given sin a= -2/5 and cos b=1/3 with a and b both in the interval (3pi/2 , 2pi), find sin(a+b)

Answer:

8 inches

Step-by-step explanation:

The volume of a hemisphere is half the volume of a sphere.

Therefore, the sum of the volumes of the two hemisphere-shaped scoops of ice cream (with diameters of 4 inches), is equal to the volume of a sphere with diameter of 4 inches.

If the melted ice cream fills the cone exactly to the top without overflowing, the volume of the cone with diameter of 4 inches must be equal to the volume of a sphere with diameter of 4 inches.

As the diameter of a circle is twice its radius, then the radius of the sphere and cone is r = 2 inches.

The formulas for the volume of a cone and the volume of a sphere are:

\(\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}\)   \(\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=\dfrac{4}{3} \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\\\end{minipage}}\)

The depth of the cone is its height.

Therefore, to calculate how deep the cone must be so that the melted ice cream will fill the cone exactly to the top without overflowing, set the two equations equal to each other, substitute r = 2, and solve for h (the depth of the cone).

\(\begin{aligned}\textsf{Volume of a cone}&=\textsf{Volume of a sphere}\\\\\dfrac{1}{3} \pi (2)^2 h & = \dfrac{4}{3} \pi (2)^3\\\\\dfrac{1}{3} \pi \cdot 4 h & = \dfrac{4}{3} \pi \cdot 8\\\\\dfrac{4}{3} \pi h& = \dfrac{32}{3} \pi \\\\\dfrac{4}{3} h& = \dfrac{32}{3} \\\\4 h& = 32 \\\\h&=\dfrac{32}{4}\\\\h&=8\; \sf inches\end{aligned}\)

Therefore, the depth of the cone must be 8 inches.

The cone must be at least 8 inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing.

1. The opening of the ice cream cone has a diameter of 4 inches. This means that the radius of the cone's opening is 4/2 = 2 inches.

2. The two hemisphere-shaped scoops of ice cream have diameters of 4 inches each. This means that the radius of each scoop is 4/2 = 2 inches.

3. When the ice cream melts, it will take up the space between the scoops and fill the cone. In order for the melted ice cream to fill the cone exactly to the top without overflowing, the depth of the cone must be equal to the combined height of the two ice cream scoops.

4. The height of each hemisphere-shaped scoop can be calculated using the formula for the volume of a sphere, which is (4/3)πr³, where r is the radius.

  - For each scoop, the radius is 2 inches, so the height of each scoop is (4/3)π(2)³ = (4/3)π(8) = (32/3)π.

5. Since there are two scoops, the combined height of the two scoops is 2 * (32/3)π = (64/3)π.

6. Therefore, the cone must be at least (64/3)π inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing. This is approximately equal to 67.03 inches.

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The 20th prize is $4400.

It is a sequence where the difference between each consecutive terms is the same.

Example:

2, 4, 6, 8 is an arithmetic sequence.

We have,

First prize = $12,000

Successive prize worth $400 less than the preceding prize.

Now,

We can make an arithmetic sequence.

12,000, 11,600, 11,200, ...

So,

a = 12,000

d = -400

The nth term of an arithmetic sequence.

= a + (n - 1)d

So,

The 20th prize.

= 12,000 + (20 -1)400

= 12,000 - 19 x 400

= 12,000 - 7600

= 4400

Thus,

20th prize = $4400

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Answer:

B, $305.11

Step-by-step explanation:

since it is in annual interest, 36 months = 3 years.

use the formula for simple interest, which is x = Prt

278 * 0.0325 * 3 = 27.105

that is the interest that you gained.

then, add the original amount that you had, which was 278.

27.105+278 = 305.105

this rounds to $305.11, which is answer choice B

As per the requirement of body fat measurement, we measure the body fat in continuous data type.

Measureable data is referred to as continuous data. The values in this data are not constant and can take on an endless number of different forms. You can also divide these measures up into smaller, independent components.

Since it may employ decimal points and have infinite values, it is more precise and comprehensive than discrete data.

The type of data that would be used to describe percent of body fat is continuous data. An example of the continuous data type is Height of a person.

