solve for b

18, b, 27, 22
(round your answer to the nearest tenth
b=[?]

Solve For B18, B, 27, 22(round Your Answer To The Nearest Tenthb=[?]

Answers

Answer 1

The length of side b for the triangle is equal to 21.8 to the nearest tenth using the sine rule.

What is the sine rule

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

Using the sine rule;

18/sin22° = b/sin27°

b = (18 × sin27°)/sin22° {cross multiplication}

b = 21.8144

Therefore, the length of side b for the triangle is equal to 21.8 to the nearest tenth using the sine rule.

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Related Questions

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Question 1 (Essay Worth 10 points)


(07. 02 HC)



A chef draws cookies randomly from a box containing 6 cookies of the same shape and size. There is 1 chocolate cookie, 3 almond cookies, and 2 butter cookies. He draws 1 cookie and then draws another cookie without replacing the first one. Find the probability of picking 1 almond cookie followed by another almond cookie, and show the equation used.





Question 2 (Essay Worth 10 points)


(07. 02 MC)



Alan is arranging 3 different stuffed toys in a row on a shelf. Create a sample space for the arrangement of a teddy bear (T), a kitten (K), and an elephant (E).





Question 3 (Essay Worth 10 points)


(07. 01 MC)



A bag has 1 red marble, 4 blue marbles, and 3 green marbles. Peter draws a marble randomly from the bag, replaces it, and then draws another marble randomly. What is the probability of drawing 2 blue marbles in a row? Explain your answer.





Question 4 (Essay Worth 10 points)


(07. 03 MC)



Chang has 2 shirts: a white one and a black one. He also has 2 pairs of pants, one blue and one tan. What is the probability, if Chang gets dressed in the dark, that he winds up wearing the white shirt and tan pants? Show your work

Answers

Question 1: The probability of picking 1 almond cookie followed by another almond cookie is 1/5.

Question 2: The probability of drawing 2 blue marbles in a row is 1/4.

Question 3: The probability of Chang wearing the white shirt and tan pants is 1/4.

In the problem, the chef draws two cookies without replacement from a box containing six cookies of three different types. The probability of picking one almond cookie followed by another almond cookie can be found by using the multiplication rule of probability.

The probability of picking the first almond cookie is 3/6, and since the first cookie is not replaced, there are now only 2 almond cookies left in the box out of a total of 5 cookies. Therefore, the probability of picking another almond cookie is 2/5. Using the multiplication rule, we multiply these probabilities together to get:

P(almond, then almond) = (3/6) x (2/5) = 1/5

In the problem, Peter draws two marbles randomly from a bag containing three different colors of marbles. The probability of drawing two blue marbles in a row can be found by using the multiplication rule of probability again.

The probability of drawing a blue marble on the first draw is 4/8, and since the marble is replaced, there are still 4 blue marbles left out of a total of 8 marbles. Therefore, the probability of drawing another blue marble on the second draw is also 4/8. Using the multiplication rule, we multiply these probabilities together to get:

P(blue, then blue) = (4/8) x (4/8) = 1/4

In the problem, Chang has two shirts and two pairs of pants, and he chooses one of each at random to wear.

The probability of him choosing the white shirt is 1/2, and the probability of him choosing the tan pants is also 1/2. Using the multiplication rule, we multiply these probabilities together to get:

P(white shirt and tan pants) = (1/2) x (1/2) = 1/4

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If you roll a number cube 96 times, how many times would you expect to roll a three or a six?

a. 36
b. 32
c. 34
d. 38
ANSWER FAST (show work please)

Answers

The calculated number of times you would expect to roll a three or a six is 32 times

How many times would you expect to roll a three or a six?

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

Cube = 96

In a cube, we have the following probability equation

P(3 or 6) = 1/6 + 1/6

When the sum is evaluated, we have

P(3 or 6) = 2/6

So, when the die is rolled 96 times, we have

Expected value = 2/6 * 96

Evaluate the products

Expected value = 32

Hence, the expected number of times is 32

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Circle W has a center at (15,–2) and has a radius of 4. Circle W' has a center of (–5,–5) with a radius of 4. What is the transformation of circle W to circle W'?

Answers

The correct answer is "Translated to the left 10 and down 3 and then reflected about the y-axis."

Understanding Transformation of Circle

Transformation is a process that changes the position, orientation, size, or shape of a geometric object. Transformations are often described using matrices, vectors, or other mathematical operations.

Types of Transformations

Translation - moving object on a straight lineRotation - turning an object around a fixed point by a certain angleScaling - changing the size of an object by a fixed factor.Reflection - flipping an object over a fixed line

From the problem statement, to move the center from (15,-2) to (-5,-5), we need to translate the circle to the left by 10 units and down by 3 units. So the first transformation is a translation to the left 10 units and down 3 units.

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P varies inversely with x. If p=7 and x=8 find the value of p when x=7

Answers

When the value of x is 7 the value of p will be equal to 8.

It is given that P varies inversely with x, so we can write that

p=k/x

where k is the proportionality constant.

here we can find the value of k by substituting the value of p and x with 7 and 8 in the relation that is given above, we get:

7=k/8

k=7*8

k=56

we the value of k to be 56 after putting the values in the relation.

Now if x is changed to 7, and k is equal to 56 we can get the value of p by putting the known values in the same relation.

p=k/x

p=56/7

p=8.

Therefore, when the value of x is 7 the value for p will be equal to 8.

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If the height is h, the leaf scar is l, how can you model the pattern using an equation?



i need explanation please

Answers

The mathematical model that pattern using an equation to represents  the height is h, the leaf scar is l is given by x = c × l × √n × cos(n × φ) , and y = c × l × √n × sin(n × φ) + h.

The pattern of leaf scars on a tree trunk is often modeled using a mathematical function called a phyllotaxis spiral.

This spiral can be represented by the polar equation,

r = c × √n

where r is the radius of the spiral,

n is the index of the leaf scar,

c is a constant that determines the tightness of the spiral,

and the angle of rotation is equal to,

θ = n × φ

where φ is the golden angle, which is approximately 137.5°.

To incorporate the height h and leaf scar size l into the model,

Make the following modifications,

Add a vertical displacement factor h to the polar equation, which shifts the spiral upward by h units.

Multiply the radius by a factor that is proportional to the size of the leaf scar l.

The modified polar equation for the phyllotaxis spiral would be,

r = c × l × √n

θ = n × φ

where r is the radius of the spiral,

n is the index of the leaf scar,

c is a constant that determines the tightness of the spiral,

l is the size of the leaf scar,

and φ is the golden angle.

To convert this polar equation to a Cartesian equation that relates x and y coordinates,

x = r × cos(θ)

y = r × sin(θ) + h

Substituting the expressions for r and θ from above, we get,

x = c × l × √n × cos(n × φ)

y = c × l × √n × sin(n × φ) + h

Therefore, mathematical equation that models the phyllotaxis spiral of leaf scars on a tree trunk, taking into account the height h and the size of the leaf scar l is

x = c × l × √n × cos(n × φ)

y = c × l × √n × sin(n × φ) + h

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The diagram below shows the side view of a ramp used to help load and unload a moving van. Which measurement is closest to the length of the ramp in feet?

Answers

Measurement is closest to the length of the ramp in feet is 33 feet

Let AB = 26 ft and BC = 19.5 ft

Let AC be the length of the ramp

Let's use the Pythagorean theorem to find the length of the ramp:

AC² = AB² + BC²

where AC is the hypotenuse (the unknown side), and AB and BC are the other two sides given.

Substituting the given values, we get:

AC² = 26² + 19.5²

AC² = 676 + 380.25

AC² = 1056.25

AC = [tex]\sqrt{1056.25}[/tex]

AC = 32.5

Rounding to the nearest feet

AC = 33

Therefore, the measurement closest to the length of the ramp in feet is 33 feet.

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On december 17, 1787, delaware was the first state to join the union followed by pennsylvania on december 12 and newjersey on december 18. Chris wanted to list the thirteen states in chronological order as they continued to join the union. How many combinations are possible

Answers

There are no other combinations to consider.

