The answers to the given questions about annual interest are given below:
a. $4,415.25b. $4,376.70c. 2.27986 yearsHow to solvea.
A = 4,000 (1 + 0.05/2)^(2 x 2)
= $4,415.25
b.
A = 4,000 x e^(0.045 x 2)
= $4,376.70
c. $100 more than option 2 = 4,376.70 + 100
= $4,476.70
t (in years) = ln(4,476.70/4,000) / ln(1 + 0.05/2)
= 2.27986 years
Annual interest denotes the rate of interest levied or gained on a loan or investment for a duration of one year. This indicates the portion, expressed as a percentage, of the original amount that is utilized for interest payments or gained as a profit within a twelve-month period.
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X squared minus 14 minus 4x
The factor form of the given expression is [tex]x^2 - 14 - 4x = (x - 4)(x - 14).[/tex]
To factor the expression x^2 - 14 - 4x, we can use the technique of grouping.
First, we can rearrange the terms as:
x^2 - 4x - 14
Next, we can factor out a common factor of x from the first two terms:
x(x - 4) - 14
Then, we can factor out a negative 1 from the last two terms:
x(x - 4) - 1(14)
Finally, we can write the expression as the product of two binomials:
(x - 4)(x - 14)
Therefore, the factored form of x^2 - 14 - 4x is (x - 4)(x - 14).
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Find the area and perimeter of the figure. (Hint: Don't forget your units!)
8cm
1
1
5cm
6cm
Answer:
Area of parallelogram:
8 × 5 = 40 square centimeters
Perimeter of parallelogram:
2(8 + 6) = 2 × 14 = 28 centimeters
Val's whole-house central air conditioner uses 4,000 watts when running. Val runs the AC 7 hours per summer day. Electricity costs (10 cents)/(1 kilowatt-hour). How much does Val's AC cost to run for a summer month of 30 days?
The electricity cost for the Val's AC to run for a summer month of 30 days is $84.
Given that,
Val's whole-house central air conditioner uses 4,000 watts when running.
Val runs the AC 7 hours per summer day.
Electricity costs (10 cents)/(1 kilowatt-hour).
Total electricity used for the whole house = 4000 watts = 4 kilowatts
Number of hours that the AC runs = 7 hours
Cost of electricity = (10 cents)/(1 kilowatt-hour).
Cost of electricity for 4 kilowatts for 1 hour = 10 × 4 = 40 cents
Cost of electricity for 4 kilowatts for 7 hours = 40 × 7 = 280 cents
= $2.80
Cost of electricity for a summer month of 30 days = $2.80 × 30
= $84
Hence the total cost for the electricity is $84.
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PLEASE HELP (WILL GIVE BRAINLIEST
Answer:
cm^3 can be used to represent volume.
An article is sold for Rs.150 at a gain. Had it been sold for Rs.135 there would have been a loss equal to 50% of the original gain. Find the cost price of the article.
The cost price of the article, which is sold for Rs. 150 at a gain but if sold for Rs. 135 would have resulted in a loss equal to 50% of the original gain, is Rs. 127.50.
How the cost of the article is determined:The cost price is the difference between the selling price and the profit or gain.
The difference is determined by subtraction.
Selling price of the article = Rs. 150
Loss if sold at Rs. 135 = 50% of the original gain
Original gain = Rs. 15 (Rs. 150 - Rs. 135)
50% of the original gain = Rs. 7.50 (Rs. 15 x 50%)
Cost price of the article = Rs. 127.50 (Rs. 135 - Rs. 7.50)
Thus, the cost price is Rs. 127.50.
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The capacity of a swimming pool is given by C = l × w × , where l is the length, w is the width, d1 is the depth of the shallow end, and d2 is the depth of the deep end of the pool.
Select all the correct statements.
The correct statements about the capacity of swimming pool are (a) and (d)
The capacity of a swimming pool is given by C = l × w × (d₁ + d₂)/2
where l is the length,
w is the width,
d₁ is the depth of the shallow end,
and d₂ is the depth of the deep end of the pool.