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Step-by-step explanation:

-4 + 2 + 4f = 8 - 3f

-2+4f=8-3f

7f=10

f=10/7

Step-by-step explanation:

\( - 4 + 2 + 4f = 8 - 3f \\ - 2 + 4f = 8 - 3f \\ - 4f - 3f = - 2 - 8 \\ \frac{ - 7f }{ - 7} = \frac{ - 10}{ - 7} \\ f = \frac{10}{7} \)

Answer:

the people who picked birds and cats : 10/40 = 1/4

The specific heat of the given sample is approximately 239.6 J/(kg·°C). This value indicates the amount of heat energy required to raise the temperature of 1 kilogram of the sample by 1 degree Celsius.

To determine the specific heat of the given sample, we can use the formula Q = mcΔT, where Q is the heat energy added, m is the mass of the sample, c is the specific heat, and ΔT is the change in temperature. By rearranging the formula, we can solve for c.

In this case, we are given the heat energy Q = 1.25 × 10^4 J, the mass m = 28.4 N (weight in newtons), and the change in temperature ΔT = 18.0 °C. To calculate the specific heat c, we rearrange the formula Q = mcΔT and solve for c.

First, we convert the weight from newtons to kilograms by dividing it by the acceleration due to gravity (9.8 m/s^2). So, the mass of the sample in kilograms is 28.4 N / 9.8 m/s^2 = 2.90 kg.

Substituting the given values into the formula, we have 1.25 × 10^4 J = c × 2.90 kg × 18.0 °C. Now, we can solve for c by dividing both sides of the equation by (2.90 kg × 18.0 °C):

c = (1.25 × 10^4 J) / (2.90 kg × 18.0 °C) ≈ 239.6 J/(kg·°C).

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Answer:

the slope is 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

The coordinate of S is (-2, -1). If you move it right, it will add 3 to the x-coordinate. This will then become 1. If you move it down, it will make it negative, making it -4. This will then become -1 - 4 = -5. Then, the S' will be located at (1, -5)

The new coordinates of S' will be located at (1, -5)  after translating 3 units right and 4 units down.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.

For example, If shift up by 1 unit,  add 1 to the function

If shift down by 4 units, subtract 4 from the function

The original coordinate of S is (-2, -1).

To determine the triangle shown in the diagram is translated 3 units right and 4 units down

The x-coordinate will increase by 3 if we move it to the right.

This will then become 1.

If we shift it downward, it will become negative and read as -4.

This will then become -1 - 4 = -5.

So, the coordinate of S' will be located at (1, -5)

Hence, the new coordinates of S' will be located at (1, -5)  after translating 3 units right and 4 units down.

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Answer:

Step-by-step explanation:

16+116 is 120%

132 is 120%

divide everything by 6

22 is 20%

x everything by 5

110 is 10%

Stefan spent $110 originally

132-110

= profit

profit=22

Answer:

110           22

Step-by-step explanation:

120%= 116+16

100% of 132 is 110

132-110=22

The probability that a German child recognized both Spongebob and Squidward is approximately 0.6786 or 67.86%.

First we can use the formula for conditional probability to solve this problem:

P(Spongebob and Squidward) = P(Squidward | Spongebob) * P(Spongebob)

We know that 87% of children recognized Spongebob, so P(Spongebob) = 0.87. We also know that among those who recognized Spongebob, 78% recognized Squidward, so P(Squidward | Spongebob) = 0.78.

Substituting these values into the formula, we get:

P(Spongebob and Squidward) = 0.78 * 0.87 = 0.6786

Rounding this to four decimal places, we get:

P(Spongebob and Squidward) ≈ 0.6786

Therefore, the probability that a German child recognized both Spongebob and Squidward is approximately 0.6786 or 67.86%.

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Answer:

Cost of Wedding cakes = x = $150

Cost of Birthday cakes = y = $40

Step-by-step explanation:

Let us represent:

Cost of Wedding cakes = x

Cost of Birthday cakes = y

Crazy cakes makes wedding cakes and birthday cakes. One week they made 2 wedding cakes and 5 birthday cakes and made $500.

