Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 90 miles per hour. The westbound train travels at 100 miles per hour. How long will it take for the two trains to be 418 miles apart?

Answer:

so 189(from 189.66) lower box tickets are sold and 18 upper box tickets are sold

Step-by-step explanation:

lets take "x" as the # of lower box tickets

and "y" as the number of upper box tickets

so in total the number of tickets sold was 208

so  x+y=208

next, we know that each lower box ticket costs 12.50 and each upper box tickets costs 10 and the total amount of money spent was $2187.50 so:

12.5x+10y=2187.50

lets subtract "x" from both sides in first equation to find value of y

y=208-x

now substitute y in equation number 2:

12.5x-10(208-x)=2187.5

12.5x-2080+10x=2187.5

22.5x-2080=2187.5

22.5x=4267.5

x=189.666

so 189 tickets lower box tickets were purchased now, substitute 190 in equation 1 to find value of "y"

y=208-190

y=18

so 189(from 189.66) lower box tickets are sold and 18 upper box tickets are sold

Answer:

Step-by-step explanation:

its m<2=degrees

Answer:

m∠1 = 131

m∠2 = 49

m∠2 = 112

Step-by-step explanation:

Step-by-step explanation:

C

Answer:

The answer is C

Step-by-step explanation:

I took the test and got it right :)

hopefully this helps you :)

pls mark brainlest ;)

Answer:

Length: 9

Width: 3

Perimeter: 24

Step-by-step explanation:

First you can set up a few equations. You know that L x W is your area, or 27.

L * W = 27

Then you also know that your length is equal to three times the width.

L = 3W

So you can substitute L into the first equation to solve for W.

3W * W = 27

3W^2 = 27

W^2 = 9

W = 3

Then you can plug 3 into either equation to solve for your length.

L = 3(3)

L = 9

Then your perimeter is just 2L + 2W

2(9) + 2(3) = 24

Answer:

Step-by-step explanation:

Let the dimensions of the rectangle be length = L and width = W. Then P = perimeter = 2L + 2W.  A = area of rectangle = L * W.  Finally, L = 3W.

Here A = 27 units^2 = W*(3W) = (3*W^2), or 3W^2 = 27 units^2, or

W^2 = 9 units^2, or W = 3 units.  Then L = 3W = 3(3 units) = 9 units.

The length of the rectangle is 9 units.  See above.

The perimeter of the rectangle is 2(9 units) + 2(3 units) = 24 units.

Answer:

1/8

Step-by-step explanation:

You must divide by common multipliers. so you can first divide the numerator and denominator by 10, which would make it 6/48, and then do that again with 6. Which then would give you the answer of 1/8.

Answer:

The answer is D.

Step-by-step explanation:

In $1 there are 4 quarters. Having $2 you would multiply 4 by 2 to get how many quarters there are in $2

Answer:

The answer is D.  

Step-by-step explanation:

In $1 there are 4 quarters. Having $2 you would multiply 4 by 2 to get how many quarters there are in $2

Answer:

4/45.

Step-by-step explanation:

There are a total of 15 marbles in the bowl, so:

P(red) = 5/15 = 1/3

P(blue) = 4/15

Required probability = 1/3 * 4/15

= 4/45

Answer:

P(red, blue) = (5/15)*(4/15) = 4/45

Answer:

all the phones produced during the day in question.

Step-by-step explanation:

Okay, we are given the following data or information or parameters in the question above and they are; 2 % of the phones produced per day are defective, the quality of a day's production was checked by sampling 50 samples randomly.

Therefore, the best option or Explanation that best Define the population of interest to the manufacturer is; ''all the phones produced during the day in question''.

Also, the 50 phones that are sampled randomly and 2% which are defective is a condition that the manufacturer should be interested in.

Answer:

2x^2 -5x +5

Step-by-step explanation:

f(x)=2x^2-8x+6 and g(x)=3x-1

f(x)+g(x)  = 2x^2-8x+6 +3x-1

Combine like terms

             = 2x^2 -5x +5

Answer:

2x^2 -5x +5

Step-by-step explanation:

Answer:

Velocity = distance / time

Velocity = (9/10) / (3/8)

Velocity = (9/10) * (8/3) = 72 / 30 =24 / 10 = 2.4 miles per hour

Therefore, you could walk 4.8 miles in 2 hours.

Step-by-step explanation:

Answer:4.8 miles

Step-by-step explanation:

3/8 of an hour to walk 9/10 of a mile

2 hour to walk ____

Distance walked in 2hr=(2x9/10) ➗ 3/8

Distance walked in 2hr=18/10 ➗ 3/8

Distance walked in 2hr=18/10 x 8/3

Distance walked in 2hr=(18x8) ➗ (10x3)

Distance walked in 2hr=144 ➗ 30

Distance walked in 2hr=4.8 miles

Answer:

27

Step-by-step explanation:

Answer:

18Πin3

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

3 over 2 down.

Answer:

Cylinder A has a volume of 35.34 and Cylinder B has a volume of 58.9, the cylinder B has the greater volume.

Step-by-step explanation:

B= (3.14) 2.5 x 3h = 58.9     Cylinder B = 58.9

A= (3.14) 1.5 x 5h = 35.34     Cylinder A = 35.34

Answer:

6q or 6 * q

Step-by-step explanation:

As you do not know what the value of the variable q is, you are essentially changing it from word form to expression form.

"product" in math means multiply, so you are multiplying 6 with q.

6q is your answer.

~

Answer:

6+9=15

6×9=54

Step-by-step explanation:

didnt know which one you wanted but hope this helps

Answer:

B

Step-by-step explanation:

i would say the answer is B, as the angles and information given heavily indicate that AB is the same as DF. As we now know this, we can rule out answers C and D. We then can rule out A, as 'both being a side of an equilateral triangle' does not prove that they are identical lines.

Answer:

10.05 for 12 quarts

Step-by-step explanation:

Answer:

1. x=13

2.x=1

Step-by-step explanation:

Answer:

9 ripe tomatoes

1 1/4 red onion

4/5 garlic cloves

6 jalapeños

2/3 cup fresh cilantro

6 teaspoons ground cumin

5 1/2 teaspoons

3 teaspoons salt

30 ounces crushed tomato (2 cans)

9 ounces dices green chilies (2 cans)

Answer:

a) The number of claims decrease from 1990 to 1996.

b) The relative extrema is a minimum and happens approximately in 1996 (t=5.688). This means the moment when the number of claims stop decreasing and start to increase.

Step-by-step explanation:

The monthly average number of unemployment claims in a certain county is given by:

[tex]C(t)=24.31t^2-276.58t+2035[/tex]

With t: number of years after 1990.

We have to determine in what years the number of claims decrease and the relative extreme value.

We can find this by analizing the first derivative.

When the first derivative is equal to zero, this indicates an extreme value, which can be a maximum or minimum.

When the first derivative is positive, it indicates that the function is increasing. On the contrary, when the first derivative is negative, it indicates that the function is decreasing.

The first derivative is:

[tex]\dfrac{dC}{dt}=24.31(2t)-276.58(1)+0\\\\\\\dfrac{dC}{dt}=48.62t-276.58[/tex]

Then, we can calculate the extreme value:

[tex]\dfrac{dC}{dt}=48.62t-276.58=0\\\\\\48.62t=276.58\\\\\\t=\dfrac{276.58}{48.62}=5.688\approx 6[/tex]

This extreme value happens for t=6 (year 1996).

If we calculate the value of the first derivative for t=5, that is previous to the extreme value, we can find if the function was increasing or decreasing:

[tex]\dfrac{dC}{dt}(5)=48.62*5-276.58=243.10-276.58=-33.48<0[/tex]

As the value is  negative, we know that the number of claims was decreasing from t=0 to t=6 (from 1990 to 1996), and then reach a minimum and start to increase from them (from 1996 onwards).

Answer:

About 68% (is that an answer choice?)

Step-by-step explanation:

In a normal distribution (a bell curve), about 68 percent of the data is in the range between one standard deviation below the mean to one standard deviation above.  If your mean is 27, and the standard deviation is 3, then one deviation below to one above would be 27 - 3  to 27 + 3, or 24 - 30.

Answer:

P=32

A=60

Step-by-step explanation:

If you ever need to graph something quickly I recommend using Desmos (it's an online graphing calculator).

The sides end up looking like this: [tex]l=10, w=6[/tex]

Perimeter is [tex]2l+2w=2(10)+2(6)=20+12=32[/tex]

Area is [tex](10)(6)=60[/tex]

good luck!

Answer:

Step-by-step explanation:

The question says,

A roulette wheel has 38 slots, of which 18 are black, 18 are red,and 2 are green. When the wheel is spun, the ball is equally likely to come to rest in any of the slots. One of the simplest wagers chooses red or black. A bet of $1 on red returns $2 if the ball lands in a red slot. Otherwise, the player loses his dollar. When gamblers bet on red or black, the two green slots belong to the house. Because the probability of winning $2 is 18/38, the mean payoff from a $1 bet is twice 18/38, or 94.7 cents. Explain what the law of large numbers tells us about what will happen if a gambler makes very many betson red.

The law of large numbers tells us that as the gambler makes many bets, they will have an average payoff of which is equivalent to 0.947.

Therefore, if the gambler makes n bets of $1, and as the n grows/increase large, they will have only $0.947*n out of the original $n.

That is as n increases the gamblers will get $0.947 in n places

More generally, as the gambler makes a large number of bets on red, they will lose money.

Answer:

The value increases

Step-by-step explanation:

the smaller the divisor, the larger the quotient.

Answer:

  $3840

Step-by-step explanation:

The total cost is ...

  (6 hr)(cost per hr) +(120 persons)(food cost per person)

  = 6($190) +120($15 +7.50)

  = $3840

The booking at Hotel 3 would cost $3840.

Answer:

  6

Step-by-step explanation:

The slope (m) can be found using the formula ...

  m = (y2 -y1)/(x2 -x1)

Any pair of points will do. We can use the first two.

  m = (2 -(-10))/(17 -15) = 12/2

  m = 6

The slope of the line is 6.

Answer:  6

Step-by-step explanation:

Answer:

Please, read the answer below.

Step-by-step explanation:

You have the following function:

[tex]f(x)=12x^4-4x^2+5[/tex]

(a) To find the intervals of increase or decrease of f(x) you first calculate the derivative of f(x):

[tex]\frac{df}{dx}=\frac{d}{dx}[12x^4-4x^2+5]\\\\\frac{df}{dx}=12(4)x^3-4(2)x=48x^3-8x[/tex]   (2)

Next, you equal the derivative to zero and obtain the roots of the obtained polynomial:

[tex]48x^3-8x=0\\\\6x^3-x=0\\\\x(6x^2-1)=0[/tex]

Then, you have the following roots for x:

[tex]x_1=0\\\\x_{2,3}=\pm \sqrt{\frac{1}{6}}[/tex] =  ±0.40

Hence, there are three special points.

Next, you evaluate the derivative (expression (2)) for the x values close to the x1, x2 and x3. The values of the derivative give to us the value of the slope of a tangent line in that point, and so, if the function increases or decreases:

First interval, for a number lower than -0.40

[tex]48(-0.41)^3-8(-0.41)=-0.02<0[/tex]

The function decreases in the interval:

[tex](-\inft,-\frac{1}{\sqrt{6}})[/tex]

It is necessary that after x=-0.40 the function increases until the next special point, that is x=0. Then, the interval in which the function increases is:

[tex](-\frac{1}{\sqrt{6}},0)[/tex]

By symmetry, from the point x=0 until x=0.40 the function decreases.

[tex](0,\frac{1}{\sqrt{6}})[/tex]

Next, you evaluate the expression (2) for a number higher than 0.40:

[tex]48(0.41)^3-8(0.41)=0.02>0[/tex]

Then, the function increases for the following interval:

[tex](\frac{1}{\sqrt{6}},+\infty)[/tex]

(b) Due to the results obtained in the previous step you can conclude that the local minimum are:

[tex]x_{min}=-\frac{1}{\sqrt{6}}\\\\x_{min}=\frac{1}{\sqrt{6}}[/tex]

[tex]P_1(-\frac{1}{\sqrt{6}},f(-\frac{1}{\sqrt{6}}))=P_1(-\frac{1}{\sqrt{6}},4.66)\\\\P_2(\frac{1}{\sqrt{6}},f(\frac{1}{\sqrt{6}}))=P_2(\frac{1}{\sqrt{6}},4.66)[/tex]

[tex]P_1(-\frac{1}{\sqrt{6}},0)\\\\P_2(\frac{1}{\sqrt{6}},0)[/tex]

(these are the point in which the function change of a decrease to an increase)

The same reason as before. There in one local maximum:

[tex]x_{max}=0[/tex]

[tex]P(0,f(0))=P(0,5)[/tex]

(c) The inflection points are calculated by using the second derivative:

[tex]\frac{d^2f}{dx^2}=144x^2-8=0\\\\x^2=\frac{8}{144}=\frac{1}{18}\\\\x=\pm \frac{1}{\sqrt{18}}[/tex]

Then , there are two inflection points , given by:

[tex]P_1(-\frac{1}{\sqrt{18}},f(-\frac{1}{\sqrt{18}}))=P_1(-\frac{1}{\sqrt{18}},4.82)\\\\P_2(\frac{1}{\sqrt{18}},f(\frac{1}{\sqrt{18}}))=P_2(\frac{1}{\sqrt{18}},4.82)[/tex]

Answer:

100

Step-by-step explanation:

(b/2)^2

b= -20

(-20/2)^2

(-10)^2

100

Answer:

a)The 80% of confidence interval for the Population 'μ' is

(29.9121 ,33.4879)

b) Margin of error of mean '  'μ' is  =  1.7879

Step-by-step explanation:

step(i):-

Given random sample 'n' =28

The mean of the sample x⁻ =31.7 min

The standard deviation of the sample's' =7.2

Step(ii):-

80% of confidence intervals:

The 80% of confidence interval for the Population 'μ' is determined by

[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{s}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{s}{\sqrt{n} } )[/tex]

Degrees of freedom

γ = n-1 = 28-1 =27

[tex]t_{\frac{\alpha }{2} } = t_{\frac{0.20}{2} } = t_{0.1} = 1.314[/tex]

The 80% of confidence interval for the Population 'μ' is determined by

[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{s}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{s}{\sqrt{n} } )[/tex]

[tex](31.7-1.314 X \frac{7.2}{\sqrt{28} } , 31.7+1.314 X\frac{7.2}{\sqrt{28} } )[/tex]

(31.7 -1.7879 , 31.7 +1.7879)

(29.9121 ,33.4879)

b)

Margin of error of mean is determined by

[tex]M.E = {\frac{t_{\frac{\alpha }{2} } s}{\sqrt{n} } }[/tex]

[tex]M.E = {\frac{1.314 X 7.2}{\sqrt{28} } }[/tex]

Margin of error =1.7879