If \(x = \sqrt{a^{sin^{-1}t}}\),\(y =\sqrt{a^{cos^{-1}t}}\), show that \(\frac{dy}{dx}= -\frac{y}{x}\).
Please help & don't spam!
Answers
Step-by-step explanation:
\(\sf x = \sqrt{a^{sin^{-1} \ t}}\\\\\\Derivative \ rule:\boxed{\dfrac{d(\sqrt{x})}{dx}=\dfrac{1}{2}*x^{\frac{-1}{2}}=\dfrac{1}{2\sqrt{x}}}\)
\(\sf \dfrac{d(\sqrt{a^{sin^{-1} \ t}}}{dt}=\dfrac{1}{2\sqrt{a^{sin^{-1} \ t}}}*\dfrac{d(a^{sin^{-1} \ t})}{dt}\\\\\\Derivative \ rule: \boxed{\dfrac{d(a^{x})}{dx}=log \ a *a^{x}}\)
\(\sf = \dfrac{1}{2\sqrt{a^{sin^{-1}} \ t}}*a^{sin^{-1} \ t}* log \ a *\dfrac{d(Sin^{-1} \ t)}{dt}\\\\\)
\(Derivative \ rule:\boxed{\dfrac{d(sin^{-1} \ x}{dx}=\dfrac{1}{\sqrt{1-x^2}}}\)
\(\sf = \dfrac{1}{2\sqrt{a^{sin^{-1} \ t}}}*a^{Sin^{-1} \ t}*log \ a*\dfrac{1}{\sqrt{1-x^2}}}}}\\\\ = \dfrac{a^{Sin^{-1} \ t}*log \ a}{2\sqrt{a^{sin^{-1} \ t}}*\sqrt{1-x^2}}\)
\(\boxed{ \dfrac{a^{sin^{-1} \ t}}{\sqrt{a^{sin^{-1} \ t}}}=\dfrac{\sqrt{a^{sin^{-1} \ t}}*\sqrt{a^{sin^{-1} \ t}}}{\sqrt{a^{sin^{-1} \ t}}} = \sqrt{a^{sin^{-1} \ t}}}\)
\(\sf = \dfrac{a^{sin^{-1} \ t}*log \ a}{2\sqrt{1-x^2}}\)
\(\sf \dfrac{dy}{dt}=\dfrac{d(a^{cos^{-1} \ t})}{dt}\)
\(= \dfrac{1}{2\sqrt{a^{cos^{-1} \ t}}}*a^{cos^{-1} \ t}*log \ a *\dfrac{-1}{\sqrt{1-x^2}}}\\\\\\=\dfrac{(-1)*a^{cos^{-1} \ t}*log \ a}{2*\sqrt{a^{cos^{-1} \ t}}*\sqrt{1-x^2}}\)
\(\sf = \dfrac{(-1)*\sqrt{a^{Cos^{-1} \ t}}* log \ a }{2\sqrt{1-x^2}}\\\\\)
\(\sf \bf \dfrac{dy}{dx}=\dfrac{dy}{dt} \div \dfrac{dx}{dt}\\\)
\(\sf \bf = \dfrac{(-1)*\sqrt{a^{cos^{-1} \ t}}*log \ a}{2*\sqrt{1-x^2}} \ \div \dfrac{\sqrt{a^{sin^{-1} \ t}} *log \ a}{2*\sqrt{1-x^2}}\\\\\\=\dfrac{(-1)*\sqrt{a^{cos^{-1} \ t}}*log \ a}{2*\sqrt{1-x^2}} \ * \dfrac{2*\sqrt{1-x^2}}{\sqrt{a^{sin^{-1} \ t}} *log \ a}\\\\= \dfrac{(-1)* \sqrt{a^{cos^{-1} \ t}} }{\sqrt{a^{sin^{-1} \ t}}}\\\\= \dfrac{-y}{x}\)
\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)
Let's solve ~
\(\qquad \sf \dashrightarrow \: x = \sqrt{ {a}^{sin {}^{ - 1}t } } \)
here, let's differentiate it with respect to t ~
\(\sf \dashrightarrow \: \dfrac{dx}{dt} = \dfrac{1}{2 \sqrt{a {}^{sin {}^{ - 1}t } } } \times a {}^{sin {}^{ - 1}t } \sdot ln(a) \times \dfrac{1}{ \sqrt{1 - {x}^{2} } }\)
\(\sf \dashrightarrow \: \dfrac{dx}{dt} = \dfrac{ \sqrt{ {a}^{sin {}^{ - 1}t } } \sdot ln(a)}{2 \sqrt{1 - {x}^{2} } } \)
\(\sf \dashrightarrow \: \cfrac{dt}{dx} = \dfrac{2 \sqrt{1 - {x}^{2} } }{ \sqrt{a {}^{sin {}^{ - 1} t} \sdot ln(a)} }\)
Smililarly,
\(\sf \dashrightarrow \: \dfrac{dy}{dt} = \dfrac{1}{2 \sqrt{a {}^{cos{}^{ - 1}t } } } \times a {}^{cos {}^{ - 1}t } \sdot ln(a) \times \dfrac{ - 1}{ \sqrt{1 - {x}^{2} } }\)
\(\sf \dashrightarrow \: \dfrac{dy}{dt} = - \dfrac{ \sqrt{ {a}^{cos {}^{ - 1}t } } \sdot ln(a)}{2 \sqrt{1 - {x}^{2} } }\)
Now : Lets get Required result ~
\(\sf \dashrightarrow \: \dfrac{dy}{dx} = \dfrac{dy }{dt} \times \dfrac{dt}{dx} \)
\(\sf \dashrightarrow \cfrac{dy}{dx} = - \dfrac{\sqrt{ {a}^{cos {}^{ - 1}t } \sdot \cancel{ ln(a)}}}{ \cancel{2 \sqrt{1 - {x}^{2}}}} \sdot \dfrac{ \cancel{2 \sqrt{1 - {x}^{2}} } }{ \sqrt{a {}^{sin {}^{ - 1} t} }\sdot \cancel{ln(a)}}\)
\(\sf \dashrightarrow \cfrac{dy}{dx} = - \dfrac{\sqrt{ {a}^{cos {}^{ - 1}t } }}{ \sqrt{a {}^{sin {}^{ - 1} t} }}\)
\(\sf \dashrightarrow \cfrac{dy}{dx} = - \dfrac{y}{x} \)
[ since y = \(\sf{\sqrt{a^{cos^{-1}t}} } \) and x = \(\sf{\sqrt{a^{sin^{-1}t}} } \) ]
Related Questions
The ratio of a to b is 4/7. If a is 16, find the value of b.
Answers
Answer:
B=28
Step-by-step explanation:
A community garden offers two different square-shaped plots of growing space. The larger plot measures one square meter greater than the smaller one. The combined lengths of the two gardens is 3+2 radical 2 meters. What is the area of garden 1?
Answers
Answer:
3 + 2√(2)
Step-by-step explanation:
Since the larger plot is 1²m greater than the smaller one.
Let x denote the length of the smaller one, this implies that the larger would be x + 1.
Since the combined length is 3 + 2√(2) we have:
x + (x + 1) = 3 + 2√(2)
2x + 1 = 3 + 2√(2)
2x = 2 + 2√(2)
x = 1 + √(2)
This is the length of the smaller plot. It's area would therefore be:
x² = [1 + √(2)]² = 1 + 2√(2) + 2 = 3 + 2√(2)
HELP ONLY DO 3,1,2 ITS ONLY # PROBLEMS PLZZZZZZZZZZZZZZZZZZZZZZ
Answers
Answer:
3. 68.44
2.25 percent
1.86
Find the missing value to the nearest hundredth sin= 7/25
Answers
Answer:
16.26
Step-by-step explanation:
I am not completely sure what the problem is asking, but I believe that you are just supposed to take the inverse of sine. So, in your calculator, make sure it is in degrees mode, then usually you have to click the 2nd key and then sine. You use the inverse of sine when two sides are given, but you are not given the angle.
It should look like:
\(sin^{-1}(\frac{7}{25})\), which is approximately 16.26.
Hopefully this is right, if not, please let me know. Good luck.
Describe a data set where the mean would be the most appropriate measure of center. Describe a data set where the mean is not the most appropriate measure of center. What measure of center should be used and why
Answers
1. You should use the median to describe the measure of the center of a data set when an outlier is present in a data set.
Having an outlier will skew the mean of the data.
This means it will adjust the average to be smaller or greater than what the actual numbers are showing.
The median should be used as the measure of center in these circumstances.
2) Using a box plot, you can find the range and interquartile range.
What is the range?The range is the distance from the smallest number to the largest. The interquartile range is the distance from the first quartile to the third quartile.
All these values are found on a box plot.
3)The best measure of spread to describe symmetrical data sets is the mean absolute deviation.
This tells us how far on average the numbers are spread out from the mean.
4) See the answer given in 1 for the explanation. An example would be a student who scores 8, 9, 10, 9, 10, and 2 on 6 quizzes.
The mean would be an average of 8, which is not a good number to represent the score this student normally gets.
The median of 9 is a better number to show how this student normally performs.
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The data below are the ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly selected adults. What is the best predicted value for y given x = 64? Assume that the variables x and y have a significant correlation.
Age, x 38 41 45 48 51 53 57 61 65
Pressure, y 116 120 123 131 142 145 148 150 152
Answers
Using linear regression, the best predicted value for systolic blood pressure (y) given age (x) = 64 is approximately 151.63 mmHg.
To determine the best anticipated value for y given x = 64, we can use linear regression.
The correlation coefficient, r, is first calculated using the formula: r = [(xi - X)(yi - Y)] / [sqrt(xi - X)**sqrt(yi - Y)**sqrt(r)]
where X and Y are, respectively, the sample means of x and y.
Using the supplied data, we have:
X = (38+41+45+48+51+53+57+61+65)/9 = 51
Y = (116+120+123+141+142+145+148+150+152)/9 = 136 xi - X - yi - Y = 464 xi - X - yi - Y - xi - xi - xi - xi - xi - xi - xi - xi - xi - xi
The result is: r = 464 / [sqrt(1120) * sqrt(2804)]. ≈ 0.942
Given the strong correlation between the variables, we can apply linear regression to choose the line that best fits the data: y = a + bx, where a denotes the y-intercept and b the slope of the line. The formulas below can be used to determine the values of a and b.
Where Sx and Sy are the sample standard deviations of x and y, respectively, b = r * (Sy/Sx) a = Y - b*X.
Using the supplied data, we have:
sqrt[(xi - X)2/(n-1)] = Sx = sqrt(1120/8) ≈ 11.83
Sqrt[(yi - Y)2/(n-1)] = Sy = sqrt(2804/8) ≈ 9.38
We thus have:
A =Y - b*X - 69.19 b = r * (Sy/Sx)
Therefore, y = 69.19 + 1.28x is the line of best fit.
We add x = 64 to the equation to determine the best anticipated value for y given that x = 64:
y = 69.19 + 1.28(64) ≈ 151.63
As a result, 151.63 mmHg is the value for y that can be best predicted for x = 64.
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5k + 7 + 3k help me
Fast
Answers
Answer:
8k+7
Step-by-step explanation:
Like terms!
5k+3k=8k
( 1,-2), gradient = -3
Answers
Answer:
if you are required to find the equation of a straight line use the formula y-y1= m (x-x1)
y+2=-3(x-1)
y+2=-3x+3
y= -3x+3-2
y -3x+1
hope this helps
Answer:
y = -3x + 1
Step-by-step explanation:
(y -(-2)) = -3(x-1)
y+ 2 = -3x+ 3
y = -3x + 1
Thabang save money by putting coins in a money box. The money box has 600 coins that consist of 20 cents and 50 cents
So calculate how many 50 cents pieces are in the container if there are 220 pieces of 20 cents
Answers
The number of 50 cents in the container is 380 fifty cents
How to find the number of 50 cents in the container?Since Thabang save money by putting coins in a money box. The money box has 600 coins that consist of 20 cents and 50 cents
To calculate how many 50 cents pieces are in the container if there are 220 pieces of 20 cents, we proceed as follows.
Let
x = number of 20 cents and y = number of 50 centsSince the total number of cents in the container is 600, we have that
x + y = 600
So, making y subject of the formula, we have that
y = 600 - x
Since x = 220
y = 600 - 220
= 380
So, there are 380 fifty cents
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What is the area of a triangle with a base of 4 7/8 ft and a height of 8 ft? (ignore the clicked answer it was an accident lol)
Answers
Answer:
A = 19 \(\frac{1}{2} \) ft²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = \(\frac{1}{2} \) bh ( b is the base and h the height ) , then
A = \(\frac{1}{2} \) × 4 \(\frac{7}{8} \) × 8 ( change mixed number to improper fraction )
= \(\frac{1}{2} \) × \(\frac{39}{8} \) × 8 ( cancel 8 on numerator/ denominator )
= \(\frac{1}{2} \) × 39
= \(\frac{39}{2} \)
= 19 \(\frac{1}{2} \) ft²
Simplify the expression .
After simplifying the given expression, the exponent of x is(_)
and the exponent of y is(_)
Answers
Answer:
x^33 y^0 x is to the 33 y is to the 0
Step-by-step explanation:
Answer:
^33
y^0
Step-by-step explanation:
First simplify x^8y/x^-39
Which then gets you
x^47 y^-26'/x^14 y^-5 y^-21
Then you simplify x^47/x^14
Which gets you
x^33 y^26/y^-5 v^-21
Then simplify y^-26/y^-5
Which gets you afterwards
x^33/y^21 y^-21
Then you just simplify the numbers that are left x^33/y^21 y^-21
Then you get
X^33
(and since x^33 equals y^0 then)
Y^0
Hope this helped!
what is the center of the dilation
Answers
Answer:
C
Step-by-step explanation:
If you draw a straight line through all the corresponding vertices, where the three vertices meet up at is the center of dilation, they all meat up at point C so C is the center of dilation.
don’t get it. someone help. algebra 1!
Answers
Have a great day/night !
Answer:
+2
Step-by-step explanation:
and what is the correct expression? help please
Answers
Meg wants to send her grandmother 135 letters. she sends 9 letters each month for 3 months. what is a good estimate for how many more letters meg needs to send to reach her goal?
Answers
Meg still needs to send approximately 108 more letters to reach her goal of 135 letters. Meg has already sent 9 letters each month for 3 months.
Meg wants to send her grandmother 135 letters. she sends 9 letters each month for 3 months. To find a good estimate for how many more letters Meg needs to send to reach her goal of 135 letters, we subtract the letters sent so far from the total goal:
Meg has already sent 9 letters each month for 3 months which totals 9*3 = 27 letters sent so fa by her.
Number of letters Meg still needs to send = Total goal - Letters sent so far,
= 135 - 27
= 108 letters
Therefore, a good estimate for how many more letters Meg needs to send to reach her goal is approximately 108 letters.
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Select the correct answer from the drop-down menu.
Triangle ABC is shown with angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees.
In this triangle, the product of tan A and tan C is
.
Answers
In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.
The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.
We have to find the product of tan A and tan C.
In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.
So, we have, tan A = tan C
Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.
Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.
Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.
Answer: `(BC)^2/(AB)^2`.
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Please i need help i don't understand
Answers
Answer:
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign
Step-by-step explanation:
Triangle ABC is similar to Triangle PQR what is the value of X in centimeters
Answers
Answer:
x=19.5cm
Step-by-step explanation:
15÷10= 1.5
13x1.5
=19.5cm
Select all the expressions that equal 6 to the power of-10.
6−5⋅62
(16)5
(6−5)2
6−367
65⋅6−36−8
Answers
Answer:
I will say answer A but I don't know
Step-by-step explanation:
The mean time required to repair breakdowns of a certain copying machine is 93 minutes. The company which manufactures the machines claims that breakdowns of its newer model are easier to fix. To test this claim, a sample of 18 breakdowns of the new model were observed, resulting in a mean repair time of 86.8 minutes with a standard deviation of 14.6 minutes. Using a significance level of a = 0.10, determine if the new copy machines are faster to repair. State clearly what your null and alternative hypotheses are, show your work, and state your conclusion.
Answers
A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.
To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:
Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.
Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.
Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:
t = (sample mean - population mean) / (sample standard deviation / √(sample size))
Given:
Population mean (μ) = 93 minutes
Sample mean (\(\bar x\)) = 86.8 minutes
Sample standard deviation (s) = 14.6 minutes
Sample size (n) = 18
Significance level (α) = 0.10
Calculating the test statistic:
t = (86.8 - 93) / (14.6 / sqrt(18))
t = -6.2 / (14.6 / 4.24264)
t ≈ -2.677
The degrees of freedom for this test is n - 1 = 18 - 1 = 17.
Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.
Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.
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what is 40 x 90 in multiplacation
Answers
Answer:
3600
Step-by-step explanation:
We multiple 40 x 90 which is equal to 4 x 10 x 9 x 10.
4 x 9 = 36 and 10 x 10 = 100, so 40 x 90 = 36 x 100 = 3600.
Answer:
The answer is 3,600
Step-by-step explanation:
40x90=3,600
Look at picture for step by step!
Hope this helps!
By: BrainlyAnime
Brainliest would be appreciated!
I need help please
Answers
Answer:
Um, I don't think you took the pic correctly... there is only one option showing.
Step-by-step explanation:
All I can say is good luck andd the first one should NOT be checkmarked.
Hope u pass! gl :)
(-11x^2 + 1.4x - 3) + (4x^2 - 2.7x + 8)
Answers
\(\underline{\boxed{\sf{-7x^2 - \frac{13}{10} x +5}}}\)
Solution :-\(\sf{(-11x^2 + 1.4x - 3) + (4x^2 - 2.7x + 8)}\)
Remove the parentheses:
\(\sf{-11x^2 + 1.4x - 3 + 4x^2 - 2.7x + 8}\)
Convert decimal to fraction:
\(\sf{-11x^2 + \frac{14}{10} x - 3 + 4x^2 - \frac{27}{10} x + 8}\)
Reduce fraction to the lowest term by canceling the greatest common factor:
\(\sf{-11x^2 + \frac{7}{5} x - 3 + 4x^2 - \frac{27}{10}x + 8}\)
Combine like terms:
\(\sf{-7x^2 - \frac{13}{10} x +5}\)
2 students given a english test. The probability of student A passing the test is 0.95 while the probability of student B is 0.8 :
a) probability of both pass the exam
b) exactly one student pass the exam
c) at least one student pass the exam
Answers
a) The probability of both students passing the exam is the product of their individual probabilities of passing the exam:
P(A passes and B passes) = P(A passes) × P(B passes) = 0.95 × 0.8 = 0.76
b) The probability of exactly one student passing the exam can be calculated as the sum of the probabilities of A passing and B failing, and the probability of A failing and B passing:
P(A passes and B fails) + P(A fails and B passes) = (0.95 × 0.2) + (0.05 × 0.8) = 0.19
c) The probability of at least one student passing the exam is the complement of the probability that both students fail the exam:
P(at least one student passes) = 1 - P(A fails and B fails) = 1 - (0.05 × 0.2) = 0.99
Therefore, the probability of at least one student passing the exam is 0.99.
Pls. Help find these answers?!
Answers
Answer:
12
Step-by-step explanation:
Answer:
1) 12 boxes
2) 3, 6, 12
3) 12
4) 110 degrees
Step-by-step explanation:
1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.
Length: 4 boxes
Width: 3 boxes
4 x 3 = 12
12 boxes
2)
10% of 30 is 0.1 times 30.
0.1 x 30 = 30/10 = 3
20% of 30 is 0.2 times 20.
0.2 x 30 = 30/5 = 6
40% of 30 is 0.4 times 20.
0.4 x 30 = 30/2.5 = 12
3) Count the cubes. Reminder there are 2 boxes you cannot see.
Top Layer: 2
Middle Layer: 4
Back Bottom Layer: 4
Front Bottom Layer: 2
2 + 4 + 4 + 2 = 12
4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.
180/18 (The angle of each section)
10
11 Sections
10 x 11 = 110
Use the drawing tool(s) to form the correct answer on the provided number line. Will brought a 144-ounce cooler filled with water to soccer practice. He used 16 ounces from the cooler to fill his water bottle. He then took out 16 plastic cups for his teammates and put the same amount of water in each cup. Find and graph the number of ounces of water, x, that Will could have put in each cup.
Answers
According to the information, we can infer that the number of ounces of water, x, that Will could have put in each cup is 8 ounces.
What is the number of ounces of water "x" that Will could have put in each cup?Will initially had a cooler filled with 144 ounces of water. After using 16 ounces to fill his water bottle, there were 144 - 16 = 128 ounces of water remaining in the cooler.
Will then took out 16 plastic cups for his teammates. Since the same amount of water was put in each cup, the remaining amount of water, 128 ounces, needs to be divided equally among the cups.
Dividing 128 ounces by 16 cups gives us 8 ounces of water for each cup.
So, Will could have put 8 ounces of water in each cup.
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Your family drives to 3 locations on a trip. The distance between the locations is 47.8, 72, and 65.9 miles. What is the total number of miles driven?
Answers
Answer: 185.7 miles
Step-by-step explanation:
To find the total distance, add the smaller distances together.
47.8 + 72 + 65.9 = 185.7
the number of gears a machine can make varies directly as the time it operates. if it can make 3058 gears in 3 hours, how many gears can it make in 9 hours?
Answers
The machine can make approximately 9140.67 gears in 9 hours, as if it can make 3058 gears in 3 hours
The number of gears a machine can make varies directly with the time it operates.
In this scenario, we know that the machine can make 3058 gears in 3 hours. To find out how many gears it can make in 9 hours, we can set up a proportion.
Let's denote the number of gears the machine can make in 3 hours as "x" and the number of gears it can make in 9 hours as "y".
The proportion can be written as:
x/3 = y/9
To solve for y, we can cross-multiply:
3 * y = 9 * x
Now we can substitute the given value of x (3058) into the equation:
3 * y = 9 * 3058
Simplifying the equation:
3 * y = 9 * 3058
3 * y = 27422
To solve for y, we divide both sides of the equation by 3:
y = 27422 / 3
Using long division, we find that:
y ≈ 9140.67
Therefore, the machine can make approximately 9140.67 gears in 9 hours.
It's important to note that the number of gears produced by a machine may not always be a whole number, especially when dealing with proportions.
In this case, the value is rounded to two decimal places for simplicity.
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OFFERING 88 POINTS AND BRAINLIEST TO THE FIRST ANSWER PLEASE HELP ME FAST
Answers
Answer
\(168in^{2}\)
Step-by-step explanation:
SA=2(wl+hl+hw)
2·(6·2+9·2+9·6)
=168
Candace surveyed every 10th student that walked onto campus. She asked them if they were planning to read any books over the summer. She ended up surveying 50 people. 15 of them said yes. If there are 1000 students at her school, predict about how many will be reading over the summer.
Answers
Answer:
not whoever wrote this question. every 10th person is surveyed. she surveyed 50 people. that mean 500 people and 50 surveyed people. then at the end the teacher said there is 1000 students. your teacher wrote you a bad question with no right answers.