Weights of the Pacific yellowfin tuna follow a normal distribution with mean weight 68 pounds and standard deviation 12 pounds. For a randomly caught Pacific yellowfin tuna, what is the probability that the weight is less than 50 pounds

Hi

1/5 is mint  : so  30*1/5 = 6

1/2 of what remain is chocolate :  which mean  (30-6) /2 = 24/2 = 12

So vanilla will be :  30-6-12 =  30-18 = 12

recap :  6 mint, 12 chocolate and 12 vanilla.

So the measure of angle HLK is 45 degrees.

In geometry, an arc is a part of a curve that is typically a segment of a circle. It is defined by any two points on the curve, which are called its endpoints, and by all the points that lie along the curve between those two endpoints. An arc can be measured by its degree measure, which is the measure of the central angle that intercepts the arc, or by its length, which is the distance between its endpoints along the curve. In the context of a circle, an arc is also called a circular arc.

Here,

Since the measure of minor arc HK is 90°, we know that angle HJK is also 90°, since it is an inscribed angle that intercepts the same arc.

By the inscribed angle theorem, the measure of angle HLK is half the measure of arc HK. Therefore,

measure of angle HLK = 1/2 * measure of arc HK

= 1/2 * 90°

= 45°

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We need to round up to the nearest integer, the required sample size is 76 households.

To estimate the required sample size, we can use the formula:

[tex]n = (z^2 * s^2) / E^2[/tex]

Where:

z is the z-score corresponding to the confidence level (90% = 1.645)

s is the standard deviation of the population (square root of the variance, so s = sqrt(3.61) = 1.898)

E is the maximum error allowed (0.15 gallons)

Plugging in the values, we get:

[tex]n = (1.645^2 * 1.898^2) / 0.15^2[/tex]

n = 75.57

Since we need to round up to the nearest integer, the required sample size is 76 households.

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Using the height formula of the trapezoid, we know that the height is 5000m respectively.

In geometry, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid in American and Canadian English or a trapezium in British and other forms of English.

In Euclidean geometry, a trapezoid is a convex quadrilateral by definition.

The bases of the trapezoid are the parallel sides.

There are four sides to a trapezoid.

A trapezium is another name for a trapezoid.

It features two parallel sides that are not equal and two nonparallel sides.

So, find the height of the trapezoid as follows:

Formula: h = 2A/a+b

a = 8mm, b = 6 mm

A = 35 mm²

Unit conversion:

a = 8*10⁻³mm

b = 6*10⁻³mm

Using the formula:

h = 2A/a+b

h = 2*35/8*10⁻³+6*10⁻³

h = 5000m

Therefore, using the height formula of the trapezoid, we know that the height is 5000m respectively.

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Every point on the graph of g(x) is 1 unit higher than the corresponding point on the graph of f(x).

Given that

f(x) = 4(0.5)^x and g(x) = 4(0.5)^x + 1

The graphs of the functions f(x) = 4(0.5)^x and g(x) = 4(0.5)^x + 1 are both exponential functions with a base of 0.5.

The only difference between these two functions is the addition of a constant term of 1 to the second function.

This constant term shifts the graph of g(x) vertically upward by 1 unit compared to the graph of f(x).

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Complete question

Describe how the graph of f(x) = 4(0.5)^x compares to the graph of g(x) = 4(0.5)^x +1

Answer:

351-7 cm³

Step-by-step explanation:

Volume a cylinder = π r² h

π = 3.14

r = radius = 4cm

h = height = 7cm

Then:

Volume = 3.14 * 4² * 7

volume = 3.14 * 16 * 7

volume = 351.7 cm³

The equation with the fewest symbols is 30x - 18, which represents the simplified form of the given expression.

An equation is a mathematical statement that shows the equality between two expressions. The given expression is not an equation since there is no equality sign present. However, we can simplify the expression to get an equivalent equation with the fewest symbols.

To simplify the expression, we use the distributive property of multiplication over addition/subtraction. We multiply 6 with each term inside the parentheses, i.e., 5x and -3. This gives us:

6(5x - 3) = 6(5x) - 6(3) = 30x - 18

This simplified expression is an equation that shows the equality between the left-hand side (LHS) and the right-hand side (RHS). The LHS is 30x - 18, and the RHS is also 30x - 18, which means that they are equal.

Therefore, the equation with the fewest symbols is 30x - 18, which represents the simplified form of the given expression.

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Answer:

C. DEFG and VWXY

Step-by-step explanation:

It is the better answer choice here

Answer:

12312

Step-by-step explanation:

add the 11485 to 827 to figure out how many times did the red team do

Answer:

The equation for the alternating current can be described by: y = 155 sin(120πt)

Where y is the voltage in volts (V) and t is the time in seconds (s).

To find the value of y when t = 1/90 s:

y = 155 sin(120π(1/90))

y ≈ 30.8 V

To approximate the value of t when y = 100 V for the first time, we need to solve the equation for t:

100 = 155 sin(120πt)

sin(120πt) = 100/155

t = arcsin(100/155)/(120π)

t ≈ 0.001 s

Therefore, the value of t when y = 100 V for the first time is approximately 0.001 seconds

According to the equation, the monthly fee that Sara paid was $60.

Let's start by assigning some variables. Let x be the monthly fee that Sara paid and let y be the number of months that Sara was a member of the gym. We know that Sara paid $15.95 to become a member, so her total cost can be represented by the equation:

Total Cost = Initial Cost + Monthly Fee x Number of Months

$735.95 = $15.95 + x x y

Now we have an equation with two variables. To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting $15.95 from both sides of the equation:

$720 = x x y

Next, we need to solve for x. Since we don't know the value of y, we can't solve for x directly. However, we do know that Sara was a member for 12 months, so we can substitute y = 12 into the equation:

$720 = x x 12

Now we can solve for x by dividing both sides by 12:

$60 = x

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Since the gravitational force is directly proportional to the mass, we can see that Satellite D has the greatest mass and therefore the greatest gravitational force with Earth. Therefore, the correct option is D.

To determine which satellite has the greatest gravitational force with Earth, we need to use the formula for gravitational force, which is:

force = (G x m1 x m2) / r^2

where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of the objects.

Since the mass of Earth is much greater than any of the satellites, we can assume that the distance between Earth and each satellite is the same. Therefore, we can compare the gravitational force of each satellite with Earth by calculating:

force = (G x Earth's mass x satellite's mass) / distance^2

Using this formula and plugging in the given values, we get:

For Satellite A: force = (G x Earth's mass x 375 kg) / (320 km)^2

For Satellite B: force = (G x Earth's mass x 250 kg) / (320 km)^2

For Satellite C: force = (G x Earth's mass x 50 kg) / (320 km)^2

For Satellite D: force = (G x Earth's mass x 500 kg) / (320 km)^2

Therefore, the correct option is D.

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If sin (α) =(5)/(13) in Quadrant I and cos(β) = (-12)/(13) in Quadrant II, then sin(α + β ) = -120/169 .So, the answer is option 1).

To evaluate sin(α + β), we can use the trigonometric identity:

sin(α + β) = sin α cos β + cos α sin β

First, we need to find cos α. Since sin α is positive and in Quadrant I, we can use the Pythagorean identity to find cos α:

cos α = √(1 - sin² α) = √(1 - (5/13)²) = √(1 - 25/169) = √(144/169) = 12/13

Next, we need to find sin β. Since cos β is negative and in Quadrant II, we can use the Pythagorean identity to find sin β:

sin β = -√(1 - cos² β) = -√(1 - (-12/13)²) = -√(1 - 144/169) = -√(25/169) = -5/13

Now we have all the values we need to evaluate sin(α + β):

sin(α + β) = sin α cos β + cos α sin β

= (5/13)(-12/13) + (12/13)(-5/13)

= -60/169 - 60/169

= -120/169

Therefore, the answer is option 1) -120/169.

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We got x = 149.53 by using Pythagorean theorem.

angle of semicircle is always be 90°.

[tex]172^2=85^2+x^2[/tex]

[tex]29584=7225+x^2[/tex]

[tex]x^2=29584-7225[/tex]

[tex]=22359[/tex]

[tex]x=\sqrt{22359}[/tex]

[tex]\boxed{\bold{x=149.53}}[/tex]

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Answer:

20 miles

Step-by-step explanation:

1 hr= 2.8 miles

7hrs=2.8×7

2.8×7= 19.6

19.6 to 1dp is 20

Answer:

81

Step-by-step explanation:

for the volume you just multiple length, height, and depth

Answer: 81.

Step-by-step explanation:

9 x 3 x 3 . LxWxH  brother!

Based on the medians, we can conclude that Bus 47 typically has a faster travel time than Bus 18. The median travel time for Bus 47 is 16 minutes, which is 3 minutes faster than the median travel time for Bus 18, which is 13 minutes.

To determine which bus typically has the faster travel time, we need to compare the measures of center for each data set. Since the data sets are relatively small and appear to have some outliers, the median is the more appropriate measure of center to use in this case, as it is less affected by extreme values than the mean.

For Bus 47, the median is 16, which means that half of the students take less than 16 minutes to travel to school on that bus, and half take more than 16 minutes.

For Bus 18, the median is 13, which means that half of the students take less than 13 minutes to travel to school on that bus, and half take more than 13 minutes.

Therefore, based on the medians, we can conclude that Bus 47 typically has a faster travel time than Bus 18. The median travel time for Bus 47 is 16 minutes, which is 3 minutes faster than the median travel time for Bus 18, which is 13 minutes.

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If the cabinets are 34 inches tall, 24 inches deep, and 16 inches wide, the volume of the kitchen cabinets is 16,384 cubic inches.

To find the volume of the rectangular prisms-shaped kitchen cabinets, we need to multiply the three dimensions: height, depth, and width. We are given the following measurements:

Height = 34 inches

Depth = 24 inches

Width = 16 inches

So the formula for the volume is:

Volume = Height x Depth x Width

Substituting the given values, we get:

Volume = 34 x 24 x 16

Volume = 16,384 cubic inches

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The Standard Normal Table is a tool that is used to calculate probabilities associated with the standard normal distribution.

When using the Standard Normal Table, we can find the area to the left of z < -2.34 by first locating the value -2.3 in the left-hand column of the table and the value -0.04 in the top row of the table.

Then, we find the intersection of the row and column to locate the corresponding value of 0.0099. This value represents the area to the left of -2.3 on the standard normal distribution.

To find the area to the left of -2.34, we need to adjust the value by subtracting the area to the left of -2.34 from the area to the left of -2.3.

The standard normal distribution is symmetric around the mean of 0. It means the area to the right of -2.3 is the same as the area to the left of 2.3.

Therefore, the area to the left of z < -2.34 is the area to the left of -2.3 (0.0099) minus the area between -2.34 and -2.3 (0.0040), which equals 0.0059. So, the area to the left of z < -2.34 is 0.0059.

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Answer:

Step-by-step explanation:

In the equation h=6d, the independent variable is d, which represents the number of days. The dependent variable is h, which represents the height of the plant that depends on the number of days it has been growing.

The length of JL is 20.572.

An angle is a geometric figure formed by two rays or lines that share a common endpoint, called the vertex of the angle. Angles are measured in degrees or radians, and they are used to describe the relationships between lines and shapes in geometry.

The size of an angle is determined by the amount of rotation needed to bring one of the rays into coincidence with the other. A full rotation around the vertex is equivalent to 360 degrees or 2π radians. A right angle, which is formed by one ray perpendicular to another, has a measure of 90 degrees or π/2 radians.

Angles can be classified according to their measures as acute angles (less than 90 degrees), right angles (exactly 90 degrees), obtuse angles (between 90 and 180 degrees), straight angles (exactly 180 degrees), and reflex angles (between 180 and 360 degrees).

Angles also have a number of important properties and relationships, such as vertical angles (formed by two intersecting lines and are congruent), complementary angles (two angles whose measures sum up to 90 degrees), and supplementary angles (two angles whose measures sum up to 180 degrees).

cos  A= (leg adjacent to ∠A)/hypotenuse: cos(∠KLM)= [tex]\frac{LM}{KL}[/tex]

Substitute, LM= 7, KL= 12 : cos(∠KLM)= [tex]\frac{7}{12}[/tex]

Calculate cos(∠KLM)= [tex]\frac{7}{12}[/tex] : ∠KLM= 54.315°

Representing same angles: ∠JLK= ∠KLM

Substitute ∠KLM= 54.315° into ∠JLK= ∠KLM ⇒∠JLK= 54.315°

cos  A= (leg adjacent to ∠A)/hypotenuse: cos(∠JLK)=[tex]\frac{KL}{JL}[/tex]

Substitute, KL= 12, ∠JLK= 54.315°  ⇒ cos(∠JLK)= [tex]\frac{12}{JL}[/tex]

Calculate cos(54.315°)=[tex]\frac{12}{JL}[/tex] ⇒ JL= 20.572

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The complete question is:

The mean number of states will be 6.

The percentage of students who visited more than 7 states will be 20%.

The mean number of states will be:

= 120 / 20

= 6.

The percentage of students who visited more than 7 states will be:

= 4/20 × 100

= 20%

The number of students who visited 7 or 8 states compare to the number of students who visited 5 states or less as they're both 7 each. This implies that they're equal.

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x = 108 is 3.10 standard deviations to the left of the mean.

The standard deviation (SD, also written as the Greek symbol sigma or the Latin letter s) is a statistic that is used to express how much a group of data values vary from one another.

The z-score when x = 108 is:

z = (108 - 153) / 14.5

z = -3.10

This tells us that x = 108 is 3.10 standard deviations to the left of the mean.