2x + 5y = 500..... Equation 1

The next week they made 1 wedding cake and 7 birthday cakes but only made $430.

x + 7y = 430..... Equation 2

x = 430 - 7y

We substitute 430 - 7y for x in Equation 1

2x + 5y = 500..... Equation 1

2(430 - 7y ) + 5y = 500

860 - 14y + 5y = 500

860 - 500 = 14y - 5y

360 = 9y

y = 360/9

y = $40

Solving for x

x = 430 - 7y

x = 430 - 7(40)

x = 430 - 280

x = $150

Therefore:

Cost of Wedding cakes = x = $150

Cost of Birthday cakes = y = $40

The stream velocity has no influence on the amount of dissolved load it contains. The amount of dissolved material depends on erosion and deposition carried out in the watercourse. These are affected by factors such as the slope of the land, the resistance of the material to erosion, the size of the sediments transported, etc.

Stream velocity plays an important role in the transport of sediments and dissolved loads in a watercourse. It affects the erosion and deposition processes that occur in the watercourse, which in turn affect the amount of sediment and dissolved load that is carried by the stream. For example, faster stream velocities can cause more erosion of the stream bed, leading to more material being carried in the water.

Sediment is any particulate matter that is transported by a fluid, and it can come in many different forms. The three main types of sediment are:

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Since the standard deviation of data set B (3.1) is greater than that of data set A (2.5), it can be concluded that data set B has more variation or spread than data set A. Thus, the answer is data set B.

The data set that has more variation (spread) between the two, data set A and data set B can be determined by comparing their standard deviations.

This is because standard deviation measures how far apart the data points in a set are from the mean.

A larger standard deviation indicates more spread or variation in the data.

Let's compare the standard deviations of the two data sets:

a) Data set A has a mean of 12 and a standard deviation of 2.5b) Data set B has a mean of 12 and a standard deviation of 3.1

Since the standard deviation of data set B (3.1) is greater than that of data set A (2.5), it can be concluded that data set B has more variation or spread than data set A.

Thus, the answer is data set B.

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You are approximately 161.5566 feet away from the base of the tree.

To determine the distance from the base of the tree, we can use trigonometry and the concept of tangent.

Let's denote the distance from the base of the tree as "x."

We have a right triangle formed by the tree, the distance from the base, and the angle of elevation. The opposite side of the triangle is the height of the tree, which is 280 feet, and the adjacent side is the distance from the base, denoted as "x."

Using the tangent function, we have:

tan(60°) = opposite/adjacent

tan(60°) = 280/x

To solve for x, we can rearrange the equation:

x = 280 / tan(60°)

Using a calculator, we can evaluate the expression:

x ≈ 280 / 1.7321 ≈ 161.5566

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Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \(\frac{2}{3}\) x - 6 ← is in slope- intercept form

with slope m = \(\frac{2}{3}\)

Parallel lines have equal slopes , then

y = \(\frac{2}{3}\) x + c ← is the partial equation

To find c substitute (9, 2) into the partial equation

2 = 6 + c ⇒ c = 2 - 6 = - 4

y = \(\frac{2}{3}\) x - 4 ← equation of parallel line

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

Given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{\frac{2}{3} }\) = - \(\frac{3}{2}\) , then

y = - \(\frac{3}{2}\) x + c ← is the partial equation

To find c substitute (9, 2) into the partial equation

2 = - \(\frac{27}{2}\) + c ⇒ c = 2 + \(\frac{27}{2}\) = \(\frac{31}{2}\)

y = - \(\frac{3}{2}\) x + \(\frac{31}{2}\) ← equation of perpendicular line

Answer:

-9/8

Step-by-step explanation:

3x + 9 + 4x + x

Collect like terms

3x + 4x + x = -9

8x = -9

Divide both sides by 8

8x/8 = -9/8

x = -9/8

Answer:

-2

Step-by-step explanation:

Answer:

y = -2

Step-by-step explanation:

y = 14 - 2(8)

y = 14 - 16

y = -2

The expressions 2, 3, 4, and 5 are equivalent to 10.08.

We need to determine which of the given expressions are equivalent to 10.08.

As per the question, simplify each expression and see if it equals 10.08.

1). 13.117 + 1.3 = 14.417

Thus, this is not equivalent to 10.08

2). 2.88 x 3.5 = 10.08

Thus, this is equivalent to 10.08

3). 21.168 ÷ 2.1 = 10.08

Thus, this is equivalent to 10.08

4). 168 x 0.06 = 10.08

Thus, this is equivalent to 10.08

5). 201.6 x 0.05 = 10.08

Thus, this is equivalent to 10.08

Therefore, expressions 2, 3, 4, and 5 are equivalent to 10.08.

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Answer:

540

Step-by-step explanation:

540 =18% of 97.2

Done please

it's quotient it's a synthax error..

Step-by-step explanation:

kya tablet side apply the side of the wall has 22 M and 20 m

Answer:

I'm not so sure but it's 90°

Drinking iced coffee more often is associated with feeling more awake is most likely correlation and causation.

A relationship that most likely reflects correlation and causation is "Drinking iced coffee more often is associated with feeling more awake." The reason for this is that drinking iced coffee directly affects the level of alertness, which causes a change in the feeling of being awake.

This relationship suggests a cause-and-effect relationship between drinking iced coffee and feeling awake.

On the other hand, "Drinking iced coffee more often is associated with using a fan more often" and "Drinking iced coffee more often is associated with wearing shorts more often" do not reflect a cause-and-effect relationship.

The two variables are merely associated with each other, but there is no direct cause-and-effect relationship between them. It could be that both variables are related to a third factor, such as the weather, or that they are simply independent of each other.

In conclusion, when determining whether a relationship reflects correlation and causation, it is important to consider if there is a direct cause-and-effect relationship between the two variables.

Hence, the correct answer is c.

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--The given question is incomplete; the complete question is

"Each of these relationships reflects a correlation. Which relationship most likely reflects correlation and causation?

a. Drinking iced coffee more often is associated with using a fan more often.

b. Drinking iced coffee more often is associated with wearing shorts more often.

c. Drinking iced coffee more often is associated with feeling more awake."--

Step-by-step explanation:

this is your answer..........

Answer:

-7, 14, 21, and 42

Step-by-step explanation:

7•-1=-7

7•2=14

7•3=21

7•6=42

Answer:

Step-by-step explanation:

You want to compare various statistics related to Graduates and Non-graduates based on the given stem-and-leaf plot.

The number of responses in the 40s can be found by counting the leaves that have a stem of 4:

  Graduates: 6

  Non-graduates: 8

More Non-graduates had responses in the 40s.

The range for each group is found by subtracting the minimum value from the maximum:

  Graduates: 56 -21 = 35

  Non-graduates: 53 -23 = 30

The median of the group of 17 Graduates is the 9th element in the list, 41.

The median of the group of 18 Non-graduates is the average of the 9th and 10th elements in the list:

  (39+40)/2 = 39.5 . . . . . . less than 41

Graduates had the greater median number of hours.

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If volleyball team purchased 15 jackets, 12 pairs of sweatpants for $348 and basketball team purchases 8 jackets , 8 pairs of sweatpants for $200, the the system of equations that represent the situation is (b)  \(15x+12y = 348\) and \(8x+8y = 200\) .

let the number of jackets purchased be = x ;

let the number of pairs of sweatshirts purchased be = y ;

the volley ball team purchased 15 jackets and 12 pairs of sweatpants for $348 ,

that means the equation that represents the situation is :

\(15x+12y = 348\) .

Also given that , the basketball team purchased 8 jackets and 8 pairs of sweatpants for $200 ,

that means the equation that represents the situation is :

\(8x+8y = 200\) .

Therefore , the system of equations are \(15x+12y = 348\) and \(8x+8y = 200\) .

The given question is incomplete , the complete question is

A sports apparel supplier offers teams the option of purchasing extra apparel for players. A volleyball team purchases 15 jackets and 12 pairs of sweatpants for $348. A basketball team purchases 8 jackets and 8 pairs of sweatpants for $200. Let x represent the price of a jacket and let y represent the price of a pair of sweatpants. Which system of equations can be used to find the price of each item ?

(a) 8x + 8y = 200  ;  12x + 15y = 348   ;

(b) 8x + 8y = 200  ; 15x + 12y = 348 ;  

(c) 8x + 8y = 348  ;  12x + 15y = 200 ;  

(d) 8x + 8y = 348 ;  15x + 12y = 200 .

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Answer:

Since (2, 4) belongs to the line the constant of proportionality is 4 / 2 = 2.