If C = 9,216 ft, l = 48 ft, w = 24 ft, and d₂ = 12 ft, then d₁ would be,
9216 = 48 × 24 × (d₁ + 12)/2
d₁ + 12 = (9216 × 2) / (48 × 24)
d₁ + 12 = 16
d₁ = 4 ft
And formula for the depth of the shallow end would be,
d₁ = (2C/lw) - d₂
Therefore, the correct statements are (a) and (d)
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The complete question is:
The capacity of a swimming pool is given by C = l × w × (d1 + d2)/2, where l is the length, w is the width, d 1 is the depth of the shallow end, and d 2 is the depth of the deep end of the pool.
Select all the correct statements.
a) The depth of the shallow end is given by d1 = 2C/lw - d2.
b) If C = 9,216 ft, l = 48 ft, w = 24 ft, and d2 = 16 ft, then d1 = 4 ft.
c) The depth of the shallow end is given by 2C - d2/lw .
d) If C = 9,216 ft, l = 48 ft, w = 24 ft, and d2 = 12 ft, then d1 = 4 ft.
Find the 15th term of the geometric sequence 9, 18, 36, ...
Answer: 147,456
Step-by-step explanation: 9, 18, 36, 72, 144, 288, 576, 1,152, 2,304, 4,608, 9,216, 18,432, 36,864, 73,728, 147,456
What is the density of a billiard ball with a radius 1.5 inches and a mass of 250g?
Answer: The density of the billiard ball is 6.67 g/cm^3.
Step-by-step explanation:
URGENT STATISTICS AND PROBABILITIES
Answer:
the expected point value is -1/5, so it is not advantageous to guess.
Step-by-step explanation:
1(1/5)+(-1/2)(4/5)
1/5-2/5
-1/5
A jet can fly (8 x 10^3) miles per hour. How far can it fly in a day?
The jet can fly a distance of 192,000 miles in a day, assuming it can maintain a speed of 8 x 10³ miles per hour for 24 hours.
There are 24 hours in a day, so the distance the jet can fly in a day is:
Distance = Speed x Time
where Time is the duration of the flight.
If we assume that the jet can fly continuously for 24 hours without refueling or stopping, then the time of the flight is 24 hours.
Therefore, we have:
Distance = Speed x Time
=8 x 10³ miles/hour x (24 hours)
= 192,000 miles
Therefore, the jet can fly a distance of 192,000 miles in a day, assuming it can maintain a speed of 8 x 10³ miles per hour for 24 hours.
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1. Dave plays golf almost every day. The data set shown are his scores for his last 40 rounds of golf.
a. Construct a tally and frequency table for this data using class intervals 70-74, 75-79, 80-84, 85 - 89.
b. What percentage of Dave's scores were more than 84?
c. What percentage of Dave's scores were less than 75?
d. Copy and complete the following: More scores were in the interval..............than in any other interval.
More scores were in the interval 75-79 than any other interval
How to solvea. Class Interval Frequency
70-74 8
75-79 16
80-84 12
85-89 4
b. The % more than 84 = 4/40 x 100
=10%/
c. The % less than 75 = 8/40 x 100
= 20%
d. More scores were in the interval 75-79 than any other interval
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wo ships, the Queen Elizabeth and the Queen Mary, are parallel to the shore and 35 km apart. How far is each ship from a lighthouse if the Queen Elizabeth is at an angle of 68° and the Queen Mary is at an angle of 45° to the lighthouse
find the following arc measures
The measure of the angles are;
<KL = 23 degrees
m<LON is 23 degrees
m<OM = 113 degrees
m<KNL = 23 degrees
m<NL = 157 degrees
How to determine the measures of the arcTo determine the measures of the arc, we need to note the following;
Angles on a straight line is equal to 180 degreesAngle at right angle is equal to 90 degreesFrom the information shown in the diagram, we have;
<KL +<KM = 90 degrees
Now, substitute the values
<KL + 67 = 90
collect like terms
<KL = 23 degrees
m<LON and <KL are corresponding angles
Then, m<LON is 23 degrees
m<OM = m<LON + 90 degrees
Substitute the values
m<OM = 113 degrees
m<KNL = 23 degrees
m<NL = 90 + <LM
Substitute the values
m<NL = 157 degrees
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Jonna is sewing a front cover for a circular pillow. The pillow has a diameter of 15 inches. To sew the front cover, she must cut the fabric two inches wider than the pillow all the way around. What is the minimum area, in square inches, of the piece of fabric she will use?
