
L2=78+4=82
W2=46+4=50
Area=L2×W2-L1×W1
82×50-78×46
Ans- 512ft^2
is A and B can do a piece of work in 6 and 12day respectively how m
any part of work can they do in 4 day
Answer:
6 * 12 / (6+12) = 72 / 18
If they work together they can finish in 4 days.
Source: http://www.1728.org/work.htm
Step-by-step explanation:
please solve asap thanks
Answer:
6x+36=180
6x=144
x=24
Step-by-step explanation:
this is the correct answer
Please help
A. SAS
B. AAS
C. HA
D. LL
E. ASA
F. HL
Answer:
Option B, AAS
Option C, HA
Option E, ASA
these three options applies
find the surface area of the cylinder and round to nearest tenth HURRY HURRY
Answer:
Does the answer help you?
What is the range & domain of the set
R: {(-6, 14), (10,19), (4, -9), (3, 2), (6, -13)}
Answer:
Domain { -6,3,4,6,10}
The range is the output values, listed from smallest to largest with no repeats
Range { -13,-9,2,14,19}
Step-by-step explanation:
The domain is the input values, listed from smallest to largest with no repeats
Domain { -6,3,4,6,10}
The range is the output values, listed from smallest to largest with no repeats
Range { -13,-9,2,14,19}
Answer:
Range: 14, 19, -9, 2, -13
Domain: -6, 10, 4, 3, 6
Step-by-step explanation:
I don't know but this is it I think .
Please help! The question is in the image
Answer:
I am pretty sure that your answer would be 3.
Step-by-step explanation:
The reason why is because if B if half of line segment AD and AD is equal to 12, then B must be equal to 6 since half of 12 is 6. Next, since C is the mid-point for line segment BD then C must be 3 since half of 6 is 3. And finally, that means line segment BC is three since it is 1/2 of BD.
Hope this helps! :)
Answer:
BC = 3
Step-by-step explanation:
If B is the midpoint of AD, that means AB = BD
AD = 12 so BD = 1/2 of AD and BD = 6
If C is the midpoint of BD, that means BC = CD
BD = 6 so BC = 1/2 of BD and BC = 3
You are planning to attend college next year. The total cost of tuition and textbooks is $10,000. If you go to school, your room and board will cost you $5,000. If you did not go to school, however, you would live at home, and your total room and board would only be $1,000. Additionally, if you did not go to college, you would work a job making $20,000 for the year.
1. In terms of room and board alone, what would be opportunity cost of attending college. Be sure to explain your answer
2. What are the explicit costs of attending school? How much should be included for room and board?
3. What would be the implicit cost of attending college next year?
4. What would be the total opportunity cost of attending college next year?
Opportunity Cost of attending college, in terms of room and board is $4000 . Explicit Cost, Implicit Cost of attending college is $14000, $20000. Total Opportunity Cost of attending college is $34000
1. Opportunity Cost is the cost of next best alternate foregone, as in value of sacrifice made, while choosing an alternative.
Money foregone to attend college, in room & board = room & board cost with college - room & board cost without college = 5000 - 1000 = 40002. Explicit Cost is the actual out of pocket cash expenses outflow, done for choosing an option. Eg : Cash expenditures
In this case, cash expenses for attending college = 140003. Implicit Cost is the implied estimated cost of self supplied factors of production, like value of self labour & self owned land etc.
In this case : Value of self labour, sacrificed for attending college, ie the salary which could have earned by doing job meanwhile = 200004. Total opportunity cost of attending college = Explicit Cost + Implicit Cost = 14000 + 20000 = 34000
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find the value of the trigonometric ratio
Answer:
ur box cannot be opend repain the window
Step-by-step explanation:
please mark this answer as brainlist
Which graph shows a set of ordered pairs that represent a function?
Answer:
Graph C.
*See attachment below
Step-by-step explanation:
A graph that shows a set of ordered pairs representing a function would have each x-value being plotted against only one y-value. That is, every x-value must have exactly one y-value. Every x-value must not have more than 1 y-value being plotted against it.
The graph that shows this is the graph in option as shown in the attachment below.
20. simplify each of the following: see the above picture
and get 40 points
Answer:
[tex]i)14 + 4 \sqrt{6} [/tex]
[tex]ii) \sqrt{10} + 28[/tex]
[tex]iii) 243[/tex]
Step-by-step explanation:
[tex]i)(2 \sqrt{3} + \sqrt{2} {)}^{2} [/tex]
➡️ [tex]12 + 4 \sqrt{6} + 2[/tex]
➡️ [tex]14 + 4 \sqrt{6} [/tex] ✅
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
[tex]ii)(3 \sqrt{5} - \sqrt{2} ) \times ( \sqrt{2} + 2 \sqrt{5} )[/tex]
➡️ [tex]3 \sqrt{10} + 30 - 2 - 2 \sqrt{10} [/tex]
➡️ [tex] \sqrt{10} + 28[/tex] ✅
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
[tex]iii)3 \sqrt{81} \times 3 \sqrt{9} [/tex]
➡️ [tex]3 \times 9 \times 3 \times 3[/tex]
➡️ [tex]243[/tex] ✅
You decide to go on a 4 day backpacking trip. The first day you walk 8 miles at northeast, on the second day, you walk 4 miles at eastsouth, and on the third day you walk 3 miles at southwest. On the fourth day you need to head straight back to your car. How far do you have to walk, and in what direction
Answer:5
Step-by-step explanation:
Where the above parameters are given, you need to walk a distance of approximately √41 miles back to your car.
