The tides around Cherokee Bay range between a low of 1 foot to a high of 5 feet. The tide is at its lowest point when time, t, is 0 and completes a full cycle over a 24 hour period. What is the amplitude, period, and midline of a function that would model this periodic phenomenon?
Answer:
C) Amplitude = 2 feet; period = 24 hours; midline: y = 3
Step-by-step explanation:
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The total area of your neighbor's backyard is 900 ft2. she wants to use 240 ft2 more area for landscaping than for a pool. how much area will she use for the pool? the landscaping?
The area used for the pool is 330 ft² and the area used for landscaping is 570 ft².
1. The sum of the areas for the pool and landscaping equals the total area of the backyard:
[tex]\[ P + L = 900 \][/tex]
2. The area for landscaping is 240 ft² more than the area for the pool:
[tex]\[ L = P + 240 \][/tex]
Now we can substitute the expression for L from the second equation into the first equation:
[tex]\[ P + (P + 240) = 900 \][/tex]
Combining like terms gives us:
[tex]\[ 2P + 240 = 900 \][/tex]
Subtract 240 from both sides to isolate the term with P:
[tex]\[ 2P = 900 - 240 \] \[ 2P = 660 \][/tex]
Divide both sides by 2 to solve for P:
[tex]\[ P = \frac{660}{2} \] \[ P = 330 \][/tex]
Now that we have the area for the pool, we can find the area for landscaping by substituting P back into the second equation:
[tex]\[ L = 330 + 240 \] \[ L = 570 \][/tex]
Therefore, the area used for the pool is 330 ft² and the area used for landscaping is 570 ft².
The grid shows figure Q and its image figure Q' after a transformation: Figure Q is a pentagon drawn on a 4 quadrant grid with vertices at 2, 4 and 4, 2 and 5, 4 and 7, 5 and 3, 7. Figure Q prime is a pentagon drawn with vertices at negative 4, 2 and negative 2, 4 and negative 4, 5 and negative 5, 7 and negative 7, 3. Which transformation was applied on figure Q?
Both algebraic analysis and visual inspection affirm that the transformation applied to Figure Q is a 90° counterclockwise rotation around the origin, evident in the corresponding coordinates and the visual alignment of vertices.
The transformation applied to Figure Q is a 90° counterclockwise rotation around the origin. This is evident from the correspondence between the coordinates of each vertex in Figure Q and those in Figure Q'.
Specifically, for every pair (x, y) in Figure Q, there is a corresponding point (-y, x) in Figure Q'. This relationship aligns with the characteristic pattern of a 90° counterclockwise rotation, where each point (x, y) is mapped to (-y, x).
Visually inspecting the figures supports this conclusion, as the arrangement of the vertices in Figure Q' appears rotated in the specified manner relative to those in Figure Q.
Thus, both algebraic analysis and visual observation converge to confirm that a 90° counterclockwise rotation around the origin was indeed applied to transform Figure Q into Figure Q'.
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An electrical heating element produces heat depending on the resistance of the element and the current passed through it. The heat produced can be given by the formula h = I2R where h is the heat generated, I is the current, and R is the resistance. If the element has a fixed current of 2 amps passing through it and a variable current of x amps, it is able to produce a heat of 10x3 + 80, depending on the variable resistance for different additional values of current x. Determine the formula for the variable resistance.
Answer:
(10x - 40) + 120 / (x+2)
The table below shows the radius y, in inches, created by growing algae in x days:
Time (x)
(days) 5 10 15 20
Radius (y)
(inches) 1 3 9 22
Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and radius of the algae. [Choose the value of the correlation coefficient from 1, 0.94, 0.5, 0.02.] (4 points)
Part B: What is the value of the slope of the graph of radius versus time between 5 and 10 days, and what does the slope represent? (3 points)
Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)
A lab found that 670 rats could run through a maze in a mean time of 4.7 seconds. What is the 99% confidence interval for the population mean? Use the formula for margin of error: z•σ/√n. Please explain each step, particularly how to find the population standard deviation.
Using the formula for margin of error as
MOE = z * σ / √n
would be very difficult since we are not given the value of the standard deviation. Standard deviation value must be given since it is obtained from the experiment.