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Answer:

[tex]\frac{12}{5}[/tex] = 12 ÷ 5

[tex]\frac{1}{4}[/tex] = 1 ÷ 4

[tex]\frac{3}{8}[/tex] = 3 ÷ 8

[tex]\frac{9}{2}[/tex] = 9 ÷ 2

a. The correlation coefficient: ≈ -0.184

b. The correlation coefficient r ≈ -0.184, which is close to 0. This suggests that there is a weak negative correlation between the x and y values in the data.'

To find the line of best fit using a linear regression algorithm, we need to find the slope (m) and y-intercept (b) of the equation in the form y = mx + b.

We will start by calculating some statistics from the given data.

First, let's find the means of x and y:

x_mean = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) / 9 = 45 / 9 = 5

y_mean = (8 + 4.037 + 7.200 + 4.180 + 4.763 + 1 + 1.047 + 2.436 + 1.844) / 9 ≈ 34.507 / 9 ≈ 3.834

Next, we need to find the sum of the product of the differences between each point and the mean for both x and y:

Σ((x - x_mean) * (y - y_mean)) = (1 - 5) * (8 - 3.834) + (2 - 5) * (4.037 - 3.834) + ... + (9 - 5) * (1.844 - 3.834) ≈ -8.311

We also need to find the sum of the squared differences between each x and the mean of x:

Σ((x - x_mean)^2) = (1 - 5)^2 + (2 - 5)^2 + ... + (9 - 5)^2 = 60

Now, we can calculate the slope (m):

m = Σ((x - x_mean) * (y - y_mean)) / Σ((x - x_mean)^2) ≈ -8.311 / 60 ≈ -0.1385

To find the y-intercept (b), use the formula:

b = y_mean - m * x_mean ≈ 3.834 - (-0.1385) * 5 ≈ 4.525

Now we have the line of best fit equation:

y = -0.1385x + 4.525

a. To find the correlation coefficient (r), we need to divide the covariance of x and y by the product of the standard deviations of x and y.

First, let's find the covariance:

cov(x, y) = Σ((x - x_mean) * (y - y_mean)) / (n - 1) ≈ -8.311 / 8 ≈ -1.039

Next, find the standard deviations of x and y:

sd_x = sqrt(Σ((x - x_mean)^2) / (n - 1)) = sqrt(60 / 8) ≈ 2.738

sd_y = sqrt(Σ((y - y_mean)^2) / (n - 1))

sd_y = sqrt((8 - 3.834)^2 + (4.037 - 3.834)^2 + ... + (1.844 - 3.834)^2) / 8 ≈ sqrt(33.904) / 8 ≈ sqrt(4.238) ≈ 2.058

Now we can calculate the correlation coefficient:

r = cov(x, y) / (sd_x * sd_y) ≈ -1.039 / (2.738 * 2.058) ≈ -0.184

b. The correlation coefficient r ≈ -0.184, which is close to 0. This suggests that there is a weak negative correlation between the x and y values in the data.'

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When the temperature increases and the water vapor content in the air stays the same, the relative humidity decreases. This is because warmer air can hold more moisture than colder air, and therefore the ratio of the actual amount of water vapor in the air to the maximum amount of water vapor that the air can hold decreases as the air temperature increases.

Relative humidity depends on two factors: the amount of water vapor present in the air and the maximum amount of water vapor that the air can hold at a given temperature. As the temperature rises, so does the amount of water vapor that the air can hold, since warm air has more energy to hold the water molecules in vapor form. This reduces the ratio of the actual amount of water vapor in the air to the maximum amount of water vapor the air can hold, resulting in lower relative humidity.

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There are 813 minutes in between 17:53 to 7.26 .

Time can be represented in two formats, that is in a twelve - hour format and in a twenty four - hour format.

Here the time 17:53 and 7:26 is represented in twenty four - hour format where the day is divided in twenty four hours and time runs from midnight and ends at midnight.

(If the time 17:53 and 7:26 was represented in twelve - hour format then it would have AM and PM to denote if the time is from midnight till noon or noon till midnight, which is clearly not the case.)

Thus, from 17:53 to 7.26 there is 13 hours and 33 minutes.

We know one hour has 60 minutes. Therefore by method of conversion of hours to minutes we get,

Number of minutes between 17:53 to 7.26 = {(13*60) + 33} = 780+33 = 813

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Answer:

Step-by-step explanation:

The correct answer is option D, 1078[tex]\pi[/tex] [tex]cm^{3}[/tex].

The volume of the cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h.

Radius = 7cm Height = 22cm.

Substituting the value in the formula, we get

[tex]\pi[/tex]*[tex]7^{2}[/tex]*22 = 1078[tex]\pi[/tex].

Hence the Answer is 1078[tex]\pi[/tex].

Answer:

3386.64 cm3

Step-by-step explanation:

i use this formula    π r² h