How to compute the aboveTo calculate the total distance you need to walk, you can use the Pythagorean theorem since you have a right triangle formed by the north and east displacements.
Distance = √((Distance north)² + (Distance east)²)
= √((5 miles)² + (4 miles)²)
= √(25 miles + 16 miles)
= √41 miles
Hence, you need to walk a distance of approximately √41 miles back to your car.
As for the direction, based on the net displacements, you are 5 miles north and 4 miles east of your car, so the direction would be a combination of north and east, often referred to as northeast.
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The height of a triangle is 2 times the base. The area is 4 square inches. Find the base.
The base of the triangle is
inches.
Answer:
2 Inches
Step-by-step explanation:
Area of a triangle = (1/2)* Base * Hight
lets consider the base of the triangle is X inches,
then, Hight of the triangle is 2X
Then the Area of the Angle is = (1/2)*X*2X
4 = x^{2}
X = 2
Find the largest positive integer that will divide 542, 436, 398 leaving reminders 7, 11, 15 respectively
Answer:
17
Step-by-step explanation:
Here in this question for finding the numbers that will divide 398, 436 and 542 leaving remainder 7, 11 and 15 respectively we have to first subtract the remainder of the following. By this step we find the highest common factor of the numbers.
And then the required number is the HCF of the following numbers that are formed when the remainder are subtracted from them.
Clearly, the required number is the HCF of the numbers 398−7=391,436−11=425, and, 542−15=527
We will find the HCF of 391, 425 and 527 by prime factorization method.
391=17×23425=52×17527=17×31
Hence, HCF of 391, 4250 and 527 is 17 because the greatest common factor from all the numbers is 17 only.
So we can say that the largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively is 17.
Note: - whenever we face such a type of question the key concept for solving this question is whenever in the question it is asking about the largest number it divides. You should always think about the highest common factor i.e. HCF. we have to subtract remainder because you have to find a factor that means it should be perfectly divisible so to make divisible we subtract remainder. because remainder is the extra number so on subtracting remainder it becomes divisible.
I’m having trouble with this
Answer:
this will give you the answer: for cylinder
V = 3×2^2×7 = 84cm
this will give you the answer for cone:
V = 3× 2^2 × 6/3 = 24cm
then we just add
84 + 24 = 108cm^3
Step-by-step explanation:
hope it helps!
9.2% written as a decimal is
the answer will be 0.092 as a decimal
If two angles are complementary, find the measure of each of angle.
Answer:
B: 30 and 60
Step-by-step explanation:
First, let's set up an equation. Since the two angles are complementary, we can write the equation like this:
2p + p = 90
Now, let's solve it!
2p + p = 90
Combine like terms:
3p = 90
Divide each side by 3 to isolate p:
3p/3 = 90/3
p = 30
Now that we know how many degrees one of our angles is, we can subtract that from 90 to get both of the complementary angles.
90 - 30 = 60
Therefore, the two angles that are complementary in this case are 30 and 60 degrees.
11. A surveyor at point S discovers that the angle between peaks A and B is 3 times as large as the angle
between peaks B and C. The surveyor knows that ZASC is a right angle. Find mzASs and m2BSC.
The measures of the angles between the peaks are;
m∠BSC = 22.5°
m∠ASB = 67.5°
The reason for arriving at the above angles is as follows:
The known values are;
The location of the surveyor = Point S
The angle between peaks A and B = m∠ASB = 3 times as large as the angle between peaks B and C = 3 × m∠BSC
The measure of angle m∠ASC = A right angle = 90°
Required:
To find m∠ASB and m∠BSC
From the given diagram, we have;
m∠ASC = 90°
m∠ASC = m∠ASB + m∠BSC (angle addition postulate)
m∠ASB = 3 × m∠BSC
∴ m∠ASC = 3 × m∠BSC + m∠BSC = 4 × m∠BSC
m∠ASC = 4 × m∠BSC = 90°
m∠BSC = 90°/4 = 22.5°
m∠BSC = 22.5°
m∠ASB = 3 × m∠BSC
∴ m∠ASB = 3 × 22.5° = 67.5°
m∠ASB = 67.5°
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Please find the answer
9514 1404 393
Answer:
-0.84
Step-by-step explanation:
In decimal, the expression is ...
-1.34 +1.50 -1.00 = -0.84
__
As fractions, the expression is ...
-67/50 +75/50 -50/50 = (-67+75-50)/50 = -42/50 = -21/25