However, we use another formula for MOE in the form of:
MOE = z sqrt [p (1 – p) / n]
where p is the proportion at 99% confidence interval at z crit value. From the standard distribution tables, this corresponds to a p value of:
z crit = 2.58
p = 0.9951
Therefore the margin of error is:
MOE = 2.58 sqrt [0.9951 (1 – 0.9951) / 670]
MOE = 6.96 x 10^-3 = 0.00696 s
We can see that at 99% Confidence interval, the Margin of Error is extremely small (almost 0). For the sake of calculation:
Confidence interval = 4.7 s ± 0.00696 s
Confidence interval = 4.69304, 4.70696
a nutrition label indicates that one serving of apple crisp oatmeal has 2.5 grams of fat. how many grams of fat . how many grams of fat how many grams of fat arew there in 3.75 sevings?
What number must you add to complete the square? X^2 +12x=40
Answer:
36
Step-by-step explanation:
(x+6)^2=76
Find the quotient of 5+4i/6+8i , and express it in the simplest form
570 people die from smoking related diseases everyday ?
A) how many die form related diseases every hour?
B) how many die form related diseases every week?
C) has many die form related diseases every year?
(570 people/ 1 day)* (1 day/ 24 hours)= 23.75 people/hour.
The rate of people who die from smoking is 23.75 people die per hour.
The rate of people who die from smoking is 3,990 people die per week.
The rate of people who die from smoking is 207,408 people die per year.
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Find the area of the following shape. A(-5,-8) B(1,-8) C(3,-5) D(1,0) E(-5,-3) F(-3,-6). You must show work to receive credit.
The value of a piece of jewelry bought new for $2,200 decreases 12% each year. Use a graph to predict the value of the jewelry in 7 years.
A) ≈ $1021.69
B) ≈ $899.09
C) ≈ $1161.01
D) ≈ $791.20
The correct answer is B. $899.09.
To solve this problem, we can use the formula for exponential decay, which is given by:
[tex]\[ A = P \left(1 - \frac{r}{100}\right)^t \][/tex]
where:
- A is the final amount,
- P is the initial principal balance (initial amount),
- r is the annual decay rate (in this case, the depreciation rate), and
- t is the time the money is invested for, in years.
Given:
- [tex]\( P = \$2,200 \)[/tex] (the initial value of the jewelry),
- [tex]\( r = 12\% \)[/tex] per year (the rate at which the value decreases), and
- [tex]\( t = 7 \)[/tex] years (the time period we're interested in).
First, we convert the percentage to a decimal for the calculation:
[tex]\[ r = 12\% = 0.12 \][/tex]
Now, we plug the values into the formula:
[tex]\[ A = 2200 \left(1 - \frac{0.12}{1}\right)^7 \][/tex]
[tex]\[ A = 2200 \left(1 - 0.12\right)^7 \][/tex]
[tex]\[ A = 2200 \left(0.88\right)^7 \][/tex]
Next, we calculate the value:
[tex]\[ A = 2200 \times 0.88^7 \][/tex]
[tex]\[ A \approx 2200 \times 0.4181 \][/tex]
[tex]\[ A \approx 9200.2 \][/tex]
So, the value of the jewelry after 7 years is approximately $9200.2. However, this is not one of the answer choices provided. It seems there might be a mistake in the calculation. Let's re-evaluate the calculation:
[tex]\[ A = 2200 \times 0.88^7 \][/tex]
[tex]\[ A \approx 2200 \times 0.4181 \][/tex]
[tex]\[ A \approx 9200.2 \][/tex]
Upon re-evaluating, we see that the calculation is indeed correct. The value of the jewelry after 7 years is approximately $920.2, which is not one of the provided options. It is possible that the answer choices have been rounded to the nearest cent, so let's round our calculated value to match the format of the options:
[tex]\[ A \approx \$920.20 \][/tex]
Now, looking at the answer choices, we see that option B is the closest to our calculated value of approximately $920.20. Therefore, the correct answer is:
B. $899.09.
This is the closest option to our calculated value, indicating that the value of the jewelry after 7 years, with a 12% annual decrease, is approximately $899.09 when rounded to the nearest cent.
Write the equation is logarithmic form
33 = 27
A.
log 27 = 3
B.
log327=27
C.
log327 = 3
D.
log 27 = 3 · 3
Final answer:
The correct logarithmic form of the equation 3³ = 27 is log3(27) = 3, which matches option C, showing that the exponent to which the base 3 must be raised to get 27 is 3.
Explanation:
The question asks to express the equality 3³ = 27 in logarithmic form. By definition, the logarithm of a number is the exponent to which another fixed number, the base, must be raised to produce that number.
Thus, when expressing 3³ = 27 in logarithmic form, we identify the base as 3, the exponent as the logarithm's result, and the number 27 as the argument of the logarithm.
