The solutions for x between 0 and 2π are: x = π/2, (5π)/6, and (11π)/6.
To solve the equation 5 + sin(3x) = 4 for x on the unit circle, where x is between 0 and 2π, follow these steps:
1. Subtract 5 from both sides: sin(3x) = -1
2. Determine the angle for which sin is -1: sin(3x) = sin(3π/2)
3. Since the sine function has a period of 2π, the general solution is: 3x = 3π/2 + 2πk, where k is an integer.
4. Divide both sides by 3: x = π/2 + (2πk)/3
Now, find the values of x between 0 and 2π by trying different integer values of k:
- If k = 0, x = π/2
- If k = 1, x = π/2 + 2π/3 = (5π)/6
- If k = 2, x = π/2 + 4π/3 = (11π)/6
Thus, the solutions for x between 0 and 2π are: x = π/2, (5π)/6, and (11π)/6.
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Which expressions represent the length of side MN?
Choose 2 answers:
A. 4 • sin (65)
B. 1. 9 • cos (65)
C. 4/sin (65)
D. 1. 9/cos (65)
PLEASE HELP!!
Expressions A and B represent the length of side MN.
How can the length of side MN be expressed?The two expressions that represent the length of side MN are A) 4•sin(65) and B) 1.9•cos(65). The length of side MN can be found using the trigonometric ratios of sine and cosine in a right triangle.
The angle of 65 degrees is opposite to side MN and the hypotenuse of the triangle is given as 4 units. Using the sine ratio, we can find the length of MN as 4•sin(65). Similarly, using the cosine ratio, we can find the length of MN as 1.9•cos(65).
Therefore, expressions A and B both represent the length of side MN, and they have been obtained by using different trigonometric ratios.
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A study reports that in 20102010 the population of the United States was 308,745,538308,745,538 people and the land area was approximately 3,531,9053,531,905 square miles. Based on the study, what was the population density, in people per square mile, of the United States in 20102010? Round your answer to the nearest tenth.
The population density is 87.4, under the condition that a study report shows that in 2010 the population of the United States was counted to be 308,745,538 people and the land area is approximately 3,531,905 square miles.
Now to evaluate the population density of the United States in 2010, here we have to use the principles of division
Population density = Population / Land area
Staging the values from the study
Population density = 308,745,538 / 3,531,905
The evaluated Population density = 87.4 people per square mile
Then, the United State's population density in 2010 was evaluated as 87.4 people per square mile.
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The complete question is
A study reports that in 2010 the population of the United States was 308,745,538 people and the land area was approximately 3,531,905 square miles. Based on the study, what was the population density, in people per square mile, of the United States in 2010? Round your answer to the nearest tenth.
Alana saved 1,200.00 to buy a pool table, but decided instead to charge it to her credit card.If the credit card had an interest rate of 13.5% for 6 months with no other fees, and she made no other purchases, what was her cost of credit of using the credit card instead of paying cash?
11. Consider the image shown. What is the measure of angle DEB?
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The supplementary angles of the given angles are 154 degrees, 136 degrees, 135 degrees, 44 degrees, 45 degrees, and 26 degrees, respectively.
Supplementary Angles of Given Angles
Supplementary angles are pairs of angles that add up to 180 degrees. To find the supplementary angle of each given angle, we simply subtract the angle from 180 degrees.
Therefore, the supplementary angles of the given angles are:
The supplementary angle of 26 degrees is 154 degrees (180 - 26 = 154).
The supplementary angle of 44 degrees is 136 degrees (180 - 44 = 136).
The supplementary angle of 45 degrees is 135 degrees (180 - 45 = 135).
The supplementary angle of 136 degrees is 44 degrees (180 - 136 = 44).
The supplementary angle of 135 degrees is 45 degrees (180 - 135 = 45).
The supplementary angle of 154 degrees is 26 degrees (180 - 154 = 26).
