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Two cyclists, 68 miles apart, start riding toward each other at the same time. One cycles 3 miles per hour faster than the other, and they meet after 4 hours of riding.

a. Write an equation using the information as it is given above that can be solved to answer this problem.

Use the variable r to represent the speed of the slower cyclist. b. What are the speeds of the two cyclists? _______________

the median of restaurant b's cleanliness ratings is 2.

the median of restaurant b's food quality ratings is 4.

the median of restaurant b's service ratings is 3.

:))

Step-by-step explanation:

√19200cm²

=138.56cm

then the highest possible volume

=(138.56)³

=2660195.926cm³

The largest possible volume of the box is; V = 25600 cm³

Let us denote the following of the square box;

Length = x

Width = y

height = h

Formula for volume of a box is;

V = length * width * height

Thus; V = xyh

but we are dealing with a square box and as such, the base sides are all equal and so; x = y. Thus;

V = x²h

The box has an open top and as such, the surface are of the box is;

S = x² + 4xh

We are given S = 19200 cm². Thus;

19200 = x² + 4xh

h = (19200 - x²)/4x

Put (19200 - x²)/4x for h in volume equation to get;

V = x²(19200 - x²)/4x

V = 4800x - 0.25x³

To get largest possible volume, it will be dimensions when dV/dx = 0. Thus;

dV/dx = 4800 - 0.75x²

At dV/dx = 0, we have;

4800 - 0.75x² = 0

0.75x² = 4800

x² = 4800/0.75

x² = 6400

x = √6400

x = 80 cm

From h = (19200 - x²)/4x;

h = (19200 - 80²)/(4 × 80)

h = (19200 - 6400)/3200

h = 4 cm

Largest possible volume = 80² × 4

Largest possible volume = 25600 cm³

Read more at; https://brainly.com/question/19053087

Answer:

(a) Temperature: Numerical

(b) Traffic congestion: Categorical

Step-by-step explanation:

Required

Determine the variable type

(a) Temperature

Temperatures are measured in numeric values e.g. 22 degree Fahrenheit, etc.

Hence, the variable is numerical

(b) Traffic congestion

From the question, we understand that the traffic congestion are divided into three categories i.e. light, medium....

Hence, the variable is categorical

Step-by-step explanation:

We need to prove that ,

cot x / csc x - csc x / cot x = - tan x sec x .

LHS :-

> cot x / csc x - csc x / cot x

> cos x / sin x ÷ csc x - sin x × csc x / cos x

> cosx - 1/ cos x

> cos² x - 1 / cos x

> - sin²x / cosx

> -sin x / cos x × sin x

> -tan x sin x

= RHS

Hence Proved !

Answer:

The call more is cheaper than talk-now.

Step-by-step explanation:

The companies charge a flat fee plus an added cost for each minute or part of a minute used for two companies are as follows :

Call-More: C = 0.40t + 25 Talk-Now: C = 0.15t + 40

We need to find which company is cheaper if a customer talks for 50 minutes.

For call more,

C = 0.40(50) + 25 = 45 units

For talk-now,

C = 0.15(50) + 40 = 47.5 units

So, it can be seen that call more is cheaper than talk-now.

Answer:

0.5587 = 55.87% probability that the sample mean would differ from the true mean by less than 1.1 dollars.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The cost of 5 gallons of ice cream has a variance of 64 with a mean of 34 dollars during the summer.

This means that [tex]\sigma = \sqrt{64} = 8, \mu = 34[/tex]

Sample of 38

This means that [tex]n = 38, s = \frac{8}{\sqrt{38}}[/tex]

What is the probability that the sample mean would differ from the true mean by less than 1.1 dollars ?

P-value of Z when X = 34 + 1.1 = 35.1 subtracted by the p-value of Z when X = 34 - 1.1 = 32.9. So

X = 35.1

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{35.1 - 34}{\frac{8}{\sqrt{38}}}[/tex]

[tex]Z = 0.77[/tex]

[tex]Z = 0.77[/tex] has a p-value of 0.77935

X = 32.9

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{32.9 - 34}{\frac{8}{\sqrt{38}}}[/tex]

[tex]Z = -0.77[/tex]

[tex]Z = -0.77[/tex] has a p-value of 0.22065

0.77935 - 0.22065 = 0.5587

0.5587 = 55.87% probability that the sample mean would differ from the true mean by less than 1.1 dollars.

Step-by-step explanation:

3x-2x=5+10 [taking variables on one side and constant on other]

x=15

soln:

3x-5= 2x+10

3x -5+5=2x+10+5 [ adding 5 on both side]

3x=2x+15

3x-2x=2x+15-2x [subtracting 2x on both side]

x=15

Ans=15

Answer:

[tex]x = 15[/tex]

Step-by-step explanation:

[tex]3x - 5 = 10 + 2x[/tex]

[tex]3x - 2x = 10 + 5[/tex]

[tex]1x = 15[/tex]

[tex]x = 15[/tex]

Answer:

2

Step-by-step explanation:

8*8 is 64

Since it looks like the empty box is an exponent, and there are 2 8s being multiplied, the answer is 2

Answer:

D = -23

Step-by-step explanation:

Answer:

D) -23

Step-by-step explanation:

Definitely

Answer:

4 places after the decimal.

the result is 0.0215

Step-by-step explanation:

I assume the expression is really

43 / (2⁴ × 5³)

this is the same as

(((((((43 / 2) / 2) / 2) / 2) / 5) / 5) / 5)

since the starting value is an odd number, the first division by 2 creates a first position after the decimal point, and it must be a 5, as the result is xx.5

the second division by 2 splits again the uneven end .5 in half, creating a second position after the decimal point again ending in 5, as the result is now xx.x5

the third division by 2 does the same thing with that last 5 and creates a third position after the decimal point ending again in 5, as the result is now xx.xx5

the fourth division by 2 does again the same thing, a fourth position after the decimal point is created ending in 5. now xx.xxx5

in essence, every division of the 0.5 part by 2 is the same as a multiplication by 0.5, which squares 0.5 leading to 0.5². the next division did the same thing leading to 0.5³.

and finally the fourth division to 0.5⁴.

0.5⁴ = (5/10)⁴ = 5⁴/10⁴

so, now we start to divide this result by 5. since the positions after the decimal point are divisible by 5 without remainder, as we have 5⁴ to work with.

every divisible by 5 takes one of these powers away.

so, we go from 5⁴/10⁴ to 5³/10⁴ to 5²/10⁴ to 5/10⁴.

all the time we maintain the 10⁴ in the denominator of the fraction. and that determines the positions after the decimal point.

so, after all the individual divisions we come to and end and are still limited to the 4 positions after the decimal point.

Answer:

The probability that exactly 12 buyers would prefer green

=0.00555

Step-by-step explanation:

We are given that

p=50%=50/100=0.50

n=14

We have to find the probability that exactly 12 buyers would prefer green.

q=1-p

q=1-0.50=0.50

Using binomial distribution formula

[tex]P(X=x)=nC_r p^r q^{n-r}[/tex]

[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^{14-12}[/tex]

[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^2[/tex]

[tex]P(x=12)=14C_{12}(0.50)^{14}[/tex]

[tex]P(x=12)=\frac{14!}{12!2!}(0.50)^{14}[/tex]

[tex]P(x=12)=\frac{14\times 13\times 12!}{12!2\times 1}(0.50)^{14}[/tex]

[tex]P(x=12)=91\cdot (0.50)^{14}[/tex]

[tex]P(x=12)=0.00555[/tex]

Hence, the probability that exactly 12 buyers would prefer green

=0.00555

Answer:

Step-by-step explanation:

Answer:

2x(4x-4+1)

Step-by-step explanation:

i hope it will help you

Answer:

x=1/2

Step-by-step explanation:

press the calculator

8x²-8x+2=0

x=1/2

min,x=1/2

min,y=0

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The attachment shows the ordered pairs (x, f(x)) and their graph.

Answer:

[tex]Pr = 0.153[/tex]

Step-by-step explanation:

Given

[tex]p = 15.3\%[/tex]

Required

Probability of alarm not working

[tex]p = 15.3\%[/tex] implies that the alarm has a probability of not working on a given day.

So, the probability that the alarm will not work on an exam date is:

[tex]Pr = 15.3\%[/tex]

Express as decimal

[tex]Pr = 0.153[/tex]

Answer:

Step-by-step explanation:

4*(n +5) - 2*(5 + 7n) = -70

4*n + 4*5 + 5*(-2) + 7n*(-2) = -70

4n + 20 - 10 - 14n = -70

4n - 14n + 20 - 10 = -70

- 10n + 10 = -70

Subtract 10 from both sides

-10n = -70 - 10

-10n = -80

Divide both sides by (-10)

n = -80/-10

n = 8

Step-by-step explanation:

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Answer:

8 pairs of large glasses and 12 pairs of small ones

Step-by-step explanation:

Let's say the number of large frames she buys is l, and the number of small frames is s. She buys 20 frames of assorted sizes, but they can only be small or large. Therefore, s + l = 20.

Next, the total cost of large frames is 12 dollars for each frame. Therefore, the total cost for the large frames is equal to 12 * l. Similarly, the total cost for the small frames is equal to 5 * s. The total cost of all frames is equal to 156, so

12* l + 5 * s = 156

s + l = 20

In the second equation, we can subtract l from both sides to get

s = 20 - l

We can then plug that into the first equation to get

12 * l + 5 * (20-l) = 156

12 * l + 100 - 5*l = 156

subtract both sides by 100 to isolate the variable and its coefficient

12 * l  -  5 * l = 56

7 * l = 56

divide both sides by 7 to isolate the l

l = 8

The woman buys 8 pairs of large glasses. The number of small glasses is equal to 20-l=20-8=12

Answer:

652 cases

Step-by-step explanation:

The formula for percentage increase is 100 times the final-initial/final value. If we plug the numbers in and calculate, we get 652 cases. Have a great day!

Answer:

8.2 miles per minute

Step-by-step explanation:

Given

See attachment for graph

Required

The rate of Tyler's graph

This means that we calculate the slope (m) of the graph using:

[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]

So, we have:

[tex](x_1 ,y_1) = (0,0)[/tex]

[tex](x_1 ,y_1) = (1,8.2)[/tex]

So, we have:

[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]

[tex]m = \frac{0 - 8.2}{0 - 1}[/tex]

[tex]m = \frac{-8.2}{- 1}[/tex]

[tex]m = 8.2}[/tex]

Answer:

0.1512 = 15.12% probability that fewer than four tornadoes occur in a three-week period.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

In a given region, the number of tornadoes in a one-week period is modeled by a Poisson distribution with mean 2

Three weeks, so [tex]\mu = 2*3 = 6[/tex]

Calculate the probability that fewer than four tornadoes occur in a three-week period.

This is:

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-6}*6^{0}}{(0)!} = 0.0025[/tex]

[tex]P(X = 1) = \frac{e^{-6}*6^{1}}{(1)!} = 0.0149[/tex]

[tex]P(X = 2) = \frac{e^{-6}*6^{2}}{(2)!} = 0.0446[/tex]

[tex]P(X = 3) = \frac{e^{-6}*6^{3}}{(3)!} = 0.0892[/tex]

Then

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0025 + 0.0149 + 0.0446 + 0.0892 = 0.1512[/tex]

0.1512 = 15.12% probability that fewer than four tornadoes occur in a three-week period.

Answer:

the answer is 50 but I don't know if

tan graph and its tax because tax=0

Hey there!

(4 + 21) - (1 - 71)

4 + 21 = 25

= 25 - (1 - 71)

1 - 71 = -70

= 25 - (-70)

= 25 + 70

= 95

Answer: 95

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

Step-by-step explanation:

I have this saved on my computer in notepad b/c this type of question get asked sooo often :/

point P1 (-4,-2)  in the form (x1,y1)

point P2(3,1)  in the form (x2,y2)

slope = m

m = (y2-y1) / (x2-x1)

My suggestion is copy that above and save it on your computer for questions like this

now use it

Point 1  , P1 = (2,-4)   in the form (x1,y1)

Point 2 , P2 = (4,-1)  in the form (x2,y2)

m = [ -1-(-4) ]  /  [ 4-2]

m =  (-1+4) / 2

m = 3 / 2

so now we know the slope is  3/2  :)  

Answer:

s = -4

Step-by-step explanation:

Your goal is to manipulate the equation so you can isolate s

9s + 20 = -16

Subtract 20 from both sides to get:

9s = -36

Divide both sides by 9 so s is alone

you end up with s = -4

Answer:

s  = -4

Step-by-step explanation:

9s+20=−16

Subtract 20 from each side

9s +20 -20 = -16 -20

9s = -36

Divide by 9

9s/9 = -36/9

s  = -4

Answer:

Yes, it is possible to have  a relation on the set {a, b, c} that is both symmetric and transitive but not reflexive

Step-by-step explanation:

Let

Set A={a,b,c}

Now, define a relation R on set A is given by

R={(a,a),(a,b),(b,a),(b,b)}

For reflexive

A relation is called reflexive if (a,a)[tex]\in R[/tex] for every element a[tex]\in A[/tex]

[tex](c,c)\notin R[/tex]

Therefore, the relation R is  not reflexive.

For symmetric

If [tex](a,b)\in R[/tex] then [tex](b,a)\in R[/tex]

We have

[tex](a,b)\in R[/tex] and [tex](b,a)\in R[/tex]

Hence, R is symmetric.

For transitive

If (a,b)[tex]\in R[/tex] and (b,c)[tex]\in R[/tex] then (a,c)[tex]\in R[/tex]

Here,

[tex](a,a)\in R[/tex] and [tex](a,b)\in R[/tex]

[tex]\implies (a,b)\in R[/tex]

[tex](a,b)\in R[/tex] and [tex](b,a)\in R[/tex]

[tex]\implies (a,a)\in R[/tex]

Therefore, R is transitive.

Yes, it is possible to have  a relation on the set {a, b, c} that is both symmetric and transitive but not reflexive.

Answer:

Point D

Step-by-step explanation:

The intersection(s) of lines represents where they cross or intersect. We can see that lines AD and DE cross or intersect as Point D, hence the answer being Point D.

Answer: Point D

Step-by-step explanation: The intersection of two figures is the set of points that is contained in both figures. In the diagram shown, D is the intersection of lines AD and DE because D is the point contained by both line AD and DE.

Answer:

I think that answer would be B.

Step-by-step explanation: