Show, using the Mean Value Theorem, that sin xsin y ≤ x − y| for all real numbers x and y. b) Prove, using a), that sinx is uniformly continuous on R.

Therefore, if Randa cleanses plates five times, she will use 2 1/2 gallons more than 20 gallons of water.

In the US, the gallon is a measurement unit for substances like milk, fuel, and water. If the petrol in your vehicle is nearly depleted, you should stop and get at least a couple extra gallons. A gallon is equal to 4 pints, or 3.785 gallons, of liquid.

To find out how many gallons of water Randa will use if she washes dishes five times, we need to multiply the amount of water she uses each time by the number of times she washes dishes:

4 1/2 gallons per wash x 5 washes = 22 1/2 gallons

Therefore, Randa will use 22 1/2 gallons of water if she washes dishes five times.

To find out how much more than 20 gallons of water she will use, we need to subtract 20 from the total amount of water she will use:

22 1/2 gallons - 20 gallons = 2 1/2 gallons

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Answer:

25°

Step-by-step explanation:

Since ∠DBC = 130°, ∠DBC + ∠ABD = 180° (sum of angles on a straight line is 180°). Solving for ∠ABD:

∠DBC + ∠ABD = 180°

130 + ∠ABD  = 180°

∠ABD = 180° - 130°

∠ABD = 50°

∠ABD  is bisected by line BE, therefore ∠ABD = ∠EBA + ∠DBE (angle addition postulate).

The angle addition postulate states that if w is the interior of xyz then ∠XYZ = ∠XYW + ∠ZYW

Since E is the interior of ∠ABD, then:

∠ABD = ∠EBA + ∠DBE

But ∠EBA = ∠DBE

∠ABD = 2∠EBA

50 = 2∠EBA

∠EBA = 25°

Answer:

King usually becomes the most emotional during moments of reflection or when he is expressing his views on civil rights and justice. King's message of hope, courage, and resilience encourages individuals to stand up for what is right and to never give up in the face of injustice.

Dr. King utilises passion in his lectures to accentuate his message and to connect with his audience on an emotional level. He frequently speaks about the sorrow and injustice that his people have endured, eliciting an emotional response from his audience. He also inspires his audience to believe in the prospect of a brighter future, which instills hope and motivation. Furthermore, he frequently employs metaphors and analogies to underline his ideas, which may be extremely effective.

King is generally the most emotional when he is reflecting or expressing his ideas on civil rights and justice. In these times, he sends a message of hope, strength, and endurance. King usually uses compelling metaphors and parables to highlight the necessity of equality and justice. He highlights the power of our actions to effect change and the importance of never losing hope in the face of hardship. He frequently urges for unity among all races and sexes and opposes all types of prejudice. He also discusses the power of love, understanding, and mutual respect in bridging gaps and creating a better society.

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Total sales = $450*40= $18000

Commision = 18000*0.025 = $450

--------------------------------------------------------------------------------------

Total earnings = 30000 + commision

comission = 4*175000*0.13 = 91000

Total earnings = 30000+91000 = $121000

If the parametric equations for x and y are both non-constant linear functions of t, then curve must be a line.

A curve (sometimes known as a curved line in ancient texts) is a mathematical entity that is similar to a line but does not have to be straight.

A curve may be conceived of intuitively as the trace left by a moving point. "The [curved] line[a] is [...] the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which [...] will leave from its imaginary moving some vestige in length, exempt of any width," Euclid wrote more than 2000 years ago.

Let x = at+b and y = ct+d

Then,

\(\frac{x-b}{a}=\frac{y-d}{c}=t xc-bc=ay-adxc-ay+ad-bc=0\)

Which is linear equation in x and y.

Therefore, curve is always a line.

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Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

Based on the information given, if Ozzie uses his coupon and pays 7% sales tax, the amount tax that he will pay for two dozen cookies is $10.18 (Option C).

Given:

The sale price is 85% of the original price, and the coupon

This means that Ozzie will pay 95% of that.

The added tax causes the resulting price to be multiplied by 107%, so for 2 dozen cookies.

Hence, Ozzie to compute how much tax Ozzie will pay, we say:

 2(5.89)(0.85)(0.95)(1.07)

= $10.18

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Answer:

\(x\leq 9\)

Step-by-step explanation:

So we have the inequality:

\(5x\leq 45\)

Divide both sides by 5:

\(x\leq 9\)

And, we're done!

This means that the solution of the inequality is all values less than or equal to 9.

I hope this helps!

Answer:

\(x \leq 9\)

Step-by-step explanation:

\(5x\leq45\\\\\frac{5x\leq45}{5}\\\\ \boxed{x\leq9}\)

Hope this helps.

\(7\frac{1}{2}\implies 7.5\hspace{5em}1\frac{1}{4}\implies 1.25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{Monday through Friday} }{\stackrel{ days }{(5)}\stackrel{ rate }{(10.80)}\stackrel{ hours }{(7.5)}}~~ + ~~\stackrel{ Saturday }{\stackrel{ days }{(1)}\stackrel{ rate }{(10.80)(1.25)}\stackrel{ hours }{(7.5)}} \\\\\\ 405~~ + ~~101.25\implies \text{\LARGE 506.25}\)

Answer:

need more info, can't solve if it's very hard to read.

Step-by-step explanation:

Answer: 16 + 2x^2/y (Also said 16 + 2x to the power of 2/y

Step-by-step explanation: You have to divide before multiplying, adding or subtracting. Hope this helps!

Answer:

The correct option is (6, 0) is located on the x-axis.

Step-by-step explanation:

Given that we plot (6, 0) and (0, 5) on the xy–plane. We know that in (6, 0) 6 is the x-coordinate and 0 is the y-coordinate while in (0, 5) 0 is the x-coordinate and 5 is the y-coordinate.

Therefore, (6, 0) can be found on the x–axis not on the origin because it has shifted from 0 to 6 and (0, 5) can be found on the y-axis not on the origin because it has shifted from 0 to 5.

Hence, the correct option is (6, 0) is located on the x-axis.

Answer:

x-axis

Step-by-step explanation:

The speed of the air or water increases and its pressure decreases as it circles the longer-path side of the sail or keel. The air or water will attempt to migrate from the side of high pressure to the side of low pressure as it moves along the sail or keel in response to the consequent pressure difference.

Theoretical displacement hull speed is determined by the following equation: velocity in knots = 1.35 x waterline length in feet squared.

Use x to symbolise the slower boat's speed.

Therefore, the faster boat's speed would be x + 20 mph.

They met for 8 hours, hence the distance they travelled overall during that period is depicted as

Distance: (x + 20) * 8 + x * 8

Thus, we have

Distance: 16x plus 160

At twilight, the two boats were separated by 400 kilometres.

The distance equation is as follows.

400 = 16x + 160

Analyze similar terms

16x = 240

multiply by 16

x = 15

Remember that

20 mph faster boat equals x.

Thus, we have

Speedier boat = 15 plus 20

Speedier boat = 35

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The three main examples of parallel lines are railway track, sidewalk edges and ladder rails

Given,

Parallel lines;-

Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines can also be said to meet at infinity.

We have to the examples of parallel lines;

Here,

Examples of parallel lines in real life are railroad tracks, sidewalk edges, ladder rails, endless rail tracks, opposing sides of a ruler, opposite edges of a pen, and eraser

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Answer:

Beta radiation

(0,0) is a saddle point and (4/3,4/3) is a point relatively maximum when the function is f(x,y) = -x³+4xy-2y²+1.

Given that,

We have to find use the second derivative test to locate any critical points and decide whether each critical point is a maximum, minimum, saddle point, or none of these for the activities that follow.

f(x)=-x³+4xy-2y²+1

We know that,

Take f(x,y) = -x³+4xy-2y²+1

\(f_{x}\)=d/dx f(x,y)= -3x²+4y

\(f_{y}\)= d/dy f(x,y)= 4x-4y

for critical points, putting \(f_{x}\) and \(f_{y}\) =0

That is

\(f_{x}\)=0

-3x²+4y=0   ----->equation(1)

\(f_{y}\) =0

4x-4y=0

x=y

Then equation(1)

-3x²+4y=0

-3y²+4y=0

y=0 and y=4/3

Same x=0 and x=4/3

The critical points are (0,0) and (4/3,4/3).

Now, calculating \(f_{xx},f_{yy}, f_{xy},\)

So,

\(f_{xx}\)= -6x

\(f_{yy}\)=-4

\(f_{xy}\)=4

So, for (0,0)

\(f_{xx}\)= 0, \(f_{yy}\)=-4 \(f_{xy}\)=4

D= \(f_{xx}\). \(f_{yy}\)- \(f_{xy}\)

D= 0.(-4)-(4)²

D=-16

D<0

(0,0) is a saddle point.

So, for (4/3,4/3)

\(f_{xx}\)= -8, \(f_{yy}\)=-4 \(f_{xy}\)=4

D= \(f_{xx}\). \(f_{yy}\)- \(f_{xy}\)

D= -8.(-4)-(4)²

D=16

D>0

(4/3,4/3) is a point relatively maximum.

Therefore, (0,0) is a saddle point and (4/3,4/3) is a point relatively maximum when the function is f(x,y) = -x³+4xy-2y²+1.

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Answer:

92.99

Step-by-step explanation:

Step-by-step explanation:

hope it helps.

Answer:

x=±√9 or x= 3, x=-3

Step-by-step explanation:

The problem requires us to find the x.

So we must isolate the variable, as so-

\(5x^2-45=0\\5x^2=45\) (add 45 to both sides)

Now we can divide both sides by -

\(5x^2=45\\x^2=9\)

Now we must square root both sides to find the root of x.

\(\sqrt{x^2} =\sqrt{9}\)

x=±√9

or x= 3, x=-3

Answer:

f = 3

Step-by-step explanation:

8 = 2f + 2

-2         -2

6 = 2f

/2    /2

3 = f

Optically active compounds can rotate plane-polarized light in

A - Clockwise rotation

B - Counterclockwise rotation

C - Dextrorotatory

D - Levorotatory

Optically active compounds can rotate the plane of polarization of light, which can be either clockwise or counterclockwise. The direction of rotation is usually expressed as either dextrorotatory (abbreviated as +) or levorotatory (abbreviated as -), depending on whether the compound rotates the plane of polarization to the right or left, respectively.

For example, a compound that rotates the plane of polarization to the right (clockwise) is said to be dextrorotatory (+), while a compound that rotates the plane of polarization to the left (counterclockwise) is said to be levorotatory (-).

Therefore, A corresponds to clockwise rotation, B corresponds to counterclockwise rotation, C corresponds to dextrorotatory, and D corresponds to levorotatory.

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The answer is option A. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity.

Probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is 0.0229.Round to four decimal places as needed.Based on the calculations the elevator does not appear to be safe.The solution for the given problem is as follows:

Given that, the maximum capacity of the elevator is 1884 lb - 12 passengers.

We can write as below:

Maximum capacity per person=1884/12=157lb.

And, weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.Thus, Z = (157-165) / (32 / √12) = -1.7321Then, P(Z > -1.7321) = 0.9586

Hence, the probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is:P(Z > -1.7321) = 1 - P(Z < -1.7321) = 1 - 0.0229 = 0.9771 (rounded off to 4 decimal places).This probability is greater than 5% and therefore, the elevator does not appear to be safe.

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Answer: 48 in.

Step-by-step explanation:

Given

Mr. Simon bought 32 feet of rope

If he used \(\frac{7}{8}\) of it i.e.

\(\dfrac{7}{8}\times 32=28\ ft\)

\(28\ ft\) is used to secure a tree

Rope left is

\(\Rightarrow 32-28=4\ ft\ or\ 4\times 12=48\ in.\)

Answer:

y = -3x+10/ - 8

Step-by-step explanation:

5x - 8y = 2x + 10

let's start by  subtracting 5x to both sides(to stay equal)

and so that  we can get rid  the left side of the equation:

5x - 8y = 2x + 10

-5x          -5x    

-8y = -3x+10

devide both side by -8

(to get rid of the left side so it will become only "Y")

-8y = -3x+10

                      divide (by - 8)

-8        -8            

y = -3x+10/ - 8

and there you have it!

Step-by-step explanation:

Since Total workers = Permanent + Temporary workers,

w = 44 + t.

Hence when t = 5, w = 44 + 5 = 49.

Answer:

199.5

Step-by-step explanation:

3 is not greater than 5

Answer:

199.5

Step-by-step explanation:

The tenth place is the first number to the right of the decimal, in this case, it is 5. In order to know whether or not to raise it to 6 or keep it as 5, we have to look at the hundredth's value. If the number is 5 or higher, we change 5 to 6. If the number is 4 or lower, we keep the 5. In this case, the number is 3, which is 4 or lower. We keep the 5 as it is and get rid off all the numbers behind it. Resulting in:

199.5

Answer:

Taylor walked 35 minutes

Step-by-step explanation:

4:25

+:35

=5:00.

once a clock hits 60 it's automatically turned to the next hour so since 25 + 35 = 50 it's automatically turned to 5:00

The volume of ball is 32.49 cubic centimeter.

What is volume ?

 Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area occupied within an object's three-dimensional bounds is referred to as its volume. The object's capacity is another name for it.

Here ,

The volume of a ball = 32490 cubic millimeters

To convert into cubic millimeter into cubic centimeter by dividing by 1000, Then,

=>  32490/1000

=> 32.49 cubic centimeter.

Hence the volume of ball in cubic centimeter is 32.49 .

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The wage of 2001 in terms of wage in 2012 is option A $14.97

Given,

Mack's wages in 2001 = $7 per hour

Mack's wages in 2012 = $12 per hour

The CPI in 2001 = 94

The CPI in 2012 = 201

We have to fins the wage of 2001 in terms of wage in 2012;

CPI;- Consumer Price Index

The CPI is calculated by the Bureau of Labor Statistics each month using a sample of 94,000 prices. To determine the overall change in prices, the index for each good or service is weighted according to its share of recent consumer spending.

Here,

The wage of 2001 in terms of wage in 2012 = (CPI in present year / CPI in past year) x Wage of earlier year

= (201 / 94) x 7

= 14.97

That is,

The wage of 2001 in terms of wage in 2012 is option A $14.97

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