For this exercise you need to use the following formula:
[tex]FV=PV\mleft(1+r\mright)^n[/tex]Where "FV" is the future value, "PV" is the present value, "r" is the interest rate (in decimal form), and "n" number of periods.
In this case, analyzing the information given in the exercise, you can identify that:
[tex]PV=200[/tex]Remember that a percent can be written in Decimal form by dividing it by 100. Then:
[tex]\frac{3}{100}=0.03[/tex]Since she earns interest at 3% per annum and it is compounded monthly, you can determine that the interest rate per month is:
[tex]r=\frac{0.03}{12}=0.0025[/tex]Knowing that 1 year has 12 months, you know that:
[tex](12)(1.5\text{ }years)=18\text{ }months[/tex]Then:
[tex]n=18[/tex]Therefore, you can substitute all those values into the formula and then evaluate, in order to find the future value of Joan’s investment after 1.5 years:
[tex]\begin{gathered} FV=PV(1+r)^n \\ FV=(200)(1+0.0025)^{18} \\ FV=(200)(1.0025)^{18} \end{gathered}[/tex][tex]FV\approx209.19[/tex]Hence, the answer is: $209.19 (approximately).
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
600
Step-by-step explanation:
[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]
A line that describes a proportional relationship between x and y is graphed on a coordinate grid. The line passes through (6, 2). Through what other point must the line pass?
The other point through which a line that describes a proportional relationship must pass is the point (0, 0)
What is a proportional relationship?A proportional relationship is one in which each the ratio of the x and y–values of each point on the line of the function is a constant.
The given relationship described by the line = A proportional relationship
The given point on the line = (6, 2)
Required; The other point through which the line must pass.
Given that the relationship described by the line, the ratio of all points on the line is a constant and each point (x, y) can be expressed in the form;
y = K•x
Which gives;
[tex] \displaystyle{ K = \frac{y}{x} }[/tex]
Where, K is a constant which is not equal to zero.
From the zero product property, which states that the product of all numbers and zero is also zero, we have;
When x = 0, k × 0 = 0 = y
A point through the line must pass is therefore; (0, 0)
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The graph below represents the number of siblings each student in a class has.
Given;
There are given that the graph represents the number of siblings.
Explanation:
According to the given graph:
The frequency of the number of siblings is:
[tex]6,7,4,4,3,2[/tex]Now,
We need to find the value of the range:
So,
From the concept of range:
The value of the difference between the highest data and lowest data will be representing the value of the range:
So,
The highest number is 7 and the lowest data is 2:
So,
[tex]\begin{gathered} Range=7-2 \\ =5 \end{gathered}[/tex]Final answer:
Hence, the value of the range is 5.
simplifylog(z) - log(18)
You have the following expression:
log(z) - log(18)
By the properties of logarithms, consider that the subtraction of two logarithms is equal to the logarithm of the quotient of the arguments:
log(z) - log(18) = log(z/18)
Hence, the answer is log(z/18)
What are the coordinates of point Q?
O (-3,0)
O (0, -3)
O (0, 3)
O (3, 0)
I SEEN HELP ASAP. are these following triangles similar? Yes or no and explain
Given data:
The given length of the EC is CD=9.
The given length of the CD is CD=10.
The given length of TV is TV=27.
The given length of TU is TU=30.
The ratio of the corresponding sides is,
[tex]\frac{EC}{CD}=\frac{TV}{TU}[/tex]Susbtitute the given values in the above expression.
[tex]\begin{gathered} \frac{9}{10}=\frac{27}{30} \\ =\frac{9}{10} \end{gathered}[/tex]Thus, the ratio of the corresponding sides is equal so they are similar.
-45g – 9g
Factor the algebraic expression
Answer:
-54g or -9g(5+1)
Step-by-step explanation:
-45g - 9g
-9g(5+1)
I'm not sure which form you want it in lol. -9g(6)
:]
Answer:
-9g ( 5 + 1 )
Step-by-step explanation:
-45g - 9g
-(45g - 9g)
common factor or less number = 9
-9g (5 + 1)
sent help please urgent
What is this answer 467 x 48=
Long Multiplication
1. Arrange the numbers one on top of the other and line up the place values in columns. The number with the most digits is usually placed on top as the multiplicand.
This will be written as follows:
467
x 48
---------------
2. Starting with the ones digit of the bottom number, the multiplier, multiply it by the last digit in the top number.
This product is 8*7 = 56
3. If that answer is greater than nine, write the ones place as the answer and carry the tens digit.
We should write 6 and carry 5:
467
x 48
---------------
6 (carry 5)
4. Proceed right to left. Multiply the ones digit of the bottom number to the next digit to the left in the top number. If you carried a digit, add it to the result and write the answer below the equals line. If you need to carry again, do so.
The next product is 8*6 = 48. Adding the carry: 48+5=53, Write 3, carry 5:
467
x 48
---------------
36 (carry 5)
Multiply 8*4 = 32. Add the carry 5: 32+5 = 37. Write the full number because it's the last of the products of this step:
467
x 48
---------------
3736
5. When you've multiplied the ones digit by every digit in the top number, move to the tens digit in the bottom number.
Multiply as above, but this time write your answers in a new row, shifted one digit place to the left.
Multiply 4*7 = 28. Write 8, carry 2.
467
x 48
---------------
3736
8 (carry 2)
Multiply 4*6=24. Add 2: 24+2=26. Write 6, carry 2:
467
x 48
---------------
3736
68 (carry 2)
Multiply 4*4=16. Add 2: 16+2=18. Write the full number:
467
x 48
---------------
3736
1868
6. When you finish multiplying, draw another answer line below your last row of answer numbers.
467
x 48
---------------
3736
1868
----------------
7. Use long addition to add your number columns from right to left, carrying as you normally do for long addition.
467
x 48
---------------
3736
1868
----------------
22416
Meals in a hospital cafeteria are discounted 15% for all hospital employees what will an employee pay for the grilled chicken lunch which cost a non employee $8.00
Given that the meals in a hospital cafeteria are discounted 15% for all hospital employees,
The price an employee will pay for the grill chicken lunch worth of $8.00 will be,
[tex]\text{ \$8.00}-(15\text{ \% of \$8.00)}[/tex][tex]\begin{gathered} \text{ \$8.00-(}\frac{\text{15}}{100}\times\text{ \$8.00)} \\ \text{ \$8.00-(0.15}\times\text{ \$8.00)}=\text{\$8.00- \$1.2=\$6.8} \end{gathered}[/tex]Hence, the hospital employee will pay $6.8 for the grilled chicken lunch.
When using a counterexample to prove a conditional statement false, which must be true about the counterexample?
There must be infinite counterexamples.
The counterexample must satisfy the hypothesis of the conditional statement.
There must be at least one example under which the conditional statement is true.
The counterexample must satisfy the conclusion of the conditional statement.
The counterexample must satisfy the hypothesis of the conditional statement which is the correct answer would be option (B).
What is a Counterexample?A counterexample is an example in which the hypothesis is correct but the conclusion is incorrect.
Since A counterexample is used to show that a conditional assertion is untrue.
So, just one counterexample is required to prove a statement untrue.
Also, when employing a counterexample to prove a conditional assertion untrue.
The counterexample must then meet the hypothesis of the conditional statement.
As a result, the correct statement concerning the counterexample is;
The conditional statement's hypothesis must be satisfied by the counterexample.
Hence, the correct answer would be option (B).
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Graph the solution set of the second linear any quality
Solution
- The inequality is:
[tex]7y\ge6x+21[/tex]- The graph of the inequality is graphed using a graphing calculator as follows:
To analyze the variation of vitamin supplement tablets, you randomly select and weigh 14 tablets. The results are shown below: 500.000 499.995 500.010 499.997 500.015 499.988 500.000 499.996 500.020 500.002 499.998 499.996 500.003 500.000 a. Assume this sample is taken from a normally distributed population. Construct a 90% level of confidence for the population variance and population standard deviation. b. For quality control, the population standard deviation of the tablets weights should be less than 0.015 milligrams. Does the confidence interval you constructed for the population standard deviation suggest that it is at an acceptable level? Explain your reasoning.
Answer:
a.
[tex]\begin{gathered} 0.000041\leq\sigma^2\leq0.00015 \\ 0.0064\leq\sigma\leq0.0125 \end{gathered}[/tex]b. The standard deviation is at an acceptable level
Explanation:
The confidence interval for the variance can be calculated as:
[tex]\frac{(n-1)s^2}{\chi^2_{\frac{\propto}{2}}}\leq\sigma^2\leq\frac{(n-1)s^2}{\chi^2_{1-\frac{\propto}{2}}}[/tex]Where n is the size of the sample, s² is the variance of the sample, (1-∝) is the level of confidence, and χ² is the value of chi-square with n-1 degrees of freedom.
In this case, we get that n is 14 tablets, s² is 0.000071, and 1-∝ = 90%, so ∝ is 10%.
Then, the values of chi-square with 13 (14 -1) degrees of freedom is:
[tex]\begin{gathered} \chi^2_{\frac{\propto}{2}}=22.36 \\ \chi^2_{1-\frac{\propto}{2}}=5.89 \end{gathered}[/tex]Therefore, the interval of confidence for the population variance is:
[tex]\begin{gathered} \frac{(14-1)(0.000071)}{22.36}\leq\sigma^2\leq\frac{(14-1)(0.000071)}{5.89} \\ 0.000041\leq\sigma^2\leq0.00015 \end{gathered}[/tex]Then, the standard deviation is the square root of the variance, so the interval of confidence for the population standard deviation is:
[tex]\begin{gathered} \sqrt[]{0.000041}\leq\sigma\leq\sqrt[]{0.00015} \\ 0.0064\leq\sigma\leq0.0125 \end{gathered}[/tex]Finally, since the upper limit of the interval for the standard deviation is less than 0.15 milligrams, we can say that the population standard deviation is at an acceptable level with a confidence level of 90%
Find the volume of this sphere.Use 3 for TT..V ?20 ftV ==Tr3Hint: The radius (r) is1/2 of the diameter.
From the problem, the diameter of the sphere is 20 ft.
Note that radius is half of diameter, so the radius will be r = 20/2 = 10 ft
Using the volume formula of a sphere.
[tex]V=\frac{4}{3}\pi r^3[/tex]where π = 3
[tex]\begin{gathered} V=\frac{4}{3}(3)(10)^3 \\ V=4000 \end{gathered}[/tex]The answer is 4000 ft^3
the amount of water a washing machine uses varies directly with the number of loads of laundry washed. if a machine uses 65 gallons of water to wash 5 loads, how much water will be used to was 8 loads?
Let g represent gallons of water and let L represent loads.
Here, the gallons of water varies directly with the number of loads, thus we have:
g ∝ L
Now introduce a constant k:
g = kL
65 gallons is used to wash 5 loads, thus we have:
65 = k * 5
Let's solve for k:
65 = 5k
Divide both sides by 5:
[tex]\begin{gathered} \frac{65}{5}=\frac{5k}{5} \\ \\ 13=k \end{gathered}[/tex]To find the amount of water that will be used to wash 8 loads, we have:
g = kl
We are to find g, substitute 13 for k and 8 for l:
g = 13 x 8
g = 104
Therefore, to wash 8 loads, 104 gallons of water is needed.
ANSWER:
104
a person's blood type is denoted with the letters a, b, and O, and symbols + and - The blood type A+ is read as A positive blood type B- is read as B negative. Use the data to write a ratio for the comparison and three different ways. O+ donors to B+ Donors.the ratio using the word "to" is [] to []
Answer:
The ratio using the word "to" is;
[tex]100\text{ to 2}9[/tex]Explanation:
Given on the table;
Number of O+ donors = 100
Number of B+ donors = 29
The ratio of the O+ donors to B+ Donors is:
Number of O+ to Number of B+
Which gives;
The ratio using the word "to" is;
[tex]100\text{ to 2}9[/tex]A student bank balance at the beginning of month was $843 during the month she deposits $92’ $404’ $39 and $51 also she made withdrawal of $70 $87 and $221 what was the student’s balance at end of month?
The account balance at the end of the month is $1051.
How is the balance estimated in a bank account?To estimate the balance in a bank account, one has to add the credit to the available balance of the account and subtract the debited amount from the same.
It is given that the account balance initially is $843.
The deposited balances are $92, $404, $39 and $51.
Add the credited amount to the account balance.
So, the current amount is = $843+ $92+ $404+ $39+ $51= $1429
The withdrawal amount is $70, $87 and $221
Subtract the debited amount to the account balance.
So, the current amount is = $1429 - $70 -$87 - $221 = $1051.
So, the account balance at the end of the month is $1051.
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Assume a normal distribution and that the average phone call in a certain town lasted 9 minutes, with a standard deviation of 2 minutes. What percentage of the calls lasted less than 5 minutes?
Given the sample mean of the distribution as 9 minutes.
Also, the sample deviation as 2 minutes;
Given the z-score formula;
[tex]z=\frac{x-\mu}{\sigma}[/tex]Where;
[tex]x=5,\text{ }\mu=9\text{ and }\sigma=2[/tex][tex]\begin{gathered} z=\frac{5-9}{2} \\ z=-\frac{4}{2} \\ z=-2 \end{gathered}[/tex]Now, from the Z-table;
[tex]P(x<-2)=0.02275[/tex]Thus, the percentage of the calls lasted less than 5 minutes is 2.3%
Describe a series of transformations Matt can perform to device if the two windows are congruent
Congruent shapes are produced when the three transformations—rotations, reflections, and translations—are combined. Any pair of congruent shapes can actually be matched to one another by combining one or more of these three transformations.
Definition of transformationsAn object's shape and/or location can vary in each of the four possible transformations of a point, line, or geometric figure. Pre-Image refers to the shape of the object before transformation, whereas Image refers to the location and shape of the object after transformation.
Data Presented
We now understand that stiff transformations preserve the size and shape of the figures (reflections, translations, and rotations). The pre-image and the actual image always concur.
The following transformational skills belong to Matt:
Reflection
A reflection maintains its initial form because the Comparable locations from the pre-image to the picture remain at the same distance from the line of reflection.
Rotations as a Congruence Transformation
A rotating figure twists. Despite being the same size and shape as before, the figure appears to have toppled over. A clock is an excellent example of how the globe actually rotates. Every hour or every day, a clock's connecting arms revolve around its axis. The degree of a rotation determines what kind of rotation it is; popular rotations include those of 90, 180, and 270 degrees. Before going back to its original position, the figure rotates a full 360 degrees. the clockwise or counterclockwise direction in which a revolution happens. This data can be used to determine the degree, amount, and a revolution's speed and direction.
Congruence translational transformation
When an object or shape is transferred from one location to another without altering its size, shape, or orientation, we refer to the transfer as a movement. A translation, often known as a slide, involves moving every point on an object or shape uniformly and in one direction.
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Is y=x(x+1) a valid equation?
y = x(x + 1)
Yes, it's a valid equation, there are 2 values for x and two values for y.
In my opinion it's a continuous function because if we graph it there would not be gaps on it.
BEST answer gets 69 points
Find the sum of (9.4 x 10^6) and (3.5 x 10^5). Write the final answer in scientific notation.
a. 1.29 x 10^10 b. 12.9 x 10^11 c. 9.75 x 10^5 d. 9.75 x 10^6
Answer:
D: 9.75 * 10^6
Step-by-step explanation:
You can make it easy for yourself if you write both answers in the same form:
(9.4 * 10^6) = (9.4 *10 * 10^5 = 94*10^5) and (3.5 * 10^5) stays the same.
We can now add those numbers up easier:
(94*10^5) + (3.5*10^5) = ( 94 + 3.5 ) * 10^5 = ( 97.5 * 10^5 )
but this answer is not in the option list. We have to perform the same trick as in the beginning, but than the other way around:
(97.5 * 10^5) = (9.75 * 10) * 10^5 = 9.75 * 10^6,
which is exactly option D
2.
Tom receives $18 from his father in a week. The ratio of the amount of
money he spends to the amount of money he saves in a week is 5 : 4.
(a) What is the difference between the amount of money spent and the
amount of money saved in a week?
B) How much does Tom save in a week?
Answer:
a= 2 and b= 8
Step-by-step explanation:
a=5/9×18=10
b=4/9×18=8, then a-b=10-8=2
b=4/9×18=8
What is the domain of the square root function graphed below?
On a coordinate plane, a curve opens down to the right in quadrant 1. The curve starts at (3, 1) and goes through (4, 2) and (7, 3).
Answer:
3 ≤ x < ∞
Step-by-step explanation:
You want the domain of a square root function shifted right 3 units and up 1 unit. It goes through points (3, 1), (4, 2) and (7, 3).
DomainThe domain of a function is the set of values of the independent variable for which the function is defined. It is the horizontal extent of the graph.
The graph of the given square root function extends to the right from x=3.
The domain is 3 ≤ x < ∞. In interval notation, it is [3, ∞).
Find the equation for the line that passes through the points (-2,-6) and (6,5). Give your answer in point-slope form. You do not need to simplify
The point-slope form of the equation of a line is given by the following expression:
y - y1 = m(x - x1)
Where m is the slope of the line and (x1, y1) is a point where the line passes through.
The slope of the line can be determined with the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where (x1, y1) and (x2, y2) are two points where the line passes through. In this case we are told that the line passes through the points (-2,-6) and (6,5). By replacing the x and y coordinates of these points into the formula of the slope, taking x1 as -2, x2 as 6, y1 as -6 and y2 as 5, we get:
[tex]m=\frac{5-(-6)}{6-(-2)}=\frac{5+6}{6+2}=\frac{11}{8}[/tex]Then, the slope of the line equals 11/8, by replacing 11/8 for m into the slope-point form, we get:
y - y1 = 11/8(x - x1)
By taking one of the points, for example (-2,-6), we replace the x and y-coordinates that appear in the equation of the line, to get:
y - (-6) = 11/8(x - (-2))
y + 6 = 11/8 (x + 2)
Then, the equation of the line in slope-point form is y + 6 = 11/8 (x + 2)
The proportional relationship between cost and pints of blueberries is shown in the table.
Blueberries (in pints) 2 5
Cost (in dollars) 6.80 17
Describe what a graph of the proportional relationship would look like.
A coordinate plane with the x-axis labeled Cost (in dollars) and the y-axis labeled Blueberries (in pints) shows a line going through (0, 0) and (5, 17).
A coordinate plane with the x-axis labeled Cost (in dollars) and the y-axis labeled Blueberries (in pints) shows a line going through (0, 0) and (2, 6.80).
A coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (5, 17).
A coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (6.80, 2).
A graph of what the proportional relationship would look like is: C. a coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (5, 17).
What is a graph?In Mathematics, a graph is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).
Generally speaking, the graph of a proportional relationship between two variables is always characterized by a straight line with its data points passing through the origin (0, 0).
In this context, the x-axis of this graph would be labeled Blueberries (in pints) while the y-axis would be labeled Cost (in dollars), with the data points starting from the origin (0, 0) and passes through (5, 17) as shown in the image attached below.
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Answer:
C. a coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (5, 17).
Step-by-step explanation:
You are an executive with the Varsity Corporation in Atlanta, Georgia. The company president was scheduled to make an important sales presentation tomorrow afternoon in Seattle, Washington, but he has now asked you to take his place.
The trip consists of a 2 1/4 hour flight from Atlanta to Dallas, a 1 1/2 hour layover in Dallas, and then a 3 1/2 hour flight to Portland. There is a 1 3/4 hour layover in Portland and then a 3/4 hour flight to Seattle. Seattle is on Pacific Time, which is 3 hours earlier than Eastern Time in Atlanta.
a) If you depart Atlanta tonight at 9:30 p.m. and all flights are on schedule, what time will you arrive in Seattle?
b) If your return flight is scheduled to leave Seattle at 9:10 p.m. tomorrow night, with the same flight times and layovers in reverse, what time are you scheduled to arrive in Atlanta?
c) If the leg from Dallas back to Atlanta is 2/3 of an hour longer than scheduled due to headwinds, what time will you actually arrive?
Using operations with mixed numbers and relations between hours and minutes, it is found that:
a) You will arrive in Seattle at 4:15 am.
b) You will arrive in Atlanta at 9:50 a.m.
c) You will arrive in Atlanta at 10:30 a.m.
How to convert a mixed number to decimal?A mixed number is represented as follows:
a b/c.
In which:
a is the integer part of the number.b/c is the fractional part of the number.As a decimal, the number is given as follows:
a + (b/c).