Therefore, the supplementary angles of the given angles are 154 degrees, 136 degrees, 135 degrees, 44 degrees, 45 degrees, and 26 degrees, respectively.
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8. The scatter plot shows the relationship between the number
of chapters and the total number of pages for several books.
Use the trend line to predict how many pages would be in a
book with 19 chapters.
Pages
11
1220+----
1200
180+
160-
(140+
120-
100+
80
60+
40+
20+
Chapters
0 2
4 6 8 10 12 14 16 18 20
Answer: So, according to this prediction, a book with 19 chapters would have approximately 950 pages. However, keep in mind that this is just a prediction based on the trend line, and there may be some variability in the actual number of pages for a book with 19 chapters.
Step-by-step explanation:
Unfortunately, I cannot see the scatter plot you are referring to. However, I can explain how to use a trend line to predict the number of pages in a book with 19 chapters.
A trend line is a line that represents the general direction or tendency of the data in a scatter plot. To use a trend line to predict the number of pages in a book with 19 chapters, you would first need to determine the equation of the trend line.
This equation usually takes the form y = mx + b, where y is the dependent variable (in this case, the total number of pages), x is the independent variable (in this case, the number of chapters), m is the slope of the line, and b is the y-intercept (the value of y when x is 0).
Once you have the equation of the trend line, you can plug in the value x = 19 and solve for y to get the predicted number of pages in a book with 19 chapters.
For example, if the equation of the trend line is y = 50x + 200, then the predicted number of pages for a book with 19 chapters would be:
y = 50(19) + 200
y = 950
So, according to this prediction, a book with 19 chapters would have approximately 950 pages. However, keep in mind that this is just a prediction based on the trend line, and there may be some variability in the actual number of pages for a book with 19 chapters.
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The two-way table shows the number of houses on the market in the castillos’ price range. a 6-column table has 4 rows. the first column has entries 1 bathroom, 2 bathrooms, 3 bathrooms, total. the second column is labeled 1 bedroom with entries 67, 0, 0, 67. the third column is labeled 2 bedrooms with entries 21, 6, 18, 45. the fourth column is labeled 3 bedrooms with entries 0, 24, 16, 40. the fifth column is labeled 4 bedrooms with entries 0, 0, 56, 56. the sixth column is labeled total with entries 88, 30, 90, 208. what is the probability that a randomly selected house with 2 bathrooms has 3 bedrooms? 0.2 0.4 0.6 0.8
The probability that a randomly selected house with 2 bathrooms has 3 is: 0.8.
So, the fourth option is correct.
We have given that,
The two-way table shows the number of houses on the market in the Castillos’ price range.
A 6-column table has 4 rows.
The first column has entries 1 bathroom, 2 bathrooms and 3 bathrooms, in total.
The second column is labeled 1 bedroom with entries 67, 0, 0, 67.
The third column is labeled 2 bedrooms with entries 21, 6, 18, 45.
We are only considering the houses that have 2 bathrooms.
There are a total of 30 of these houses.
Out of these 30, 24 have 3 bedrooms.
What is the formula for probability?
The probability of an event can only be between 0 and 1 and can also be written as a percentage.
This makes the probability 24/30, which is 0.8.
Therefore, the probability that a randomly selected house with 2 bathrooms has 3 is: 0.8.
So, the fourth option is correct.
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I need help Please !!!!!!!!!!!!!!!!!!!!!!!!!!
Can someone help me ASAP please? It’s due tomorrow. Show work please!! I will give brainliest if it’s correct and has work.
Answer:
Step-by-step explanation:
There are 12 possible cards you can choose.
There are 3 possible results for the spinner.
There are 2 possible results for the coin toss.
When doing all 3 events:
Total possibilities [tex]=12\times 3 \times 2=72.[/tex]
SOLUTION: 72
Escribe a cuáles de las bolsas anteriores corresponde la notación decimal aproximada a tres cifras
6.2 × 10⁴ in decimal notation is simply 62,000.
In scientific notation, a number is expressed as the product of a decimal number between 1 and 10 and a power of 10.
Now, let's talk about converting a number in scientific notation to decimal notation. Decimal notation simply means expressing a number in the standard way, using digits and a decimal point. To convert a number in scientific notation to decimal notation, we just need to evaluate the product of the decimal number and the power of 10.
In the case of 6.2 × 10⁴, the decimal number is 6.2, and the power of 10 is 4. To evaluate the product, we simply move the decimal point in 6.2 four places to the right, since the power of 10 is positive. This gives us:
6.2 × 10⁴ = 62,000
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Complete Question:
Convert to decimal notation: 6.2 × 10⁴
A tired frog is jumping across a pond. Her first jump will be her longest. She travels 300 cm. Her second jump carries her another 270 cm. How far will the frog travel before she cannot jump anymore?
S= 1560cm
S= 570cm
S= 2700cm
S= 3000cm
The frog will travel a total distance of 1650 cm before she cannot jump anymore. None of the options given are correct.
To find the total distance the frog will travel, we need to add up the distances of all her jumps. Given that her first jump is her longest at 300 cm and her second jump is 270 cm, we can assume that each subsequent jump is shorter than the one before it.
The difference between the first jump and the second jump is 30 cm. So let's assume that the common difference between each jump is 30 cm. So the frog takes a total of 10 jumps before she cannot jump anymore.
The total distance the frog will travel is:
300 + 270 + (240 + 210 + 180 + 150 + 120 + 90 + 60 + 30) = 1650 cm
So here none of the options are correct.
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Which graphs represent functions?
4
←
4
•
4
4 -2
++
Graph A
4
2
2
2
4
4
2 4
Graph C
X
-4
-2
4
-2
2
-2-
4
Graph B
у
4-
2
-2
Graph D
4
4
Help me— My brain goes brrr in this question word problem thing ; - ;
A table tennis ball has a radius of 0. 04m. Estimate how many table tennis balls you could fit into the coin building! [search up what it is—]
( Width: 20m | height: 110m )
- How did you calculate your estimate?
- Explain how accurate you think your prediction is?
( Show Work. )
Number of balls ≈ [tex]1.03 * 10^9[/tex]
To calculate how many table tennis balls can fit into the coin building, we need to first figure out the volume of the building and the volume of the table tennis ball.
Then, we can divide the volume of the building by the volume of the ball to get an estimate of the number of balls that can fit inside.
The volume of a table tennis ball can be calculated using the formula for the volume of a sphere, which is:
V = (4/3)πr³
where V is the volume, π is pi (approximately 3.14), and r is the radius of the ball. In this case, the radius is given as 0.04m, so we can plug that in and get:
V = (4/3) x 3.14 x 0.04³
[tex]V =2.14 * 10^{-5} m^3[/tex]
Next, we need to find the volume of the coin building. The building has a width of 20m and a height of 110m, but we don't know its depth.
Let's assume that the building is a rectangular prism with a depth of 10m. Then, we can calculate its volume using the formula:
V = l x w x h
where l is the length, w is the width, and h is the height. Plugging in the given values, we get:
V = 20 x 10 x 110
V = 22000 m³
Now, we can divide the volume of the building by the volume of the ball to get an estimate of how many balls can fit inside:
Number of balls ≈ [tex]V_building / V_ball[/tex]
Number of balls ≈ 22000 / 2.14 x [tex]10^-5[/tex]
Number of balls ≈ [tex]1.03 * 10^9[/tex]
So we can estimate that approximately 1.03 billion table tennis balls can fit into the coin building.
As for the accuracy of this prediction, it's important to keep in mind that we made some assumptions and estimations in our calculations.
For example, we assumed that the building is a rectangular prism with a depth of 10m, which may not be completely accurate.
Additionally, we rounded some of our values and used approximations for pi.
Therefore, our estimate should be considered as a rough approximation rather than an exact calculation. Nonetheless, it gives us an idea of the scale of the building and how many objects it can hold.
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In ΔRST, s = 990 inches, ∠S=8° and ∠T=60°. Find the area of ΔRST, to the nearest square inch
The area of ΔRST, to the nearest square inch is,
Area = 29,17,735.54 square inches
We have,
In ΔRST, s = 990 inches, ∠S=8° and ∠T=60°.
Apply sine rule formula,
sin S / s = sin T / t
sin 8° / 990 = sin 60° / t
0.14 / 990 = 0.87 / t
0.14t = 990 x 0.87
0.14t = 861.3
t = 6,152 inches
Here, ∠R = 180° - (8 + 60)°
∠R = 180 - 68
∠R = 112°
sin S / s = sin R / r
sin 8° / 990 = sin 112° / r
0.14 / 990 = 0.92 / r
0.14r = 0.92 x 990
0.14r = 910.8
r = 910.8 / 0.14
r = 6505 inches
We use the formula
Heron's formula = √s(s - a)(s - b)(s - c)
Where s = a + b + c/2
Solving for s
s = 990 + 6505 + 6,152 /2
s = 6823.5
Solving for the area of the triangle
= √6823.5 × (6823.5 - 990) × (6823.5 - 6,152) × (6823.5 - 6505)
= √6823.5 x 5833.5 x 671.5 x 318.5
= 29,17,735.54 square inches
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36 A bicycle rental company charges a fixed rental fee for the first
30 minutes and a cost per minute for each additional minute. The
table shows the linear relationship between the total cost in dollars
to rent a bicycle and the number of additional minutes a bicycle
is rented.
Bicycle Rental
Number of Additional Minutes Total Cost (dollars)
15
3.05
20
$0.17 per min
$0.35 per min
$0.07 per min
$0.56 per min
35
55
3.40
4.45
5.85
What is the rate of change of the total cost in dollars with respect to
the number of additional minutes?
Answer:
C
Step-by-step explanation:
Since the rate is linear, we can subtract a larger amount of minutes by a smaller one and a larger cost by a smaller one.
For example:
20 - 15 = 5
3.40 - 3.05 = 0.35
Since you want to find the amount it takes per minute, you divide the 5 by 5 to make it one minute. You also divide the 0.35 by 5 in which you get 7.
explain how using a table is similar to using a double number line and how it is different
Using a table is similar to using a double number line because the relation between the corresponding would never change.
Given that,
To explain how using a table is similar to using a double number line and how it is different.
What is a number line?A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.
Here,
Let assuming some values, in tabulated form,
x y
1 -1
2 -2
3 -3
Now calibrating the x and y in the number line
x = 1 2 3
----------
y = -1 -2 -3
-----------
When comparing the corresponding relationship it remains the same, where it is a table or number line.
Thus, using a table is similar to using a double number line because the relation between the corresponding would never change.
Harold, Rhonda, and Brad added water to beakers in science class. The line plot shows the amount of water, in cups, that they added to each of 14 beakers.
In the given line plot, the data represents the amount of water, in cups, that Harold, Rhonda, and Brad added to each of 14 beakers in their science class.
A line plot is a way to represent data that involves marking a number line for each data point and placing an “X” above the number that represents the value of that data point.
The line plot shows that most of the beakers were filled with either 1 or 2 cups of water. Specifically, there are 5 beakers with 1 cup of water and 6 beakers with 2 cups of water. There are also 2 beakers with 3 cups of water and 1 beaker with 4 cups of water.
The line plot provides a visual representation of the data that allows the viewer to quickly understand the distribution of the data. By seeing that most of the data is clustered around 1 and 2 cups of water, one can infer that the students were likely instructed to add a specific amount of water to each beaker. However, the presence of a few outliers, such as the beaker with 4 cups of water, suggests that some of the students may have made errors in their measurements or not followed the instructions closely.
Overall, the line plot provides a quick and easy way to visualize the distribution of the data and identify any outliers or patterns in the data. It is a useful tool for representing small to medium-sized datasets and is commonly used in education, research, and data analysis.
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Answer:
if this is study island than the answer is:
All of the beakers with more than of a cup of water added to them were filled by Harold. Harold added a total of
4
cup(s) of water to his beakers.
All of the beakers with exactly of a cup of water added to them were filled by Rhonda. Rhonda added a total of
15/8 or 1 7/8
cup(s) of water to her beakers.
Brad filled the rest of the beakers. Brad added a total of
13/8 or 1 5/8
cup(s) of water to his beakers.
Step-by-step explanation:
Triangle G Y K is shown. Angle G K Y is a right angle. Angle K G Y is 60 degrees and angle G Y K is 30 degrees. The length of G K is 27.
Given right triangle GYK, what is the value of tan(G)?
One-half
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction
StartRoot 3 EndRoot
The value of tanG is √3
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
The value of KY
Tan 30 = 27/KY
1/√3 = 27/KY
KY = 27√3
Tan G = 27√3/27
tanG = √3
therefore the value of tanG is √3
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An ant travels 33cm in walking completely around the edges of a rectangle. If the rectangle is twice as long as it is wide, how long is the shortest side?
Rectangle: w = 5.5cm, l = 11cm. Shortest side is width.
+
ent will
A circle with center (7,3) and radius of 5 is graphed below with a square inscribed in
the circle.
+
Dillon says to write the equation of the tangent line you need the opposite-reciprocal
slope of the slope of the radius and Chelsey says you need to use the same slope as
the radius. Who is correct and why? Write the equation of the tangent line.
Part B: Find the perimeter of BCDE.
Part C: Find the area of BCDE.
Part D: Prove BCDE is a square.
Chelsey is correct that we use the same slope as the radius to write the equation of the tangent line, even though the slope of the radius is undefined at the points of tangency.
The perimeter will be 20 ✓2 units.
The area will be 50 units²
How to explain the informationChelsey is correct, and the reason is that a tangent line to a circle at a given point is always perpendicular to the radius of the circle at that point. This means that the slope of the tangent line and the slope of the radius at the point of tangency are negative reciprocals of each other.
Chelsey is correct that we use the same slope as the radius to write the equation of the tangent line.
The perimeter will be:
= 4 × BC
= 20 ✓2
The area will be:
= BC²
= (5✓2)²
= 50
It should be noted that BCDE is a square as EBC is 90°.
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If a photo measures 4 inches by 6 inches is places in a frame that measure 2 inches wide all around what percent of the fear is the photo itsel
The photo takes up 30% of the framed area.
To calculate the percentage of the frame that is taken up by the photo, we first need to calculate the dimensions of the framed photo. If the photo measures 4 inches by 6 inches, the dimensions of the framed photo will be 8 inches by 10 inches (adding 2 inches to each side).
To calculate the area of the frame, we need to subtract the area of the photo from the area of the framed photo. The area of the photo is 4 inches x 6 inches = 24 square inches. The area of the framed photo is 8 inches x 10 inches = 80 square inches. So, the area of the frame is 80 square inches - 24 square inches = 56 square inches.
To calculate the percentage of the frame that is taken up by the photo, we divide the area of the photo by the area of the framed photo and multiply by 100.
24 square inches / 80 square inches x 100 = 30%
Therefore, the photo takes up 30% of the framed area.
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The equation relates the sound level, , in decibels (dB), of a noise with an intensity of I to the smallest sound intensity that can be heard by the human ear, (approximately watts/meter2).
The maximum intensity of a car horn is approximately 0. 01 watts/meter2. Based on this information, which value is closest to the maximum sound level, in decibels, of a car horn?
.
100 dB
10 dB
1,000 dB
10,000 dB
The equation relates the sound level, in decibels (dB), of a noise with an intensity of I to the smallest sound intensity that can be heard by the human ear, which is approximately 1 x 10^-12 watts/meter2.
Using this equation and the given maximum intensity of a car horn (0.01 watts/meter2), we can find the maximum sound level in decibels:
Sound level = 10 log (0.01/1 x 10^-12)
Sound level = 10 log (1 x 10^10)
Sound level = 100 dB
Therefore, the value that is closest to the maximum sound level in decibels of a car horn is 100 dB.
The scores on the last math quiz are summarized in the following frequency table:
Score
10
9
8
7
6
5
4
3
2
1
0
Frequency
6
7
5
3
2
1
1
0
0
0
0
The information is then put into the following histogram:
A histogram has score on the x-axis, and frequency on the y-axis. A score of 4 has a frequency of 1; 5, 1; 6, 2; 7, 3; 8, 5; 9, 7; 10, 6.
Calculate the mean, median, mode, and midrange of this quiz distribution and explain whether the distribution is skewed to the left or to the right.
a.
Mean = 9, median = 8.2, mode = 7, midrange = 9; skewed to the left.
b.
Mean = 8.2, median = 9, mode = 9, midrange = 7; skewed to the left.
c.
Mean = 8.2, median = 9, mode = 9, midrange = 7; skewed to the right.
d.
Mean = 9, median = 8.2, mode = 7, midrange = 9; skewed to the right.
Please select the best answer from the choices provided
The correct option regarding the data is B. Mean = 8.2, median = 9, mode = 9, midrange = 7; skewed to the left.
How to explain the dataA histogram has score on the x-axis, and frequency on the y-axis. A score of 4 has a frequency of 1; 5, 1; 6, 2; 7, 3; 8, 5; 9, 7; 10, 6.
It shtbe noted that Mean = 8.2, median = 9, mode = 9, midrange = 7; skewed to the left.
This statement describes a distribution with a mean equal to the median and a mode that is likely less than the mean and the median. The fact that the distribution is skewed to the left indicates that the tail of the distribution is longer on the left side, and that there may be some low outliers that are pulling the mean towards the left.
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A survey found that the relationship between the years of education a person has and that person's yearly income in his or her first job after completing schooling can be modeled by the equation y - 1200x
7000, where x is the number of years of education and y is the yearly income. According to the model, how much does 1 year of education add to a person's yearly incomo?
А $1200
B
$5800
$7000
D
$8200
Answer:
The equation provided is y = 1200x + 7000, where y is the yearly income and x is the number of years of education.
To determine how much 1 year of education adds to a person's yearly income, we need to find the change in y when x increases by 1.
Let's plug in x and x+1 into the equation to find the corresponding yearly incomes:
When x = 1, y = 1200(1) + 7000 = $8200
When x = 2, y = 1200(2) + 7000 = $9400
The difference between these two yearly incomes is:
9400 - 8200 = $1200
Therefore, 1 year of education adds $1200 to a person's yearly income according to the model.
The answer is (A) $1200.
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Find the missing side
17 cm
1319
a
area = 25 cm²
Answer:
a= 2.9cm
Step-by-step explanation:
area =25 so 17a=50
50/17=2.941176...
Dos personas reciben a los carros que entran a un estacionamiento. La primera persona entrega un boleto verde cada dos carros que entran. La segunda persona entrega un boleto azul cada tres carros que entran. ¿Qué número ocupará en la fila el tercer carro que recibirá boletos de ambos colores?
Por lo tanto, el tercer carro que recibirá boletos de ambos colores ocupará la posición número 18 en la fila.
Hola, entiendo que quieres saber en qué posición de la fila se encontrará el tercer carro que recibirá boletos de ambos colores (verde y azul). Para esto, vamos a analizar la situación:
- La primera persona entrega un boleto verde cada 2 carros.
- La segunda persona entrega un boleto azul cada 3 carros.
Un carro que recibe boletos de ambos colores será aquel que ocupa una posición que es múltiplo común de 2 y 3. El mínimo común múltiplo (MCM) de 2 y 3 es 6. Por lo tanto, cada 6 carros, habrá uno que reciba boletos de ambos colores.
Para encontrar el tercer carro que recibirá boletos de ambos colores, simplemente multiplicamos el MCM (6) por la cantidad de carros que buscamos (3):
6 × 3 = 18
Por lo tanto, el tercer carro que recibirá boletos ición número 18 en la fila.
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Find the ordered pair (s,t) that satisfies the system
s/2+5/t=3
3t-6s=9
The ordered pair (s,t) that satisfies the system are (1/2,4) and (1,5).
We can use the second equation to solve for one of the variables in terms of the other. Let's solve for t:
3t - 6s = 9
3t = 6s + 9
t = (2s + 3)
Now we can substitute this expression for t into the first equation and solve for s:
s/2 + 5/t = 3
s/2 + 5/(2s + 3) = 3
Multiplying both sides by the denominator (2s + 3) gives:
s(2s + 3)/2 + 5 = 3(2s + 3)
Simplifying and collecting like terms yields:
2s^2 + 3s + 10 = 6s + 9
2s^2 - 3s + 1 = 0
This quadratic equation can be factored as:
(2s - 1)(s - 1) = 0
So s = 1/2 or s = 1.
Now we can substitute these values for s into the equation we derived for t:
If s=1/2 then t=2(1/2)+3=4
If s=1 then t=2(1)+3=5
Therefore, the ordered pairs that satisfy the system are (1/2,4) and (1,5).
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please help me I don't understand how to do these.
Given: SD⊥HT ; SH≅ST
Prove: SHD=STD
Step-by-step explanation:
For this given problem we have the following statements and reasons:
1) SD is vertical to HT,
Reason: Given
2) SDH and SDT are right angles
Reason: Right angle congruence theorem
3) SH=≈ST
Reason: Given
4) BD=≈BD
Reason: Reflexive property
5) SHD=≈STD
Reason: SAS
The function
models the DVD sales, in billions of dollars, from 1999 to 2017, where
is the number of years since 1999.
What is the average rate of change of DVD sales, in billion of dollars, per year for the period from 2001 to 2008? Round your answer to the nearest tenth, if necessary.
The average rate of change of DVD sales is 723.1 billion dollars.
How to determine average rate of change of DVD sales?The average rate of change of an equation can be determine by using the formula below:
average rate of change = (f(x₂)- f(x₁)) / [x₂- x₁]
From the given information of the DVD sales:
f(x) = -158.8x² + 2469.9x + 3010.5
x₁ = 2001 - 1999 = 2
x₂ = 2008 - 1999 = 9
average rate of change = ([-158.8(9)² + 2469.9(9) + 3010.5] - [-158.8(2)² + 2469.9(2) + 3010.5]) / (9-2)
= (12376.8 - 7315.1)/(7)
= 723.1 billion dollars
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Complete Question
Check image attached
Solve for x, t, r and round to the nearest hundredth
Answer:
x = 14°
t = 12.367 ~ 12.4
r = 2.999 ~ 3
Step-by-step explanation:
1st we can find x by sum theory which is the sum of all side equal to 180° .
x + 90° + 76° = 180 °
x + 166° = 180°
x= 180° - 166°
x = 14° ... So the unknown angle is 14°
and we also can solve hypotenus t and adjecent r by using sin amd cos respectively by angle 76° .
sin(76) = 12/t
sin(76) t = 12 ....... criss cross it
t = 12 / sin(76) ....... divided both side by sin(76)
t = 12.367 ~ 12.4 ....... result
And
cos(76) = r / 12.4
r = cos(76) × 12.4 .......criss cross
r = 2.999 ~ 3 ....... amswer and i approximate it
Given the objective Function: Revenue = 75x+85y and the critical points: (0,0) (180,120) (300,0)