The vertical distance between (7, -22) and (7, 12) is 34 units.
Explanation:
We can calculate the vertical distance by finding the difference between the y-coordinates of the two points.
Vertical distance = difference in y-coordinates = 12 - (-22) = 34
Therefore, the vertical distance between the two points is 34 units.
The ceiling of Stacy's living room is a square that is 25 ft long on each side. Stacy knows the diagonal of the ceiling from corner to corner must be longer than 25 ft, but she doesn't know how long it is.
Solve for the length of the diagonal of Stacy's ceiling in two ways:
(a) Using the Pythagorean Theorem.
(b) Using trigonometry
The length of the diagonal of Stacy's ceiling using the Pythagorean Theorem and trigonometry is 35.36 ft.
(a) Using the Pythagorean Theorem:
Since the ceiling is a square, we can treat it as two right triangles. Let's call the length of the diagonal 'd'. Now, we can apply the Pythagorean Theorem (a² + b² = c²) to one of the right triangles:
a² + b² = d²
25² + 25² = d²
625 + 625 = d²
1250 = d²
Now, take the square root of both sides:
√1250 = d
d ≈ 35.36 ft
(b) Using trigonometry:
In one of the right triangles, the angle between the two sides of the square (25 ft each) is 45 degrees. We can use the tangent function (tan) to relate the angle to the side lengths:
tan(45) = opposite side / adjacent side
tan(45) = 25 / 25
Since tan(45) = 1, we have 1 = 1, which confirms the angle is 45 degrees. Now, we can use the sine or cosine function to find the diagonal:
sin(45) = opposite side / hypotenuse
sin(45) = 25 / d
OR
cos(45) = adjacent side / hypotenuse
cos(45) = 25 / d
Both functions give us the same result since the angles are 45 degrees. Solving for 'd':
d = 25 / sin(45)
d ≈ 35.36 ft
So, the length of the diagonal of Stacy's ceiling is approximately 35.36 ft using both methods.
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The first is kept by the albatross, which first lands in our region. The second occurs every night in shooting, swimming, fighting, singing and others. Separately, they would reveal many to you. Together, they will reveal only one to you. And whose one is it?
Based on the information provided, it is not clear what "they" refer to. However, it seems that there are two distinct events or phenomena being described here.
The first involves the albatross, which is known to be a migratory bird that visits certain regions at certain times of the year. It is unclear what exactly is being "kept" by the albatross, but it could be some sort of information or knowledge that is unique to this bird.
The second event or phenomenon is described as happening every night and involving various activities such as shooting, swimming, fighting, and singing.
It is unclear what this refers to exactly, but it could be some sort of nightly ritual or tradition that takes place in a particular community or region.
The statement that "separately, they would reveal many to you" suggests that each of these phenomena has its own unique insights or knowledge to offer.
However, the statement that "together, they will reveal only one to you" implies that there is some sort of deeper connection or meaning between these two events that is not immediately apparent.
The question of "whose one is it?" suggests that there is some sort of ownership or responsibility associated with this revelation.
It is unclear who this refers to, but it could be interpreted as asking who is responsible for uncovering the deeper meaning or connection between these two phenomena.
In summary, the information provided is somewhat cryptic and open to interpretation. However, it seems that there are two distinct events or phenomena being described, and that there is some sort of deeper connection or meaning between them that is not immediately apparent.
The question of who is responsible for uncovering this connection remains unanswered.
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[tex]4^3\sqrt{-88}[/tex]
Help I don't know where the negative goes.
if you meant simplification
[tex]4^3\sqrt{-88}\implies 64\sqrt{-88}\implies 64\sqrt{(-1)(2^2)(2)(11)}\implies 64(2)\sqrt{(-1)(2)(11)} \\\\\\ 128\sqrt{(2)(11)}\cdot \sqrt{-1}\implies 128\sqrt{22}~i[/tex]
At a craft shop, a painter decided to paint a welcome sign to take home. An image of the sign is shown. A five-sided figure with a flat top labeled 5 and one-half feet. A height labeled 4 feet. The length of the entire image is 9 ft. There is a point coming out of the right side of the image that is created by two line segments. What is the area of the sign? 19 square feet 22 square feet 29 square feet 36 square feet Question 2(Multiple Choice Worth 2 points) (Volume of Rectangular Prisms MC) A family is building a sandbox for their yard that is shaped like a rectangular prism. They would like for the box to have a volume of 43,972.5 in3. If they already have the length measured at 71.5 inches and the width at 60 inches, what is the height needed to reach the desired volume? 5.25 inches 10.25 inches 131.5 inches 283.5 inches Question 3(Multiple Choice Worth 2 points) (Perimeter and Area on the Coordinate Plane MC) An office manager needs to cover the front face of a rectangular box with a label for shipping. The vertices of the face are (–8, 4), (4, 4), (–8, –2), and (4, –2). What is the area, in square inches, of the label needed to cover the face of the box? 18 in2 36 in2 60 in2 72 in2 Question 4(Multiple Choice Worth 2 points) (Perimeter and Area on the Coordinate Plane MC) The vertices of a rectangle are plotted in the image shown. A graph with the x-axis and y-axis labeled and starting at negative 8, with tick marks every one unit up to positive 8. There are four points plotted at negative 2, 6, then 3, 6, then negative 2, negative 3, and at 3, negative 3. What is the perimeter of the rectangle created by the points? 14 units 19 units 28 units 45 units Question 5(Multiple Choice Worth 2 points) (Volume of Rectangular Prisms MC) What is the volume of a rectangular prism with a length of fourteen and one-fifth yards, a width of 7 yards, and a height of 8 yards? seven hundred ninety-five and one-fifth yd3 seven hundred thirty-nine and one-fifth yd3 four hundred fifty-two and four
The area of the sign can be calculated by finding the area of the trapezoid shape. The formula for the area of a trapezoid is A = (1/2) * (base1 + base2) * height. In this case, the bases are 5.5 feet (half of 11 feet, which is the flat top of the five-sided figure) and 9 feet (the entire length of the image), and the height is 4 feet. Plugging these values into the formula, we get:
A = (1/2) * (5.5 + 9) * 4
A = (1/2) * 14.5 * 4
A = 7.25 * 4
A = 29
So, the area of the sign is 29 square feet.
The volume of a rectangular prism is calculated by multiplying its length, width, and height. In this case, the length is given as 71.5 inches, the width is given as 60 inches, and the volume is given as 43,972.5 in^3. We can solve for the height by dividing the volume by the product of the length and width:
Height = Volume / (Length * Width)
Height = 43,972.5 / (71.5 * 60)
Height ≈ 10.25 inches
So, the height needed to reach the desired volume is approximately 10.25 inches.
The area of the rectangular box face can be calculated by finding the length of the sides of the rectangle using the given coordinates, and then using the formula for the area of a rectangle, which is A = length * width. In this case, the length is the difference between the x-coordinates of the two points on the x-axis (4 - (-8) = 12) and the width is the difference between the y-coordinates of the two points on the y-axis (4 - (-2) = 6). Plugging these values into the formula, we get:
A = 12 * 6
A = 72
So, the area of the label needed to cover the face of the box is 72 square inches.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, we can use the given coordinates of the four points to find the lengths of the sides. The length is the difference between the x-coordinates of the two points on the x-axis (3 - (-2) = 5) and the width is the difference between the y-coordinates of the two points on the y-axis (6 - (-3) = 9). Since the opposite sides of a rectangle have equal lengths, the perimeter is twice the sum of the length and width:
Perimeter = 2 * (Length + Width)
Perimeter = 2 * (5 + 9)
Perimeter = 2 * 14
Perimeter = 28
So, the perimeter of the rectangle created by the points is 28 units.
The volume of a rectangular prism is calculated by multiplying its length, width, and height. In this case, the length is given as 14.2 yards (14 and one-fifth yards), the width is given as 7 yards, and the height is given as 8 yards. Plugging these values into the formula, we get:
Volume = Length * Width * Height
Volume = 14.2 * 7 * 8
Volume ≈ 795.2
So, the volume of the rectangular prism is approximately 795.2 cubic yards. Answer: seven hundred ninety-five and one-fifth yd3
A person sleeps in a tent while camping.
which equation correctly determines the
amount of material used, m, to construct
the fully enclosed tent.
a. =(8∙9)+2(7.5∙8)
b. =(8∙9)+2(7.5∙8)+2(1
2∙9∙6)
c. =2(8∙9)+2(7.5∙8)+(1
2 ∙9∙6)`
d. =3(8∙9)+2(1
2 ∙9∙6)
.m The correct equation to determine the amount of material used, m, to construct the fully enclosed tent is:
c. =2(8∙9)+2(7.5∙8)+(12∙9∙6)
To determine the amount of material used to construct the fully enclosed tent, we need to consider the surface area of the tent. The tent is fully enclosed, so we need to calculate the area of all the sides.
Option a. =(8∙9)+2(7.5∙8) calculates the area of the top and two sides of the tent. This does not include the front and back of the tent, so it is not the correct equation.
Option b. =(8∙9)+2(7.5∙8)+2(12∙9∙6) calculates the area of the top, two sides, front and back of the tent, but it also includes an extra term of 2(12∙9∙6) which is not necessary for a fully enclosed tent. This option overestimates the amount of material used.
Option c. =2(8∙9)+2(7.5∙8)+(12∙9∙6) calculates the area of the top, bottom, and all four sides of the tent. This is the correct equation to determine the amount of material used in a fully enclosed tent.
Option d. =3(8∙9)+2(12∙9∙6) overestimates the amount of material used because it includes an extra term of 3(8∙9) which is not necessary for a fully enclosed tent.
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Kyra bought a ""trick"" coin that lands on heads with a probability of 0. 4. Which frequency table would Kyra most likely generate by flipping the coin many times?
Don't mind the answer c because I don't know if that's right
Kyra's trick coin is more likely to generate a frequency table with a higher count of tails than heads, reflecting the 0.4 probability of landing on heads and the 0.6 probability of landing on tails.
Kyra's "trick" coin has a probability of 0.4 for landing on heads, meaning that it is more likely to land on tails. If Kyra flips the coin many times, she will likely generate a frequency table that shows a higher frequency of tails than heads.
A possible frequency table might look like this:
| Outcome | Frequency |
|---------|-----------|
| Heads | 40 |
| Tails | 60 |
In this table, the coin landed on heads 40 times and tails 60 times, representing the probability of 0.4 for heads and 0.6 for tails (since the total probability must equal 1). The more times Kyra flips the coin, the closer the relative frequencies will get to the actual probabilities. It's important to note that this is just an example, and the exact frequency counts may vary in practice due to randomness.
To summarize, Kyra's trick coin is more likely to generate a frequency table with a higher count of tails than heads.
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2. The town's five traffic enforcement officers hand out 14, 8, 10, 4, and
15 "good driving" citations. What part of the total number of citations do
the top two officers hand out?
The top two officers hand out approximately 56.86% of the good driving citations.
The given good traffic citations are = 14, 8, 10, 4, and 15.
Among the above citations, the top two officers get top 2 values for their good driving. The top two values are 14 and 15.
Lets add those top two good traffic citations and divide it by the total number of citations to find out the percentage the top two officers hand out.
Total number of citations = 14 + 8 + 10 + 4 + 15 = 51
Citations get by top two officers = 14 + 15 = 29
percentage handout by top two officers = 29 / 51 = 0.5686.
To convert the obtained value in to peercentage multiply it by 100.
so, 0.5686 x 100 = 56.86%
From the above analysis, we can conclude that the 56.86% of the citations could be hand out by the top two officers.
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"Francine made 11 long distance calls in March. The calls ranged from 11 minutes to 25 minutes in length. If Francine pays 0. 99 per minute for long distance calls, which is the closest to the total cost of her calls?"
The closest value to the total cost of Francine's calls is $191.07
To find the total cost of Francine's calls, we need to know the total number of minutes she spent on the phone. We can calculate this by adding up the lengths of all 11 calls:
Total minutes = 11 + 14 + 12 + 20 + 25 + 16 + 11 + 22 + 18 + 19 + 15 = 193
The total cost of Francine's calls can then be found by multiplying the total number of minutes by the cost per minute:
Total cost = 193 * 0.99
= 191.07
Therefore, the closest value to the total cost of Francine's calls is $191.07.
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Your local dry cleaners is running a special. The dry cleaner is offering a 13% discount for any drop off that is over $40. Also, they are running a neighborhood special of an additional 5% off. Given this information, determine the decay factor corresponding to each percent decrease. A. 34. 8; 33. 06 c. 0. 87; 0. 95 b. 0. 384; 0. 3306 d. 87; 95
The decay factor corresponding to each percent decrease is 0.87. The correct option is c. The customer would save a total of $17.35, or 17.35% off the original price.
To determine the decay factor corresponding to each percent decrease, we need to use the formula:
decay factor = (100% - percent decrease)/100%
For the first discount of 13%, the decay factor would be:
decay factor = (100% - 13%)/100% = 0.87
For the additional neighborhood discount of 5%, the decay factor would be:
decay factor = (100% - 5%)/100% = 0.95
So the correct answer is option C, with a decay factor of 0.87 for the 13% discount and 0.95 for the neighborhood discount.
These decay factors represent how much of the original price is left after the discount has been applied. For example, if the original price was $100, after the 13% discount, the price would be:
price after first discount = $100 x 0.87 = $87
Then, after the additional 5% discount, the final price would be:
final price = $87 x 0.95 = $82.65
So the customer would save a total of $17.35, or 17.35% off the original price.
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Solve for X. Round to the nearest tenth, if necessary.
The value of x to the nearest tenth is 1.4
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(θ) = opp/hyp
cos(θ)= adj/hyp
tan( θ) = opp/adj
x is opposite side to angle F and 32 is adjascent to angle F.
therefore;
tan F = opp/adj
tan23 = x/3.2
x = tan23 × 3.2
x = 1.4
therefore the value of x to the nearest tenth is 1.4
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A regular size chocolate bar was 5 4/9 inches long. if the king size bar is 3 2/5 inches longer, what is the length of the king size bar?
please help me!!!!
Answer:
8 38/48
Step-by-step explanation:
Estimate 4/5-1/3=
A 3/2
B 1/2
C 0
D 1
The estimate is 7/15.
The given expression is
4/5-1/3
We see that the denominators of both functions are different
So, the numerators can't be added/subtracted directly.
For this, we need to find the equivalent fraction of the given fractions, and the equivalent fractions should have the same denominator.
Now, the denominators are 5 and 3.
To have a common denominator in both fractions, we find the LCM of the denominators.
∴ The LCM of 5 and 3 = 15
Converting the fraction 4/5 into a fraction with 15 as the denominator,
4/5=4×3/5×3=12/15.
The same for 1/3
1/3= 1×5/3×5=5/15
Replacing 4/5 and 1/3 with the equivalent fractions in the given expression, we get,
12/15-5/15=(12-5)/15=7/15
Hence, the estimate is 7/15.
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A globe company currently manufactures a globe that is 18 inches in diameter if the dimensions of the globe are reduced by half what would the volume be 
The volume of the new globe would be 381.51 cubic inches, which is half the volume of the original globe.
The volume of a sphere is given by the formula:
V = (4/3)πr³
where r is the radius of the sphere.
If the diameter of the globe is reduced by half, then the new diameter would be 9 inches, and the new radius would be half of that, or 4.5 inches.
The new volume would be:
V' = (4/3)π(4.5)³
= (4/3)×3.14×(91.125)
= 381.51 cubic inches
Therefore, the volume of the new globe would be 381.51 cubic inches, which is half the volume of the original globe.
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The expected increase (I) of a population of organisms is directly proportional to the current population (n). If a sample of 240 organisms increases by 20, by how many will a population of 600 increase?
A population of 600 organisms is expected to increase by 50.
To solve this problem
We can use the equation I = k * n to determine whether the anticipated growth (I) of an organism population is directly related to the size of the current population (n).
Where k is a proportionality constant that connects the anticipated growth to the current population.
We can use the details provided in the problem to determine the value of k. We can write: 20 = k * 240 to represent an increase of 20 in a sample of 240 organisms.
We can calculate k as follows: k = 20 / 240 = 1 / 12.
Now that we know the value of k, we can use it to calculate the predicted growth for a population of 600:
I = (1 / 12) * 600 = 50
Therefore, a population of 600 organisms is expected to increase by 50.
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PLEASE HELP QUICK!! Which is the best measure of central tendency for the data set below? { 10, 18, 13, 11, 62, 12, 17, 15} A. Median because there is an outlier B. Mean because there is no outlier C. There is no way to tell D. Mode because there is an outlier
The best measure of central tendency for the data set below { 10, 18, 13, 11, 62, 12, 17, 15} is option B- Mean because there is no outlier.
The best measure of central tendency for the given data set depends on the nature of the data and what you want to represent.
If you want to find the middle value of the data set that is not affected by the outlier, then the median is the best measure of central tendency. In this case, the median is 13, as it is the middle value when the data is arranged in ascending order.
If you want to find the typical or average value of the data set, then the mean is the best measure of central tendency. In this case, the mean is approximately 20, calculated by adding all the values and dividing by the total number of values.
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write down the relation between AD and BC from the given figure from the attachment.
The figure that we have is an equilateral triangle. AD is the height of the triangle while BC represents the length of one of the sides. To get the length of one of the sides, we can use the expression;
S= 2/sqrt3 * h
What is the relationship between AD and BC?To get the relationship between AD and BC, we need to first note that the shape is an equilateral triangle. Next, we identify AD as the height of the triangle and BC as the length of one of the three equal sides.
So, the relationship between the height and sides is obtained with the formula: S= 2/sqrt3 * h or S = 1.1547 * h.
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Consider the three points P (3,0,0), Q (0,0,-9), and R (0, -6,0). (a) Find a non-zero vector orthogonal to the plane through the points P, Q, and R. (b) Find the area of the parallelogram with sides PQ and PR.
(a) To find a non-zero vector orthogonal to the plane through the points P, Q, and R, we need to take the cross product of two vectors in the plane. One way to do this is to subtract one point from another to get a vector, and then take the cross product of the two resulting vectors. For example, we could subtract point Q from point P to get the vector PQ, and subtract point R from point P to get the vector PR. Then, taking the cross product of PQ and PR will give us a vector orthogonal to the plane:PQ = <-3, 0, -9>PR = <-3, -6, 0>PQ x PR = <54, 27, 18>Therefore, the vector <54, 27, 18> is orthogonal to the plane through the points P, Q, and R.(b) To find the area of the parallelogram with sides PQ and PR, we need to find the length of the projection of PQ onto PR, and then multiply by the length of PR. The projection of PQ onto PR is given by:proj_PR(PQ) = (PQ · u) uwhere u is a unit vector in the direction of PR, and · denotes the dot product. Since PR = <-3, -6, 0>, we can take u = <-1/sqrt(10), -3/sqrt(10), 0>, which is a unit vector in the direction of PR. Then:proj_PR(PQ) = (PQ · u) u = (-3/sqrt(10)) <-1/sqrt(10), -3/sqrt(10), 0> = <9/10, 27/10, 0>The length of this vector is sqrt((9/10)^2 + (27/10)^2 + 0^2) = 3sqrt(10), so the area of the parallelogram is:A = |PQ| |proj_PR(PQ)| = sqrt((-3)^2 + 0^2 + (-9)^2) * 3sqrt(10) = 27sqrt(10)
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A. Orthogonal vector = (0, -27, 18)
B. The area of the parallelogram with sides PQ and PR is 1053 square units.
(a) To find a non-zero vector orthogonal to the plane through points P, Q, and R, we need to compute the cross product of vectors PQ and PR.
Vector PQ = Q - P = (-3, 0, -9)
Vector PR = R - P = (-3, -6, 0)
Cross product PQ x PR = (i, j, k) × ((-3, 0, -9), (-3, -6, 0))
= i(0 * 0 - (-9) * (-6)) - j(-3 * 0 - (-3) * (-9)) + k(-3 * -6 - 0 * (-3))
= i(0) - j(27) + k(18)
Orthogonal vector = (0, -27, 18)
(b) To find the area of the parallelogram with sides PQ and PR, we can use the magnitude of the cross product of PQ and PR.
Magnitude of PQ x PR = ||(0, -27, 18)||
= √(0^2 + (-27)^2 + 18^2)
= √(729 + 324)
= √1053
The area of the parallelogram with sides PQ and PR is 1053 square units.
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tim can paint a room in 6 hours . bella can paint the same room in 4 hours . how many hours would it take tim and bella to paint the room while working together y=kx+b
please help me now.
Answer: 3
Step-by-step explanation:
Answer:
2hrs 24 mins
Step-by-step explanation:
Ok so let's make this problem a bit simpler by splitting it up.
Tim paints a room in 6 hours.
So, we can also say that she paints 1/6 of that room in 1 hour
Bella paints it in 4 hours
So, we can also say that she paints 1/4 of that room in 1 hour
Now, lets see what we have:
Bella: 1/4 every hour
Tim: 1/6 every hour
The problem states that they are working together, so we need to add the values we have:
1/4 + 1/6
We cannot just add them, we must make them have the same common denominator.
LCD is 12, you can find that by just doing the times tables for 4 and 6 and seeing what number they match on first.
3/12 + 2/12 = 5/12
So, tim and bella working together paint 5/12 of a room in 1 hour.
They paint 5/12 of a room in 60 minutes
They paint 1/12 of the room in 12 minutes(divide both values by 5)
So if they paint 1/12 of the room in 12 minutes, we can multiply both values by 12 to get our answer.
They paint the full room in 144 minutes(12*12).
144 minutes is 2 hours and 24 minutes
Solve for f(-2).
f(x) = -3x + 3
f(-2) = [?]
Answer:
f(-2) = 9
Step-by-step explanation:
f(x) = -3x + 3 Solve for f(-2).
f(-2) = -3(-2) + 3
f(-2) = 6 + 3
f(-2) = 9
Which of these words has a vertical line of symmetry? A BOB B HOD с TOT D KID E COOK
Answer:
A BOB, C TOT
Step-by-step explanation:
If we draw a vertical line throgh the word the left side is the mirror image of the right.
A quadrilateral has a total area of 36. 18 square inches. One of the sides measures 6. 7 inches. How long is the other side? inches
(do not include any words in the answer blank)
The length of the other side of the quadrilateral is 10.67 inches.
The other side of the quadrilateral measures 10.67 inches. This can be found by using the formula for the area of a quadrilateral, which is (1/2) x diagonal x height. We know the total area and one side length, so we can solve for the height. The height is 10.67 inches, which is the length of the other side.
To find the length of the other side of the quadrilateral, we need to use the formula for the area of a quadrilateral, which is (1/2) x diagonal x height.
We know the total area of the quadrilateral is 36.18 square inches, and we can assume that the side given (6.7 inches) is one of the diagonals. We can solve for the height, which represents the length of the other side.
