Answers
The relationship between the squares formed by the sides of a right triangle is defined by Pythagorean Theorem, which states that the square on the hypotenuse side is the sum of the squares on the other two sides.
How can the Pythagorean Theorem describe the relationship between the sides of a right triangle?According to Pythagorean Theorem, the square formed by the side length of the hypotenuse side of right triangle is equivalent to the sum of the squares formed by the lengths of the other two sides
Let a, b, and c represent the lengths of the sides of the right triangle, where;
a = The length of the hypotenuse side
b = The length of a leg of the right triangle
c = The length of the other leg of the right triangle
The area of each squares are therefore;
Area of the square formed by the hypotenuse side = a²
Area of the square formed by the legs = b² and c²
Therefore; a² = b² + c²
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Related Questions
The equation y = –1.25x + 13.5
represents the gallons of water
y left in an inflatable pool after
x minutes. Select all the true
statements.
A. When the time starts, there
are 13.5 gallons of water in
the pool.
B. The tub is being filled at a rate
of 1.25 gallons per minute.
C. The water is draining at a rate
of 1.25 gallons per minute.
D. When the time starts, there
are 1.25 gallons of water in
the pool.
E. The water is draining at a rate
of 13.5 gallons per minute.
F. When the time starts, there
are 12.25 gallons of water in
the pool.
Answers
The two true statements are:
A "When the time starts, there are 13.5 gallons of water in the pool."
C "The water is draining at a rate of 1.25 gallons per minute."
Which statements are true?Here we have the linaer equation y = –1.25x + 13.5 that represents the gallons of water y left in an inflatable pool after x minutes.
And we want to see which of the given statements are true.
We can see that the slope is -1.25, this means that the volume of water is reducing (due to the negative sign) then the statement C is true.
We also can see that the y-intercept is 13.5, that would be the initial volume of water in the pool, then the statement A "When the time starts, there are 13.5 gallons of water in the pool." is also true.
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PLEASE HELP SERIOUSLY!
A. Determine whether the following statements are true or false.
1. The higher the percentile rank of a score, the greater the percent of scores above that score.
2. A mark of 75% always has a percentile rank of 75.
3. A mark of 75% might have a percentile rank of 75.
4. It is possible to have a mark of 95% and a percentile rank of 40.
5. The higher the percentile rank, the better that score is compared to other scores.
6.A percentile rank of 80, indicates that 80% of the scores are above that score.
7. PR50 is the median.
8. Two equal scores will have the same percentile rank.
Answers
Answer:
**Statement | True or False**
---|---
**1. The higher the percentile rank of a score, the greater the percent of scores above that score.** | True
**2. A mark of 75% always has a percentile rank of 75.** | False. A mark of 75% could have a percentile rank of 75 if it is the median score. However, it could also have a percentile rank of 60, 65, 80, or any other percentile rank, depending on the distribution of scores.
**3. A mark of 75% might have a percentile rank of 75.** | True. See above.
**4. It is possible to have a mark of 95% and a percentile rank of 40.** | True. For example, if there are 100 students in a class, and 95 of them get 100% on a test, then the student who gets 95% will have a percentile rank of 40.
**5. The higher the percentile rank, the better that score is compared to other scores.** | True. A higher percentile rank indicates that a score is better than more of the other scores.
**6.A percentile rank of 80, indicates that 80% of the scores are above that score.** | False. A percentile rank of 80 indicates that 80% of the scores are **at or below** that score.
**7. PR50 is the median.** | True. The median is the middle score in a distribution. By definition, half of the scores will be at or below the median, and half of the scores will be at or above the median. Therefore, the percentile rank of the median is 50.
**8. Two equal scores will have the same percentile rank.** | True. Two equal scores will always have the same percentile rank.
Step-by-step explanation:
A rectangle that is 7 feet wide has an area of 56 square feet
Answers
The length of the rectangle is 8 feet given it is 7 feet wide and has an area of 56 square feet.
