Oak Street intersects with Mill Avenue. The traffic light on Oak Street follows a cycle. It is green for 35 seconds, yellow for 5 seconds, and red for 20 seconds. As you travel along Oak and approach the intersection, what is the probability that the first color you see is red? Write the probability as a simplified fraction. Incorrect feedback has been removed from the screen. Fill in the blank text field 1

Answer:

Option (3)

Step-by-step explanation:

Given : 3x + 12 = 8x - 18

To prove : x = 6

        Statements                  Reasons

1). 3x + 12 = 8x - 18                 1). Given

2). 12 = 5x - 18                       2). Subtraction property of equality

3). 30 = 5x                             3). Addition property of equality

4). 6 = x                                  4). Division property of equality

5). x = 6                                  5). Symmetric property

For step 1 in the given proof Option (3) will be the answer.

The distance that the train travel is 240.3 kilometers.

Since the train leaves at 14:56 and arrives at 16:43, the time taken will be the subtraction of the time. This will be:

= 16.43 - 14:56

= 1 hour 47 minutes

= 1.78 hours

Since the speed is 135km per hour. The distance will be:

= Speed × Time

= 135 × 1.78

= 240.3 kilometers

The distance is 240.3 kilometers.

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Answer: 29

Step-by-step explanation: since m is the midpoint, then the two sides are equal

4x + 13 = 3x + 17

4x - 3x = 17 - 13

x = 4

Therefore

BM = 3x + 17

BM = 3(4) + 17

BM = 12 + 17

BM = 29

Answer:

3.14159265359 and so on

Step-by-step explanation:

a. the relative decay rate of radium-226 is 0.000433 per year.

b. The function that models the mass remaining after t years is \(m(t) = 22 * e^(-0.000433*t)\)

c. After 4000 years, only 5.39 mg of the original 22 mg sample of radium-226 will remain.

The relative decay rate r can be calculated using the formula:

r = ln(2) / t1/2

where t1/2 is the half-life of the substance. Substituting the value

r = ln(2) / 1600 = 0.000433

Therefore, the relative decay rate of radium-226 is 0.000433 per year.

(b) The function that models the mass remaining after t years is

\(m(t) = m0 * e^(-r*t)\)

where m₀is the initial mass of the substance, r is the relative decay rate, and e is the base of the natural logarithm.

Substitute the given values

\(m(t) = 22 * e^(-0.000433*t)\)

(c) To find how much of the sample will remain after 4000 years, we can substitute t = 4000 in the above function:

\(m(4000) = 22 * e^(-0.000433*4000)\)

= 5.39 mg

Therefore, after 4000 years, only 5.39 mg of the original 22 mg sample of radium-226 will remain.

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Answer:

lolololololololololololololololololololololo

Answer:

#1 is 8

#2 is -18

Step-by-step explanation:

#1

13-5=8

#2

-13 - 5= -18

Answer:

Wrigley Gum at Store 1 (since it has the lowest unit price)

Step-by-step explanation:

To find the best deal, you solve for unit price. The price for each item (total price / total units)

Store 1

1.29/14=$0.092

1.19/15=$0.079

Store 2

7.81/81=$0.096

0.55/5=$0.11

Store 3

3.98/10=$0.398

9.98/100=$0.0998

Given:

The population, P, of six towns with time t in years are given by the following exponential equations:

(i) \(P=1000(1.08)^t\)

(ii) \(P = 600 (1.12)^2\)

(iii) \(P =2500 (0.9)^t\)

(iv) \(P=1200 (1.185)^t\)

(v) \(P=800 (0.78)^t\)

(vi) \(P=2000 (0.99)^t\)

To find:

The town whose population is decreasing the fastest.

Solution:

The general form of an exponential function is:

\(P(t)=ab^t\)

Where, a is the initial value, b is the growth or decay factor.

If b>1, then the function is increasing and if 0<b<1, then the function is decreasing.

The values of b for six towns are 1.08, 1.12, 0.9, 1.185, 0.78, 0.99 respectively. The minimum value of b is 0.78, so the population of (v) town  \(P=800 (0.78)^t\) is decreasing the fastest.

Therefore, the correct option is b.

Answer:

False

Step-by-step explanation:

A line is a simple geometric shape that extends in both the directions, but a line segment has two defined endpoints. So, the answer is false. My mistake.

Answer:

line segment have 2 end points and a line has no end pionts so it just keeps going so False

Step-by-step explanation:

false

Answer:

Perimeter of XYZ = Perimeter of QRP

Step-by-step explanation:

Since congruent then

P of XYZ = P of QRP

Answer:

8 cm

Step-by-step explanation:

:)

Answer:

Hi there!

The correct answer is: 5

Step-by-step explanation:

Essentially they replace x with 14, so all you have to do is plug 14 into the equation. 14 multiplied by 1/2 is 7, because it's the same thing as 14 divided by 2. Then you minus 2 from 7, and you get 5.

Answer:

3+9+12+15+16+18+23+24+28+29+35+37+44+46+47+52+59+83/20 =29

median=(29+35)/2=32

modal = 0

Answer:

32 glasses

Step-by-step explanation:

To solve this we will first find out how many glasses one bottle of grape juice can fill.

Equation:

8/2 = 4

This means one bottle of grape juice can fill four glasses. Now all we have to do is multiply 4 glasses of grape juice by the number of bottles.

Equation:

8 * 4 = 32

32 glasses

As per the mathematical operation both Jillian and Samuel are correct.

Given expression = 30+40+70,

The methodology by Jillian = added 30 and 40 and then 70

The methodology by Samuel = added 30 and 70 and then 40.

Determining the result of the given equation:

30 + 40 + 70

= 140

Reviewing the operations of both Jillian and Samuel

Jillian

He added 30 and 40 and then 70:

30 + 40 = 70

70 + 70 = 140

Samuel

He added 30 and 70 and then 40

30 + 70 = 100

100 + 40 = 140

The result of both mathematical operations is 140. Thus, it can be stated that both are correct.

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The graph of y = 14x+9 is bounded by the x-axis and the interval [0, L]. To find the area of the region, find the integral of y = 14x+9 in the interval, which is 7L² + 9L. This area is the region bounded by the x-axis and the graph.

We are given a graph of y = 14x+9 that looks like this:g raph{(y-9)/14 = x [-5.07, 6.03, -2.39, 19.31]}We are also given an interval [0, L] and are asked to find the region bounded by the x-axis and the graph in this interval.Therefore, we need to find the integral of the function y = 14x+9 in the interval [0, L], which will give us the area of the region we are looking for. The integral will be:

∫[0, L] (14x+9) dx

= [7x² + 9x] [0, L]

= (7L² + 9L) - (0 + 0)

= 7L² + 9L

Therefore, the area of the region bounded by the x-axis and the graph in the interval [0, L] is 7L² + 9L. This is the  found the region bounded by the x axis and the graph y = 14x+9 in the interval [0,L].

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Answer:

40%

Step-by-step explanation:

2/5 can be converted to 40/100 by multiplying the numerator and denominator by 20.

40/100 is equivalent to 40%.

When we rotate a figure 90° counterclockwise each point changes thorugh the following rule.

then, since the initial coordinates of the figure are given, apply the transformation to each point

If we look at the flags shown, the correct ubication of the flag is:

Answer:

v = 9 , − 9

Step-by-step explanation:

Take the root of both sides and solve.

Answer:

if you're solving by the square root I think the answer would be 9 or -9 it's either one of those

Step-by-step explanation:

\(1 + 5a + 7a^{2}+a+3\\\)

so you have \(7a^{2}\)

5a + a = 6 a

and 1 + 3 = 4

Answer: \(7a^{2} + 6a + 4\)

Answer:

7a² + 6a + 4

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ 1 + 5a + 7a² + a + 3

Let's simplify the expression,

→ 1 + 5a + 7a² + a + 3

→ 7a² + 5a + a + 1 + 3

→ (7a²) + (5a + a) + (1 + 3)

→ 7a² + (6a) + (4)

→ 7a² + 6a + 4

Hence, answer is 7a² + 6a + 4.

Answer: X = 1 and X = 3

Step-by-step explanation:

By filling in both the possible X values (1 and 3) you get two equations.

5|1-2| + 3 = 8

5|3-2| + 3 = 8

Both of these equations when simplified equal eight on both sides because the first one has the absolute value of -1 times 5 plus 3 which is eight. The second equation is the same besides the fact that it's the absolute value of 1, not -1 but it makes no difference.

Answer:

1) 98°

2) 65°

Step-by-step explanation:

Sum of the angles in any triangle = 180°

in first triangle the third inner angle =  180 - (18 + 80) = 82 then measure of (1) = 180 - 82 = 98°

The missing interior angle of the second triangle = 180 - 124 = 56° then measure of (2) = 180 - (59+56) = 65°

The amount left is an illustration of equivalent expressions.

All three expressions can be used to represent the amount left

The given parameters are:

\(\mathbf{Paycheck =X}\)

\(\mathbf{Savings =20\%}\)

The amount left is:

\(\mathbf{Amount = Paycheck \times (1 - Savings)}\)

So, we have:

\(\mathbf{Amount = X\times (1 - 20\%)}\)

Substitute 250 for A

\(\mathbf{Amount = 250 \times (1 - 20\%)}\)

Express percentage as decimal

\(\mathbf{Amount = 250 \times (1 - 0.20)}\)

\(\mathbf{Amount = 250 \times 0.80}\) ---- this represents option (A)

Expand \(\mathbf{Amount = 250 \times (1 - 20\%)}\)

\(\mathbf{Amount = 250 - 250 \times 20\%}\)

\(\mathbf{Amount = 250 - 250 \times 0.20}\) ---- this represents option (B)

Express 250 as X in \(\mathbf{Amount = 250 - 250 \times 0.20}\)

\(\mathbf{Amount = X - X \times 0.20}\) ---- this represents option (C)

Hence, all three expressions can be used to represent the amount left

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The values in b are compared with the true volume. And we conclude that b is precise and accurate.

Accuracy determines how closely measured values match the actual value. The degree to which two measured values are inside a certain range, or how closely they agree, is called precision.

First calculate the mean of a, b, and c. We get, the mean of a is 87.63, the mean of b is 87.06, and the mean of c is 87.77.

From the values in "a", we can tell there is no good agreement between the given values, and just one (87.1) value is near to the true value. So a is neither precise nor accurate.

From the values in "b", we can tell these given values are reasonably close to the true value and exhibit good agreement. So b is precise and accurate.

From the values in "c", we can tell there is a considerable agreement between the given values but they are not very close to the true value. So c is precise but not accurate.

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Answer:

$7.03

Step-by-step explanation: