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The distance between P and R of the ship bearing correct to the nearest metre is equal to 112 using the cosine rule.

Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.

Let ∆PQR be the triangle formed with bearings so that:

angle Q = 26° + 90° {alternate angles}

angle Q = 116°

PQ = 53m

QR = 78m

The distance between P and R is calculated using the cosine rule as follows:

PR² = 53² + 78² - 2(53)(78)cos116° {cosine rule}

PR² = 8893 + 3624.4526

PR = √12517.4526 {take square root of both sides}

PR = 111.8814

Therefore, the distance between P and R of the ship bearing correct to the nearest metre is equal to 112 using the cosine rule.

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Navern's manufacturing cycle efficiency (MCE) for its elevators is: 41.4%

The formula for obtaining the manufacturing cycle efficiency is value-added time divided by the production cycle time * 100. In the data given, the process and inspection times qualify as a value-added time

Process time = 23 days

Inspection time = 13 days

Value added time = 23 + 13 = 36days

The production cycle time = Move time + process time + queue time + inspection time + wait time

= 22 + 12 + 23 + 13 + 17 days

= 87 days

So, the manufacturing efficiency time = 36/87 * 100

= 41.4%

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Answer:

074°

Step-by-step explanation:

the bearing of Y from X is the measure of the angle from the north line (N) at X in a clockwise direction to Y , that is ∠ NXY

∠ NXY = 180° - 106° = 74°

the 3- figure bearing of Y from X is 074°

Answer:

the answer are 2 and 6 ok

Answer:

2 and 6

Step-by-step explanation:

Take integers to be X and Y

X*Y=12

X + Y = 8

from the second equation, X= 8-Y

put X in the first Equation

(8-Y)Y = 12

Expand the equation

-Y² + 8Y - 12 = 0

Factorize the above equation

(-Y + 2) (Y - 6) = 0

Y = 2 and Y = 6

choose any value of Y.

so Y = 6,

put Y in X + Y = 8

X + 6 = 8

X = 2

therefore the integers are 2 and 6

1/x^7

Step-by-step explanation:

To the 7th power is positive. It's the first one.

Hope this helps, have a good day!

it is A because X is unknown u can put 0 as a denominator so it 1 the X is still unknown and your exponents are 0

Answer:

126

Step-by-step explanation:

(−3/10)(4.2)(−100)

Since the product of -10 & 10 is -100, we can rewrite as-you may call this associative property I guess since I still haven't rearranged the factors:

(−3/10)(4.2)((−10)(10))

Associative property:

(-3/10)(4.2)(-10)(10)

Commutative property:

(-3/10)(-10)(4.2)(10)

Associative property:

((-3/10)(-10))((4.2)(10))

Simplifying:

(3)(42)

Simplifying:

126

The value of product is 126.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The expression is;

⇒ (−3/10)(4.2)(−100)

Since, Apply Commutative property in multiplication as;

⇒ (−3/10)(4.2)(−100) = -3 × 1/10 × 4.2 × -100

                             = -3 × 4.2 × -100 × 1/10

                             = 126

And, Apply associative property;

⇒ (−3/10)(4.2)(−100) = (-3/10) (4 + 0.2) (-100)

                             = 3 × 10 (4 + 0.2)

                             = 30 (4 + 0.2)

                             = 30 × 4 + 30 × 0.2

                             = 120 + 6

                             = 126

Thus, The value of product is 126.

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The sum of these 40 sampled numbers follows option D: normal distribution, if X follows Poisson distribution.

The likelihood that a certain number of events will occur in a specific period of time or space, provided that they do so with a known constant mean rate and the Poisson distribution describes the distribution of events, regardless of the time since the previous event. When the mean is high, the sum of the Poisson distribution resembles a normal distribution.

The "normal distribution," a continuous probability distribution that is symmetrical at the mean and has a bell-shaped curve. It is also known as the bell curve or the Gaussian distribution. Several natural phenomena, including height, weight, blood pressure, and others, have a normal distribution.

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Answer:

(A) 45x +455= 905

10 hours of labor

Step-by-step explanation:

Start by defining the variable x:

Let x be the number of hours of labor.

Total bill= parts +labor

905= 455 +45x

(A) 45x +455= 905

_____

Solving for x:

45x +455= 905

Bring constants to the other side of the equation:

45x= 905 -455

45x= 450

x= 450 ÷45

x= 10

Since $45 is an hourly rate, the units of x we are looking at is hours.

Thus, 10 hours of labor is needed to complete the job.

Answer:

x=6

Step-by-step explanation:

Answer: x=6

Step-by-step explanation: 5•6+3=33

Good luck! :)

The length of James's rectangular yard, given a fence perimeter of 20 feet and a width of 2 feet, is 8 feet, equivalent to 96 inches.

Given: Perimeter (P) = 20 feet, Width (W) = 2 feet,

Conversion factor: 1 foot = 12 inches

Using the formula for perimeter: P = 2L + 2W

Substitute the given values: 20 = 2L + 2(2)

Simplify: 20 = 2L + 4

Subtract 4 from both sides: 16 = 2L

Divide by 2: L = 8 feet

Convert feet to inches: Length (in inches) = 8 feet * 12 inches/foot = 96 inches

So, the length of the rectangular yard is 96 inches.

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To find the length of James' rectangular yard in inches, we can use the perimeter formula P = 2L + 2W. Given that the perimeter is 20 feet and the width is 2 feet, we can substitute these values into the formula and solve for the length in inches. The length of James' rectangular yard is 108 inches.

To find the length of James' rectangular yard in inches, we can use the perimeter formula P = 2L + 2W. Given that the perimeter is 20 feet and the width is 2 feet, we can substitute these values into the formula. However, since we need the length in inches, we will convert the feet to inches using the conversion factor of 1 foot = 12 inches.

Let's solve:

The length of James' rectangular yard is 108 inches.

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Answer:

The biggest differentiating factor between a function and NOT a function

is that a function gives only one output for any given input. so no matter how many times you use the same value in the function, you will get the same output

A relation which is not a function will have 2 or more outputs for a single input

So if we have more than 1 similar input values in the table and given them different outputs, the relation will NOT be a function

I will take 2 similar inputs "1" and give them different outputs, the rest of the table can be randomly filled

x         y

1         4

3        7

5        9

1         2

Answer:

9

Step-by-step explanation:

18 x 1/2

18/2

9

Answer: 9

Step-by-step explanation:

Parenthesis first, so 8+10 =18 .

18 multiplied by 1/2 = 9

Answer:

See diagram below.

====================================================

Explanation:

Start at the lower left corner of the entire figure. Move 20 ft directly to the right until reach the end of the driveway at the bottom. Now move 10 ft up so you reach the other side of the driveway (the 26 ft side). In the process of moving 10 ft up, mark a new line segment. I've done so in red in the diagram below.

I've also drawn a green box. The red line and green box form a shape of a flag on a flagpole. The pole being 10 ft tall and the green box (flag) is a 6 by 3 rectangle. The 6 is from 26-20 = 6 and the 3 is from 10-7 = 3. Note how I'm subtracting the opposite side values to help figure out the dimensions of this green box.

The 10 ft by 20 ft portion of the driveway is 10*20 = 200 square feet. The green box adds on another 18 sq ft because 6*3 = 18. In all, we have 200+18 = 218 square feet for the driveway.

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

If you want to know the area of the garden, then we first compute the overall area of everything shown. That's 32*14 = 448 square feet. Subtract off the driveway's area to get 448-218 = 230. Therefore, the garden's area is 230 square feet.

Answer:

Simplest form of expression:

-3+2x

Answer:

2x - 3 (or) -3 + 2x

Step-by-step explanation:

Given equation,

→ (-+ 3) - 2 (-x)

The simplest form will be,

→ (-+ 3) - 2 (-x)

→ -3 + (-2 × -x)

→ -3 + 2x

→ 2x - 3

Thus, the answer is 2x - 3.

The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

From the question, we have the following parameters that can be used in our computation:

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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A formula without free variables is a formula that does not contain any variables that are not quantified.

Sentences are commonly referred to as formulas devoid of any unrestricted variables. These statements hold a truth value independent of the variable values, hence the reason.

Open formulas are frequently referred to as formulas with free variables. These are not actually declarations; instead, they are arrangements that can transform into declarations by allotting definite values to the independent variables.

Formulas without free variables are often easier to work with than formulas with free variables.

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To earn an A grade, a student needs to score at least 82.8 , calculated using the inverse normal cumulative distribution function with a mean of 70, a standard deviation of 10, and a 10th percentile of 0.10.

Given that the grades are normally distributed with a mean of 70 and a standard deviation of 10.

We need to find the score which is at the 10th percentile of the distribution.

Using the standard normal distribution table, we can find the z-score that corresponds to the 10th percentile.

From the table, we can see that the z-score is approximately -1.28.

Using the formula for standardizing a normal distribution:

z = (x - μ) / σ

where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.

Substituting the given values, we have:

-1.28 = (x - 70) / 10

Solving for x, we get:

x = (-1.28 * 10) + 70

x = 82.8

Therefore, a student would need to earn a score of approximately 82.8 to receive an A grade.

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Answer: -27

Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.

3, 9, -3, 3, -9, -3, -15, -9, -21, ?

We can start by looking at the differences between consecutive terms in the list:

9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12

Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:

-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21

Therefore, we predict that the most probable next number in the list is -27.

To find the probability that Naomi selects both white balls, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes:

Naomi selects 2 balls without replacement, so the total number of outcomes is the number of ways she can choose 2 balls out of the total number of balls in the bag. This can be calculated using combinations:

Total outcomes = C(20, 2) = (20!)/(2!(20-2)!) = (20 * 19)/(2 * 1) = 190

Number of favorable outcomes:

Naomi needs to select 2 white balls. There are 2 white balls in the bag, so the number of favorable outcomes is the number of ways she can choose 2 white balls out of the 2 white balls in the bag:

Favorable outcomes = C(2, 2) = 1

Probability = Favorable outcomes / Total outcomes = 1/190

Therefore, the correct answer is (G) 1/190.

9514 1404 393

Answer:

Step-by-step explanation:

A cube that is 1/3 ft on a side will fit 3 in a foot. In terms of the 1/3 ft small cube, the dimensions of the prism are ...

  1 1/3 ft = 4 small cubes

  1 ft = 3 small cubes

  2 1/3 ft = 7 small cubes

Then the volume in terms of small cubes is ...

  V = LWH = (4)(3)(7) = 84 small cubes

__

There are 3×3×3 = 27 small cubes in a 1-ft unit cube, so the prism volume in terms of unit cubes is ...

  84/27 = 3 1/9 . . . unit cubes

__

Additional comment

The largest dimension of the prism is just over 2 ft, so the maximum number of unit (1 ft) cubes that will fit is 2. To fill the volume with 3 1/9 unit cubes, those would have to be cut and fit into the space.

Answer:

A:84 B:?

Step-by-step explanation:

In preparing to construct a one-sample t interval for a population mean, suppose we are not sure if the population distribution is Normal. In option (c) A boxplot of the data has a large outlier, we would not be safe constructing the interval based on an SRS of size 24 from the population.

What is a sample?

A sample is characterised as a more manageable and compact version of a bigger group. A smaller population that possesses the traits of a bigger group. When the population size is too big to include all participants or observations in the test, a sample is utilised in statistical analysis.

Constructing a one-sample t interval for a population mean is generally safe when the population is not Normal, as long as the sample size is large enough (usually at least 30) or the sample is taken from a population that is not too skewed or has outliers.

Therefore, options (a), (b), and (e) suggest that the sample may come from a population that is roughly Normal or can be transformed to be Normal, and so constructing the interval based on an SRS of size 24 would be safe.

Option (d) suggests that the sample standard deviation is large, but this does not necessarily mean that constructing the interval would not be safe.

It may reduce the precision of the interval, but as long as the sample size is sufficient, the interval can still be constructed.

Option (c) suggests that the sample has a large outlier, which may significantly affect the distribution of the sample and the calculation of the interval.

Therefore, in this circumstance, constructing the interval based on an SRS of size 24 would not be safe.

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ANSWER

LMNO is a parallelogram

EXPLANATION

Segments LM and NO are parallel, because they are both horizontal lines. Also, they are congruent because the horizontal distance between the endpoints is the same for both segments:

Then, segments LO and NM are parallel too. We can prove this with the slope

The slope is:

For both segments, the rise is 5 - which is the height of the parallelogram - and the run is 2. Therefore they have the same slope, so they are parallel.

Hence, LMNO is a parallelogram.

That is correct.

Sqrt 5 x sqrt20

Apply the radical rule to get sqrt( 5 x 20)

Simplify to get sqrt(100)

Sqrt(100) = 10

Solution:

Option A

Option B

Option C

Option D

Option C is correct.

Answer:

5

Step-by-step explanation:

Part A: 4 x 6 = 24 - 5 = 19 = 19, and v= is equal to or less than. Because 19 is the same as 19, saying it is larger than is false.

Part B (of two):

The answer is incorrect: 4 x 4 = 16 + 3 = 19 = 23.

20 + 3 = 23 = 23 = 4 x 5 = 20 x 5 = 20 x 5 = 20 x 5 = 20 x True, but we should also consider the other possibilities.

Incorrect: 4 x 6 = 24 + 3 = 27 = 23

Incorrect: 4 x 7 = 28 + 3 = 31 = 23

Incorrect: 4 x 8 = 32 + 3 = 35 = 23

As a result, 5 is the correct response!

Answer:

m = 5

Step-by-step explanation:

Given , x = m, y = 5 (from (m,5) )

5x - y = 20

=> 5m - 5 = 20

=> 5m = 20 + 5

=> 5m = 25

=> m = 25/5

=> m = 5