A rectangle is a geometric figure with four straight sides and four right angles, where the opposite sides are parallel and equal in length. In this case, we are given that the rectangle has a width of 7 feet and an area of 56 square feet. The area of a rectangle is calculated by multiplying its length (L) and width (W), expressed as A = L × W.
We are provided with the width, W = 7 feet, and the area, A = 56 square feet. To find the length of the rectangle, we can rearrange the area formula:
L = A ÷ W
Substituting the given values, we have:
L = 56 ÷ 7
L = 8 feet
Hence, the length of the rectangle is 8 feet. To summarize, a rectangle with a width of 7 feet and an area of 56 square feet has a length of 8 feet. The dimensions of the rectangle are 7 feet by 8 feet.
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anyone know the dba questions for unit 8 algebra 1 honors
Answers
a) The distance the ball rebounds on the fifth bounce is approximately 7.59 ft.
b) The total distance the ball has traveled after the fifth bounce is approximately 52.61 ft.
What is the explanation for the above response?Let's denote the height of the ball after its nth bounce by h_n. Then we can express the relationship between the height of the ball after each bounce in terms of a recursive formula:
h_0 = 16 (initial height)
h_1 = (3/4) * h_0 (rebound distance after the first fall)
h_2 = (3/4) * h_1 (rebound distance after the second fall)
h_3 = (3/4) * h_2 (rebound distance after the third fall)
h_4 = (3/4) * h_3 (rebound distance after the fourth fall)
h_5 = (3/4) * h_4 (rebound distance after the fifth fall)
a) To find the distance the ball rebounds on the fifth bounce, we need to calculate h_5:
h_5 = (3/4) * h_4
= (3/4) * ((3/4) * ((3/4) * ((3/4) * 16)))
= (3/4)^5 * 16
= 7.59375 ft
Therefore, the ball rebounds approximately 7.59 ft on the fifth bounce.
b) To find the total distance the ball has traveled after the fifth bounce, we need to add up all of the distances traveled during the falls and rebounds:
total distance = distance of first fall + rebound distance after first fall + rebound distance after second fall + rebound distance after third fall + rebound distance after fourth fall + rebound distance after fifth fall
total distance = 16 + (3/4) * 16 + (3/4)^2 * 16 + (3/4)^3 * 16 + (3/4)^4 * 16 + (3/4)^5 * 16
total distance = 16 + 12 + 9 + 6.75 + 5.0625 + 3.7969
total distance = 52.6094 ft
Therefore, the ball travels approximately 52.61 ft after the fifth bounce.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Be sure to show and explain all work using mathematical formulas and terminology. A bouncy ball is dropped from a height of 16ft and always rebounds ¼ of the distance of the previous fall.
a) What distance does it rebound the 5th time?
b) What is the total distance the ball has travelled after this time?
An athletic Beld is a 50 yd-by-100 yd rectangle, with a semicircle at each of the short sides. Arunning track 10 yd wide surrounds the field. If the track is divided into eight lanes of equal width, with lane 1 being the inner-most and lane 8 being the outer-most lane, what is the distance around the along the inside edge of each lane?
Answers
The distance along the inside edge of each lane is 170 yards, 180 yards, 190 yards, 200 yards, 210 yards, 220 yards, 230 yards, and 240 yards.
Length of the Beld = 100 yd
Width of the Beld = 50 yd
The radius of the lane = 50/2 = 25 yards
To calculate the length of the overall length of the lane including semicircles is:
100 yards + 2 × 25 yards = 150 yards
The length of the innermost lane is:
150 yards + 2 × 10 yards = 170 yards
To calculate the length of the other lanes is:
170 yards + 10 yards = 180 yards
The length of lane 3 is:
180 yards + 10 yards = 190 yards
The distance between the two lanes is 10 yards. Then the remaining lengths of the lanes will be 200 yards, 210 yards, 220 yards, 230 yards, and 240 yards
Therefore, we can conclude that the distance between the two lanes along the inside edge of each lane is 10 yards.
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if 2x + 3y = 6x - 5y, find the value of x/y.
Answers
Answer: 2
Step-by-step explanation:
Answer:
[tex] \frac{dy}{dx} = \frac{4}{9} [/tex]
Step-by-step explanation:
sol,
2x+3y-6x+6y=0
f(x,y)=2x+3y-6x+6y
f(X,-y)=2x+3y-6y,fx=?
f(x-y)=2x+3y-6y,fy=?
fx=-4
fy=9
[tex] \frac{d}{y} = \frac{ - 4}{9} [/tex]
now,
[tex] \frac{dy}{dx} = \frac{4}{9} [/tex]
Write each of teh following expressions without using absolute value.
|y-x|, if y>x
Answers
The expression |y-x| without absolute value is simply: y-x
In mathematics, the absolute value refers to the magnitude or numerical value of a real number without considering its sign. It gives the distance of the number from zero on the number line. The absolute value of a number x is denoted by |x| and is defined as follows:
If x is positive or zero, then |x| = x.
If x is negative, then |x| = -x (the negative sign is removed).
Since y > x, the difference (y-x) will be positive. The absolute value of a positive number is the number itself. Therefore, the expression |y-x| without absolute value is simply: y-x
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A sales person in the stereo store is given a choice of two different compensation plans. One plan offers a weekly salary of $250 plus a commission of $25 for each serial sold. The other plan offers no salary will pays $50 commission on each stereo sold her daughter plan offers no celer sales person in the stereo store is given a choice of two different compensation plans
Answers
10 stereos must the salesperson sell to make that same amount of money under both plans.
How many stereos must the salesperson sell ?Assume that in order for the salesperson to earn the same amount of money under both schemes, x stereos must be sold.
The salesperson will be paid a salary of $250 + $25 for each stereo sold under the first strategy. So, these are the total earnings:
First plan's total profits are $250 plus $25.
Instead of receiving a salary under the second proposal, the salesperson would be compensated with a $50 commission for each stereo sold. So, these are the total earnings:
Total income under the second plan equals $50x
We can set the two equations for total earnings to be equal in order to determine the value of x:
$250 + $25x = $50x
When we simplify the equation, we obtain:
$250 = $25x
x = 10
The sales person must thus sell 10 stereos in order to.
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ldentify the relationship between the angles. y : x
Answers
Answer:
there both symmetrical
Answer:
Congruent
Step-by-step explanation:
When visualizing how two angles are related, try squashing the two parallel lines into each other. When you do that with these angles, they go from appearing like =\= to appearing like -\-, with x and y being catty-corner from each other.
Because the parallel lines are straight, x and y are both half of a pair that adds up to 180. However, x and y aren't sharing a straight line, so they cannot add up to 180 with each other. That leaves only one possibility, that x and y have the same angle measure.
9x - 3x = 3x(3) is it true
Answers
Answer:
It is not true since 9x - 3x = 6x and
3x(3) = 9x.
Answer:
Not true b/c
Step-by-step explanation:
9x-3x=6x
and3x(3)=9x
6x is not equal to 9x
Suppose that in 1682, a man bought a diamond for $32. Suppose that the man had instead put the $32 in the bank at 3% interest compounded continuously. What would that $32 have been worth in 2003? In 2003, the $32 would have been worth $ (Do not round until the final answer. Then round to the nearest dollar as needed.)
Answers
If a man bought a diamond for $32 in 1682 and the man had instead put the $32 in the bank at 3% interest compounded continuously, then the value of the diamond in 2003 would be $554,311.
The given problem is related to exponential growth. In this problem, the continuous compounding formula will be used to find the value of $32 in 2003.
The formula for continuous compounding is given by:
A = Pert Where,
P is the principal amount,
r is the annual interest rate,
e is the Euler's number which is approximately 2.71828, and
t is the time in years.
Using the formula, we get:
A = 32e^(0.03 x 321)
A = 32e^9.63
A = 32 x 17322.23
A = $ 554311.36
Thus, $32 invested at 3% compounded continuously from 1682 to 2003 would be worth $554,311.
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In circle m, secants pamd and pbc are drawn from point p such that mbc = 100 and mcd = 62°. which
of the following is the measure of p?
(1) 19
(2) 22
(3) 34
(4) 40
Answers
In the circle, the measure of p is 34 (option 3).
First, we know that angle MBC is an exterior angle to triangle PBC. Therefore, the measure of angle PBC is equal to the sum of angles MBC and MCB, which is 100 + (1/2)(angle MCP) = 100 + (1/2)(angle MQP).
Similarly, angle MCD is an exterior angle to triangle PCD. Therefore, the measure of angle PDC is equal to the sum of angles MCD and MDC, which is 62 + (1/2)(angle MPQ) = 62 + (1/2)(angle MQP).
Since angle PBC and angle PDC are both subtended by the same arc BC, they are equal. Therefore, we can set the expressions for these angles equal to each other and solve for angle MQP:
100 + (1/2)(angle MQP) = 62 + (1/2)(angle MQP)
38 = (1/2)(angle MQP)
angle MQP = 76 degrees
Finally, we can use the fact that angles MPQ and MQP form a linear pair, so they add up to 180 degrees. Therefore, angle MPQ is 180 - 76 = 104 degrees.
Since angle MPQ is an exterior angle to triangle PAB, we can use the exterior angle theorem to find the measure of angle P, as follows:
angle P = angle MPQ + angle PAB = 104 + 100 = 204 degrees
However, angles in a circle cannot be greater than 180 degrees, so we need to subtract 180 from angle P to get the actual measure of angle P:
angle P = 214 - 180 = 34 degrees
Therefore, the answer is option (3).
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Scientists estimate that the mass of the sun is 1. 9891 x 1030 kg. How many zeros are in this
number when it is written in standard notation?
A 26
B 30
C 35
D 25
Answers
The total number of zeros in the mass of the sun when written in standard notation is 30, which is option B.
When we write the number in standard notation, we move the decimal point to the left or right to express the number in terms of powers of 10. In this case, we can write the mass of the sun as:
1.9891 x 10^30
To count the number of zeros in this number, we only need to count the number of digits to the right of the decimal point, which is zero in this case. Then we add the exponent, which tells us the number of places we need to move the decimal point to the right to express the number in standard notation. In this case, the exponent is 30, so we need to move the decimal point 30 places to the right, which means adding 30 zeros.
Therefore, the total number of zeros in the mass of the sun when written in standard notation is 30, which is option B.
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The table shows the number of jelly beans in a dish. If Jeremy randomly selects a jelly bean, what is the probability that it is NOT lemon or orange?
Jelly Bean Type Number in Dish
grape 10
lemon 8
orange 14
cherry 16
Group of answer choices
1/4
11/24
1/2
13/24
Answers
The probability of Jeremy selecting a jelly bean that is not lemon or orange is: 26/48 = 0.54 or 54%.
To find the probability that Jeremy randomly selects a jelly bean that is not lemon or orange, we need to first find the total number of jelly beans that are not lemon or orange.
The number of grape jelly beans is 10, the number of cherry jelly beans is 16, so the total number of jelly beans that are not lemon or orange is:
10 + 16 = 26
The total number of jelly beans in the dish is:
10 + 8 + 14 + 16 = 48
Therefore, the probability of Jeremy selecting a jelly bean that is not lemon or orange is:
26/48 = 0.54 or 54%.
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A pet border keeps a dog-to-cat ratio 5;2. If the boarder has room for 98 animals then how many of them can be dogs?
Answers
Answer:
70 dogs
Step-by-step explanation:
sum the parts of the ratio , 5 + 2 = 7 parts
divide total by 7 to find the value of one part of the ratio
98 ÷ 7 = 14 ← value of 1 part of the ratio , then
5 × 14 = 70 ← number of dogs
Question 11 (Multiple Choice Worth 5 points)
(Laws of Exponents with Integer Exponents MC)
Choose the expression that is equivalent to
9
92
Answers
Therefore, the equivalent expression to [tex]9^2[/tex] is 81.
How to solve equation?To solve an equation, you need to isolate the variable on one side of the equation, typically the left side, and simplify the other side until you are left with an expression that has only the variable you are trying to solve for.
Here are the general steps to solve an equation:
Start by simplifying both sides of the equation as much as possible. This may involve distributing or combining like terms.
Get all terms with the variable you are solving for on one side of the equation. To do this, you can add or subtract terms from both sides of the equation. For example, if you have the equation 2x + 5 = 9, you can subtract 5 from both sides to get 2x = 4.
Isolate the variable by dividing both sides of the equation by its coefficient. In the above example, you can divide both sides by 2 to get x = 2.
Check your solution by plugging it back into the original equation and verifying that both sides of the equation are equal.
[tex]a^m/a^n = a^{(m-n)}[/tex]
to simplify the expression.
The expression [tex]9^2[/tex] means 9 multiplied by itself 2 times:
[tex]9^2 = 9 * 9[/tex]
Using the laws of exponents, we can rewrite this expression as:
[tex]9^2 = 9^{(1+1)} (since 2 = 1 + 1)[/tex]
Then, using the rule that [tex]a^{(m+n)} = a^m * a^n[/tex], we have:
[tex]9^2 = 9^1 *9^1[/tex]
Finally, using the fact that. [tex]a^1 = a[/tex] for any value of a, we get:
We can use the rule of exponents that states:
[tex]9^2 = 9 * 9 = 81[/tex]
Therefore, the equivalent expression to [tex]9^2[/tex] is 81
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A triangular roof is built so that its height is half its base. If the base of the roof is 32 feet long, what is the area of the roof?
Answers
If the base of the roof is 32 feet long, then the area of the triangular roof is 256 square feet.
In the given scenario, we are provided with information about a triangular roof. It is mentioned that the base of the roof is 32 feet long, and we need to determine the area of the triangular roof.
To calculate the area of a triangle, we need to know the length of the base and the height. In this case, we are given that the height is half the length of the base, which can be expressed as h = (1/2) * b.
Since we are given that the base length, b, is 32 feet, we can substitute this value into the height equation to find the height of the triangle: h = (1/2) * 32 feet = 16 feet.
Now that we have the base length (b = 32 feet) and the height (h = 16 feet), we can use the formula for the area of a triangle: A = (1/2) * b * h.
Substituting the values, we have A = (1/2) * 32 feet * 16 feet = 256 square feet.
Therefore, the area of the triangular roof is determined to be 256 square feet. This represents the amount of surface area covered by the triangular section of the roof.
Let the base of the triangular roof be denoted by b, and its height be denoted by h. We are given that
h = (1/2) * b, and that
b = 32 feet.
We can use this information to find the area A of the roof as follows:
A = (1/2) * b * h
= (1/2) * 32 feet * (1/2) * 32 feet
= 256 square feet
Therefore, the area of the triangular roof is 256 square feet.
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Researchers pose a question can pant sizes be predicted from a man's height? A random sample of 20 males and their pant size versus height
Answers
Answer:
Yes, there is evidence at the 10% significance level, but not at the 5% level
Step-by-step explanation:
Look at the p-value in bottom left corner (in the Height row).
It is less than 0.1, but greater than 0.05. Thus, Yes, there is evidence at the 10% significance level, but not at the 5% level. Got it right.
The areas of two triangles are 50 cm2 and 98 cm2. what is the ratio of their perimeters?
a ) 25/49
b ) 50/98
c ) 625/2401
d ) 5/7
e ) 2500/9604
Answers
The ratio of the perimeters is 14/5, which simplifies to 70/25, which reduces to 14/5. So the answer is (d) 5/7.
Let's use the fact that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths. If we let the corresponding side lengths be a and b, then we have:
(area of first triangle)/(area of second triangle) = (a^2)/(b^2)
We are given that the areas of the two triangles are 50 cm^2 and 98 cm^2, respectively. Let's call the side lengths of the first triangle a1, a2, and a3, and the side lengths of the second triangle b1, b2, and b3. Then we have:
(50)/(98) = (a1a2)/(b1b2)
We don't know the actual values of a1, a2, b1, and b2, but we can find the ratio of their perimeters by adding up the side lengths of each triangle. Let's call the perimeters of the first and second triangles P1 and P2, respectively. Then we have:
P1 = a1 + a2 + a3
P2 = b1 + b2 + b3
Dividing P1 by P2, we get:
P1/P2 = (a1 + a2 + a3)/(b1 + b2 + b3)
We can rewrite the ratios of the side lengths using the equation we found earlier:
P1/P2 = [(a1a2)/(b1b2)]*[(a1 + a2 + a3)/(a1 + a2 + a3)]
P1/P2 = [(a1a2)/(b1b2)]*1
P1/P2 = (a1a2)/(b1b2)
We still don't know the values of a1, a2, b1, and b2, but we can eliminate them by using the equation we found earlier:
(50)/(98) = (a1a2)/(b1b2)
Simplifying this expression, we get:
(a1/a2) = sqrt((98/50)*(b1/b2))
We can use this to substitute for one of the ratios of side lengths in the equation for P1/P2:
P1/P2 = [(a1a2)/(b1b2)]*[(a1 + a2 + a3)/(a1 + a2 + a3)]
P1/P2 = [sqrt((98/50)(b1/b2))][(a1 + a2 + a3)/(a1 + a2 + a3)]
P1/P2 = sqrt((98/50)*(b1/b2))
Now we can substitute the given values to get:
P1/P2 = sqrt((98/50)(b1/b2)) = sqrt((98/50)(2/1)) = sqrt(196/50) = 14/5
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7.) The Goody's store manager charted
the number of coats sold compared
with the outside temperature. What
kind of relationship would you expect
between the variables?
Answers
It is also possible that there may not be a clear relationship between the two variables or that there may be other factors that influence the number of coats sold, such as seasonal trends or fashion trends.
What is variable?In mathematics, a variable is a symbol or letter that represents a quantity that can vary or take on different values in a given situation or equation. Variables are commonly denoted by letters such as x, y, z, a, b, c, etc. They are used to represent unknown or changing quantities in mathematical expressions or equations.
For example, in the equation y = 2x + 3, x and y are variables. x represents an unknown value, while y represents the value that results from the equation for a particular value of x. In this case, the variable x can take on different values, and the corresponding value of y will change accordingly.
Variables are used in a wide range of mathematical concepts, such as algebra, calculus, and statistics, to represent and manipulate different quantities and relationships between them.
It is reasonable to expect that there is a negative correlation between the number of coats sold and the outside temperature. In other words, as the temperature gets colder, the number of coats sold would increase, and as the temperature gets warmer, the number of coats sold would decrease. This is because colder temperatures would typically prompt people to buy more coats to stay warm, while warmer temperatures would make people less likely to buy coats. However, it is also possible that there may not be a clear relationship between the two variables or that there may be other factors that influence the number of coats sold, such as seasonal trends or fashion trends.
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Suppose that f(x) = (x + 6)/(2-6) (A) Find all critical values of f. If there are no critical values, enter- None. If there are more than one, enter them separated by commas. Critical value(s) =?
Answers
The function f(x) = (x + 6)/(2-6) does not have any critical values. A critical value of a function is a value of x where the derivative of the function is either zero or undefined.
However, in this case, the denominator of f(x) is a constant, so the derivative of f(x) is simply the derivative of the numerator divided by the constant denominator.
The derivative of the numerator is 1, so the derivative of f(x) is simply 1/(2-6) = -1/4. Since the derivative is a constant, it is never zero or undefined, and so there are no critical values for this function.Explanation: To find the critical values of a function, we need to find the values of x where the derivative of the function is either zero or undefined. However, in this case, the denominator of f(x) is a constant, so the derivative of f(x) is simply the derivative of the numerator divided by the constant denominator. The derivative of the numerator is 1, so the derivative of f(x) is simply 1/(2-6) = -1/4. Since the derivative is a constant, it is never zero or undefined, and so there are no critical values for this function. Therefore, the answer is None.
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The outside temperature was 4°C for the next six hours the temperature changed at a mean rate of -0. 8°C per hour for the next two hours what was the final temperature
Answers
The final temperature after the next 8 hours (6 hours at -0.8°C per hour, followed by 2 hours at -0.8°C per hour) will be -2.4°C.
The final temperature can be calculated by subtracting the total temperature change from the initial temperature of 4°C.
The total temperature change during the next six hours can be calculated by multiplying the mean rate of -0.8°C per hour by the number of hours, which is 6.
-0.8°C/hour x 6 hours = -4.8°C
Therefore, the temperature after the next six hours will be:
4°C - 4.8°C = -0.8°C
For the next two hours, the temperature changed at a mean rate of -0.8°C per hour. This means the temperature decreased by:
-0.8°C/hour x 2 hours = -1.6°C
So the final temperature will be:
-0.8°C - 1.6°C = -2.4°C.
Therefore, the final temperature after the next 8 hours (6 hours at -0.8°C per hour, followed by 2 hours at -0.8°C per hour) will be -2.4°C.
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A car can be rented for $75 per week plus $0. 15 per mile. How many miles can be driven if you have at most $180 to spend for weekly transportation
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You can drive at most 700 miles within the $180 budget for weekly transportation.
To determine how many miles can be driven with a budget of $180 for weekly transportation, we'll use the given information: $75 per week for car rental and $0.15 per mile driven. First, subtract the weekly rental cost from the total budget:
$180 - $75 = $105
Now, divide the remaining budget by the cost per mile to find the maximum number of miles that can be driven:
$105 ÷ $0.15 ≈ 700 miles
So, you can drive at most 700 miles within the $180 budget for weekly transportation.
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Question 13 of 13 > Attempt 6 Find an equation of the plane passing through the three points given P = (1,7,4), Q = (3,12,12). R = (8,11,7) (Use symbolic notation and fractions where needed. Give you answer in the form ax + by + cz = d.)
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The equation of the plane passing through the three points P, Q, and R is -29x + 50y - 23z = 229
To find the equation of the plane passing through the three points P, Q, and R, we need to first find two vectors in the plane. We can do this by subtracting P from Q and R to get:
Q - P = (3-1, 12-7, 12-4) = (2, 5, 8)
R - P = (8-1, 11-7, 7-4) = (7, 4, 3)
Next, we can take the cross product of these two vectors to get a vector that is perpendicular to the plane:
(2, 5, 8) x (7, 4, 3) = (-29, 50, -23)
Now we have the equation of the plane in the form ax + by + cz = d, where (a, b, c) is the normal vector we just found and (x, y, z) is any point on the plane (we can use one of the three given points):
-29x + 50y - 23z = d (equation of plane)
To find the value of d, we can substitute one of the points, say P:
-29(1) + 50(7) - 23(4) = d
-29 + 350 - 92 = d
d = 229
Therefore, the equation of the plane passing through the three points P, Q, and R is:
-29x + 50y - 23z = 229
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The pattern of a soccer ball contains regular hexagons and regular pentagons. The figure below shows what a section of the pattern would look like on a flat surface. What is the measure of each gap between the hexagons in degrees?
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Answer:
In this pattern, there are 12 regular pentagons and 20 regular hexagons. Each hexagon shares a vertex with three pentagons and each pentagon shares a vertex with five hexagons.
To find the measure of each gap between the hexagons, we can use the fact that the sum of the angles around any vertex in a regular polygon is always 360 degrees. Let x be the measure of the angle between two adjacent pentagons, and y be the measure of each angle at the center of a hexagon.
At each vertex of the pattern, there are three pentagons and three hexagons meeting. Thus, we have:
3(108) + 3y = 360
Simplifying, we get:
324 + 3y = 360
3y = 36
y = 12
Therefore, each angle at the center of a hexagon measures 12 degrees. Since there are six angles around the center of a hexagon, the total angle around the center of a hexagon is 6(12) = 72 degrees.
To find the measure of each gap between the hexagons, we need to subtract the angle of the hexagon from 180 degrees (since the sum of the angles of a triangle is 180 degrees). Thus, the measure of each gap between the hexagons is:
180 - 72 = 108 degrees
Step-by-step explanation:
This sont Use a calculator or program to compute the first 10 iterations of Newton's method for the given function and initial approximation, f(x) = 2 sin x + 3x + 3, Xo = 1.5 Complete the table. (Do not round until the final answer. Then found to six decimal places as needed) k k XX 1 6 2 7 3 8 4 9 5 10
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given: function f(x) = 2sin(x) + 3x + 3 ,Xo=1.5
1. Compute the derivative of the function, f'(x).
2. Use the iterative formula: Xₖ₊₁ = Xₖ - f(Xₖ) / f'(Xₖ)
3. Repeat the process 10 times.
First, let's find the derivative of f(x):
f'(x) = 2cos(x) + 3
Now, use the iterative formula to compute the iterations:
X₁ = X₀ - f(X₀) / f'(X₀)
X₂ = X₁ - f(X₁) / f'(X₁)
...
X₁₀ = X₉ - f(X₉) / f'(X₉)
Remember to not round any values until the final answer, and then round to six decimal places. Since I cannot actually compute the iterations, I encourage you to use a calculator or program to find the values for each Xₖ using the provided formula.
2 Decide if each statement about r = 6 is true or false. Choose True or False for each statement. a. The equation has the same solution as fr = 3. True False
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Answer:
Step-by-step explanation:
True
A quantity with an initial value of 390 decays continuously at a rate of 5% per decade. What is the value of the quantity after 51 years, to the nearest hundredth?
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The value of the quantity after 51 years, rounded to the nearest hundredth, is 499.92.
Since a decade is a period of 10 years, a decay rate of 5% per decade can be converted to a continuous decay rate as follows:
Continuous decay rate = (1 + decay rate per decade[tex])^{(1/10)[/tex] - 1
In this case, the decay rate per decade is 5%, which can be expressed as 0.05.
Continuous decay rate = (1 + 0.05[tex])^{(1/10)[/tex] - 1
Continuous decay rate ≈ 0.0048767
Now we can use the formula for continuous decay:
A = A0[tex]e^{rt[/tex]
In this case, the initial value A0 is 390, the continuous decay rate r is 0.0048767, and the time elapsed t is 51 years.
Substituting these values into the formula, we have:
A = 390 [tex]e^{(0.0048767)( 51)[/tex]
A ≈ 499.9202826
Therefore, the value of the quantity after 51 years, rounded to the nearest hundredth, is 499.92.
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PLEASE HELP WILL MARK BRANLIEST !!!
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If password begin with capital letter followed by lower case letter, and end with symbol , then the number of unique passwords which can be created using letters and symbols are 47525504.
The password must have 6 characters and the first character must be a capital letter, so, we have 26 choices for the first character.
For the second character, we have 26 choices for a lower-case letter.
For the third, fourth, and fifth characters, we can choose from any of the 26 letters (upper or lower case).
For the last character, we have 4 choices for the symbol
So, total number of unique passwords that can be created is:
⇒ 26 × 26 × 26 × 26 × 26 × 4 = 26⁵ × 4 = 47525504.
Therefore, there are 47525504 unique passwords that can be created using these letters and symbols.
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Write an inequality and a word sentence that represent the graph. Let x represent the unknown number.
A number line. The number line is shaded left of an open circle at 1.
Inequality:
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The word sentence for the given number line represents the X is greater than zero. The inequality is the X is not less than or equal to zero.
In the given number line the values are from negative infinity to positive infinity. Though the number line is having all values, there is some part that is shaded only on certain parts of the number line. The part is from number 1 to positive infinity marking zero as a circle.
The circle represents the value starts counting from the next step. In the given number line circle is shaded at number zero and the value started from the next value which is number 1 onwards to positive infinity.
So, the given number line represents X is greater than zero and X is not less than or equal to zero.
In mathematical words,
X < 0 and X≠0
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Given question is not having enough information to solve, for better understanding attaching the number line image below.