Answer:
-16r^2 - 10r
Step-by-step explanation:
To simplify the expression -2r(8r+5), you can use the distributive property of multiplication over addition.
-2r(8r+5) = -2r * 8r - 2r * 5
First, let's simplify -2r * 8r:
-2r * 8r = -16r^2
Next, let's simplify -2r * 5:
-2r * 5 = -10r
Putting it all together, the simplified expression is:
-2r(8r+5) = -16r^2 - 10r
Please help me with this one thanks
The wrapping paper that she need, not including any overlap is B. B 340 in²
How to calculate the valueTo find the area of wrapping paper needed, we need to find the total surface area of the box.
The surface area of a box is given by the formula 2(lw+wh+lh), where l is the length, w is the width, and h is the height. In this case, l=15 in, w=10 in, and h=2 in.
Substituting these values into the formula, we get 2(15×10+10×2+15×2)=340 in².
Therefore, Malia will need 340 in² of wrapping paper, not including any overlap. The answer is B.
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The American Automobile Association (AAA) reported that families planning to travel over the Labor Day weekend would spend an average of $749 (The Associated Press, August 12, 2012). Assume that the amount spent is normally distributed with a standard deviation of $225.
a. What is the probability that family expenses for the weekend will be less than $400?
b. What is the probability that family expenses for the weekend will be $800 or more?
c. What is the probability that family expenses for the weekend will be between $500 and $1000?
d. What are the Labor Day weekend expenses for 5% of the families with the most expensive travel plans?
a. The probability will be less than $400 is approximately 4.78%. b. The probability will be $800 or more is approximately 34.13%. c. The probability will be between $500 and $1000 is approximately 68.27%. d. The most expensive travel plans are approximately $1,170 or more.
a. To find the probability that family expenses for the weekend will be less than $400, we need to standardize the value using the formula z = (x - μ) / σ, where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation. In this case, x = $400, μ = $749, and σ = $225. So, z = (400 - 749) / 225 = -1.56. Using a standard normal distribution table or calculator, we can find that the probability of a standard normal variable being less than -1.56 is approximately 0.0594. Therefore, the probability that family expenses for the weekend will be less than $400 is about 0.0594 or 5.94%.
b. To find the probability that family expenses for the weekend will be $800 or more, we again need to standardize the value. In this case, x = $800, μ = $749, and σ = $225. So, z = (800 - 749) / 225 = 0.227. Using a standard normal distribution table or calculator, we can find that the probability of a standard normal variable being greater than 0.227 is approximately 0.409. Therefore, the probability that family expenses for the weekend will be $800 or more is about 0.409 or 40.9%.
c. To find the probability that family expenses for the weekend will be between $500 and $1000, we need to standardize both values and then find the area between them. For $500, z = (500 - 749) / 225 = -1.11, and for $1000, z = (1000 - 749) / 225 = 1.11. Using a standard normal distribution table or calculator, we can find that the probability of a standard normal variable being less than -1.11 is approximately 0.1335 and the probability of a standard normal variable being less than 1.11 is approximately 0.8664. Therefore, the probability that family expenses for the weekend will be between $500 and $1000 is about 0.8664 - 0.1335 = 0.7329 or 73.29%.
d. To find the Labor Day weekend expenses for 5% of the families with the most expensive travel plans, we need to find the z-score corresponding to the 95th percentile of the normal distribution. This can be done using a standard normal distribution table or calculator, and we find that the z-score is approximately 1.645. Then, we can use the formula x = μ + zσ, where x is the value we want to find, μ is the mean, σ is the standard deviation, and z is the z-score we just found. Plugging in the values, we get x = 749 + 1.645(225) = $1,100.13. Therefore, the Labor Day weekend expenses for 5% of the families with the most expensive travel plans is about $1,100.13 or higher.
According to the American Automobile Association (AAA), families planning to travel over the Labor Day weekend are expected to spend an average of $749, with a standard deviation of $225. Assuming the amount spent is normally distributed:
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Mr. Vern is lining his rectangular pool on all sides and the bottom He wants to know how many square feet he will be covering. The deep, 30 feet wide and 40 feet long. What equation should Mr. V determine the total area in square feet being covered?, Mr. Vern is lining his rectangular pool on all sides and the bottom with pool liner. He wants to know how many square feet he will be covering. The pool is 5 feet deep, 30 feet wide and 40 feet long. What equation should Mr. Vern use to determine the total area in square feet being covered?
The linear equation be 2lw + 2lh + 2wh + lb and total area is 2200 square feet.
Assume that,
l is the length of the pool (40 feet),
w is the width of the pool (30 feet),
h is the height of the pool (5 feet),
And b is the depth of the pool (also 5 feet).
To determine the total area of the pool liner needed to line the rectangular pool on all sides and the bottom, Mr. Vern can use the following equation:
Total area = 2lw + 2lh + 2wh + lb,
Plugging in the values, we get:
Total area = 2(40)(5) + 2(30)(5) + 2(30)(5) + (40)(30) Total area = 400 + 300 + 300 + 1200 Total area = 2200
Therefore, Mr. Vern would need to cover a total area of 2200 square feet with pool liner to line his rectangular pool on all sides and the bottom.
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find the length of the diagonal of a square whose side is 4CM
the diagonal is 4cm
so, we know that a square has equal length on all sides. the way to find the diagnol of a square that its sides are 4cm you have to multiple the base and the height of the triangle that is created.
the type for that is : (a×b)÷2 so it will be (4×4)÷2=4
hope that helps!
The next model of a sports car will cost 12. 4% more than the current model. The current model costs 49,000. How much will the price increase in dollars? What will be the price of the next model?
1. Increase in price:
2. Price of next model:
Answer:
1. $6,076
2. $55076
Step-by-step explanation:
price increase: 49,000x12.4%
12.4%=0.124
49,000x0.124=6,076
price of next model:49000x0.124=6076
6076+49000=55076
A square of area 36 cm² is cut to make two rectangles, A and B.
Area = 36 cm²
The ratio of area A to area B is 2:1
Work out the dimensions of rectangles A and B.
Rectangle A
Length:
Width:
Rectangle B
Length:
Width:
Terms and Definitions
what is the key word ?
Acceleration - a change in velocity over time and how fast that change happened
the difference between the final velocity and the initial velocity
Acceleration rate of change of velocity can be written as
a = (v₁ - v₀)/t.
The given keyword is,
Acceleration
Since we know that,
Acceleration has both a magnitude and a direction, it is a vector quantity. Additionally, it is the first derivative of velocity with respect to time or the second derivative of position with respect to time.
Now let,
a = is the acceleration
v₁ is the final velocity
v₀ is the initial velocity
t is the time interval
Δv is the small change in the velocity
Therefore,
The acceleration = ( final velocity - initial velocity)/time
Thus,
The acceleration be,
⇒ a = (v₁ - v₀)/t
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express tan(t) in terms of sin(t), if the terminal point determined by t is in quadrant i.
if the terminal point determined by t is in quadrant I, then tan(t) = sin(t)/sqrt(1 - sin^2(t)).
If the terminal point determined by t is in quadrant I, then both sine and tangent are positive. We can use the identity:
tan(t) = sin(t)/cos(t)
to express tangent in terms of sine. Since the terminal point is in quadrant I, cosine is positive, so we can use the Pythagorean identity:
sin^2(t) + cos^2(t) = 1
to solve for cosine:
cos(t) = sqrt(1 - sin^2(t))
Substituting this expression for cosine in the formula for tangent, we get:
tan(t) = sin(t)/cos(t) = sin(t)/sqrt(1 - sin^2(t))
what is quadrant?
A quadrant is one of the four regions that a coordinate plane is divided into by the x-axis and the y-axis. The x-axis is a horizontal line that runs left and right through the plane, and the y-axis is a vertical line that runs up and down through the plane. The point where the x-axis and the y-axis intersect is called the origin.
Each quadrant is labeled with a Roman numeral (I, II, III, or IV) to distinguish it from the others. Quadrant I is the region in the upper-right corner of the plane, where both the x and y coordinates are positive. Quadrant II is the region in the upper-left corner of the plane, where the x-coordinate is negative and the y-coordinate is positive.
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find the values of X and Y using the given chord secant and tangent lengths
Check the picture below.
[tex]x^2=(5+25)(5)\implies x^2=150\implies x=\sqrt{150}\implies x=5\sqrt{6} \\\\[-0.35em] ~\dotfill\\\\ x^2=(10+y)(10)\implies (\sqrt{150})^2=100+10y\implies 150=100+10y \\\\\\ 50=10y\implies \cfrac{50}{10}=y\implies 5=y[/tex]
Find the measures of angles
∠1 and ∠8 given that
m∠2 = 5x − 22 and m∠6 = 4x − 6, and r ∥ s cut by a
transversal t
Unfortunately, the diagram or additional information is needed to determine the measures of angles ∠1 and ∠8. The given information about angles ∠2 and ∠6 and the fact that r ∥ s cut by a transversal t do not provide enough information to solve for the measures of angles ∠1 and ∠8.
To find the measures of angles ∠1 and ∠8, we need additional information about the angles or the lines r, s, and t in the diagram. It's possible that the diagram was not provided or the question is incomplete. Without more information, it's not possible to provide a complete answer to this question.
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Unfortunately, the diagram or additional information is needed to determine the measures of angles ∠1 and ∠8. The given information about angles ∠2 and ∠6 and the fact that r ∥ s cut by a transversal t do not provide enough information to solve for the measures of angles ∠1 and ∠8.
To find the measures of angles ∠1 and ∠8, we need additional information about the angles or the lines r, s, and t in the diagram. It's possible that the diagram was not provided or the question is incomplete. Without more information, it's not possible to provide a complete answer to this question.
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What is the derivative of x^2 + 2x + 3?
Answer:
2x+2
Step-by-step explanation:
Answer:
2x + 2
Step-by-step explanation:
Differentiate using the Power Rule,
d/dx [x^n] = nx^n−1
can you hellp me if you can hellp me
Answer:
Solution,
Given,
radius of the circle(r)=9 cm
circumference of the circle(c)=?
We know that;
[tex]C=2{\pi}r[/tex]
[tex] \: \: \: \: = 2 \times 3.14 \times 9[/tex]
[tex]\: \: \: \: = 56.52[/tex]
Thus,the circumference of the circle is 56.52 cm.
The radius of a circle is 18 ft. Find its circumference in terms of
�
π.
Answer:
Circumference = 36π
Step-by-step explanation:
The formula for circumference is C = πd, where
C is the circumference,and d is the diameterWe know that the diameter is simply 2 * the radius, so the diameter of the circle is 36 cm as 2 * a radius of 18 cm = 36 cm.
To find the circumference in terms of π, we simply multiply 36 and π, but don't simplify, approximate, etc.
Thus, the circumference in terms of π is C = 36π
state if the 3 numbers can be the measures of the sides of a triangle or not 1) 7, 5, 4 - ________ 2) 3, 6, 2 - ________ 3) 5, 2, 4 - ________ 4) 8, 2, 8 - ________ 5) 9, 6, 5 -________
7, 5, 4 numbers can be the measures of the sides of a triangle.
For series 3, 6, 2, numbers cannot be the measures of the sides of a triangle.For series 5, 2, 4, numbers can be able to the measures of the sides of a triangle.For series 8, 2, 8, numbers can be able to measures of the sides of a triangle For series 9, 6, 5, numbers can be the measures of the sides of a triangle.What is the measures of the sides of a triangle?To know if the three given numbers above in the question can be the measures of the sides of a triangle, one need to use the Triangle Inequality Theorem,
The law states that the sum of the lengths of any two sides of a triangle is one that needs to be greater than the length of the third side. Hence using it, one can say that:
Series 7, 5, 4 can be the measures of the sides of a triangle due to the fact that 7 is lesser than the sum of 5 and 4.
Series 3, 6, 2 cannot be the measures of the sides of a triangle because 6 is said to be greater than the sum of 3 and 2, and this violate the Triangle Inequality Theorem.
Series , 5, 2, 4, the three numbers can be the measures of the sides of a triangle due to the fact that the sum of any two sides is greater than the third side of 5. The same applies to the others.
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How do you prove csc^4 x - cot^4 x = csc^2 x + cot^2 x
To prove the equation csc^4(x) - cot^4(x) = csc^2(x) + cot^2(x), we can start by expressing the trigonometric functions csc(x) and cot(x) in terms of sine and cosine:
csc(x) = 1/sin(x)
cot(x) = cos(x)/sin(x)
Substituting these expressions into the equation, we get:
(1/sin(x))^4 - (cos(x)/sin(x))^4 = (1/sin(x))^2 + (cos(x)/sin(x))^2
Next, we simplify each term separately:
(1/sin(x))^4 = 1/sin^4(x)
(cos(x)/sin(x))^4 = cos^4(x)/sin^4(x)
Expanding the powers, we have:
1/sin^4(x) - cos^4(x)/sin^4(x) = 1/sin^2(x) + cos^2(x)/sin^2(x)
Combining the fractions on the left side:
(1 - cos^4(x))/sin^4(x) = (1 + cos^2(x))/sin^2(x)
Now, let's simplify the left side:
1 - cos^4(x) = sin^4(x)
Using the identity sin^2(x) + cos^2(x) = 1, we can rewrite the equation as:
sin^4(x) = sin^4(x)
The equation simplifies to an identity, showing that the original equation csc^4(x) - cot^4(x) = csc^2(x) + cot^2(x) is true for all values of x.
Therefore, we have proved the given equation.
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A university is researching the impact of including seaweed in cattle feed. They assign feed with and without seaweed to be fed to cows at two
different dairy farms. The two-way table shows randomly collected data on 200 dairy cows from the two farms about whether or not their feed
includes seaweed.
Based on the data in the table, if a cow is randomly selected from farm B, what is the probability that its feed includes seaweed?
Without Seaweed?
A. 0.649
B. 0.620
C. 0.370
D. 0.597
Based on the data in the table, if a cow is randomly selected from farm B, the probability that its feed includes seaweed is 0.597 (Option D) and without is 0.57
How did we arrive at this?Note that the total number of feed with sea weed is 74.
And the total number of cows on the farm B is 124.
Thus, the cows whose feed includes seaweed is 74/124
= 0.59677419354
≈ 0.597
The Probability of those whose feed is without sea weed is
Note that the total number of feed without sea weed is 40.
And the total number of cows on the farm B is 76.
Thus, the probability is 40/70
= 0.5714285714
≈ 0.571
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a 90% confidence interval for a population mean is (10, 20). what is the margin of error of the interval?
the margin of error for the 90% confidence interval is 5.
the margin of error is equal to half the width of the confidence interval. Therefore, to find the margin of error, we need to find the width of the interval and divide it by 2.
The width of the interval is found by subtracting the lower bound (10) from the upper bound (20), which gives us 10. Dividing this by 2 gives us the margin of error, which is 5.
the margin of error for the 90% confidence interval is 5.
The margin of error for the given 90% confidence interval is 5.
A confidence interval (CI) is an estimated range of values within which the population mean is likely to fall, with a certain level of confidence (in this case, 90%). The CI is given as (10, 20). To find the margin of error, follow these steps:
1. Calculate the midpoint of the interval by averaging the lower and upper limits: (10 + 20) / 2 = 15.
2. Subtract the lower limit from the midpoint: 15 - 10 = 5.
The margin of error for the given 90% confidence interval (10, 20) is 5. This means that we are 90% confident that the population mean lies within 5 units of the midpoint value (15).
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A cone has a volume of 1256cm.The vertical height of the cone is 14cm.Find the radius of the cone (Take π 22/7)
Answer:
The answer is 9 cm to the nearest cm
Step-by-step explanation:
[tex]volume \: of \: a \: cone = \frac{1}{3} \pi {r}^{2} h[/tex]
1256=1/3×22/7×r²×14
1256=1/3×22×2×r²
3768=44r²
44r²/44=3768/44
r²=942/11
take square root of both sides
r=9 cm to the nearest cm
Help please im trying to check my answer
Answer:
(a) 66 cm³
Step-by-step explanation:
You want the volume of a right triangular prism with a base right triangle that has a leg length of 3 cm and a hypotenuse of 5 cm. The height of the prism is 11 cm.
BaseThe base triangle is a 3-4-5 right triangle, so will have an area of ...
A = (1/2)bh
A = (1/2)(4 cm)(3 cm) = 6 cm²
VolumeThe volume of the prism is ...
V = Bh . . . . . where B is the base area
V = (6 cm²)(11 cm) = 66 cm³
The volume of the prism is 66 cubic centimeters.
__
Additional comment
As you can see, the "work" is greatly simplified by the recognition of the {3, 4, 5} right triangle. If you must use the Pythagorean theorem to find the missing side length, you will find it to be ...
b = √(c² -a²) = √(5² -3²) = √16 = 4
The answer can be estimated by realizing the missing dimension is less than 5. The volume of a rectangular prism of side lengths 3, 5, and 11 would be 3·5·11 = 165 cm³. A triangular prism with the same overall dimensions would have 1/2 that volume, or 82.5 cm³. Since the prism shown has a side length less than 5, its volume will be smaller than 82.5 cm³. The only reasonable answer is 66 cm³.
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please help asap i need help ASAP!!!
The cost of variation is $3 per guest.
The equation of a line is y=mx+b
m is slope and b is the y intercept of the given equation
The ratio of the rise to the run, or rise divided by the run is known as slope and represents the steepness of line in the coordinate plane.
Constant of variation is slope in the given question.
From the graph number of guests taken in the x axis and cost is taken in the y axis
The Constant of variation which passes through two points (x₁, y₁) and (x₂, y₂) is
The formula to find slope is m=y₂-y₁/x₂-x₁
Here the two points from graph are (30, 90) and (20, 60)
Now plug in these values to find the constant of variation or slope
constant of variation = 90-60/30-20
=30/10
=3
Hence, the cost of variation is $3 per guest.
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Find Vector A + B
….
The sum of magnitude of vectors is 17.4 and direction is 88 degree.
Hence, option 3 is correct.
Given that,
Vector A: magnitude = 12 and direction = 60 degree
Vector B: magnitude = 10 and direction = 150 degree
Find the x and y components using the following formulas,
Ax = AcosΘ and Ay = AsinΘ
Substitute the values,
Ax = 12cos(60) and Ax = 6
Ay = 12sin(60) and Ay = 10.39
For vector B,
By using the same formulas,
Bx = 10cos(150) and Bx = -5
By = 10sin(150) and By = 7.66
We have the x and y components of both vectors,
Add them,
Rx = Ax + Bx
⇒ Rx = 6 + (-5)
⇒ Rx = 1
⇒ Ry = Ay + By
⇒ Ry = 10.39 + 7.66
⇒ Ry = 18.05
Finally, we can find the magnitude and direction of the resulting vector,
Magnitude = √(R²x + R²y)
Therefore, after putting values we get,
Magnitude = 17.4
Direction = [tex]tan^{-1}[/tex](Ry/Rx)
= [tex]tan^{-1}[/tex](18.05/1)
= 88 degrees
Therefore, the sum of the two vectors is a vector with magnitude 17.4 and direction 88 degrees.
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URGENT! Please help
What is the value of 7 for the following data to three decimal places?
A. 0.852
B. 0.930
C. 0.659
D. 0.964
Answer:
Option B
Step-by-step explanation:
Given that two variables in the table as
Total Average
x 2 6 7 8 12 35 7
y 15 13 9 8 5 50 10
xy 30 78 63 64 60 295 59
(x-7)^2 25 1 0 1 25 52 10.4
(y-10)^2 25 9 1 4 25 64 12.8
Var x = 10.4 and std dev x = 3.225
Var Y = 12.8 and std dev Y = 3.578
Cov (xy) = E(xy)-E(x) E(Y)=59-70=-11
Correlation coefficient r
= Cov /sx sy = -11/(3.225)(3.578)=-0.9532
Round off to get
r=-0.953
Henceoption B is right.
I hope my answer helped! <3
What are your options in regards to the null hypothesis after you collect your data?
After you collect your data, you have several options in regards to the null hypothesis. First, you could fail to reject the null hypothesis.
The data did not provide enough evidence to support the alternative hypothesis, and you accept the null hypothesis as the most likely explanation. Second, you could reject the null hypothesis. This means that your data provided enough evidence to support the alternative hypothesis, and you reject the null hypothesis as the most likely explanation. To neither accept nor reject the null hypothesis. The less common option and occurs when your data does not provide enough evidence to reject the null hypothesis, but also does not provide enough evidence to accept it as the most likely explanation.
The null hypothesis after you collect your data include failing to reject it, rejecting it, or neither accepting nor rejecting it.
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Write an equation of the parabola that has its x intercepts at (-3,0) and (4,0) and its y intercept at (0,-6)
the x-intercepts in a function are pretty much just its roots or solutions, so let's reword that
what's the equation of a parabola with roots at -3 and 4 that it passes through (0 , -6)?
[tex]\begin{cases} x = -3 &\implies x +3=0\\ x = 4 &\implies x -4=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +3 )( x -4 ) = \stackrel{0}{y}}\hspace{5em}\textit{we also know that } \begin{cases} x=0\\ y=-6 \end{cases} \\\\\\ a ( 0 +3 )( 0 -4 ) = -6\implies -12a=-6\implies a=\cfrac{-6}{-12}\implies a=\cfrac{1}{2} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1}{2}( x +3 )( x -4 ) =y\implies \cfrac{1}{2}(x^2-x-12)=y\implies \boxed{\cfrac{x^2}{2}-\cfrac{x}{2}-6=y}[/tex]
Check the picture below.
Dan works on a horse farm. There are 10 horses on the farm and they each eat 140
pounds of hay in a week. Dan buys new hay for the farm every week. Where should
Dan purchase hay from if he does not want any hay leftover at the end of the week?
How many bales should he purchase?
The number of bales purchased for the farm is n = 7 bales
Given data ,
Dan works on a horse farm. There are 10 horses on the farm and they each eat 140 pounds of hay in a week
Now , Dan buys new hay for the farm every week
To find the total amount of hay needed for the week, we multiply the amount consumed by each horse by the number of horses:
Total hay needed = 10 horses x 140 pounds/horse = 1400 pounds
To determine the number of bales needed, we divide the total hay needed by the weight of each bale:
Number of bales needed = Total hay needed / Weight of each bale
On simplifying the equation , we get
Number of bales needed for agri supply = 1400 / 75 = 18.667
Number of bales needed for farm supply = 1400 / 150 = 9.33
Number of bales needed for tractor supply = 1400 / 200 = 7 bales
Number of bales needed ≈ 7 bales when there is not leftover
Hence , there is no leftover at the end of the week if he purchases 7 bales from the tractor supply
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The complete question is attached below :
Dan works on a horse farm. There are 10 horses on the farm and they each eat 140 pounds of hay in a week. Dan buys new hay for the farm every week. Where should Dan purchase hay from if he does not want any hay leftover at the end of the week? How many bales should he purchase?
Let F(x)={sin(x+1)ex−1x<−1−1≤x
Find limx→-1+F(x)
To find the limit of F(x) as x approaches -1, we need to evaluate the left-hand and right-hand limits separately and check if they are equal.
For x < -1, F(x) = sin(x + 1) * e^(x - 1). Since we are interested in the limit as x approaches -1, we consider values of x that are approaching -1 from the left side.Let's evaluate the left-hand limit:
lim(x→-1-) F(x) = lim(x→-1-) sin(x + 1) * e^(x - 1)
As x approaches -1 from the left side, sin(x + 1) approaches sin(0) = 0, and e^(x - 1) approaches e^(-2).
Therefore, lim(x→-1-) F(x) = 0 * e^(-2) = 0.
Now, let's evaluate the right-hand limit:
lim(x→-1+) F(x) = lim(x→-1+) F(x)
For x greater than or equal to -1, F(x) is not defined.
Since the left-hand limit and the right-hand limit are not equal, the limit of F(x) as x approaches -1 does not exist.
Therefore, lim(x→-1+) F(x) is undefined.
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Points D(2; 5), E (-4;-4), F(0; 2) and G(-4;9) are given. Find MDG: What can you conclude about the line segments DE and DG?
Answer:
Step-by-step explanation:
To find MDG, we need to calculate the length of line segment DG.
Using the distance formula, the length of a line segment between two points (x1, y1) and (x2, y2) is given by:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the length of line segment DG:
DG = √((-4 - 2)^2 + (9 - 5)^2)
= √((-6)^2 + (4)^2)
= √(36 + 16)
= √52
= 2√13
Therefore, MDG is equal to 2√13.
Now, let's analyze the line segments DE and DG:
Line segment DE: The coordinates of D are (2, 5) and the coordinates of E are (-4, -4). By calculating the length of DE using the distance formula, we can determine the length of DE.
DE = √((-4 - 2)^2 + (-4 - 5)^2)
= √((-6)^2 + (-9)^2)
= √(36 + 81)
= √117
= √(9 * 13)
= 3√13
Therefore, the length of line segment DE is 3√13.
Line segment DG: We have already calculated the length of DG as 2√13.
From the calculations, we can conclude that DE and DG have different lengths. DE is 3√13 while DG is 2√13.
In summary, line segments DE and DG have different lengths.
This number line shows the solution set for the inequality x≥9
Calculate the number of ceiling boards measuring 5cm by 10cm required to cover a square room of 5m
The number of ceiling boards in the room is 5000
Calculating the number of ceiling boardsFrom the question, we have the following parameters that can be used in our computation:
Measurement = 5 cm by 10 cm
Room = square of 5 m dimension
The area of the room is calculated as
Area = (5 m)²
When evaluated, we have
Area = 25 m²
The area of the board is
Area = 5 cm * 10 cm
So, we have
Area = 50 cm²
So, we have
Boards = (25 m²)/(50 cm²)
Evaluate the quotient
Boards = 5000
Hence, the number of boards is 5000
Read more about areas at
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Jeff made $243. 75 last week. If he worked 25 hours, how much is he paid for 1 hour of work?
To find out how much Jeff is paid per hour of work, we need to divide his total earnings by the number of hours he worked.
Total earnings: $243.75
Number of hours worked: 25
Hourly pay rate: Total earnings / Number of hours worked
Hourly pay rate: $243.75 / 25 = $9.75
Therefore, Jeff is paid $9.75 per hour of work
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