Answer:
Step-by-step explanation:
To determine the minimum area of the piece of fabric Jonna needs, we need to calculate the diameter of the circle after adding 2 inches to the radius.
The radius of the pillow is half its diameter, which is 15/2 = 7.5 inches.
When Jonna adds 2 inches to the radius, the new radius becomes 7.5 + 2 = 9.5 inches.
The diameter of the circle with the new radius is 2 x 9.5 = 19 inches.
Therefore, Jonna needs to cut a circular piece of fabric with a diameter of 19 inches.
To calculate the minimum area of the fabric, we need to use the formula for the area of a circle:
Area = π x (radius)^2
The radius is 9.5 inches, so:
Area = π x (9.5)^2
Area = π x 90.25
Area ≈ 283.77 square inches
Therefore, Jonna needs a piece of fabric with a minimum area of approximately 283.77 square inches.
Which of the following table represents probability distribution
Answer:
b
Step-by-step explanation:
What does the song reveal about the goals of the Nazi Party?
Adolescents who loved jazz and were drawn to American, British culture in general, as well as conformity and discipline in the army, made up the swing youths in Nazi Germany.
Germany saw significant turmoil in politics in the late 1930s as a result of Hitler's ascension to power and the real-world consequences of his virulent anti-Semitism.
He described how in the Nazi era, there were groups of young people in Vienna who would get together in private, dancing to American bounce music, and express opposition to the brutal Nazi reality through their behavior and attire.
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The question is incomplete, Complete question probably will be:
What does the song Swing Heil reveal about the goals of the Nazi Party?
The table below shows information about the thickness of each of the books on a shelf. Work out an estimate for the mean book thickness. Give your answer as a decimal. Thickness, x (mm) 0< x≤2 2< x≤4 4< x≤6 Frequency 4 9 7
Answer:
3.2mm
Step-by-step explanation:
Answer:
3.2mm
Step-by-step explanation:
a doctor has 7 patients to visit how many different ways can she make her rounds if she visits each patient only once
There is only one way for the doctor to visit all seven patients exactly once.
A combination is a way of selecting items from a larger set, where the order of the items is not important. In this problem, we need to select seven patients out of a larger set of seven patients, so we can use the formula for the number of combinations of n items taken r at a time:
C(n,r) = n! / (r!(n-r)!)
where n is the total number of items, r is the number of items to be selected, and the exclamation mark represents the factorial function.
In this case, we need to find the number of combinations of 7 patients taken 7 at a time, which can be written as:
C(7,7) = 7! / (7!(7-7)!) = 7! / (7!0!) = 1
The order in which she visits the patients does not matter since each patient is visited only once.
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if there are 18 triangles in a polygon how many sides has the polygon
The number of sides of a polygon that has 18 triangles would be 20 sides.
How to find the number of sides ?To determine the number of sides in a polygon consisting of 18 triangles, we can calculate the sum of the interior angles. Each triangle has total interior angle sum of 180 degrees, and since there are 18 triangles, the sum of those angles would be 18 multiplied by 180, which comes to 3, 240 degrees.
Applying the given formula for calculating the interior angles of a polygon, we obtain that (n - 2) multiplied by 180 stands for the sum of all angles within it, with n being the number of sides.
Hence, rearranging the equation gives n :
n = (sum of interior angles ÷ 180) + 2
n = (3240 ÷ 180) + 2 = 20
There must be precisely 20 sides in that particular polygon.
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100 POINTS!!! PLS ANSWER ASAP
The number of toys owned by eight classmates is shown below:
4, 3, 4, 5, 6, 6, 8, 4
Part A: What is the mean of the data? Show your work. (4 points)
Part B: Use your answer from Part A to calculate the mean absolute deviation for the data. Show your work. (6 points)
Answer:
the answer for part A is. 5
the absolute deviation is. 1
Step-by-step explanation:
to find the answer for part A add all numbers and divide it by 8
4+3+4+5+6+6+8+5/840/85 is the answersFor part B
4-5= |-1|= 1
3-5= |-2|= 2
4-5= |-1| =1
5-5= |0| =0
6-5= |1 | =1
6-5= |1 | =1
8-5= |3| =3
5-5= |0| =0
Then add all the number and divided them by 8
1+2+1+0+1+1+3+0/89/89/8 is the answerMAY I GET BRAINLIEST
on a 28 question test there are 2-point questions, 4-point, and 5- point questions. the test is worth a total of 100 points. there are twice as many 2 point questions as 5point questions on the test how many 2point questions are on the test
Answer:
Number of 2-point questions on the test as per given condition is equals to 8.
Total number of questions in a test = 28
Total points allotted for test = 100
Questions distribution as per points :
2-point questions, 4-point questions, and 5-point questions
'x' represents the 5-point questions
As per condition given,
Number of 2-point questions = 2x
Number of( 2-point + 4-point + 5-point ) questions = 28
⇒ 2x + 4-point questions + x = 28
⇒ 4-point questions = 28 - 3x
Substitute the value in the given condition of the equation we get,
2(2x)+4(28-3x)+5(x) = 100
4x+112-12x+5x=100
112-3x=100
x=4
please help me with this
Answer: okay ill help
Step-by-step explanation:
Ferrese
2. (errencer feld acceed
rest
As and ove rect
The x-coordinate of 4s recex is 45
The x-ceerdinate of is rectex is
The coordinate os recex 45
he rease othe reser at
The true statements are
Its x-intercepts are (0,0) and (11,0)The x-coordinate of its vertex is 5.5How to find the true statementsTo find the true statements about the graph that represents y = -2x(x - 11), we need to analyze the equation and its properties.
x-intercepts by setting y = 0 and solving for x:
form the equation we have y = -2x(x - 11)
0 = -2x(x - 11)
0 = x(x - 11)
x = 0
x = 11
The x-intercepts are at (0,0) and (11,0).
Now let's find the vertex of the parabola. The vertex is located at the x-coordinate x = -b / 2a,
y = -2x^2 + 22x
given that
a = -2,
b = 22
x coordinate of the vertex is found by
= -22 / (2 * -2)
= 22 / 4
= 5.5
so we can say that the true statement is: The x-coordinate of its vertex is 5.5
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diego is buying a pumpkin that weighs 12.8 pounds. pumpkins cost $0.60 per pound. how much will diego pay for his pumpkin
As pumpkins cost $0.60 per pound Diego will pay $7.68 for his pumpkin.
To find out how much Diego will pay for his pumpkin, we need to multiply the weight of the pumpkin by the cost per pound:
Cost = weight × cost per pound
In this case, the weight is 12.8 pounds and the cost per pound is $0.60:
Cost = 12.8 pounds × $0.60/pound
Simplifying the expression, we get:
Cost = $7.68
Therefore, Diego will pay $7.68 for his pumpkin.
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Drag the tiles to the correct boxes to complete the pairs.
Match each system of linear equations with the correct number of solutions.
One solution
62
地址
3x - y
-
y =
Infinitely many solutions
-
= 4
2y = 8
-4x - 5
-4x + 1
-3x + y
2x
ee
4y
= 7
=
-8
Reset
Next
No solution.
In the given system of linear equations we get,
3x - y = 4, 6x - 2y = 8 has no solution.
y = -4x - 5, y = -4x + 1 has infinitely many solutions.
- 3x + y = 7, 2x - 4y = -8 has exactly one solution.
System of linear equations can have one solution or infinitely many solution or no solution based on their form.
If two lines are parallel to each other (that is, both linear equations have same slope) then the system of linear equations has no solutions.
A system of linear equation with infinitely many solutions has both the sides of equations equal.
When a system of linear equation has exactly one value of the variables which makes the equations satisfy is said to have one solution.
Here the system of linear equations are as,
3x - y = 4
6x - 2y = 8
The two equations of the system of linear equations are parallel to each other and hence has no solution.
y = -4x - 5
y = -4x + 1
The two equations of the system of linear equations has both the sides equal to each other and hence has infinitely many solutions.
- 3x + y = 7
2x - 4y = -8
The two equations of the system of linear equations has exactly one value of x and y which satisfies the conditions and hence has one solution.
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A virus takes 18 days to grow from 160 to 240. How many days will it take to
grow from 160 to 600? Round to the nearest whole number.
The virus will thus increase from 160 to 600 in around 10 days.
What is virus ?
A virus is a submicroscopic infectious agent that only reproduces inside of an organism's live cells.
We can resolve this issue using a proportion. Let x be the period of time needed for the virus to multiply from 160 to 600. Then: (240 - 160) / 18 = (600 - 160) / x
This equation may be written as
80/18 = 440/x.
Cross-multiplying:
80x = 18 * 440
80 divided by both sides yields x = 9.9
We obtain x = 10 by rounding to the next full value.
Therefore, The virus will thus increase from 160 to 600 in around 10 days.
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The entries in Table I are the probabilities that a random variable having the standard normal distribution will take on a value between 0 andz. They are given by the area of the gray region under the curve in the figure. TABLET NORMAL-CURVE AREAS 2 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.1 0.2 0.3 0.4 0.5 0.0000 0.0398 0.0793 0.1179 0.1554 0.1915 0.0080 0.0478 0.0871 0.1255 0.1628 0.1985 0.0120 0.0517 0.0910 0.1293 0.1664 0.2019 0.2357 0.2673 0.2967 0.3238 0.3485 0.0160 0.0557 0.0948 0.1331 0.1700 0.2054 0.2389 0.2704 0.2995 0.3264 0.3508 0.0199 0.0596 0.0987 0.1368 0.1736 0.2088 0.0239 0.0636 0.1026 0.1406 0.1772 0.2123 0.0279 0.0675 0.1064 0.1443 0.1808 0.2157 0.0319 0.0714 0.1103 0.1480 0.1844 0.2190 0.0359 0.0753 0.1141 0.1517 0.1879 0.2224 0.2549 0.2852 0.3133 0.3389 0.3621 0.2257 0.0040 0.0438 0.0832 0.1217 0.1591 0.1950 0.2291 0.2611 0.2910 0.3186 0.3438 0.3665 0.3869 0.4049 0.4207 0.4345 0.4463 0.4564 0.4648 0.4719 0.4778 0.6 0.7 0.8 0.9 1.0 0.2580 0.2881 0.3159 0.3413 0.2324 0.2642 0.2939 0.3212 0.3461 0.2422 0.2734 0.3023 0.3289 0.3531 0.2454 0.2764 0.3051 0.3315 0.3554 0.2517 0.2823 0.3106 0.3365 0.3599 0.2486 0.2794 0.3078 0.3340 0.3577 0.3790 0.3980 0.4147 0.4292 0.4418 1.1 1.2 1.3 1.4 1.5 0.3749 0.3944 0.4113 0.4265 0.4394 0.3770 0.3962 0.4131 0.4279 0.4406 0.3810 0.3997 0.4162 0.4306 0.4429 0.3643 0.3849 0.4032 0.4192 0.4332 0.4452 0.4554 0.4641 0.4713 0.4772 0.3686 0.3888 0.4066 0.4222 0.4357 0.4474 0.4573 0.4656 0.4725 0.4783 0.3708 0.3907 0.4082 0.4236 0.4370 0.4484 0.4582 0.4664 0.4732 0.4788 0.3729 0.3925 0.4099 0.4251 0.4382 0.4495 0.4591 0.4671 0.4738 0.4793 0.3830 0.4015 0.4177 0.4319 0.4441 0.4545 0.4633 0.4706 0.4767 0.4817 1.6 1.7 1.8 1.9 2.0 0.450S 0.4599 0.4678 0.4744 0.4798 0.4515 0.4608 0.4685 0.4750 0.4803 0.4525 0.4616 0.4692 0.4756 0.4808 0.4535 0.4625 0.4699 0.4761 0.4812 2.1 2.2 2.3 2.4 2.5 0.4826 0.4864 0.4896 0.4920 0.4940 0.4830 0.4868 0.4898 0.4922 0.4941 0.4834 0.4871 0.4901 0.4925 0.4943 0.4850 0.4884 0.4911 0.4932 0.4949 0.4854 0.4887 0.4913 0.4934 0.4951 0.4857 0.4890 0.4916 0.4936 0.4952 0.4821 0.4861 0.4893 0.4918 0.4938 0.4953 0.4965 0.4974 0.4981 0.4987 0.4838 0.4875 0.4904 0.4927 0.4945 0.4959 0.4969 0.4977 0.4984 0.4988 0.4842 0.4846 0.4878 0.4881 0.4906 0.4909 0.4929 0.4931 0.4946 0.4948 0.4960 0.4961 0.4970 0.4971 0.4978 0.4979 0.4984 0.4985 0.4989 0.4989 2.6 2.7 2.8 2.9 3.0 0.4955 0.4966 0.4975 0.4982 0.4987 0.4956 0.4967 0.4976 0.4982 0.4987 0.4957 0.4968 0.4977 0.4983 0.4988 0.4962 0.4972 0.4979 0.4985 0.4989 0.4963 0.4973 0.4980 0.4986 0.4990 0.4964 0.4974 0.4981 0.4986 0.4990 Also, for 3 - 4.0, 5.0 and 6.0, the areas are 0.49997, 0.4999997, and 0.499999999. ^ The entries in Table II are values for which the area to their right under the 1 distribution with given degrees of freedom (the gray area in the figure) is equal toa. TABLE II VALUE OF d.f. Fo.050 os 0.005 d.. 63.657 9.925 1 2 3 4 6.314 2.920 2.353 2.132 2.015 12.706 4.303 3.182 2.776 2.571 0.010 31.821 6.965 4.541 3.747 3.365 1 2 3 4 5.841 4.604 4.032 S S 6 7 6 7 8 1.943 1.895 1.860 1.833 1.812 2.447 2.365 2.306 2.262 2.228 3.143 2.998 2.896 2.821 2.764 3.707 3.499 3.355 3.250 3.169 8 9 9 10 10 11 12 1.796 1.782 1.771 1.761 1.753 13 14 15 2.201 2.179 2.160 2.145 2.131 2.718 2.681 2.650 2.624 2.602 3.106 3.055 3.012 2.977 2.947 11 12 13 15 16 16 17 18 19 20 1.746 1.740 1.734 1.729 1.725 2.120 2.110 2.101 2.093 2.086 2.583 2.567 2.552 2.921 2.898 2.878 2.861 2.845 17 18 19 2.539 2.528 20 21 22 23 24 25 1.721 1.717 1.714 1.711 1.708 2.080 2.074 2.069 2.064 2.060 2.518 2.508 2.500 2.831 2.819 2.807 2.797 2.787 21 22 23 24 25 2.492 2.485 2.056 2.052 26 27 28 29 Inf. 1.706 1.703 1.701 1.699 1.645 2.479 2.473 2.467 2.462 2.326 2.779 2.771 2.763 2.048 26 27 28 29 Inf. 2.045 2.756 2.576 1.960 Question 2 (20 marks) A tutorial school has been running IELTS mock examination for many years. Below is the summary presented by the tutorial school related to the IELTS mock examination in one of the many online classes selected randomly in year 2022. IELTS score in mock examination Number of students <4 0 5 2 6 7 5 15 8 10 3 9 A report presented by this tutorial school 5 years ago indi that the population mean score of IELTS mock examination was 7.05 points and the population proportion of students got 7 points or above was 0.67. (a) Construct a 95% confidence interval estimate of population mean score a student get in the IELTS mock examination in 2022. (b) Test, at 1% level of significance, if the population proportion of students get 7 points or above in 2022 is higher than that in year 2017. (The report must include the (i) null hypothesis and alternative hypothesis, (ii) rejection region(s), (iii) calculation of test statistics, and (iv) conclusion.) (c) If the confidence interval estimate in part (a) is constructed at 99% instead of 95%, would the interval be (1) wider, (II) narrower, or (III) no change in width? (State your answer, no explanation is needed in part (C).)
please help me yalll
Answer:
13
Step-by-step explanation:
210+50 is the total number of miles that can be driven. This adds up to 260. 260 divided by 20 is miles per gallon, which equals 13.
Pls help me understand this
The radius of the circle is 36 centimetres.
The circumference of the circle is 75.36 centimetres.
How to find radius and circumference of a circle?Let's find the radius of the circle with 20 degrees arc and length of 4π centimetres.
Length of an arc = ∅ / 360 × 2πr
where
r = radius∅ = central angleTherefore,
Length of an arc = 20 / 360 × 2 × π × r
4π = 40πr / 360
4π = 1 / 9 πr
cross multiply
πr = 36π
divide both sides by π
r = 36 centimetres
radius = 36 centimetres
b.
The equilateral triangle is inscribed in the circle. Therefore, the circumference of the circle can be found as follows:
The radius of the circle can be found using trigonometric ratios as follows:
The radius is an angle bisector. Hence,
sin 30 = opposite / hypotenuse
0.5 = 6 / r
cross multiply
r = 6 / 0.5
r = 12 centimetres
Lets' find the circumference,
circumference of the circle = 2πr
circumference of the circle = 2 × π × 12
circumference of the circle = 24 × 3.14
circumference of the circle = 75.36 cm
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|x| = 9 Solve the equation. Check your solutions. Graph the solution(s) on a piece of paper.
The equation |x| = 9 has two solutions: x = 9 and x = -9. The shaded region includes all points to the left of -9 and all points to the right of 9.
The equation is given as follows:
|x| = 9
The equation |x| = 9 has two solutions: x = 9 and x = -9.
To check these solutions, we can substitute them back into the original equation and see if they satisfy it:
|x| = 9
|9| = 9 --> True
|-9| = 9 --> True
Therefore, the solutions x = 9 and x = -9 are both valid.
To graph the solution(s), we can draw a number line and mark the points x = 9 and x = -9 with closed circles (since the absolute value of x is equal to 9 at those points).
We can then shade the parts of the number line where the absolute value of x is greater than or equal to 9.
This includes all points to the right of 9 and all points to the left of -9.
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Answer
[tex]\large\textrm{There are two solutions: 9 and -9.}[/tex]
Further explanation
If we have the absolute value of x, that means x could be positive or negative.
This means that, in |x| = 9, x could be 9 or -9.
Checking
Plug the answers into the original equation.
You should get a true statement.
[tex]\rm{\mid 9\mid=9}[/tex]because the absolute value of 9 is 9 so that's a solution
[tex]\rm{\mid-9\mid=9}[/tex]the absolute value of -9 is also 9 so that's also a solution
therefore, the solutions are 9 and -9.