To determine the possible combinations, since Chris wants to list the thirteen states in chronological order as they continued to join the union, there is only one combination possible.

This is because the order is based on the dates the states joined, which is a fixed sequence. Here are the steps for listing the states:

1. Begin with Delaware, as it was the first state to join the union on December 17, 1787.
2. Follow with Pennsylvania, which joined on December 12.
3. Add New Jersey, which joined on December 18.
4. Continue listing the remaining ten states in the order they joined.

As the order is determined by the joining dates, there are no other combinations to consider.

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Olivia finds a combination of two different transformations that moves ABCD onto A" B" C" D". What is one way she might have done this?

Answers

One way Olivia might have achieved this is by performing a translation followed by a rotation.

How could Olivia have combined two different transformations to move ABCD onto A" B" C" D"?

One way Olivia might have achieved the transformation of ABCD onto A" B" C" D" is by performing a translation followed by a rotation. Here's a possible approach:

Translation: Olivia could have first translated ABCD by shifting the entire figure in a specific direction (up, down, left, or right) by a certain distance. This would result in a new position for each vertex of ABCD, creating a new figure.

Rotation: After the translation, Olivia could have performed a rotation around a point, such as the origin or a specific vertex. The rotation would change the orientation of the translated figure, aligning it with the desired position of A" B" C" D".

By combining these two transformations, Olivia could have successfully moved ABCD onto A" B" C" D" and achieved the desired configuration. It's important to note that there could be other valid combinations of transformations as well.

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Round all answers to the nearest cent. The profit (in dollars) from the sale of z palm trees is given by: P(x) = 20x - .01x² - 100 a. Find the profit at a sales level of 14 trees $ b. Find the average change in profit sales from 12 to 19 trees. $ per tree c. Find the instantaneous rate of change of profit at a sales level of 14 trees. per tree $ Let f(x) = x² - 4x. Round all answers to 2 decimal places. a. Find the slope of the secant line joining (1, f(1) and (7, f(7)). Slope of secant line = b. Find the slope of the secant line joining (5, f(5)) and (5 + h, f(5+h)). Slope of secant line = c. Find the slope of the tangent line at (5, f(5)). Slope of the tangent line = d. Find the equation of the tangent line at (5, f(5)).

Answers

a) The profit at a sales level of 14 trees is $180.40.

b) The average change in profit sales is $13.96 per tree [(ΔP/Δx) = 97.75/7].

c) The instantaneous rate of change of profit at a sales level of 14 trees is $19.72 per tree.

d) The equation of the tangent line at (5, f(5)) is y = 6x - 25.

a. To find the profit at a sales level of 14 trees, we need to evaluate the profit function at x = 14:

P(x) = 20x - 0.01x^2 - 100

P(14) = 20(14) - 0.01(14)^2 - 100 = $180.40

Therefore, the profit at a sales level of 14 trees is $180.40.

b. To find the average change in profit sales from 12 to 19 trees, we need to calculate the average rate of change of the profit function over this interval:

Δx = 19 - 12 = 7

ΔP = P(19) - P(12) = (2019 - 0.0119^2 - 100) - (2012 - 0.0112^2 - 100) = $97.75

Therefore, the average change in profit sales is $13.96 per tree [(ΔP/Δx) = 97.75/7].

c. To find the instantaneous rate of change of profit at a sales level of 14 trees, we need to find the derivative of the profit function at x = 14:

P(x) = 20x - 0.01x^2 - 100

P'(x) = 20 - 0.02x

P'(14) = 20 - 0.02(14) = $19.72

Therefore, the instantaneous rate of change of profit at a sales level of 14 trees is $19.72 per tree.

d. To find the equation of the tangent line at (5, f(5)), we need to find the slope of the tangent line and its y-intercept:

f(x) = x^2 - 4x

f'(x) = 2x - 4

f'(5) = 2(5) - 4 = 6

The slope of the tangent line at (5, f(5)) is 6.

To find the y-intercept of the tangent line, we can use the point-slope form of a line:

y - f(5) = m(x - 5)

y - (5^2 - 4*5) = 6(x - 5)

y - 5 = 6x - 30

y = 6x - 25

Therefore, the equation of the tangent line at (5, f(5)) is y = 6x - 25.

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Find the following unknowns about the circle. Round all answers to the nearest tenth.

Answers

The given circle has a radius of 11.2,

The diameter of the given circle is 22.4The circumference of the given circle is 70.336 The area of the given circle is 393.88

Given radius of the circle (r) = 11.2

The diameter of the given circle = 2*r = 2*11.2 = 22.4

The circumference of the given circle = 2πr = 2*3.14*11.2 = 70.336

The area of the given circle =  πr² = 3.14*(11.2)² = 393.88

From the above analysis, we can conclude that the diameter of the circle is 22.4 and the circumference of the circle is 70.336 and the area of the circle is 383.88.

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A factory uses 50 milligrams of red coloring powder in one batch of candle wax

how many batches of candle wax can it make with 25 grams of red coloring powder

Answers

The factory can make 500 batches of candle wax with 25 grams of red coloring powder.

For the given question the easiest and the simplest approach will be by using the unit conversion method to solve the problem.

We need to convert the unit from grams to milligrams.

So, 25 grams of red coloring powder will be equal to:

25 grams * 1000mg/grams = 25000mg.

Now it is given that it takes 50 mg to make a single batch of candle wax. So, the number of batches that can be made using 25,000 mg of red coloring powder is equal to:

25000mg/50mg per batch = 500 batches.

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in the coordinate plane, point b is located at (2, -3), Point C is reflected across the y-axis. Plot and label points b and C in the coordinate plane.​

Answers

Thus, we can label the points B and C' in the coordinate plane as follows

     |

     |

 C'  |

     |

------B(2, -3)

     |

     |

     |

Coordinate plane calculation.

To reflect a point across the y-axis, we keep the x-coordinate the same but change the sign of the y-coordinate.

Point B is located at (2, -3), so it looks like

     |

     |

     |

     |

------B(2, -3)

     |

     |

     |

     |

To reflect point C across the y-axis, we change the sign of the y-coordinate, but keep the x-coordinate the same. If point C is located at (x, y), then its reflected image, C', would be located at (-x, y).

Since we don't have the coordinates for point C, we cannot plot it accurately. However, we know that its reflected image would be located at (-x, y), so we can label it as C' for now.

So, the reflected image of point C across the y-axis, C', would be located at (-x, y). Thus, we can label the points B and C' in the coordinate plane as follows

     |

     |

 C'  |

     |

------B(2, -3)

     |

     |

     |

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Calculate the expected value for the number of asian zing wings sold. round your answer to three decimal places, if necessary.

Answers

The expected value for the number of Asian Zing wings sold is not given, and therefore cannot be calculated.

What is the given value to calculate the expected value?

The expected value is a statistical measure that represents the average outcome of a random variable. It is calculated by multiplying each possible outcome by its probability, and then summing the products. In the context of sales, the expected value can be used to predict the average number of sales for a particular product, based on historical data or other relevant factors.

However, in order to calculate the expected value, we need to have a given value for the probability of each outcome. Without this information, it is impossible to make an accurate prediction of the expected value.

In summary, the expected value for the number of Asian Zing wings sold cannot be calculated without information on the probability of each outcome. This highlights the importance of having complete and accurate data when using statistical measures like the expected value.

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A. Use the AA Similarity Theorem in writing an if-then statement to describe the illustration
or in completing the figure based on the if-then statement.
R
Н.
If:
P
Then:
AHEY​

Answers

The AA Similarity Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. We can complete the figure by drawing a line segment of length 10.5 from point A to point H.

Using this theorem, we can write the following if-then statement to describe the given illustration:

If angle RH is congruent to angle A and angle NH is congruent to angle E, then triangle PHN is similar to triangle AHE.

This means that the corresponding sides of these triangles are proportional to each other. We can use this information to complete the figure by finding the length of side AH.

Since triangle PHN is similar to triangle AHE, we can set up the following proportion:

PH/AH = HN/HE

We know that PH = 6 and HN = 8, and we want to find AH. Let x represent the length of AH.

6/x = 8/14

Cross-multiplying gives us:

6 * 14 = 8 * x

Simplifying:

84 = 8x

Dividing both sides by 8:

x = 10.5

Therefore, we can complete the figure by drawing a line segment of length 10.5 from point A to point H.

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An electrical charge of 0. 000003 coulombs is 0. 06 m away from another electrical charge of 0. 0000009 coulombs. Solve this equation

Answers

The force between the two charges is 1.69 x[tex]10^-^1^5[/tex] N

How to find the equation?

The force between two electric charges can be calculated using Coulomb's law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:

F = k * (q1 * q2) / d²

where F is the force, k is Coulomb's constant (9 x 10⁹ N m² / C²), q1 and q2 are the magnitudes of the two charges, and d is the distance between them.

Substituting the given values, we get:

F = (9 x [tex]10^9[/tex] N m² / C²) * (0.000003 C) * (0.0000009 C) / (0.06 m)²

Simplifying this expression gives:

F = 1.69 x[tex]10^-^1^5[/tex] N

Therefore, the force between the two charges is 1.69 x [tex]10^-^1^5[/tex] N.

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Test the convergence of the series: is it convergentor divergent or inconclusive or none of them

Answers

Once we apply one of these tests and determine whether the series converges or diverges, we can then further analyze the series to find its sum, if it exists.

To test the convergence of a series, we typically use one of several tests, depending on the nature of the series. Some of the commonly used tests are:

Divergence test: If the terms of a series do not approach zero, the series must diverge. The test states that if lim(n->inf) an != 0, then the series diverges.

Comparison test: If the terms of a series are positive and can be compared with a known convergent or divergent series, we can determine the convergence or divergence of the given series. If an <= bn for all n and the series sum of bn converges, then the series sum of an also converges. If an >= bn for all n and the series sum of bn diverges, then the series sum of an also diverges.

Limit comparison test: If the terms of a series are positive, we can compare the given series with a known convergent series, using the limit comparison test. If lim(n->inf) (an/bn) = L, where L is a positive finite number, then both series either converge or diverge.

Ratio test: If the terms of a series approach zero and the ratio of consecutive terms approaches a limit L, then the series converges if L < 1 and diverges if L > 1. If L = 1, the test is inconclusive.

Root test: If the terms of a series approach zero and the nth root of the absolute value of the nth term approaches a limit L, then the series converges if L < 1 and diverges if L > 1. If L = 1, the test is inconclusive.

Alternating series test: If the terms of a series alternate in sign and decrease in magnitude, then the series converges.

There are also other tests, such as integral test, p-series test, and Dirichlet test, among others, which can be used to test the convergence of certain types of series.

Once we apply one of these tests and determine whether the series converges or diverges, we can then further analyze the series to find its sum, if it exists.

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Consider the function f(x) = 7(x-2)^{2/3}. For this function there are two important intervals: (-[infinity], A) and (A, [infinity]) where A is a critical number.
A is

Answers

The critical number A is 2

To find the critical number A for the function f(x) = 7(x-2)^(2/3):

We need to first find the derivative of the function and then set it equal to zero or identify where it is undefined.

Step 1: Find the derivative of f(x).
f'(x) = d/dx[7(x-2)^(2/3)]
Using the chain rule, we get:
f'(x) = (2/3) * 7(x-2)^(-1/3) * (1)

= (14/3)(x-2)^(-1/3)

Step 2: Set the derivative equal to zero or identify where it is undefined.
The derivative will never be zero since (14/3) is a constant and (x-2)^(-1/3) will never equal zero.

However, the derivative is undefined when the exponent -1/3 leads to a division by zero in the denominator.

This occurs when (x-2) = 0.

Solving for x, we get:
x-2 = 0
x = 2

Therefore, the critical number A is 2. The two important intervals for the function f(x) = 7(x-2)^(2/3) are (-∞, 2) and (2, ∞).

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Need help to find the zeros for this quadratic equation pleaseeee

Answers

The zeros for this quadratic equation is [-1, 0].

What is the general form of a quadratic function?

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.

Next, we would solve the quadratic function by using the factorization method as follows;

y = x² + 2x + 1

x² + 2x + 1 = 0

x² + x + x + 1 = 0

x(x + 1) + 1(x + 1) = 0

(x + 1)(x + 1) = 0

x = -1.

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identify B on the following diagram: a: y-axis b origin c quadrant I d x-axis

Answers

Answer:

b

Step-by-step explanation:

point B has coordinates (0, 0 ) which is the origin

The tip of a pendulum swings through an arc whose length is 8 centimeters. If the radius of the pendulum is 26 centimeters, then what radian angle did the tip rotate through? Round your answer to the nearest hundredth

Answers

Answer: Therefore, the tip of the pendulum rotated through an angle of approximately 0.31 radians.

Step-by-step explanation:

The length of the arc traveled by the tip of the pendulum is 8 centimeters, and the radius of the pendulum is 26 centimeters. We can use the formula for the length of an arc of a circle to find the radian angle rotated through:

Length of arc = radius * angle in radians

Solving for the angle in radians, we get:

Angle in radians = Length of arc / radius

Plugging in the given values, we get:

Angle in radians = 8 / 26

Simplifying this expression, we get:

Angle in radians = 0.30769...

Rounding this value to the nearest hundredth, we get:

Angle in radians = 0.31

Therefore, the tip of the pendulum rotated through an angle of approximately 0.31 radians.

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Find the value of x such that the data set has the given mean.

102​, 120​, 103​, 112​, 110​, ​x; mean 108

Answers

The value of x in the data set is 101.

How to find mean?

The mean of a data set is the sum of all the data divided by the count n.

Therefore, let's find the mean of the data set as follows:

The mean is  the sum of the data divided by the total number of data.

Hence, let's find the value of x using the mean

108  = 102 + 120 + 103 + 112 + 110 + x  / 6

108 = 547 + x / 6

Cross multiply

108 × 6 = 547 + x

648 = 547 + x

x = 648 - 547

x = 101

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Luis takes 35 minutes to ride his bike 3 miles. He rode his bike 25 miles


last week. Which equation can be used to find t, the number of minutes


that Luis rode his bike last week?

Answers

The equation that can be used to find t, the number of minutes that Luis rode his bike last week, is t = 875/3, which represents the total time in minutes for his 25-mile ride based on the average time it took him to ride 3 miles.

We can use proportions to find the number of minutes Luis rode his bike last week. Since Luis took 35 minutes to ride 3 miles, we can set up a proportion to relate the time and distance for his entire ride: 35 minutes / 3 miles = t minutes / 25 miles

To solve for t, we cross-multiply and simplify: 35 * 25 = 3 * t, 875 = 3t, t = 875 / 3, t ≈ 291.67 minutes

Therefore, the equation that can be used to find t, the number of minutes that Luis rode his bike last week, is t = 875/3, which represents the total time in minutes for his 25-mile ride based on the average time it took him to ride 3 miles.

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Tables

Contingency Tables

10. In recent years, concerns have been expressed about adverse health effects from amalgam

dental restorations, which contain mercury. The table shows results from a study in which

some patients were treated with amalgam restorations and others were treated with composite

restorations that do not contain mercury. Use a 0. 01 significance level to find the critical value

needed to test for independence between the type of restoration and sensory disorders.

Adverse health

condition reported

No adverse health

condition reported

01136

Amalgam

36

231

Composite

28

239

(1 poin

Answers

The critical value needed to test for independence between the type of restoration and sensory disorders is 6. 635.

How to find the critical value ?

To evaluate the correlation between sensory impairments and restoration type, a chi-square test of independence can be used. To determine the critical value for this statistical test, consult the chi-square distribution table at a 0.01 significance level.

The degrees of freedom for a chi-square test of independence :

Degrees of Freedom ( df ) = ( Number of Rows - 1 ) x ( Number of Columns - 1 )

The number of rows from the table = 2

Number of columns is also = 2

The df is therefore:

df = (2 - 1) x (2 - 1) = 1 x 1 = 1

The critical value for χ² with 1 degree of freedom at a 0. 01 significance level can be founding using the Chi - Square table to be approximately 6.635.

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Full question is:

In recent years, concerns have been expressed about adverse health effects from amalgam dental restorations, which contain mercury. The table shows results from a study in which some patients were treated with amalgam restorations and others were treated with composite restorations that do not contain mercury. Use a 0. 01 significance level to find the critical value needed to test for independence between the type of restoration and sensory disorders.

Helpp pleasee!!!!!!!!

Answers

The volume of a cone with a slant height of 13 cm and radius of 5 cm is A. 100 pi cm³.

How to obtain the volume of the cone

To obtain the volume of the cone we would use the formula:

V = (1/3)πr²h

where V is the volume of the cone, r is the radius of the base of the cone, and h is the height of the cone.

Since we are given the slant height (s) of the cone, not its height (h), we would use the Pythagorean theorem to find the height of the cone:

s² = r² + h²

where s is the slant height, r is the radius of the base, and h is the height.

We are given that the slant height (s) is 13 cm, and the radius (r) is 5 cm. So, we can solve for the height (h) this way:

13² = 5² + h²

169 = 25 + h²

h² = 144

h = 12 cm

Now that we know the height of the cone, we can substitute the values into the formula for the volume:

V = (1/3)πr²h

V = (1/3)π(5²)(12)

V = (1/3)π(25)(12)

V = (1/3)π(300)

V = 100π cm³

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Which of the following numbers are less than 3/7? You must answer this

12.5%

0.3

50%

2/3

0.102

1/5

Answers

The numbers that are less than 3/7 are 1/8 and 3/10, while the numbers that are greater than 3/7 are 1/2 and 2/3. The decimal 0.102, which is equivalent to 51/500 as a fraction, is also less than 3/7.

To determine which of the given numbers are less than 3/7, we can convert them to fractions and compare them to 3/7.

12.5% is equivalent to 0.125 as a decimal or 1/8 as a fraction. To compare 1/8 and 3/7, we can convert them to a common denominator. The least common multiple of 8 and 7 is 56, so we can rewrite 1/8 as 7/56 and 3/7 as 24/56. Therefore, 1/8 is less than 3/7.

0.3 is equivalent to 3/10 as a fraction. To compare 3/10 and 3/7, we can also convert them to a common denominator. The least common multiple of 10 and 7 is 70, so we can rewrite 3/10 as 21/70 and 3/7 as 30/70. Therefore, 3/10 is less than 3/7.

50% is equivalent to 0.5 as a decimal or 1/2 as a fraction. To compare 1/2 and 3/7, we can convert 3/7 to a fraction with a denominator of 2. Multiplying the numerator and denominator of 3/7 by 2 gives us 6/14. Therefore, 1/2 is greater than 3/7.

2/3 is already a fraction, and we can compare it directly to 3/7. Multiplying the numerator and denominator of 3/7 by 3 gives us 9/21, and we can see that 2/3 is greater than 3/7.

0.102 is a decimal that is less than 1, but it can also be written as a fraction. To do so, we can place the decimal over 1 followed by the appropriate number of zeros. This gives us 102/1000, which can be simplified to 51/500. To compare 51/500 and 3/7, we can convert them to a common denominator. The least common multiple of 500 and 7 is 3500, so we can rewrite 51/500 as 357/3500 and 3/7 as 1500/3500. Therefore, 51/500 is less than 3/7.

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help asspppp.............

Answers

The value of x and y in the right triangle are 11.31 units and 8 units respectively.

The tangential ratio of ∠P and ∠Q are 16 / 12 and 12 / 16 respectively.

How to find the side and angle of a right triangle?

A right angle triangle is a triangle that has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios as follows:

tan 45 = opposite / adjacent

tan 45 = 8 / y

cross multiply

y = 8 / tan 45

y = 8  /1

y = 8 units

Therefore,

sin 45 = opposite / hypotenuse

sin 45 = 8 / x

cross multiply

x = 8 / sin 45

x = 11.313816999

x = 11.31 units

Let's find the tangent ratio of ∠p and ∠q.

Hence,

tan ∠P = 16 / 12

tan ∠Q = 12 / 16

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A bag of shapes contains 4 red circles, 3 blue circles, and 9 yellow triangles. What is the probability of drawing a shape that is red or a circle?

Answers

The probability of drawing a shape that is red or a circle is 7/16 from the bag that contains 4 red circles, 3 blue circles, and 9 yellow triangles.

Number of red circles = 4

Number of blue circles = 3

Number of yellow triangles = 9

Total number of all items = 4+3+9 = 16

Thus, the total number of possible outcomes is 16.

The probability of getting a red shape  = 4/16

The probability of getting a circle   = 4/16 + 3/16 = 7/16

To calculate the probability of drawing an item circle or red color,

P(red or circle) = P(red) + P(circle) - P(red and circle)

P(red or circle) = 4/16 + 7/16 - 4/16

P(red or circle) = 7/16

Therefore, we can conclude that the probability of drawing a shape that is red or a circle is 7/16.

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each of the following questions could be the basis for a statistical study. how would the collected data look different for each question? do you think they would lead to the same result or different results? what percentage of internet dates lead to marriage? what percentage of marriages begin with internet dates?

Answers

Answer:is 230

Step-by-step explanation:

230 i hoped i helped

Tiffany was cutting out some fabric for her friend she cut a piece that was 6 cm wide in an area of 30 cm to the power of two how long was the piece

Answers

The length of the fabric piece is 5 cm.

We are given the width and area of the fabric piece and need to find its length. Here are the steps:

1. The terms involved in this problem are width, length, and area.
2. The formula to calculate the area of a rectangle is Area = Width × Length.
3. We are given the width (6 cm) and area (30 cm²) of the fabric piece.
4. To find the length, we'll rearrange the formula: Length = Area ÷ Width.
5. Plug in the given values: Length = (30 cm²) ÷ (6 cm).
6. Perform the calculation: Length = 5 cm.

So, the length of the fabric piece is 5 cm.

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As each person entered a theatre, the manager counted how many of the 105 people had popcorn and how many had a drink. She found that out of 84 people that had popcorn, only 10 did not have a drink. Six people walked in without popcorn or a drink. Construct a two-way table summarizing the results. ​

Answers

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

|           | Popcorn | No Popcorn |

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

| Drink     |    74   |     15     |

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

| No Drink  |    10   |     6      |

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

The completed two-way table is as shown above.

We construct a two-way table summarizing the results. Let's use the information provided:

1. 105 people entered the theatre
2. 84 people had popcorn
3. 10 out of 84 people with popcorn did not have a drink
4. 6 people walked in without popcorn or a drink

Now let's construct the two-way table:

---------------------------
|           | Popcorn | No Popcorn |
---------------------------
| Drink     |    A    |     B      |
---------------------------
| No Drink  |    C    |     D      |
---------------------------

We need to fill in the values for A, B, C, and D:

1. A = People with popcorn and a drink = Total with popcorn - those without a drink = 84 - 10 = 74
2. C = People with popcorn but no drink = 10 (given in the question)
3. D = People with neither popcorn nor a drink = 6 (given in the question)
4. To find B, we need to find the total number of people with a drink. We know 105 people entered, and 6 had neither popcorn nor a drink, so there were 105 - 6 = 99 people with either popcorn or a drink. Since 84 people had popcorn, this means there were 99 - 84 = 15 people with only a drink.
5. B = People with a drink but no popcorn = 15

Now let's fill in the table:

---------------------------
|           | Popcorn | No Popcorn |
---------------------------
| Drink     |    74   |     15     |
---------------------------
| No Drink  |    10   |     6      |
---------------------------

So, the completed two-way table is as shown above.

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