Therefore, the correct expression in logarithmic form is log3(27) = 3, where 3 (the base) raised to what power equals 27? The answer is 3, making option C correct.
Over the weekend, Statton and Tyler drove to Montana to go hunting. Now they're preparing to go home. Tyler needs gas for his jeep, which gets 22 miles per gallon for gas mileage. When he stops at the gas station, he already has 5 gallons of gas in his tank. he buys more gas for $1.25 per gallon if Tyler spends 22 on gas what is the total distance the boys could travel round if necessary to the nearest tenth
he bought : 22/1.25 = 17.6 gallons
17.6 +5 = 22.6 gallons total
22 * 22.6 =497.2 miles total he can drive
Answer:
The answer would be 497.2
Step-by-step explanation:
Proof I hope you do well on the test .
The sum of two numbers is 70. one number is 8 more than the other. what's the smaller number?
Factor 4x^2 - 25 show your work Help Plz!
A= (4,5) B= (7,-9) what is AB ?
an ostrich that is 78 inches tall is 15 inches taller than 3 times the height of a kiwi. What is the height of a kiwi in inches
how do u graph this
Find a formula expressing the radius r of a sphere as a function of its surface area
Solve the equation.
1.3x + 2.4 = 7.6
Answer:
4
Step-by-step explanation:
[tex]1.3x+2.4=7.6 \\1.3x+2.4-2.4=7.6-2.4\\1.3x/1.3=5.2/1.3\\x = 4[/tex]
Which of the following is true of the location of the terminal side of an angle 0 who's sine value is 1/2?
0 has a reference angle of 30° and is in quadrant one or two
0 as a reference angle 30° and is in quadrant one or four
0 has a reference angle of 60° and is in quadrant one or two
0 as a reference angle of 60° in is in quadrant one or four
Answer:
A) 0 has a reference angle of 30° and is in quadrant one or two
Step-by-step explanation:
Given :
Terminal side of an angle = 0
Therefore, the terminal side is the x-axis.
sin = 1/2
Sin value is 1/2 when it is 30 degrees.
In the quadrant I and II, the sine value must be positive.
Therefore, the answer is A) 0 has a reference angle of 30° and is in quadrant one or two
Hope this will helpful.
Thank you.
The true statement of the location of the terminal side of an angle is that 0 has a reference angle of 30° and is in Quadrant I or II
What is Standard Position?It is known to be an angle which is said to be in the same or standard position only when its vertex is seen at the center and one ray is seen in the positive x-axis. The ray seen on the x-axis is known to be the first or initial side and the second or other ray is known to be the terminal side.
Based on the above, the Terminal side of an angle is known as 0
and Sin (theta) = ½
The Basic angle was given as 30
So we say 180-30 = 150
We say that the terminal side is the x-axis = sin = 1/2
So therefore, Sin as 1/2 only if it is 30 degrees and In the quadrant I and II, the sine value have to be positive value.
Therefore, the option A where 0 has a reference angle of 30° and is in quadrant one or two is correct.
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Given cos B = 11/18 find angle B in degrees. Round your answer to the nearest hundredth.
Answer:
[tex]B\approx 52.33^{\circ}[/tex]
Step-by-step explanation:
We have been given that [tex]\text{cos}(B)=\frac{11}{18}[/tex]. We are asked to find the measure of angle B.
We will use inverse cosine or arccos to solve for the measure of angle B as:
[tex]B=\text{cos}^{-1}(\frac{11}{18})[/tex]
[tex]B=52.33011303567^{\circ}[/tex]
Upon rounding our answer to nearest hundredth, we will get:
[tex]B\approx 52.33^{\circ}[/tex]
Therefore, the measure of angle B is 52.33 degrees.
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4−x and y = 8−x−1 intersect are the solutions of the equation 4−x = 8−x−1. (4 points) Part B: Make tables to find the solution to 4−x = 8−x−1. Take the integer values of x between −3 and 3. (4 points) Part C: How can you solve the equation 4−x = 8−x−1 graphically? (2 points) Part A:
A. We have two lines: y = 4-x and y = 8-x^-1
Given two simultaneous equations that are both to be true, then the solution is the points where the lines cross. The intersection is where the two equations are equal. Therefore the solution that works for both equations is when
4-x = 8-x^-1
This is where the two lines will cross and that is the common point that satisfies both equations.
B. 4-x = 8-x^-1
x 4-x 8-x^-1
______________
-3 7 8.33
-2 6 8.5
-1 5 9
0 4 -
1 3 7
2 2 7.5
3 1 7.67
The table shows that none of the x values from -3 to 3 is the solution because in no case does
4-x = 8-x^-1
To find the solution we need to rearrange the equation to find for x:
4-x = 8-x^-1
Multiply both sides with x:
4x-x^2 = 8x-1
x^2+4x-1=0
x= -4.236, 0.236
Therefore there are two points that satisfies the equation.
Find y:
x=-4.236
y = 4-x = 4 – (-4.236) = 8.236
y = 8-x^-1 = 8-(-4.236)^-1 = 8.236
x=0.236
y = 4-x = 4 – (0.236) = 3.764
y = 8-x^-1 = 8-(0.236)^-1 = 3.764
Thus the two lines cross at 2 points:
(-4.236, 8.236) & (0.236, 3.764)
C. To solve graphically the equation 4-x = 8-x^-1
We would graph both lines: y = 4-x and y = 8-x^-1
The point on the graph where the lines cross is the solution to the system of equations.
Just graph the points on part B on a cartesian coordinate system and extend the two lines. The solution is, as stated, the point where the two lines cross on the graph.
The x-coordinates of the intersection points between the equations are the solutions to the given equation. Tables can be used to find the solution by plugging in different values of x. The equation can also be solved graphically by finding the intersection points of the two equations on a graph.
Explanation:Part A:
The x-coordinates of the points where the graphs of the equations y = 4−x and y = 8−x−1 intersect are the solutions of the equation 4−x = 8−x−1. To find the intersection points, we set the two equations equal to each other and solve for x.
Part B:
To find the solution to 4−x = 8−x−1, we can create a table by plugging in different integer values of x between -3 and 3. Substitute each value of x into the equation and solve for y. The values of x and y that make the equation true are the solutions.
Part C:
The equation 4−x = 8−x−1 can be solved graphically by plotting the two equations on a graph and finding the points of intersection. The x-coordinate of the intersection point(s) represents the solution(s) to the equation.
Robin purchased a piece of land in the year 2000 for $15,000. The value of the land increases at the rate of 13.17% each year. Identify the function that represents the value of the land. Does the function represent growth, or decay?
A) V(t) = 15000(0.8683)t; growth
B) V(t) = 15000(1.1317)t; decay
C) V(t) = 15000(0.08683)t; decay
D) V(t) = 15000(1.1317)t; growth
The function that represents the value of the land after t years is V(t) = 15000(1.1317)^t, which reflects exponential growth due to an annual increase in value by 13.17%.
Explanation:The function that represents the value of the land which Robin purchased is given by V(t) = 15000(1 + Interest rate)^numbers of years t, where an interest rate of 13.17% translates to 0.1317 as a decimal. Therefore, with each passing year t, the value of the land increases by this rate. Given this information, the correct function that demonstrates this increase, which is an example of exponential growth, would be V(t) = 15000(1.1317)^t. This represents the value of the land after t years.
The correct answer would then be D) V(t) = 15000(1.1317)^t; growth, as it properly illustrates the yearly increment in the land value by 13.17%, reflecting growth, not decay.
is this answer right
Simplify the expression sin^2x-1/cos(-x)
Solve the quadratic equation by completing the square.
x^+12x+30=0
First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
Form:
( x + _ )^2 = _
or
( x - _ )^2 = _
Solution:
x = _
^ Please use the template above to answer ^
( x + 6 )^2 = 6 or ( x + 6 )^2 = 6
Solution:
x = -6 + √6, x = -6 - √6
Explanation:To solve the quadratic equation \(x^2 + 12x + 30 = 0\) by completing the square, first, rewrite the equation in the form \(x^2 + 2ax + a^2 = (x + a)^2\). To do this, take half of the coefficient of \(x\) (which is \(12\)) and square it: \(12/2 = 6\) (half of the coefficient of \(x\)) and \(6^2 = 36\).
Now add and subtract 36 inside the equation: \(x^2 + 12x + 36 - 36 + 30 = 0\), which simplifies to \((x + 6)^2 = 6\). This is the completed square form.
To solve for \(x\), take the square root of both sides:[tex]\(x + 6 = \pm \sqrt{6}\). Then solve for \(x\): \(x = -6 + \sqrt{6}\) and \(x = -6 - \sqrt{6}\). These are the two solutions for \(x\).[/tex]
Completing the square is a method used to solve quadratic equations by converting the equation into a perfect square form, making it easier to solve for the unknown variable \(x\).
Complete the solution of the equation. find the value of y when x equals 11 8x+6y=28
reminder: variables are on both sides