Answer:
Max area is 16
Step-by-step explanation:
If A² + B² = C², then A² + B² = 64. The largest triangle area is when both A² and B² are equal to 32, so 32 + 32 = 64.
So equal side of the triangle is √32 or about 5.6568. The area of the triangle is then 1/2(5.6568 × 5.6568) or 16.
The maximal area of a right triangle is 90.496
What is differentiation?Derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
Given:
let the perpendicular be 'x'
and base be 'y'
Using Pythagoras theorem
x² + y² = 8²
x² + y² = 64
y²= 64- x²
y = √64-x²
Now, Area of triangle
= 1/2* base* height
=xy/2
=x *√64-x²*1/2
On differentiating both side
A' = 64-2x²/√64-x²*1/2
Setting derivative function equal to zero,
64= 2x²
32=x²
x=5.656
So, Area of triangle = x *√64-x²*1/2
= 90.496
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Line AB and Line CD are parallel lines. Which translation of the plane can we use to prove angles x and y are congruent, and why?
Answer:
Option C.
Step-by-step explanation:
In the given figure we have two parallel lines AB and CD.
A transversal line FB intersect the parallel lines at point B and C.
We know that the if a transversal line intersect two parallel lines, then corresponding angles are congruent.
[tex]\angle ABC=\anle ECF[/tex]
[tex]x=y[/tex]
To prove this by translation, we need a translation along the directed line segment CB maps ine CD onto line AB and angle y onto angle x.
Therefore, the correct option is C.
A data set is summarized in the frequency table below. Using the table, determine the number of values less than or equal to 6.
Answer:
18
Step-by-step explanation:
Given the above table of the data set, the number of values less than or equal to 6 would be the sum of the frequencies of all values that is equal to or less than 6.
From the table above, we would add up the frequencies of the values of 6 and below, which is:
2 + 3 + 6 + 4 + 3 = 18
Answer = 18
The number of values less than or equal to 6 is 18
Calculation of the number of values:Here the number of values should be less than or equivalent to 6 represent the sum of the frequencies i.e. equal or less than 6
So, here the number of values should be
= 2 + 3 + 6 + 4 + 3
= 18
Hence, we can conclude that The number of values less than or equal to 6 is 18
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Find the value of y.
[tex]y^2 = 9(9+3)\\\\y^2 = 9(12)\\\\y^2 =3^2\cdot3\cdot2^2\\\\y = 6\sqrt{2}[/tex]
One grade of tea costing $3.20 per pound is mixed with another grade costing $2.00 per pound to make 20
pounds of a blend that will sell for $2.72 per pound. How much of the $3.20 grade is needed? Formulate an
equation and then solve it to find how much of the $3.20 grade is needed.
Answer:
X+y = 20... equation 1
3.2x + 2y = 54.4...equation 2
X= 12
12 of $3.2 grade is needed
Step-by-step explanation:
Let x = grade containing$ 3.2 per pound
Let y = grade containing $2.00 per pound
X+y = 20... equation 1
X3.2 +2y = 20(2.72)
3.2x + 2y = 54.4...equation 2
Multiplying equation 1 by 2
2x +2y = 40
3.2x + 2y = 54.4
1.2x = 14.4
X= 12
If x= 12
2x +2y = 40
2(12) + 2y = 40
2y = 40-24
2y = 16
Y= 8
Rewrite the equation in =+AxByC form. Use integers for A, B, and C. =−y6−6+x4
Answer:
6x + y = -18
Step-by-step explanation:
The given equation is,
y - 6 = -6(x + 4)
We have to rewrite this equation in the form of Ax + By = C
Where A, B and C are the integers.
By solving the given equation,
y - 6 = -6x - 24 [Distributive property]
y - 6 + 6 = -6x - 24 + 6 [By adding 6 on both the sides of the equation]
y = -6x - 18
y + 6x = -6x + 6x - 18
6x + y = -18
Here A = 6, B = 1 and C = -18.
Therefore, 6x + y = -18 will be the equation.
Given that 243√3 =3^a, find the value of a
Answer:
a=11/5 OR 5.5
Step-by-step explanation:
The function ƒ(x) = 2x is vertically translated 5 units down and then reflected across the y-axis. What's the new function of g(x)?
Answer:
g(x) = -2x - 5
2x becomes -2x as a reflection across the y-axis
add on -5 to shift the function 5 units down
Suppose that f(x,y) is a smooth function and that its partial derivatives have the values, fx(8,5)=2 and fy(8,5)=2. Given that f(8,5)=−2, use this information to estimate the value of f(9,6).
Answer:
f(9,6) = 2
Step-by-step explanation:
We know df = (df/dx)dx + (df/dy)dy
From the question, df/dx = fx(8,5) = 2 and df/dy = fy(8,5) = 2
Since we need to find f(9,6) and f(8,5) = -2
dx = 9 - 8 = 1 and dy = 6 - 5 = 1
f(9,6) = f(8,5) + df
df = (df/dx)dx + (df/dy)dy
df = fx(8,5)dx + fy(8,5)dy
Substituting the values of fx(8,5) = 2, fy(8,5) = 2, dx = 1 and dy = 1
df = 2 × 1 + 2 × 1
df = 2 + 2
df = 4
f(9,6) = f(8,5) + df
substituting the value of df and f(8,5) into the equation, we have
f(9,6) = -2 + 4
f(9,4) = 2
The value of f(9,6) = 2
At the city museum, child admission is $ 5.30 and adult admission is $ 9.40 . On Sunday, three times as many adult tickets as child tickets were sold, for a total sales of $ 1206.00 . How many child tickets were sold that day?
Answer:
36 tickets
Step-by-step explanation:
At a city museum, child tickets are sold for $5.30, and adult tickets are sold for $9.40
The total sales that were made are $1206
Let x represent the number of child tickets that were sold
Let y represent the number of adult tickets that was sold
5.30x +9.40y= 1206
The number of adult tickets sold was three times greater than the child tickets
y= 3x
Substitute 3x for y in the equation
5.30x + 9.40y= 1206
5.30x + 9.40(3x)= 1206
5.30x + 28.2x= 1206
33.5x= 1206
Divide both sides by the coefficient of x which is 33.5
33.5x/33.5= 1206/33.5
x = 36
Hence the number of child tickets that were sold that day is 36 tickets
Is 6/16 greater or less than 4/10
Answer:
Less than 4/10
Step-by-step explanation:
First lets convert both fractions to a common denominator:
16 and 10 can both go into 80 equally.
Now lets convert the fractions so they have a denominator of 80:
(6/16) *5 = 30/80
(4/10) *8 = 32/80
we can multiply the fractions to get just the numerator (*80)
Now compare 30 to 32. As you can see 32 is greater meaning that 6/16 is less that 4/10.
In the given figure, find AB, given thatAC = 14 andBC = 9.
Answer:
Given:
AC = 14 and BC = 9
AB = ?
Solution:
From the fig:
AC = AB + BC
Putting the values
14 = AB + 9
AB = 14 - 9
AB = 5
(you can also take AB = x or any other variable)
Step-by-step explanation:
Which two points are on the graph of y=-x+ 3?
(-1,-2), (1,4)
(1, 2), (0, -3)
(0, 3), (4, -1)
(4, -1), (1, 3)
Answer:
(0, 3), (4, -1)
(1, 2)
Step-by-step explanation:
If the answers that have been provided to you are only in pairs then it'd just be the first answer I wrote. The points (1, 2) also are on the graph of y=x+3 but if the answers aren't individual than I'd just stick with the (0, 3), (4, -1). Does that make sense? I used a graphing calculator online called Desmos, it's very good. I highly recommend it for problems like these.
I hope this helps:) Select as brainliest because I actually put work into this and tried.
Find the least common multiple of $6!$ and $(4!)^2.$
Answer:
The least common multiple of $6!$ and $(4!)^2.$
is 6×4! or 144
6. Look at the figure below.
Are triangles ABC and DEC congruent?
Explain why or why not.
Answer:
Yes
Step-by-step explanation:
They are congruent by the AAS postulate.
∠A corresponds to and is congruent to ∠D
Side BC corresponds to and is congruent to side EC
∠C is congruent to ∠C by the Vertical Angles Theorem.
So, ΔABC ≅ ΔDEC
Explain the connection between the chain rule for differentiation and the method of u-substitution for integration.
Answer:
Chain rule: [tex]\frac{d}{dx} [f[u(x)]] = \frac{df}{du} \cdot \frac{du}{dx}[/tex], u-Substitution: [tex]f\left[u(x)\right] = \int {\frac{df }{du} } \, du[/tex]
Step-by-step explanation:
Differentiation and integration are reciprocal to each other. The chain rule indicate that a composite function must be differentiated, describing an inductive approach, whereas u-substitution allows integration by simplifying the expression in a deductive manner. That is:
[tex]\frac{d}{dx} [f[u(x)]] = \frac{df}{du} \cdot \frac{du}{dx}[/tex]
Let integrate both sides in terms of x:
[tex]f[u(x)] = \int {\frac{df}{du} \frac{du}{dx} } \, dx[/tex]
[tex]f\left[u(x)\right] = \int {\frac{df }{du} } \, du[/tex]
This result indicates that f must be rewritten in terms of u and after that first derivative needs to be found before integration.
What is the product of the polynomials below? (4x^2-2x-4)(2x+4)
Answer: 8x³ + 12x² - 16x - 16
Step-by-step explanation:
(4x² - 2x - 4)(2x + 4)
= (2x + 4)(4x² - 2x - 4)
= 2x(4x² - 2x - 4) + 4(4x² - 2x - 4)
= 8x³ - 4x² - 8x + 16x² - 8x - 16
= 8x³ + (-4x² + 16x²) + (-8x - 8x) - 16
= 8x³ + 12x² - 16x - 16
A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 8% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 4% during the current year. In addition, it estimates that 15% of employees who had lost-time accidents last year will experience a lost-time accident during the current year.
a. What percentage of the employees will experience lost-time accidents in both years?
b. What percentage of the employees will suffer at least one lost-time accident over the two-year period?
Answer:
a) percentage of the employees that will experience lost-time accidents in both years = 1.2%
b) percentage of the employees that will suffer at least one lost-time accident over the two-year period = 10.8%
Step-by-step explanation:
given
percentage of lost time accident last year
P(L) = 8% = 0.08 of the employees
percentage of lost time accident current year
P(C) = 4% = 0.04 of the employees
P(C/L) = 15% = 0.15
using the probability
P(L ∩ C) = P(C/L) × P(L)
= 0.08 × 0.15 = 0.012 = 1.2%
percentage of the employees will experience lost-time accidents in both years = 1.2%
b) Using the probability of the event
P(L ∪ C) = P(L) + P(C) - P(L ∩ C)
= 0.08 + 0.04 -0.012 = 0.108 = 10.8%
percentage of the employees will suffer at least one lost-time accident over the two-year period = 10.8%
Suppose that Vera wants to test the hypothesis that women make less money than men doing the same job. According to the Bureau of Labor Statistics (BLS), the median weekly earnings for men in the professional and related occupation sector in 2015 was $1343. Vera collected median weekly earnings data for women in 2015 from a random subset of 18 positions in the professional and related occupation sector. The following is the sample data. $1811, $728, $1234, $966, $953, $1031, $990, $633, $796, $1325, $1448, $1125, $1144, $1082, $1145, $1256, $1415, $1170 Vera assumes that the women's median weekly earnings data is normally distributed, so she decides to perform a t-test at a significance level of α = 0.05 to test the null hypothesis, H0:µ=1343H0:μ=1343 against the alternative hypothesis, H1:µ<1343H1:μ<1343 , where µμ is the population mean. If the requirements for performing a t-test have not been met, only answer the final question. Otherwise, answer all five of the following questions. First, compute the mean, x⎯⎯⎯x¯ , of Vera's sample. Report your answer with two decimals of precision.
Answer:
There is sufficient evidence to conclude that women make less money than men doing the same job.
Step-by-step explanation:
The hypothesis for the test can be explained as follows:
H₀: Women does not make less money than men doing the same job, i.e. [tex]\mu\geq \$1343[/tex].
Hₐ: Women make less money than men doing the same job, i.e. [tex]\mu<\$1343[/tex].
From the provided data compute the sample mean and standard deviation:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{18}[1811+728+...+1170]=1125.11\\\\s=\sqrt{\frac{1}{n-1}\sum (X-\bar x)^{2}}=\sqrt{\frac{1}{18-1}\times 1322541.86}=278.92[/tex]
Compute the test statistic as follows:
[tex]t=\frac{\bar x-\mu}[\s/\sqrt{n}}=\frac{1125.11-1343}{278.92/\sqrt{18}}=-3.143[/tex]
The test statistic value is -3.143.
Compute the p-value as follows:
[tex]p-value=P(t_{n-1}<-3.143)=P(t_{17}<-3.143)=0.003[/tex]
*Use a t-table.
The p-value of the test is 0.003.
The p-value of the test is very small for all the commonly used significance level. The null hypothesis will be rejected.
Conclusion:
There is sufficient evidence to conclude that women make less money than men doing the same job.
Simplify the expression.
16 • 4^-4
A. 256
B. -256
C. 1/16
D. -4,096
Answer:
C. 1/16
Step-by-step explanation:
[tex]16 * 4^{-4}[/tex]
16 can be written as a power of 4.
[tex]4^2 * 4^{-4}[/tex]
The bases are same, add exponents.
[tex]4^{2+-4}[/tex]
[tex]4^{-2}[/tex]
Simplify negative exponent.
[tex]\frac{1}{4^2 }[/tex]
[tex]\frac{1}{16}[/tex]
The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the distribution's standard deviation
Answer:
15
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
30 hcchxfifififififfud7dd7d
The circle graph shows the percentage of numbered tiles in a box. If each numbered tile is equally likely to be pulled from the box, what is the probability of pulling out a tile with a 6 on it? (Hint: Remember that percents are based out of 100% and probability is represented as a fraction of 100%)
Answer: [tex]\dfrac{1}{5}[/tex]
Step-by-step explanation:
From, the circle graph in the attachment below,
The percentage of portion taken by 6 (dark blue) = 20%
So, the probability of pulling out a tile with a 6 on it = percentage of portion taken by 6 (dark blue) = 20% [Probability can also be written as a percentage]
[tex]=\dfrac{20}{100}\\\\=\dfrac{1}{5}[/tex] [we divide a percentage by 100 to convert it into fraction]
Hence, the probability of pulling out a tile with a 6 on it = [tex]\dfrac{1}{5}[/tex]
Write the equation of the line in slope intercept form that is perpendicular to the line y=-(3/2)x +7. Show your work
Answer:
the answer is y= 2/3x - 5
evaluate the expression 2(5 -(1/2m)) - 7 where m =4
Answer:
-1
Step-by-step explanation:
since m=4
we substitute in eqn which is 2(5-(1/2m))
2(5-(1/2(4)))
2(5-2)-7
=-1
What is the complete factorization of 36y2 − 1?
Answer:
36y² - 1
Factorize
We have the final answer as
[tex](y - \frac{1}{6} )(36y + 6)[/tex]
Hope this helps you
Reflection Over Parallel Lines Please complete the attached reflection. Thanks!
Answer: A(3, -5)
B(6, -2)
C(9, -2)
Step-by-step explanation:
If we have a point (x, y), and we do a reflection over the axis y = a, then the only thing that will change in our point is the value of x.
Now, the distance between x and a must remain constant before and after the reflection.
so if x - a = d
then the new position of the point will be:
(a - d, y) = (2a - x, y).
I will use that relationship for the 3 points
A)
We start with the point (1, -5)
The reflection over y = -1 leaves.
The distance between 1 and -1 is = 1 - (-1) = 2.
Then the new point is (-1 - 2, -5) = (-3, -5)
Now we do a reflection over y = 1, so D = -3 - 1 = -2
Then the new point is:
A = (1 -(-2), -5) = (3, -5)
B) (2, -2)
Reflection over y = -1.
distance, d = 2 - (-1) = 3
the point is (-1 - 3, -2) = (-4, -2)
Now, a reflection over y = 1.
The distance is D = -4 - 1 = -5
The new point is (1 - (-5), 2) = (6, -2)
C) (5, -2)
reflection over y = -1
Distance: D = 5 - ( - 1) = 6
New point: (-1 - 6, -2) = (-7, -2)
Reflection over y = 1.
Distance D = -7 - 1 = -8
New point ( 1 - (-8), -2) = (9, -2)
The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds. What is the probability of a weight between 415 pounds and the mean of 400 pounds
Answer:
The probability is [tex]P(x_1 \le X \le x_2 ) = 0.4332[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 400[/tex]
The standard deviation is [tex]\sigma = 10[/tex]
The considered values are [tex]x_1 = 400 \to x_2 = 415[/tex]
Given that the weight follows a normal distribution
i.e [tex]\approx X (\mu , \sigma )[/tex]
Now the probability of a weight between 415 pounds and the mean of 400 pounds is mathematically as
[tex]P(x_1 \le X \le x_2 ) = P(\frac{x_1 - \mu }{\sigma } \le \frac{X - \mu }{\sigma } \le \frac{x_2 - \mu }{\sigma } )[/tex]
So [tex]\frac{X - \mu }{\sigma }[/tex] is equal to Z (the standardized value of X )
Hence we have
[tex]P(x_1 \le X \le x_2 ) = P(\frac{x_1 - \mu }{\sigma } \le Z \le \frac{x_2 - \mu }{\sigma } )[/tex]
substituting values
[tex]P(x_1 \le X \le x_2 ) = P(\frac{400 - 400 }{10 } \le Z \le \frac{415 - 400}{415 } )[/tex]
[tex]P(x_1 \le X \le x_2 ) = P(0\le Z \le 1.5 )[/tex]
[tex]P(x_1 \le X \le x_2 ) = P( Z < 1.5) - P( Z < 0)[/tex]
From the standardized normal distribution table [tex]P( Z< 1.5) = 0.9332[/tex] and
[tex]P( Z < 0) = 0.5[/tex]
So
[tex]P(x_1 \le X \le x_2 ) = 0.9332 - 0.5[/tex]
[tex]P(x_1 \le X \le x_2 ) = 0.4332[/tex]
NOTE : This above values obtained from the standardized normal distribution table can also be obtained using the P(Z) calculator at (calculator dot net).
Evaluate the expression
Answer: C) tan(pi/56)
=============================================
Explanation:
I recommend using a trig identity reference sheet. The specific identity we will be using is [tex]\frac{\tan(A)-\tan(B)}{1+\tan(A)\tan(B)} = \tan(A-B)[/tex]
What we are given is in the form [tex]\frac{\tan(A)-\tan(B)}{1+\tan(A)\tan(B)}[/tex] with A = pi/7 and B = pi/8
A-B = (pi/7)-(pi/8)
A-B = pi(1/7-1/8)
A-B = pi(8/56 - 7/56)
A-B = pi*(1/56)
A-B = pi/56
Therefore,
[tex]\frac{\tan\left(\pi/7\right)-\tan(\pi/8)}{1+\tan(\pi/7)\tan(\pi/8)} = \tan\left(\pi/56\right)[/tex]
If Sara drives 60 miles per hour, it takes her 2 hours to reach her parents' house. Write an equation describing the relationship between Sara's speed and the time it takes her to get to her parents' house. (Note that speed and time are inversely proportional).
Question 17 options:
A)
s = 120∕t
B)
s = 60∕t
C)
s = 24∕t
D)
s = 30∕t
Answer: (A) .
because if you travel 60 miles per hour and i takes 2 hours yto get there you have to double 60 miles so 120 miles per 2 hours
The relationship between Sara's speed and the time it takes her to get to her parent's house will be s = 120/t so option (A) will be correct.
What are work and time?Work is the completion of any task for example if you have done your homework in 5 hours then you have done 5 hours.
Another illustration of labor is when you finish your meal in an hour, which means that you finished your work in an hour. In essence, work is the length of time it took you to complete any task.
Given that Sara drives 60 miles in 2 hours.
Distance covered by sara is = 60(2) = 120 miles.
We know that
speed = distance/time
Let's say speed is S time is t then
⇒ S = 120/t so the correct equation of the given question will be this.
For more information about the work and time relation
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An insect population in a lab has 2 ¹² insect. If the population double how many insect will be there?
Answer:
8192
Step-by-step explanation:
2 ¹²= 4096
4096 x 2 = 8192
f(x)=x^2+12x+7 f(x)=(x+_)^2+_ Rewrite the function by completing the square
Answer:
f(x) = (x + 6)² - 29
Step-by-step explanation:
Given
f(x) = x² + 12x + 7
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² + 12x
x² + 2(6)x + 36 - 36 + 7
= (x + 6)² - 29, thus
f(x) = (x + 6)² - 29
answers are 6, and -29