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A rectangle has an area of 345 square millimeters and a base of 15 millimeters. What is the height?

Using the double-angle identity and substituting the values for cosine and sine of 30 degrees, we simplified \(10 \cos 30 \sin 30\) to \(\frac{5\sqrt{3}}{2}\).

To rewrite \(10 \cos 30 \sin 30\) using a double-angle identity, we can use the identity \(\sin 2\theta = 2 \sin \theta \cos \theta\). Given that \(\cos 30 = \frac{\sqrt{3}}{2}\) and \(\sin 30 = \frac{1}{2}\), we can rewrite the expression.

To rewrite \(10 \cos 30 \sin 30\) using a double-angle identity, we can substitute \(\cos 30 = \frac{\sqrt{3}}{2}\) and \(\sin 30 = \frac{1}{2}\) into the expression.

\(10 \cos 30 \sin 30 = 10 \cdot \frac{\sqrt{3}}{2} \cdot \frac{1}{2}\)

Simplifying, we get:

\(10 \cos 30 \sin 30 = \frac{10}{2} \cdot \frac{\sqrt{3}}{2} \cdot 1\)

\(10 \cos 30 \sin 30 = 5 \cdot \frac{\sqrt{3}}{2}\)

\(10 \cos 30 \sin 30 = \frac{5\sqrt{3}}{2}\)

Therefore, \(10 \cos 30 \sin 30\) can be rewritten as \(\frac{5\sqrt{3}}{2}\).

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The expected number of boxes to be produced is given as 3,000 boxes. So, the correct answer is 0.3, indicating that the takt time in minutes is 0.3 minutes.

The production line operates for two eight-hour shifts each day, which means there are 16 hours of production time available. Since there are 60 minutes in an hour, the total available time in minutes would be 16 hours multiplied by 60 minutes, which equals 960 minutes.

The expected number of boxes to be produced is given as 3,000 boxes.

To calculate the takt time in minutes, we divide the total available time (960 minutes) by the expected number of boxes (3,000 boxes):

\(Takt time = Total available time / Expected number of boxes\)

\(Takt time = 960 / 3,000\)

By performing the calculation, we find that the takt time is approximately 0.32 minutes, which is equivalent to 0.3 minutes rounded to one decimal place.

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0.017 m/min is the height of increasing water.

What is the volume of a cylinder?

A cylinder's volume refers to the amount of interior room it has to hold a given quantity of material.

Formula to calculate the volume of a cylinder

volume = π r² h

where r is the radius of the cylinder and h is the height.

Here, we have

radius = 6m

dV/dt = 3

We have to find:  dh/dt

volume = π r² h

Differentiating both sides with respect to t, we get

dV/dt = π[2r(dr/dt)h + r²(dh/dt)]

r remains constant (r = 6), dr/dt = 0

So, dV/dt = πr²(dh/dt)

Substituting the values, we get

2 = π(6)²(dh/dt)

dh/dt = 2/(36π)

= 0.017m/min

Hence, 0.017 m/min is the height of increasing water.

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The determinant of the given matrix { [1 4 3], [3 5 1], [4 1 5]} is -71. Thus, the correct answer is (d) -71.

To compute the determinant of the matrix using cofactor expansion, we can expand along the first row:

det = 1( det ([5 1][1 5]) - 4 ( det([3 1][4 5]) ) + 3 ( det([3 5][4 1]) )

det = 1(( 5*5 - 1*1 ) - 4*( 3* 5 - 1*4 ) + 3*( 3*1 - 5*4 ))

det = 1( 25 - 1 - 4 ( 15 - 4 ) + 3 ( 3 - 20 ))

det = 1( 25 - 1 - 4 ( 11 ) + 3 (-17) )

det = 1( 25 - 1 - 44 - 51 )

det = 1( -71 )

Therefore, the determinant of the given matrix is -71.

So, the correct answer is (d) -71.

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Points:

Im sorry but imma yoink your points and not answer the question

Hol up:

There is no question here so it's ok

The angle in radians to the nearest 10th 4.9. An angle in radians is a unit of measurement for angles, defined as the ratio of the length of the arc intercepted by the angle to the radius of the circle.

The measure of an angle in radians is typically expressed as a fraction of the constant pi, which is equal to approximately 3.14. For example, a right angle has a measure of \($\frac{\pi}{2}$\) radians, while a full circle has a measure of \($2\pi$\) radians.

The circumference of the circle is given by the formula \($C=2\pi r$\),

where C is the circumference, pi is a constant equal to approximately 3.14,

r is the radius of the circle.

In this case, the radius is 5.1, so the circumference is \($2\pi(5.1)=10.2\pi$\).

The arc length is a portion of the circumference,

so we can find the measure of the angle that intercepts the arc by dividing the arc length by the circumference and multiplying by the total measure of the circle,

which is \($360^\circ$\).

The measure of the angle in radians can then be found by converting from degrees to radians using the formula \($\text{radians}=\frac{\text{degrees}}{180}\cdot\pi$\)

Plugging in the values, we get:

\($$\text{radians} = \frac{25}{10.2\pi}\cdot 360^\circ\cdot\frac{\pi}{180^\circ} \\$$= \frac{25\cdot 360^\circ}{10.2\pi\cdot 180^\circ}\\ = \frac{25\cdot 2\pi}{10.2\pi} \\= \frac{50\pi}{10.2\pi} \\= \frac{50}{10.2}$$\)

To the nearest 10th, the answer is 4.9.

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Answer:

Disagree

radius = 7 m

diameter = 14 m

Step-by-step explanation:

Formula

\(\sf Area\:of\:a\:circle=\pi r^2\)

Given:

Substitute given value into the formula and solve for r:

\(\sf \implies \pi r^2=153.88\)

\(\sf \implies r^2=\dfrac{153.88}{\pi}\)

\(\sf \implies r=\sqrt{\dfrac{153.88}{\pi}}\)

\(\sf \implies r=6.998680253\)

Therefore r ≈ 7 m

So I disagree with Nysean, as from my calculations, the approximate radius of the merry-go-round is 7 m.

Diameter = 2r

⇒ diameter of merry-go-round = 2 x 7 = 14m

So Nysean has actually given the approximate measure of the diameter rather than the radius.

The length of the diagonal for this rectangle is 13 cm.

To find the length of the diagonal for a rectangle with measurements of 5 cm by 12 cm, you can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (diagonal in this case) is equal to the sum of the squares of the other two sides (length and width).

In this case, the length is 5 cm and the width is 12 cm. Using the Pythagorean theorem:

Diagonal² = Length² + Width²
Diagonal² = 5² + 12²
Diagonal² = 25 + 144
Diagonal² = 169

Now, take the square root of 169 to find the length of the diagonal:

Diagonal = √169
Diagonal = 13 cm

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Answer:

0.20x(1000/55)

Step-by-step explanation:

Answer: 195°

Step-by-step explanation:

The sum of interior angles can be found by using this formula

(n - 2)180

(7 - 5)180

5 * 180

900 = sum of interior angles

900 - 120 = 780

Now we divide it by 4

780 ÷ 4 = 195°

The equal angles is 195°

Answer:

1962/18=109.

Division sign

Step-by-step explanation:

Answer:

1962 ÷ 18

Step-by-step explanation:

i answered in the comments before the other person

oh well

dum bots taking up answers

The probability that: either a or b occur

P(AUB)=0.9

This is further explained below.

Generally, In the fields of logic and probability, two occurrences are said to be mutually exclusive or discontinuous if it is impossible for both of them to take place at the same moment. One obvious illustration of this is the possible results of a single flip of a coin, which may produce either heads or tails, but not both at the same time.

Therefore,

P(AUB)=P(A)+P(B)

P(AUB)=0.7+0.2

P(AUB)=0.9

In conclusion,

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CQ

Suppose that a and b are mutually exclusive events for which p(a) = 0.2 and p(b) = 0.7. what is the probability that: either a or b occur7

Based on the information in the graph, we can infer that the missing numbers are: 9, 4, 19, 30, 84, 16, 8, 22, and 40.

To complete the table correctly we must identify the columns or rows with more data. These will be the easiest to complete. First of all, we must fill in those that already have a number in the total box because we can add the available numbers and later subtract them from the total to identify the missing number.

We can also find the numbers in the total cells by adding all the numbers in a column or row to find this result. Finally, the boxes that are being completed serve as clues to complete the others.

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The number of significant digits in a measurement is determined by following a specific rule. According to the rule, all non-zero digits in a measurement are considered significant. For example, in the measurement 25.4 cm, there are three significant digits (2, 5, and 4) because they are non-zero.

In addition to non-zero digits, there are two more rules to consider. The first rule states that all zeros between non-zero digits are also significant. For instance, in the measurement 1003 g, there are four significant digits (1, 0, 0, and 3) because the zero between the non-zero digits is significant.

The second rule states that trailing zeros at the end of a number are significant only if they are after the decimal point. For example, in the measurement 2.000 s, there are four significant digits (2, 0, 0, and 0) because the trailing zeros after the decimal point are significant. However, in the measurement 2000 m, there are only one significant digit (2) because the trailing zeros are not after the decimal point.

In summary, the number of significant digits in a measurement is determined by considering all non-zero digits, zeros between non-zero digits, and trailing zeros after the decimal point. These rules help in properly representing the precision and accuracy of a measurement.

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All multiple of 6 under 14 are: -12, -6, 0, 6, 12

How do we get 14 here:

√200= 14.142 (Round to thousandth place)

This is how many x we have found.

A multiple in math is the number you get when you multiply a certain number by using an integer. for example, multiples of 5 are: 10, 15, 20, 25, 30…, and so forth. Multiples of 7 are 14, 21, 28, 35, 42, 49…and many others.

In math, the meaning of a multiple is the product result of one number multiplied by another number. Here, 56 is a multiple of the integer 7. Here is an example of multiples: Fun facts. 0 is a multiple of every number as the product of 0 multiplied by any number is 0.

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Assuming the randomly throw is equally distributed along the rectangle area, the probability of hitting the square is the fraction of the area of the square with respect to the total are of the rectangle.

The area of the square is the square of its side:

And the area of the rectangle is the product of its lengths by its height:

So, the probability is the area of the square divided by the area of the rectangle:

The probability if 9%.

The probability of spinning green and rolling an even number will be 0.125.

The missing diagram is given below.

The percentage of favorable events to the total number of occurrences.

The probability of spinning green will be

Toial event = 4 {R, G, B, Y}

Favorable event = 1 {G}

P(G) = 1/4

The probability of an even number on dice will be

Toial event = 6 {1, 2, 3, 4, 5, 6}

Favorable event = 3 {2, 4, 6}

P(E) = 3/6

P(E) = 1/2

Then the probability of spinning green and rolling an even number will be

P = P(G) x P(E)

P = 1/4 x 1/2

P = 0.125

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Answer:

0.0062

Step-by-step explanation:

Given that:

Mean (μ) = 72 inches, Standard deviation (σ) = 1.2 inches.

The z score is a measure in statistics is used to determine by how many standard deviation the raw score is above or below the mean. If the raw score is above the mean, the z score is positive and if the raw score is below the mean, the z score is negative.

The z score is given as:

\(z=\frac{x-\mu}{\sigma}\)

For Clydesdale is greater than 75 inches tall, x = 75 inches, the z score is:

\(z=\frac{x-\mu}{\sigma}=\frac{75-72}{1.2} =2.5\)

The probability that a Clydesdale is greater than 75 inches tall = P(X > 75) = P(Z > 2.5) = 1 - P(Z < 2.5) = 1 - 0.9938 = 0.0062 = 0.62%

The probability that a Clydesdale is greater than 75 inches tall is 0.62%

Required area of the composite figure is 69 cm²

What is area of a composite shape?

the area covered by any composite shape. A composite shape is a shape in which some polygons are put together to form the required shape is called the area of composite shapes . These figures can consist of combinations of triangles, rectangles, squares etc. To determine the area of composite shapes, divide the composite shape into basic shapes such as square, rectangle,triangle, hexagon, etc.

Basically, a compound shape consists of basic shapes put together. This is also called a "composite" or "complex" shape. This mini-lesson explains the area of compound figures with solved examples and practice questions.

Here in this figure, we have two figures.

First one is rectangle and second one is triangle.

Length and breadth of the rectangle are 12 cm and 4 cm respectively.

So, area = Length × Breadth = 12 × 4 = 48 cm²

Again height of the triangle is (11-4) = 7 cm and base of the triangle is (12-6) = 6 cm.

So, area of the triangle = 1/2 × 7 × 6 = 3×7 = 21 cm²

Now if we add both area of rectangle and triangle then we will get area of the composite figure.

So, required area of the composite figure is ( 48+21) = 69 cm²

Therefore, option A is the correct option.

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Using the Well-Ordering Principle (WOP), it can be proven that in every tournament with n players (where n is a natural number), there is at least one top player, defined as someone who either beats every other player or beats someone who beats the other player.

We will prove this statement by contradiction. Assume that there exists a tournament with n players where there is no top player. This means that for each player, there exists either another player who beats them or a chain of players such that each player beats the next one. Now, consider the set S of all players in this tournament. Since S is a non-empty set of natural numbers, it has a least element, let's say k.

Now, player k either beats every other player in the tournament, making them a top player, or there exists a player, let's say player m, who beats player k. In the latter case, we have a chain of players: k, m, p_1, p_2, ..., p_t, where p_1 beats p_2, p_2 beats p_3, and so on until p_t.

However, this contradicts the assumption that there is no top player, as either player k beats every other player (if m does not exist), or player m beats someone who beats the other player (if m exists). Hence, by contradiction, we have shown that in every tournament with n players, there is at least one top player.

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Answer:

-0.00572

Step-by-step explanation:

0.572 143/250 57.2%

then divide:)

Answer:

rolling a sum of 9

Rolling a sum less than 5

Rolling a sum that is greater than 9 but less than 11

Step-by-step explanation:

so you have sum of 9 which is 9

sum less than 5 which is 4,3,2,1

And a sum greater than 9 but less than 11 so 10

10 +9 is greater than 11

10 +4, 10 + 3, 10 +2, 10 + 1 would work too

9+5, 9+4,9+3, 9+2 would work as well the only one who wouldn’t is 9+1 but you have more that work than don’t

Answer: b , c , e

Step-by-step explanation:

In an experiment, the variable being measured or tested is known as the dependent variable.

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The values of x and r can be determined by solving the quadratic equation   \(3xr^2 - 4xr + x = 0.\)

Let's start by expressing the terms of the geometric sequence in terms of their common ratio:

\(x, y = xr, z = xr^2.\)

Now, consider the arithmetic sequence formed by x, 2y, 3z. We can express these terms in terms of x and r:

2y = x + d,

3z = x + 2d,

where d is the common difference of the arithmetic sequence.

Substituting the expressions for y and z from the geometric sequence, we have:

2xr = x + d,

3xr^2 = x + 2d.

Simplifying these equations, we get:

2xr - x = d,

3xr^2 - x = 2d.

Now, let's solve for x and r. From the first equation, we can express d in terms of x and r:

d = 2xr - x.

Substituting this expression into the second equation, we have:

3xr^2 - x = 2(2xr - x).

Simplifying further:

3xr^2 - x = 4xr - 2x,

3xr^2 - 4xr + x = 0.

Now, we can solve this quadratic equation to find the values of x and r.

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Answer:

19 + 21 = 40.

Step-by-step explanation:

Answer:x= 2

Step-by-step explanation:

X+16/3= 3x

3(x+16/3)=3(3x) [in order to cancel out the divided by 3]

X+16=9x

16=8x

2=x