Average speed of Car 1 = 35 mph. Average speed of Car 2 = 55 mph. Time elapsed between start of Car 1 and start of Car 2 = 18 minutes.

How long before Car 2 overtakes Car 1? ___________ hour.

Answer:

[tex]\text{Area of sphere is }484\pi units^2[/tex]

Step-by-step explanation:

Given the radius of sphere 11 units

we have to find the surface area of sphere

Radius=11 units

As area of sphere can be calculated as

[tex]\text{Area}=4\pi r^2[/tex]

[tex]=4\pi (11)^2=484\pi units^2[/tex]

[tex]\text{Area of sphere is }484\pi units^2[/tex]

Answer:

p(X)=7x-20

Step-by-step explanation:

correct answer

Answer:

a)  2 red lights

b) SD = 1.26

c) mean = 10, SD = 1.26

Step-by-step explanation:

a) The number of red lights she expects to hit by day can be gotten by calculating the mean of the distribution.

[tex]E(X) = \sum xP(x)[/tex]

[tex]E(X) = (0*0.05) + (1*0.25) + (2*0.35) + (3*0.15) + (4*0.15) + (5*0.15)\\E(X) = 2.25[/tex]

Since the number of lights cannot be a decimal, she expects to hit 2 lights each day

b)

Variance, [tex]V(X) = \sum(x- \mu)^{2} P(x)[/tex]

[tex]V(X) = [(0-2.25)^{2}*0.05] + [(1-2.25)^{2}*0.25] + [(2-2.25)^{2}*0.35] + [(3-2.25)^{2}*0.15] + [(4-2.25)^{2}*0.15] + [(5-2.25)^{2}*0.05][/tex]

V(X) = 0.253 + 0.391 + 0.022 + 0.084 + 0.459 + 0.378

V(X) = 1.587

Standard Deviation, [tex]SD = \sqrt{V(X)}[/tex]

[tex]SD = \sqrt{1.587}[/tex]

SD = 1.26

c) In a 5 day work week, the commuter is expected to hit an average of 5* 2 red lights, i.e. mean = number of red lights hit per day * number of days

mean = 2 * 5

mean = 10

The standard deviation will not change, SD = 1.26

Answer:

the graph is stretched horizontally to 1/3 the original width

Step-by-step explanation:

the graph is also reflected and translated but those are rigid transformations and this is asking about the non rig transformations

The approximate value of 'x' in the diagram is 31. 64

Using the formula, tan α = opposite side/ adjacent side

Opposite side = side opposite the angle

Adjacent = the other side

IF  α  = 36°

Opposite = 23

Adjacent = x

tan 36 = 0. 727

Substitute values into the formula

tan 36° = 23/ x

0.727 = 23/ x

Make 'x' subject by cross multiplying

x * 0. 727 = 23

x = 23/ 0. 727

x = 31. 64

Thus, the approximate value of 'x' in the diagram is 31. 64

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Answer: 225 Centimeters

Step-by-step explanation:

Answer:  The below graph shows the given situation.

Step-by-step explanation:

Let x represents the number of week, and y represents the total balance in the account after x weeks.

Since, initially the amount in the account = $ 270

According to the question,

Every week $80 is saved.

Thus, the total saving in x weeks = 80 × x = 80x

Since the total amount in x weeks = Initial amount + total saving.

⇒ y = 80x + 270

Which is the equation of line that shows the given situation.

x-intercept of the line is (-27/8,0)

y-intercept = (0,270)

If x=1 y = 350

If x=2 y= 430

If x=3 y =510

Thus, the points of the line are (1,350), (2,430), (3,510)

Hence we can draw the graph with help of above information.

Graph A & C are negative

Graph B & D are positive

The coefficient closest to 0 is B

The coefficient with the least value is A

Hope this helped :3

The slope of the line passing through points J (0,0) and K (-2,8) is calculated using the slope formula and results in a slope of -4.

The question asks to calculate the slope of the line passing through points J (0,0) and K (-2,8). The slope of a line is found by the formula

slope = (y'' - y') / (x'' - x'), where (x', y') and (x'', y'') are the coordinates of two distinct points on the line. Substituting the given points into this formula gives us

slope = (8 - 0) / (-2 - 0) = 8 / -2 = -4.

To estimate the probability of getting fewer than 4 successes in a binomial distribution, we can use the normal distribution as an approximation based on the conditions np > 5 and nq > 5. By calculating the mean and standard deviation of the normal distribution, we can use a z-score to find the estimated probability. In this case, the estimated probability is approximately 0.1709.

The given question requires us to estimate the probability of getting fewer than 4 successes in a binomial distribution. To determine if we can use the normal distribution as an approximation, we need to check if both np and nq are greater than 5. In this case, np = 13 * 0.4 = 5.2 and nq = 13 * 0.6 = 7.8, so both conditions are satisfied. Thus, we can use the normal distribution as an approximation. Let's estimate P(fewer than 4) using the normal distribution.

The mean of the normal distribution is given by μ = np = 13 * 0.4 = 5.2. The standard deviation is calculated using the formula σ = √(npq), where q = 1 - p. So, q = 1 - 0.4 = 0.6. Plugging in the values, we get σ ≈ √(13 * 0.4 * 0.6) ≈ 1.789. Now, we can use the normal distribution to estimate the probability.

Using the z-score formula z = (x - μ) / σ, where x is the number of successes we want to estimate the probability for, we can find the z-score for 3.5 (less than 4). z = (3.5 - 5.2) / 1.789 ≈ -0.951. Now, we can use a standard normal distribution table or calculator to find the cumulative probability for this z-score. P(fewer than 4) = P(z < -0.951) ≈ 0.1709 (approximately). Therefore, the estimated probability of getting fewer than 4 successes in the given binomial distribution is approximately 0.1709.

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Firstly, we would have to evaluate whether a normal approximation would be useful to use. However, given our conditions where `n` is 13, `p` is 0.4, `q` (the complement of `p`) is 1 - 0.4 or 0.6, we can clearly use the normal approximation to the binomial distribution because both `np` (13 * 0.4 = 5.2) and `nq` (13 * 0.6 = 7.8) are greater than 5.

For the normal approximation, we begin by calculating the mean (µ) and standard deviation (σ) of the binomial distribution. The mean of a binomial distribution is calculated as `np` hence in our case, `np` is 13 * 0.4 which is equal to 5.2. To find the standard deviation, we use the formula `sqrt(npq)`, so in our case, we have`sqrt(13 * 0.4 * 0.6)`, which is approximately 1.76635.

Now, to find the probability of getting fewer than 4, we would calculate a z-score for the value of x = 4. This helps convert the raw scores in a dataset into a standardised form, allowing us to better understand the position of individual scores in relation to the rest of the dataset. The z-score is calculated as `z = (x - µ) / σ` . With x being 4, µ is 5.2, and σ is 1.76635, our z-score will be (4 - 5.2) / 1.76635, which gives us approximately -0.67937.

Now, the last step is to find the cumulative probability associated with this z-score. In essence, the cumulative probability associated with a z-score tells you the probability that a certain observation will occur given a standard normal distribution (which is our case, as we've standardised our dataset using the z-score). Checking a z-table, or by using the cumulative distribution function for a value of z = -0.67937, the associated probability is approximately 0.24845.
So the final probability that we will get fewer than 4 is approximately 0.24845 or 24.85% when we use the normal distribution as an approximation to the binomial distribution.

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A tilt level and a dumpy level are both surveying instruments used for measuring horizontal distances and vertical elevations. The main difference is that the tilt level has a built-in compensator that eliminates the need for manual leveling, while the dumpy level requires manual leveling before each use.

A tilt level and a dumpy level are both surveying instruments used for measuring horizontal distances and vertical elevations. However, there are some key differences between the two.

Tilt Level: A tilt level, also known as a tilting level, is a type of level that utilizes a compensator mechanism to maintain a level plane even when the instrument itself is not level. This compensator allows for accurate measurements and eliminates the need for manually leveling the instrument each time.

Dumpy Level: A dumpy level, on the other hand, is a more traditional type of level that requires manual leveling before each use. It consists of a telescope mounted on a tripod, and the instrument is adjusted using leveling screws to ensure that it is perfectly horizontal. The dumpy level does not have a compensator like the tilt level, so the instrument needs to be leveled manually to obtain accurate measurements.

In summary, the main difference between a tilt level and a dumpy level is that the tilt level has a built-in compensator that eliminates the need for manual leveling, while the dumpy level requires manual leveling before each use.

According to given question, 12 divided by 144140 is approximately 0.000083158.

To divide 12 by 144140, simply perform the division:

12 ÷ 144140 ≈ 0.000083158

So, 12 divided by 144140 is approximately 0.000083158.

Division is a mathematical operation used to distribute a quantity or a number of items into equal parts. It involves finding out how many times one number (called the divisor) can be subtracted or taken away from another number (called the dividend) until there is nothing left or the subtraction cannot be done anymore.

The result of the division is called the quotient, and it represents the number of equal parts or groups that the dividend can be divided into by the divisor. In the division expression "a ÷ b," where "a" is the dividend and "b" is the divisor, the quotient is represented by "a/b."

For example, in the division 12 ÷ 3:

12 is the dividend (the total quantity to be divided).

3 is the divisor (the number of equal parts to divide the dividend).

The quotient is 4, as 12 can be divided into 4 equal parts of size 3.

Division is the opposite operation of multiplication. If you have two numbers, the product of their multiplication can be divided by one of the numbers to get the other number. For example, 12 × 3 = 36, and 36 ÷ 3 = 12.

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The simplified form of each expression is as follows:

[tex]A. \( 729 \times 33 \) simplifies to \( 3^6 \times 33 \) B. \( 3 \times 33 \) simplifies to \( 3 \times 3 \times 11 \) or \( 3^2 \times 11 \). C. \( 729 \times 29 \) simplifies to \( 3^6 \times 29 \). D. \( 3 \times 29 \) simplifies to \( 3 \times 29 \).[/tex]

To simplify these expressions, we recognize that 729 is a power of 3, specifically [tex]\( 3^6 \)[/tex], and that 33 and 29 are prime numbers. Therefore, we can express each product in terms of its prime factors.

A. For the expression [tex]\( 729 \times 33 \)[/tex] , we know that 729 is [tex]\( 3^6 \)[/tex] and 33 is a prime number. Thus, the simplified form is [tex]\( 3^6 \times 33 \)[/tex].

[tex]B. For the expression \( 3 \times 33 \), we can further break down 33 into \( 3 \times 11 \), since 33 is the product of these two prime numbers. Therefore, the simplified form is \( 3^2 \times 11 \) or \( 3 \times 3 \times 11 \).[/tex]

[tex]C. For the expression \( 729 \times 29 \), similar to expression A, 729 is \( 3^6 \) and 29 is a prime number. Hence, the simplified form is \( 3^6 \times 29 \).[/tex]

[tex]D. For the expression \( 3 \times 29 \), both 3 and 29 are prime numbers, so the expression is already in its simplest form and cannot be simplified further. Thus, the simplified form remains \( 3 \times 29 \).[/tex]In summary, the simplified forms are:

[tex]A. \( 3^6 \times 33 \) B. \( 3^2 \times 11 \) or \( 3 \times 3 \times 11 \) C. \( 3^6 \times 29 \) D. \( 3 \times 29 \)[/tex]

Answer:

Option A. 6%

Step-by-step explanation:

250 tickets are sold at a fund raiser.

Sarah buys 15 tickets.

The probability that she will win the prize quilt = [tex]\frac{15}{250}[/tex]

                                                                              = 0.06 = 6%

The probability that Sarah will win is 6%.