4.
Which point on the number line
represents 0.3?

To answer the questions related to the probability of droplet sizes, we'll use the normal distribution with the given mean and variance. Let's solve each part of the question:

a. Probability that the size of a single droplet is less than 1500 μm:

To find this probability, we need to calculate the cumulative distribution function (CDF) of the normal distribution up to 1500 μm. We'll use the z-score formula:

z = (x - μ) / σ

Where:

x = droplet size (1500 μm)

μ = mean (1050 μm)

σ = standard deviation (square root of the variance, which is sqrt(22500 μm))

Calculating the z-score:

z = (1500 - 1050) / sqrt(22500)

= 450 / 150

= 3

Using the z-score table or a calculator, we can find that the cumulative probability corresponding to z = 3 is approximately 0.9987.

Therefore, the probability that the size of a single droplet is less than 1500 μm is approximately 0.9987.

b. Probability that the size of a single droplet is between 1000 and 1500 μm:

Similar to part (a), we need to calculate the cumulative probability for two values: 1000 μm and 1500 μm. Let's calculate the z-scores for both values:

For 1000 μm:

z_1000 = (1000 - 1050) / sqrt(22500)

For 1500 μm:

z_1500 = (1500 - 1050) / sqrt(22500)

Once we have the z-scores, we can find the corresponding cumulative probabilities using the z-score table or a calculator. Then, we subtract the probability for 1000 μm from the probability for 1500 μm to find the probability between the two values.

c. Characterizing the smallest 2% of all droplets:

To characterize the smallest 2% of droplets, we need to find the droplet size that corresponds to the 2nd percentile of the normal distribution. In other words, we need to find the value x such that the cumulative probability up to x is 0.02. We can use the z-score formula to solve for x:

z = (x - μ) / σ

We'll find the z-score corresponding to the cumulative probability 0.02 using the z-score table or a calculator. Then, we can rearrange the formula to solve for x:

x = z * σ + μ

d. Probability that at least one of five independently selected droplets exceeds 1500 μm:

To find this probability, we'll use the complement rule. The probability that none of the five droplets exceed 1500 μm is the complement of the probability that at least one of them exceeds 1500 μm. We can calculate this probability by subtracting the probability of none from 1. We'll use the probability obtained in part (a) for a single droplet.

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Answer:

\(\sf x = 1 + 2\sqrt{3}\)

Explanation:

In a right angle triangle, the hypotenuse is the longest side.

Here the given sides are (x + 1) cm, (x + 2) cm, (x + 4) cm.

where (x + 4) is the longest side among all the side lengths.

Apply Pythagoras theorem:

(leg 1)² + (leg 2)² = (hypotenuse)²

substitute values

\(\sf (x + 1)^2 + (x + 2)^2 = (x + 4)^2\)

\(\sf x^2 + 2x + 1 + x^2 + 4x + 4 = x^2 + 8x + 16\)

\(\sf x^2 + x^2 - x^2 + 2x + 4x - 8x + 1 + 4 - 16 = 0\)

\(\sf x^2 - 2x - 11 = 0\)

use quadratic formula

\(\sf \dfrac{-(-2)\pm \sqrt{(-2)^2 - 4(1)(-11)} }{2(1)}\)

\(\sf \rightarrow \dfrac{2\pm \sqrt{48} }{2}\)

\(\sf \rightarrow 1\pm \sqrt{48}\)

\(\sf \rightarrow 1\pm 2\sqrt{3}\)

\(\sf \rightarrow 1+ 2\sqrt{3} \:\ or \:\ 1 -2\sqrt{3}\)

\(\sf \rightarrow 4.46 \:\ or\:\ -2.46\)

As length can only be positive, the value of x will be 1 + 2√3.

Answer:

Step-by-step explanation:

Use the slope intercept formula.

y = mx + b

m = slope

b = y intercept

y = -2x + 1

Answer: \(n=5\)

Add -10 to each side of the equation

\(10 + -10 + 8n = 50 + -10\)

Combine like terms

\(0 + 8n = 50 + -10\\8n = 50 + -10\\8n = 40\)

Divide each side by 8

\(8n/8=40/8\\n=5\)

Answer:

n = 5

Step-by-step explanation:

8n +10 = 50

     -10    -10

     8n  = 40

      8      8

       n   = 5

The value of x = 1 does not match any of the mathematics values given (10, 12, 22, 31, 42, 55).

The given set of values for x is 10, 12, 22, 31, 42, and 55. However, none of these values equal 1. Therefore, the value of x = 1 is not present in the given set.

In mathematics and programming, the equal sign (=) is used for assignment, not for equality. So when we say "x = 1," we are assigning the value 1 to the variable x. However, in the given set, x takes the values 10, 12, 22, 31, 42, and 55, which means x can only have those specific values, not 1.

It's important to distinguish between assignment and equality. In this case, the assignment statement "x = 1" does not match any of the values in the given set. If we were looking for a value of x that equals 1, we would need to search for it in a different context or equation.

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Answer:

1.00 significant figures

The required, 0.9967 rounded to 2 significant figures is approximately 1.0.

To round 0.9967 to 2 significant figures, we look at the first two non-zero digits: 0.9967

The first two non-zero digits are 99. Since there is no third significant digit, we round according to the following rules:

If the third digit is 5 or greater, round up the second digit.

If the third digit is less than 5, leave the second digit unchanged.

In this case, the third digit is 6, which is greater than 5. So, we round up the second digit:

Thus, 0.9967 rounded to 2 significant figures is approximately 1.0.

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Answer:

30

Step-by-step explanation:

Step-by-step explanation:

\(2x + 3y = 12 \\ 3y = - 2x + 12 \\ y = - \frac{2}{3} x + 4\)

slope is -2/3

y intercept is 4

Answer:

The slope is -2/3 and the y intercept is 4

Step-by-step explanation:

2x + 3y = 12

Slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

2x + 3y = 12

Subtract 2x from each side

2x-2x+3y = -2x+12

3y = -2x+12

Divide by 3

3y/3 = -2x/3 +12/3

y = -2/3 x +4

The slope is -2/3 and the y intercept is 4

Answer: 77/12

Step-by-step explanation:

1) 11/12 * 7 = (11*7)/12 = 77/12

The next term in the sequence is 49.

To find the pattern in sequences 4, 7, 13, 22, and 34, we can examine the differences between consecutive terms. The differences are 3, 6, 9, 12. Notice that these differences are increasing by 3 each time.

From this observation, we can infer that the sequence is generated by adding consecutive odd numbers to the previous term. Starting with 4, we add 3 (the first odd number) to get 7. Then, we add 5 (the next odd number) to 7 to get 13. Continuing this pattern, we add 7 to 13 to get 22, and so on.

Based on this pattern, we can determine the next term by adding the next odd number, which is 15, to the previous term. Thus, adding 15 to 34 gives us the next term in the sequence:

34 + 15 = 49.

Therefore, the next term in the sequence is 49.

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A simplified fraction to represent the ratio where ∠A is the angle of reference is 12/13.

In order to determine the magnitude of angle A, we would apply cosine ratio because the given side lengths represent the adjacent side and hypotenuse of a right-angled triangle.

cos(θ) = Adj/Hyp

Where:

By substituting the given side lengths cosine ratio formula, we have the following;

cos(θ) = Adj/Hyp

cos(A) = 1.2/1.3

cos(A) = 1.2/1.3 × 10/10

cos(A) = 12/13

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The area of the rectangle shown on the coordinate plane is 12 square units.

What is the area of the rectangle shown on the coordinate plane?

To calculate the area of a rectangle, multiply the length by the width of the rectangle.

To find the area of the rectangle shown on the coordinate plane, first, we need to calculate the distance between the points that conforms two of the sides of the rectangle (base and height).

We can use any of the four vertex points shown on the coordinate plane, so, we will use the points:

1 - (-4, 1)

2 - (-1,-2)

3 - (-3,-4)

4 - (-6, -1)

Then, calculating the length of the sides,

Consider rectangle ABCD  with vertices A(-4, 1), B(-1, -2), C(-3, -4) and D(-6, -1). The area of the rectangle is

A = length * Width

Find the length and the width:

AB = √(-1 - (-4))² + (-2 - 1)² = √9 + 9 = √18

BC = √(-3 - (-1))² + (-4 - (-2))²  = √4 + 4 = √8

Then the area of the rectangle ABCD is

A = √18 * √8

A = 12 unit²

Hence, the area of the rectangle shown on the coordinate plane is 12 square units.

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The volume of the helium-filled balloon at 0.855 atm and 10.0 °C will be approximately 42.81 L, calculated using the ideal gas law equation.

To compute this problem, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

First, we need to convert the initial temperature of 25 °C to Kelvin:

T1 = 25 + 273.15 = 298.15 K

Next, we can rearrange the ideal gas law equation to solve for V2:

V2 = (P1 * V1 * T2) / (P2 * T1)

We have:

P1 = 1.08 atm (initial pressure)

V1 = 50.0 L (initial volume)

P2 = 0.855 atm (final pressure)

T2 = 10.0 °C (final temperature)

Converting the final temperature to Kelvin:

T2 = 10 + 273.15 = 283.15 K

Substituting the values into the equation:

V2 = (1.08 * 50.0 * 283.15) / (0.855 * 298.15)

V2 ≈ 42.81 L

Therefore, the volume of the helium-filled balloon at 0.855 atm and 10.0 °C will be approximately 42.81 L.

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The sum of the arithmetic sequence 12, 19, 26, 33..... n is 1425

Sum of  arithmetic sequence is given by the formula

S = n/2[2a + (n − 1) × d]

where

s = sum

n = number of terms

a = first term

d = common difference

The term as compared with the sequence is substituted

d = 19 - 12 = 26 - 19 = 7

S = 19/2 [2 * 12 + (19 − 1) × 7 ]

S = 19/2 [24 + 18 × 7 ]

S = 19/2 [150]

S = 1425

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Answer:

$3,096

Step-by-step explanation:

To find the total interest Mr. Quesada will pay, we need to first calculate the total amount he will pay back, and then subtract the original amount borrowed.

The total amount Mr. Quesada will pay back over 24 months is:

$629 x 24 = $15,096

Subtracting the original loan amount, we get:

$15,096 - $12,000 = $3,096

So Mr. Quesada will pay a total of $3,096 in interest over the course of the loan.

Let's plug in x = 2.

f(x) = x^2

f(2) = 2^2 ... replace every x with 2

f(2) = 4

----------

Now plug in x = 3.

f(x) = x^2

f(3) = 3^2 ... replace every x with 3

f(3) = 9

-----------

And x = 5 as well.

f(x) = x^2

f(5) = 5^2 .... replace every x with 5

f(5) = 25

-----------

We see that

f(2)+f(3) = 4+9 = 13

which is not equal to f(5) = 25.

So f(2)+f(3) = f(5) is false.

------------

Another way to phrase why it doesn't work is because (2,3,5) isn't a pythagorean triple. The equation 2^2+3^2 = 5^2 is false.

If it said f(3)+f(4) = f(5), then it would be correct because 3^2+4^2 = 5^2 is a true equation.

Answer:

12, 120,012

Step-by-step explanation:

The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.

the claim aligns with the null hypothesis, as both assert the absence of an effect, difference, or relationship between variables.

The claim and the null hypothesis are the same when the claim being made is that there is no significant difference or relationship between variables or that there is no effect or impact of a particular factor. In other words, the claim asserts that the null hypothesis is true.

For example, if the null hypothesis (H₀) states that there is no difference between the means of two groups, the corresponding claim would be that the means are indeed equal. Similarly, if the null hypothesis states that there is no correlation between two variables, the claim would be that there is indeed no significant correlation.

In such cases, the claim aligns with the null hypothesis, as both assert the absence of an effect, difference, or relationship between variables.

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A major disadvantage of correlations is that they cannot make a cause-and-effect statement.

Correlations are statistical measures that describe the size and direction of a relationship between variables.

Correlations are expressed as numbers. Correlations establish that relationships exist but do not explain if the change in one variable is caused by the change in another variable's value.

The disadvantages of correlations include:

Thus, a major disadvantage of correlations is that they cannot make a cause-and-effect statement.

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Using proportions, the amounts are given as follows:

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

We have that the amount of Twix is triple the amount of Milky ways, hence:

There are 5 fewer Snickers then Twix, hence:

Hence the amounts are given as follows:

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Answer:

65°

Step-by-step explanation:

Complementary angles add up to 90°. This means the measure of the other angle can be represented as

90° - 25°

or

65°

Answer:

The distance each bus travels is given as d=tr where

- d is distance bus travels

- t is a time bus travels

- r is the speed of the bus

:

Distance first bus travels for 4 hours is d1=4r.

Distance other bus travels for 4 hours is d2=4(r+12).

:

The total distance between them is 480 miles and since they go in opposite directions this distance is the sum of distances each bus travels.

:

d1+d2=480

4r+4(r+12)=480

4r+4r+48=480

8r+48=480

8r=432

r=432/8

r=54 mph, this is a speed of the first bus

:

r+12=66 mph, this is the speed of the second bus

Hope this helps you!!!! :D

Answer:

point-slope form, standard form, and slope-intercept form

Step-by-step explanation:

The three main types of linear functions are: point-slope form, standard form, and slope-intercept form.

Here is an image with each form

We proved that triangle abc ≅ triangle dbc.

A straight line that divides any line or any angle in equal two parts.

In the given question, line segment cb is a bisector.

Let, adc is an isosceles triangle and hence, side ac = side dc

cb is a perpendicular line on the base of triangle ad.

As per given condition line segment cb bisect the angle acd.

As a result, two equal angles ∠acb and ∠dcb is formed

And line segment cb divide the base ad of the Δacd in equal two parts.

Therefore, ab = bd, ∠acb = ∠dcb

and because of isosceles triangle ac= dc

After all these discussion for the triangle acb and triangle dcb

three side lengths are equal and also have an equal angle.

Δabc ≅Δdbc (proved)

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Answer:

im going to say c 55%

Step-by-step explanation: please let me know if its wrong so i can fix it thanks

The given line y = -2x + 3 will cross the y-axis at (0, 3).

A coordinate plane is a two-dimensional plane that consists x-axis and a y-axis. These are perpendicular to each other and will be intersected at the point called the origin.  

The coordinates of the point that lies on the y-axis are (0, y), Similarly, the coordinates of the point that lies on the x-axis are (0, x).    

Here we have

The equation of the line is y = -2x + 3  

To find the required point take x = 0

=> y = -2(0) + 3

=> y = 0 + 3

=> y = 3

Therefore,

The given line y = -2x + 3 will cross the y-axis at (0, 3).

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Answer:

3.3 for pepper and 2.7 for salt which is 6 tons in total

Step-by-step explanation:

The number of tons of hay both Salt and Pepper eat in a year is 5.5 tons.

Given that, every month, Salt eats 450 pounds of hay. Pepper is bigger, so he eats 550 pounds of hay each month.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Number of pounds of hay eaten by Salt in a year

= 450 × 12

= 5400 pounds

Number of pounds of hay eaten by Pepper in a year

= 550 × 12

= 6600 pounds

Total pounds of hay eaten by both the horses = 5400+6600

= 11000 pounds

In tons = 11000/2000

= 5.5 tons

Therefore, the number of tons of hay both Salt and Pepper eat in a year is 5.5 tons.

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