Using algebra, we can rearrange the formula to solve for the height:
Area = (1/2) x diagonal x height
36.18 = (1/2) x 6.7 x height
Multiplying both sides by 2:
72.36 = 6.7 x height
Dividing both sides by 6.7:
height = 10.67 inches
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Find the quotient of 1x10^-2 and 8x10^-2
Answer:
The first one is - 5 and the other is - 40
|x-3|+|x+2|-|x-5| if 3
|x-3|+|x+2|-|x-5| if x<-2
|x-3|+|x+2|-|x-5| if -2
pls help
i will give brainliest
|x-3|+|x+2|-|x-5| can be broken down into three separate cases based on the value of x:
(x-3) + (x+2) - (x-5) = 2x + 4
(x-3) + (x+2) - (5-x) = 2x - 6
-(x-3) - (x+2) - (5-x) = -3x - 4
We break down the expression into three separate cases based on the value of x. This is because the absolute value function creates "turning points" at which the behavior of the expression changes. We analyze the expression for each case and simplify it to obtain the final answer. The answer depends on the value of x, and we must consider the expression separately for each case.
If x ≥ 5, then the expression becomes:
(x-3) + (x+2) - (x-5) = 2x + 4
If -2 ≤ x < 3, then the expression becomes:
(x-3) + (x+2) - (5-x) = 2x - 6
If x < -2, then the expression becomes:
-(x-3) - (x+2) - (5-x) = -3x - 4
Therefore, the final answer depends on the value of x. If x is greater than or equal to 5, then the answer is 2x + 4. If x is between -2 and 3, then the answer is 2x - 6. And if x is less than -2, then the answer is -3x - 4.
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the state of new jersey is divided into 21 counties. the counties population range from just over 60,000 people to almost 1,000,000 people. The median country population is 445,349 people, and the interquaritle range is 467,983 people. what is the typical population of a new jersey county?
The typical population of a New Jersey county can be described as being around 445,349 people which is also the median population of a New Jersey country.
Based on the given information, the median population of a New Jersey county is 445,349 people. This means that half of the counties in the state have a population above this number, while the other half have a population below it.
However, it is important to note that the range of county populations in New Jersey is quite large, with some counties having as little as 60,000 people and others having almost 1,000,000 people. This indicates that there is significant variability in the population size of counties across the state.
The interquartile range (IQR) of county populations is also provided, which tells us that the middle 50% of county populations fall within a range of 467,983 people. This suggests that while there is variability in county populations, there is also some level of consistency in the distribution of populations across the state.
Overall, the typical population of a New Jersey county can be described as being around 445,349 people, with some counties having significantly larger or smaller populations.
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The radius of a right circular cone is increasing at a rate of 4 inches per second and its height is decreasing at a rate of 3 Inches per second. At what rate is the volume of the cone changing when the radius is 40 inches and the height is 20
inches?
To find the rate of change of the volume of the cone, we need to use the formula for the volume of a cone:
V = (1/3)πr^2h
Taking the derivative of both sides with respect to time, we get:
dV/dt = (1/3)π[2rh(dr/dt) + r^2(dh/dt)]
Substituting the given values:
r = 40 in (radius is increasing at a rate of 4 in/s)
h = 20 in (height is decreasing at a rate of 3 in/s)
dr/dt = 4 in/s
dh/dt = -3 in/s
Plugging these into the formula:
dV/dt = (1/3)π[2(40)(20)(4) + (40)^2(-3)]
dV/dt = (1/3)π[3200 - 4800]
dV/dt = (1/3)π(-1600)
dV/dt = -1681.99 in^3/s
Therefore, the volume of the cone is decreasing at a rate of approximately 1681.99 cubic inches per second when the radius is 40 inches and the height is 20 inches.
To find the rate at which the volume of the cone is changing, we can use the formula for the volume of a cone (V = (1/3)πr^2h) and differentiate it with respect to time (t).
Given:
dr/dt = 4 inches per second (increasing radius)
dh/dt = -3 inches per second (decreasing height)
r = 40 inches
h = 20 inches
First, let's differentiate the volume formula with respect to time:
dV/dt = d/dt[(1/3)πr^2h]
Using the product and chain rules, we get:
dV/dt = (1/3)π(2r(dr/dt)h + r^2(dh/dt))
Now, plug in the given values:
dV/dt = (1/3)π(2(40)(4)(20) + (40)^2(-3))
Simplify:
dV/dt = (1/3)π(6400 - 4800)
dV/dt = (1/3)π(1600)
Finally, calculate the rate:
dV/dt ≈ 1675.52 cubic inches per second
So, the volume of the cone is changing at a rate of approximately 1675.52 cubic inches per second.
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The points (1,5), (5,10), (7,8), and (8,1) are on the graph of the function p. Which expression belo gives the average rate of change of the function p on 5 less than or equal x less than or equal 8
Answer:
Step-by-step explanation:
Since it is x that is bound by 5≤x≤8, you should use the points (5,10) and (8,1), since a coordinate is written as (x,y).
Then, use the formula for slope, as the average rate of change means find the slope, [tex]\frac{y2-y1}{x2-x1}[/tex]
thus, plug in
[tex]\frac{1-10}{8-5}[/tex], and you get -9/3, or -3. :)
Pls help now with algebra 2 picture provided
The inverse function of f(x) = ∛(8x) + 4 is f^-1(x) = 1/8(y - 4)^3
Calculating the inverse function of f(x) = ∛(8x) + 4To find the inverse function of f(x), we need to solve for x in terms of f(x).
To find the inverse function of f(x) = ∛(8x) + 4, we can follow these steps:
Step 1: Replace f(x) with y:
y = ∛(8x) + 4
Step 2: Solve for x in terms of y:
y - 4 = ∛(8x)
Cube both sides:
(y - 4)^3 = 8x
x = 1/8(y - 4)^3
Step 3: Replace x with f^-1(x):
f^-1(x) = 1/8(y - 4)^3
Therefore, the inverse function of f(x) is f^-1(x) = 1/8(y - 4)^3
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URGENT!!!!
What is the probability that the card drawn is a black card or an eight?
Write your answers as fractions in the simplest form.
Face cards:
Red Hearts: 1♥ 2♥ 3♥ 4♥ 5♥ 6♥ 7♥ 8♥ 9♥ 10♥ J♥ Q♥ K♥
Red Diamonds: 1♦ 2♦ 3♦ 4♦ 5♦ 6♦ 7♦ 8♦ 9♦ 10♦ J♦ Q♦ K♦
Black Spades: 1♠ 2♠ 3♠ 4♠ 5♠ 6♠ 7♠ 8♠ 9♠ 10♠ J♠ Q♠ K♠
Black Clubs: 1♣ 2♣ 3♣ 4♣ 5♣ 6♣ 7♣ 8♣ 9♣ 10♣ J♣ Q♣ K♣
22
A statistical question is one where you expect to get a variety of answers. Determine whether each question can be classified as a statistical question. Select Yes or No for each question. Yes
No
How many hours a week do people exercise?
How many hours are there in a day?
How many rainbows have students seen this month?
To answer this question, determine the quantity asked for:
Answers are:
Yes - How many hours a week do people exercise?
No - How many hours are there in a day?
Yes - How many rainbows have students seen this month?
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A marine biologist is researching the population density of manatees. The marine biologist counts 550 manatees within a radius of 5 miles of a half circle off of Crystal Bay. What is the population density of the manatees? Use 3. 14 for pi, and round to the nearest whole number
The population density of manatees within a radius of 5 miles of a half circle off of Crystal Bay is approximately 14 manatees per square mile
The population density of manatees within a radius of 5 miles of a half circle off of Crystal Bay is approximately 70 manatees per square mile. To calculate this, we first need to find the area of the half circle. Using the formula for the area of a circle, A=πr^2, where r is the radius, we can find the area of the full circle with a radius of 5 miles:
A = 3.14 x 5^2
A = 78.5 square miles
Since we only want to consider the area of the half circle, we divide this by 2:
A = 78.5 / 2
A = 39.25 square miles
Now we can calculate the population density by dividing the number of manatees by the area:
Density = 550 / 39.25
Density ≈ 14
Therefore, the population density of manatees within a radius of 5 miles of a half circle off of Crystal Bay is approximately 14 manatees per square mile. Rounded to the nearest whole number, this is 14.
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