For item a, it is found that the time it takes to arrive in Seattle from Atlanta is given by the addition of these following numbers:
2.25 hours. (Atlanta to Dallas)1.5 hours. (Layover).3.5 hours (Dallas to Portland).1.75 hours (Layover).0.75 hours (Portland to Seattle).Hence the time in hours is:
2.25 + 1.5 + 3.5 + 1.75 + 0.75 = 9.75 hours = 9 hours and 45 minutes.
Seattle is 3 hours behind Atlanta, hence the time you arrive there is:
6:30 pm + 9 hours and 45 minutes = 4:15 am, as:
6:30 pm is the time in Seattle when you depart Atlanta.30 minutes + 45 minutes = 75 minutes = 1 hour and 15 minutes.9 hours and 45 minutes after 6:30 p.m. is of 4:15 a.m.For item b, we have that:
When the plane leaves Seattle, it is 0:10 am in Atlanta, as it is 3 hours ahead.9 hours and 45 minutes of flight, hence you should arrive in Atlanta at 9:50 a.m.For item c, 2/3 of an hour is 40 minutes, 40 minutes after 9:50 am is 10:30 a.m., which is the time you would arrive.
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Solve the system. Tell how many solutions the system has.-2x + 6y = 8x-3y=-3solution(s).The system has (select)(select)onenoinfinitely many
We have
-2x + 6y = 8 ...(1)
x-3y=-3 ....(2)
we need to solve the system of equations
we will multiplicate the second equation by 2
[tex]2x-6y=-6[/tex]then we sum the equation above with the first equation
[tex]-2x+2x+6y-6y=8-6[/tex]we sum similar terms, and we obtain
[tex]0=2[/tex]that's an inconsistency
so we don't have a solution
the answer is no
Write about a time you have used numbers and operations in your everyday life (outside ofmath class).
When going to the movies and we pay the ticket, most of the times (if we pay in cash) we will receive change for the bill we use.
For example, if the ticket costs $7 and we pay with $10, we will receive 10-7 = $3 as change.
We then have used math to know that the change we receive is correct.
A theme park guest takes an innertube into the wave pool. The innertube moves up and down in a way such that the height h of the innertube, in meters, above the floor of the pool can be modeled by the function h = asinbx + 5. When the wave pool is turned on, the innertube's height fluctuates between 2 meters and 8 meters, with an interval of 12 seconds between maximums. Based on the context of the problem, what are the values of a and b?
So we are told that the height of the innertube in meters is given by:
[tex]h(x)=a\sin (bx)+5[/tex]The minimum height is 2 meters, the maximum is 8 meters and the time between two consecutive maximums is 12 seconds. Here is important to note a few properties of the sine. First of all, the minimum value of sin(bx) is -1 and its maximum value is 1. Then the height of the innertube is minimum when sin(bx)=-1 and maximum when sin(bx)=1. With these two values we can build two equations for a:
[tex]\begin{gathered} \min (h)=2=a\cdot(-1)+5 \\ \max (h)=8=a\cdot1+5 \end{gathered}[/tex]So we have:
[tex]\begin{gathered} 2=-a+5 \\ 8=a+5 \end{gathered}[/tex]Substracting 5 from both sides of the second equation we get:
[tex]\begin{gathered} 8-5=a+5-5 \\ 3=a \end{gathered}[/tex]Using this in the first equation gives us:
[tex]\begin{gathered} 2=-3+5 \\ 2=2 \end{gathered}[/tex]Which confirms that a=3. Now we have to find b. For this purpose we can recal another property of the sine. Its period i.e. the distance (in this case the time) between two consecutive maximums is given by:
[tex]\frac{2\pi}{b}[/tex]Since we know this time is 12 seconds we get:
[tex]\frac{2\pi}{b}=12[/tex]If we multiply both sides by b and divide them by 12 we get:
[tex]\begin{gathered} \frac{2\pi}{b}\cdot\frac{b}{12}=12\cdot\frac{b}{12} \\ \frac{2}{12}\pi=b \\ \frac{\pi}{6}=b \end{gathered}[/tex]So we have:
[tex]a=3\text{ and }b=\frac{\pi}{6}[/tex]Which means that the answer is the second option.
Without using a calculator, order the following numbers from least to greatest.
15
14
√200
Answer:
14, 200 squared, 15
Step-by-step explanation: