Dale crosses two pedestrian crossing on his way to school each of which shows either a green or red light when he arrives if the lights at both crosins showed the same colour when dale arrived what his the probability that they both show red give your answer as a fraction in its simplest form

Answer:

-3

Step-by-step explanation:

We can calculate the experimental probability of selling a can of tomato soup, and then use that probability to predict the number of tomato soup cans sold in the next 20 cans.

Step 1: Calculate the experimental probability of selling a can of tomato soup.
Probability = (Number of tomato soup cans sold) / (Total number of cans sold)
Probability = 6 / 12 = 0.5

Step 2: Use the probability to predict the number of tomato soup cans sold in the next 20 cans.
Expected number of tomato soup cans = Probability × Total number of cans
Expected number of tomato soup cans = 0.5 × 20 = 10

Based on the experimental probability, you should expect 10 of the next 20 cans sold to be tomato soup.

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Answer:

24.6 cm^2

Step-by-step explanation:

3.28m = 328 cm

75mm = 0.075 cm

Area of rectangle: L x W

328 times 0.075 = 24.6 cm^2

Using the identity

\(\cos^2(x) = \dfrac{1+\cos(2x)}2\)

we have

\(\dfrac{2 \sin(2x) - \cos(x)}{6 - \frac{1 + \cos(2x)}2 - 4 \sin(x)} = \dfrac{4 \sin(2x) - 2 \cos(x)}{11 - \cos(2x) - 8 \sin(x)} \\\\ ~~~~~~~~ = \dfrac{2(2 \sin(2x) - 8 \cos(x)) + 14 \cos(x)}{11 - \cos(2x) - 8 \sin(x)}\)

Expand the integral as

\(\displaystyle \int \frac{2 \sin(2x) - \cos(x)}{6 - \cos^2(x) - 4 \sin(x)} \, dx \\\\ ~~~~= 2 \int \frac{2 \sin(2x) - 8 \cos(x)}{11 - \cos(2x) - 8 \sin(x)} \, dx + 14 \int \frac{\cos(x)}{11 - \cos(2x) - 8 \sin(x)} \, dx\)

In the first integral, substitute

\(y = 11 - \cos(2x) - 8 \sin(x) \implies dy = \bigg(2\sin(2x) - 8 \cos(x) \bigg) \, dx\)

In the second integral, rewrite the denominator in terms of \(\sin(x)\).

\(11 - \cos(2x) - 8\sin(x) = 11 - (1 - 2\sin^2(x)) - 8\sin(x) \\\\ ~~~~~~~~ = 10 - 8\sin(x) + 2 \sin^2(x)\)

Now substitute

\(z = \sin(x) \implies dz = \cos(x) \, dx\)

and complete the square.

\(2z^2 - 8z + 10 = 2 (z-2)^2 + 2\)

Then we have

\(\displaystyle \int \frac{2 \sin(2x) - \cos(x)}{6 - \cos^2(x) - 4 \sin(x)} \, dx = 2 \int \frac{dy}y + 7 \int \frac{dz}{(z-2)^2 + 1}\)

In the \(z\)-integral, substitute

\(w = z-2 \implies dw = dz\)

Then the integral is

\(\displaystyle \int \frac{2 \sin(2x) - \cos(x)}{6 - \cos^2(x) - 4 \sin(x)} \, dx = 2 \int \frac{dy}y + 7\int \frac{dw}{w^2 + 1} \\\\ ~~~~~~~~ = 2 \ln|y| + 7 \tan^{-1}(w) + C \\\\ ~~~~~~~~ = 2\ln|y| + 7\tan^{-1}(z - 2) + C \\\\ ~~~~~~~~ = \boxed{2\ln(11 - \cos(2x) - 8 \sin(x)) + 7 \tan^{-1}(\sin(x) - 2) + C}\)

We cannot say that this drug is effective at a 0.05 significance level.

In order to determine if the drug is effective, we need to conduct a hypothesis test. The null hypothesis, denoted as H0, states that there is no difference between the drug and the placebo, while the alternative hypothesis, denoted as Ha, states that there is a difference between the drug and the placebo.

To conduct the hypothesis test, we can use a chi-square test for independence, which compares the observed frequencies of the two groups with the expected frequencies. In this case, the observed frequencies are 19 and 27 for the placebo and drug groups, respectively.

To calculate the expected frequencies, we assume that the drug has no effect and that the proportion of people feeling better is the same in both groups. Since there are 200 people in each group, the expected frequency for each group is 200 multiplied by the overall proportion of people feeling better.

To calculate the overall proportion of people feeling better, we add the number of people feeling better in each group and divide by the total number of people: (19 + 27) / (200 + 200) = 46 / 400 = 0.115.

Now we can calculate the expected frequency for each group: 0.115 * 200 = 23 for both the placebo and drug groups.

Next, we calculate the chi-square statistic using the formula:
chi-square = Σ [(observed frequency - expected frequency)^2 / expected frequency].

For the placebo group: (19 - 23)^2 / 23 = 0.696.

For the drug group: (27 - 23)^2 / 23 = 0.696.

Now, we sum the chi-square values for each group: 0.696 + 0.696 = 1.392.

To determine if this chi-square value is statistically significant at the 0.05 significance level, we compare it to the critical chi-square value for the degrees of freedom (df). The df is calculated as (number of rows - 1) * (number of columns - 1), which in this case is (2 - 1) * (2 - 1) = 1.

Looking up the critical chi-square value for df = 1 and α = 0.05 in a chi-square distribution table, we find that the critical value is 3.841.

Since our calculated chi-square value (1.392) is less than the critical value (3.841), we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the drug is effective at a 0.05 significance level.

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Answer: x * y = 2x + 5y. Formula used: x * y = 2x + 5y. Calculation: When x = 3, and y = 5. ⇒ 2x + 5y = (2 × 3) + (5 × 5) = 6 + 25 = 31

Step-by-step explanation:

The solutions to the equation \(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)

To solve the equation \(2/x - 1 = 16/(x^2 + 3x - 4),\) we'll simplify and rearrange the equation to isolate the variable x. Here's the step-by-step solution:

1. Start with the given equation: 2/x - 1 = 16/(x^2 + 3x - 4)

2. Multiply both sides of the equation by x(x^2 + 3x - 4) to eliminate the denominators:

\(2(x^2 + 3x - 4) - x(x^2 + 3x - 4) = 16x\)

3. Simplify the equation:

\(2x^2 + 6x - 8 - x^3 - 3x^2 + 4x - 16x = 16x\)

4. Combine like terms:

  -x^3 - x^2 + 14x - 8 = 16x

5. Move all terms to one side of the equation:

\(-x^3 - x^2 - 2x - 8 = 0\)

6. Rearrange the equation in descending order:

  -x^3 - x^2 - 2x + 8 = 0

7. Try to find a factor of the equation. By trial and error, we find that x = 2 is a root of the equation.

8. Divide the equation by (x - 2):

\(-(x - 2)(x^2 + x - 4) = 0\)

9. Apply the zero product property:

  x - 2 = 0 or x^2 + x - 4 = 0

10. Solve each equation separately:

   x = 2

11. Solve the quadratic equation:

   For x^2 + x - 4 = 0, you can use the quadratic formula or factoring to solve it. The quadratic formula gives:

 \(x = (-1 ± √(1^2 - 4(1)(-4))) / (2(1)) x = (-1 ± √(1 + 16)) / 2 x = (-1 ± √17) / 2\)

Therefore, the solutions to the equation\(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)

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Answer:

Probability [Randomly choose plant Juan's mother want] = 3 / 5

Step-by-step explanation:

Given:

Total number of plant in store = 30 plants

Number of plant kind Juan's mother want = 18

Find:

Probability [Randomly choose plant Juan's mother want]

Computation:

Probability of an event = Number of favorable outcome / Total number of outcomes

Probability [Randomly choose plant Juan's mother want] = Number of plant kind Juan's mother want / Total number of plant in store

Probability [Randomly choose plant Juan's mother want] = 18 / 30

Probability [Randomly choose plant Juan's mother want] = 3 / 5

Answer:

Step-by-step explanation:

You want expressions that have values 48, 40, 24, 64 using the numbers 2, 4, 8 exactly once in each expression.

  48 = (2 +4)×8

  40 = 4×(2 +8)

  24 = 4×(8 -2)

  64 = 2×4×8

Answer:

1080

Step-by-step explanation:

Find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.

Multiples of 15:

15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, 735, 750, 765, 780, 795, 810, 825, 840, 855, 870, 885, 900, 915, 930, 945, 960, 975, 990, 1005, 1020, 1035, 1050, 1065, 1080, 1095, 1110

Multiples of 24:

24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, 288, 312, 336, 360, 384, 408, 432, 456, 480, 504, 528, 552, 576, 600, 624, 648, 672, 696, 720, 744, 768, 792, 816, 840, 864, 888, 912, 936, 960, 984, 1008, 1032, 1056, 1080, 1104, 1128

Multiples of 27:

27, 54, 81, 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486, 513, 540, 567, 594, 621, 648, 675, 702, 729, 756, 783, 810, 837, 864, 891, 918, 945, 972, 999, 1026, 1053, 1080, 1107, 1134

Therefore,

LCM(15, 24, 27) = 1080

hope it helps :)

Answer:

y=-1/3x-7

Step-by-step explanation:

Change the sign of x and flip the slope. 3/1 equals -1/3.

Answer:

17

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

i got it right on edge 2021

The value of the legs of the triangle would be hypotenuse/√2.

You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).

That is perpendicular=hypotenuse/√2

Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)

That is base=hypotenuse/√2

Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.

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Answer:

A

Step-by-step explanation:

she already has 100 dollars (100)

and is saving 20 dollars a week (20x)

Answer: If the dress orginially priced at 8080 dollars and put for 25 percent, that means that you have to move the decimal point to the left twice which will result as 0.25 and 10 percent tax ends up as 0.10. Multiply the two and the product, you have to add to the 8080!

Step-by-step explanation:

Answer:

5√5

Step-by-step explanation:

125/25=5

√25=5

Answer:  5√5

Decimial form = 11.180339888

I reccomond not using decimal form

Step-by-step explanation:

11 ft

since diameter is HALF of circumference

22 divided by 2 = 11

a. The least squares prediction equation is y = B + B1X1 + B2X2 + ε.

b. The values of B1 and B2 represent the changes in the predicted response for a one-unit increase in X1 and X2, respectively, while holding other variables constant.

To report the least squares prediction equation for the given model, we need the estimated coefficients. Since you mentioned that MINITAB was used to fit the model, I assume you have access to the output of the regression analysis. In that output, you should find the estimated coefficients for B (intercept), B1 (coefficient for X1), and B2 (coefficient for X2).

a. The least squares prediction equation can be written as:

y = B + B1X1 + B2X2 + ε

You need to substitute the estimated coefficient values into the equation. For example, if the estimated coefficients are B = 2, B1 = 0.5, and B2 = 0.8, the prediction equation would be:

y = 2 + 0.5X1 + 0.8X2 + ε

b. To interpret the values of B1 and B2 in the context of the model, consider the following:

B1 represents the change in the predicted response (y) for a one-unit increase in X1, while holding other variables constant. If X1 is a categorical variable (1 if level 2, 0 if not), then B1 represents the difference in the predicted response between level 2 and the reference level (usually level 1).

B2 represents the change in the predicted response (y) for a one-unit increase in X2, while holding other variables constant. Similarly, if X2 is a categorical variable (1 if level 3, 0 if not), then B2 represents the difference in the predicted response between level 3 and the reference level.

The interpretation of B1 and B2 will depend on the specific context of your data and the variables X1 and X2.

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The Probability that the tennis team won 9  games is 1.35% , under the given condition that the tennis team wins 73% of their game,  if they play 10 games.

Therefore, probability of winning nine games out of ten with a 73% win rate can be evaluated using the binomial distribution formula
\(P(X=k) = (n choose k) * p^k * (1-p)^{(n-k)}\)

Here
P(X=k) = probability of winning k games out of n games
n = total number of games played (n=10)
k = number of games won (k=9)
p = probability of winning a single game (p=0.73)

Staging the values in the formula
\(P(X=9) = (10 choose 9) * 0.73^9 * (1-0.73)^{(10-9)}\)
= ( 10 - 9) x (0.05) x ( 0.27)¹

= 1 x 0.05 x 0.27

= 0.0135

Converting into percentage

0.0135 x 100

= 1.35%

The probability that the tennis team won 9  games is 1.35% , under the given condition that the tennis team wins 73% of their game,  if they play 10 games.

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Answer:

31.5576

Step-by-step explanation:

Answer:

D

Step-by-step explanation

60/60 = 1

4/60 = 0.066....

1 foot would take 0.067 minute which would be 1/15

The ratio that represents the height of the climbers ascends per hour is

900 feet : 60 minutes

or

900 feet / hour

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

60 feet = 4 minutes

Multiply 15 on both sides.

15 x 60 feet = 15 x 4 minutes

900 feet - 60 minutes

This means,

900 feet per hour.

Thus,

The ratio that represents the height of the climbers ascends per hour is

900 feet : 60 minutes

or

900 feet / hour

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To find the Fourier series of the periodic function defined by f(x) = z for -π ≤ x < π and f(x + 2π) = f(x), we can use the Fourier series expansion formula and compute the coefficients for each term in the series.

The Fourier series expansion of a periodic function f(x) with period 2π is given by:

f(x) = a0 + Σ[an cos(nx) + bn sin(nx)]

To find the Fourier coefficients an and bn, we can use the formulas:

an = (1/π) ∫[f(x) cos(nx) dx]

bn = (1/π) ∫[f(x) sin(nx) dx]

In this case, the function f(x) is defined as f(x) = z for -π ≤ x < π. Since f(x + 2π) = f(x), the function is periodic with period 2π.

To compute the Fourier coefficients, we substitute the function f(x) = z into the formulas for an and bn and integrate over the interval -π to π:

an = (1/π) ∫[z cos(nx) dx] = 0 (since the integral of a constant multiplied by a cosine function over a symmetric interval is zero)

bn = (1/π) ∫[z sin(nx) dx] = (2/π) ∫[0 to π][z sin(nx) dx] = (2/π) [z/n] [cos(nx)] from 0 to π = (2z/π) [1 - cos(nπ)]

Therefore, the Fourier series for the given periodic function f(x) = z for -π ≤ x < π is:

f(x) = a0 + Σ[(2z/π) [1 - cos(nπ)] sin(nx)]

In summary, the Fourier series of the periodic function f(x) = z for -π ≤ x < π is given by f(x) = a0 + Σ[(2z/π) [1 - cos(nπ)] sin(nx)].

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The compound inequality for the given situation is $2.75x + $4.25y ≥ $65 and $2.75x + $4.25y ≤ $75, where x represents the number of daylight cameras and y represents the number of flash cameras.

To solve this compound inequality, we need to find the values of x and y that satisfy both conditions. The inequality $2.75x + $4.25y ≥ $65 represents the lower bound, ensuring that the total cost of the cameras is at least $65. The inequality $2.75x + $4.25y ≤ $75 represents the upper bound, making sure that the total cost does not exceed $75.

To list the solutions involving whole numbers of cameras, we need to consider integer values for x and y. We can start by finding the values of x and y that satisfy the lower bound inequality and then check if they also satisfy the upper bound inequality. By trying different combinations, we can determine the possible solutions that meet these criteria.

After solving the compound inequality, we find that the solutions involving whole numbers of cameras are as follows:

(x, y) = (10, 10), (11, 8), (12, 6), (13, 4), (14, 2), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0).

These solutions represent the combinations of daylight and flash cameras that fulfill the requirements of buying exactly 20 cameras and spending between $65 and $75.

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Answer:

X=8.7 (1dp)

Step-by-step explanation:

X=8.7

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The total number of possible 7-place license plates are 67600000.

Given: A 7-plate license plate. 2 places are for letters and 5 places are for numbers. To find how many different 7-plate license plates are possible

Let's solve the given problem:

The license plate has 7 places. 2 places are for letters and the remaining 5 places are for numbers.

Therefore, the total number of ways in which the 7-place license plate can fill are: Total possible ways in which the two letters can be filled × Total possible ways in which the 5 number places can be filled

= 676 × 100000

= 67600000 ways

Hence the total number of possible 7-place license plates are 67600000.

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Answer:

Answer:

The slope is 2 and the y-intercept is three

Step-by-step explanation:

So y-intercept is the point in which the line crosses the y axis.

And the slope is rise/run or rise over run so it goes over one and up two meaning it will be 2/1 and the slope is two.

Answer:

(-ab^2)^3.

Step-by-step explanation:

-a^3b^6 = (-ab^2)^3