6 radians to degrees (plane angle)

Value of x rounded to nearest tenth is 25.5 units.

Given in question,

Right angled triangle CDE

θ = 20°

CD = perpendicular = 24 units

CE = Hypotenuse = x

Therefore,

cosθ = Perpendicular/Hypotenuse

cos 20 = 24/x

0.9397 = 24/x

         x = 24/0.9397

            = 25.54

Hence, value of x rounded to nearest tenth is 25.5 units.

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Answer:

37.5%

Step-by-step explanation:

Cardi B

Step-by-step explanation:

It is decreasing in the time interval 0 < x < 2 hours.

Answer:

When \(x=0\), the value of f(x) is 1.

Each time x increases by 1, f(x) is multiplied by 4.

Equation of function: \(f(x)=1\cdot 4^x\)

Step-by-step explanation:

The detailed explanation is attached below.

Answer:

3,266.53

Step-by-step explanation:

Rounded to the nearest hundreth thousandths

Answer:10x+y+2xy^2-4x^2-4x?y[(-4,-2).(-4x+y)+10

Step-by-step explanation:

Answer:

\( \frac {x}{3} + 6 = 8 \)

Step-by-step explanation:

Let the unknown number be x.

Quotient simply means to divide a number by another number without any remainder.

For example, a quotient of 2 simply means that a number divided by 5 would have a value that is equal to 2 without any remainder; \( \frac {10}{5} = 2\)

Hence, translating the word problem in this scenario into an algebraic expression, we have;

\( \frac {x}{3} + 6 = 8 \)

Simplifying further, we have;

\( \frac {x}{3} = 8 - 6 \)

\( \frac {x}{3} = 2 \)

Cross-multiplying, we have;

x = 3 * 2

x = 6

The multiplication 3/4×8/9 can be used to address the problem in response (B). which is the correct answer that would be an option (B).

In mathematics, Multiplication operations perform Multiplying values on either side of the operator.

For example 4×2 = 8

As per option (B),

Jada rode her bike for 3/4 mile. Sarah rode her bike 8/9 the distance that Jada rode her bike.

Sarah rides her bike = Sarah rode (8/9) of the (3/4) that Jada rode.

Sarah rides her bike = 3/4 × 8/9

Therefore, this problem can be solved by performing the above multiplication.

Hence, the correct answer would be an option (B).

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5 years longer then Bill, 2x5=10.

10+2=12.

12-5=7

Hoang has be there for 12 years. Bill has for 7 years.

Answer: It is similar to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8)

Step-by-step explanation: Dilated triangles are never congruent, only similar (unless the dilation factor is exactly 1).

The coordinates of an image dilated about the origin are those of the pre-image multiplied by the dilation factor. For example,

 A' = 2A

 A'(8, -12) = 2×A(4, -6)

These facts are all you need to know to choose the correct answer (shown above).

Answer: 1/2

Step-by-step explanation:

I took the quiz!

The three inequalities will be :

1) 400 + 15x > 520

2) 520 < 400 + 15x

3) 15x > 120

Given,

In the question:

Dan’s dog-walking job pays $15 per hour.

His job as a car-wash attendant pays $400 each week.

Walking dogs to earn more than $520 in a week.

To find the which three inequalities can model this situation?

Now, According to the question:

Car wash = $400 per week

Dog - walking = $15per hour

To earn more than $520 in a week .

Let the hour be = x hour

Based on the given conditions:

Hence, The three inequalities will be :

1) 400 + 15x > 520

2) 520 < 400 + 15x

3) 15x > 120.

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Answer:

Step-by-step explanation:

We can see here that the 90% confidence interval will be: 420.2 to 585.8.

An interval of values known as a confidence interval is one that is likely to include the real value of a population parameter. A confidence interval of 95%, for instance, indicates that there is a 95% likelihood that the population parameter's real value falls inside the interval.

We will find the sample mean first:

Sample mean = sum of data points / number of data points

Sample mean = 8551 / 17 = 503

Then the standard error will be:

Standard error = population standard deviation / square root of number of data points

Standard error = 190 / √(17) = 41.7

Confidence interval = Sample mean ± 1.645 × standard error.

where 1.645 is the z-score for a 90% confidence interval.

Confidence interval = 503 ± 1.645 * 41.7 = 420.2 to 585.8

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Answer:

M=12

Step-by-step explanation:

The required length of MN in the given triangle LMN is 16 units.

A polygon with three vertices, angles and sides is called a triangle.

Given that, a triangle △ LMN, where, ∠ M ≅ ∠ L, LM = 7 and LN = 16

Since, ∠ M ≅ ∠ L

Therefore, MN ≅ LN

By the postulate :-

Sides opposite to congruent angles of a triangle are also congruent.

Therefore,

MN = LN

Since, LN = 16

Therefore, MN = 16 [By transitive property]

Hence, the required length of MN in the given triangle LMN is 16 units.

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Answer:

35 units

Step-by-step explanation:

Perimeter of rectangle ABCD =2(L + W)

L = AD or BC (we only need to calculate one of the two)

W = AB or DC. (we only need to calculate one of the two).

Distance between A(-2, 6) and D(-8, -4):

\( AD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Let,

\( A(-2, 6) = (x_1, y_1) \)

\( D(-8, -4) = (x_2, y_2) \)

\( AD = \sqrt{(-8 -(-2))^2 + (-4 - 6)^2} \)

\( AD = \sqrt{(-6)^2 + (-10)^2} \)

\( AD = \sqrt{36 + 100} = \sqrt{136} \)

\( AD = 11.7 \) (nearest tenth)

Distance between A(-2, 6) and B(3, 3):

\( AD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Let,

\( A(-2, 6) = (x_1, y_1) \)

\( B(3, 3) = (x_2, y_2) \)

\( AB = \sqrt{(3 -(-2))^2 + (3 - 6)^2} \)

\( AB = \sqrt{(5)^2 + (-3)^2} \)

\( AB = \sqrt{25 + 9} = \sqrt{34} \)

\( AB = 5.8 \) (nearest tenth)

Perimeter of rectangle ABCD =2(AD + AB)

= 2(11.7 + 5.8)

= 2(17.5)

= 35 units

The area of the figure is 596.625 in².

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

We will consider the figure to have a rectangle and a circle.

Rectangle:

Length = 28 in

Breadth = 15 in

Area = 28 x 15 = 420 in²

Semicircle:

Diameter = 15 in

Radius = 7.5 in

Area = 1/2 πr²

= 1/2 x 3.14 x 7.5²

Area = 176.625/2

Area = 88.3125

There are two semicircles so,

= 2 x 88.3125

= 176.625 in²

Now,

Area of the figure.

= 420 + 176.625

= 596.625 in²

Thus,

596.625 in² is the area of the figure.

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Answer:

2

Step-by-step explanation:

Answer:

6 and or d

Step-by-step explanation:

6x is just 6 time ? so 6 time 6 is 36 minus 3  which is greator than 21

Answer:

D

Step-by-step explanation:

6x - 3 > 21    

6x > 21 + 3

6x > 24

x > 24 ÷ 6

x > 4

So x ∈ (4, +∞)

then the only solution from given is 6

Answer:

2.75

Step-by-step explanation:

When x = 4, y = 11

when x = 1, y = 2.75

k = 2.75

The spherical coordinates of the given rectangular coordinates are (10, 0, 60).

The cartesian coordinate or rectangular coordinates describes the location of a point in space using an ordered triple where each coordinate represents a distance. The spherical coordinate system describes the location of a point in space using an ordered triple where coordinate describes one distance and two angles. In the spherical coordinate system, a point is represented by the ordered triple (ρ, θ, φ).

The equations which are used to convert from rectangular coordinates to spherical coordinates are:

ρ^2=x^2+y^2+z^2

tan⁡〖θ= y/x〗

φ=arccos⁡〖z/√(x^2+y^2+z^2 )〗

The given rectangular coordinates are (5√3, 0, 5). Hence,

ρ^2=〖(5√3)〗^2+0^2+5^2 ≈ 100

ρ ≈ √100 ≈ 10

tan⁡〖θ= 0/(5√3)=0〗

θ=  tan^(-1)⁡0=0

φ=arccos⁡〖5/√(〖(5√3)〗^2+0^2+5^2 )〗= arccos 5/10=arccos⁡0.5 ≈ 60

Note:  The question is incomplete. The complete question probably is: Convert from rectangular to spherical coordinates. (Use symbolic notation and fractions where needed. Give your answer as a point's coordinates in the form (*,*,*). (5√3, 0, 5)

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The type of scale commonly used on maps is a graphic scale, which uses a line or bar to represent distances accurately.

The type of scale used on a map is known as a map scale. It is a graphical representation that shows the relationship between distances on the map and their corresponding measurements in the real world. A map scale allows us to understand the size and proportion of features depicted on the map.

There are three main types of map scales: verbal scales, graphic scales, and representative fraction scales.

Verbal Scale: A verbal scale uses words to describe the relationship between distances on the map and real-world measurements. For example, a verbal scale might state "1 inch represents 1 mile" or "1 centimeter represents 10 kilometers." Verbal scales are commonly used on small-scale maps, where the level of detail is not as important.

Graphic Scale: A graphic scale, also known as a bar scale or linear scale, uses a line or a bar marked with specific distances. This line is divided into equal segments that represent units of measurement. By comparing the length of the line on the map to the corresponding distance in the real world, you can determine distances accurately. Graphic scales are often found on the margin or the legend of a map and are commonly used on medium- to large-scale maps.

Representative Fraction (RF) Scale: A representative fraction scale expresses the relationship between map distances and real-world distances using a ratio. For example, a representative fraction of 1:100,000 means that one unit of measurement on the map represents 100,000 of the same units in the real world. This type of scale is useful because it allows for precise calculations and conversions between map distances and real-world distances. Representative fraction scales are commonly used on topographic maps and engineering plans.

It's important to note that a map may include multiple scales to accommodate different levels of detail. For instance, a large-scale map of a city may have a more detailed scale than a small-scale map of an entire country.

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Calculating the volume of a rectangular prism is a simple process that involves multiplying the length, width, and height.

Calculating the volume of a rectangular prism is a straightforward process. A rectangular prism is a three-dimensional shape that has a length, width, and height. To find its volume, you simply multiply the length by the width by the height. The formula for calculating the volume of a rectangular prism is:
Volume = length x width x height
For example, if a rectangular prism has a length of 5 cm, a width of 4 cm, and a height of 3 cm, its volume would be:
Volume = 5 cm x 4 cm x 3 cm
Volume = 60 cubic centimeters (cm³)
It's important to ensure that all measurements are in the same unit before calculating the volume. For instance, if the length is in meters and the width and height are in centimeters, you would need to convert the length to centimeters to ensure that all measurements are in the same unit before calculating the volume.
In conclusion, calculating the volume of a rectangular prism is a simple process that involves multiplying the length, width, and height. This formula can be used for any rectangular prism regardless of its size or shape.

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Heracio used the computer 4 more hours to do homework than shop online.

To find out how many more hours Heracio used the computer to do homework than shop online, we first need to calculate the number of hours he spent on each activity.

Let's start by calculating the number of hours Heracio spent on each activity:

Shopping: 10% of 40 hours = 4 hours

Videos: 15% of 40 hours = 6 hours

Homework: 20% of 40 hours = 8 hours

Games: 20% of 40 hours = 8 hours

Social media: 25% of 40 hours = 10 hours

Now, to find out how many more hours Heracio used the computer to do homework than shop online, we need to subtract the number of hours spent shopping from the number of hours spent on homework:

8 hours (homework) - 4 hours (shopping) = 4 hours

Therefore, Heracio used the computer 4 more hours to do homework than shop online.

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Answer:

andrew

Step-by-step explanation:

Answer:

X¹= -2 + 2√33

X²= -2 - 2√33

Step-by-step explanation:

X × (X+2) = 32

X² + 2X = 32

X² + 2X - 32= 0

Δ=132

X= -2 ± 2√33

X¹= -2 + 2√33

X²= -2 - 2√33

(You can change the 2√33 to 11,5 if you want to)

Answer:

1.5 hours  

Step-by-step explanation:

Answer:

1.5 hours

Step-by-step explanation:

15 men can dig a trench 90 feet deep in 3 hours. So, first, we have to divide 90 by 3 to find the depth that 15 men can dig in 1 hour.

90/3 = 30

Next, we need to divide 30 by 15 to find how deep 1 man can dig in 1 hour.

30/15=2.

Now, since there are 16 men in this second project, we need to multiply 16 by 2 to find how much 16 men can dig in 1 hour.

16x2 = 32.

Finally, we have to add 16 to get 48.

Since we added the depth for 1 hour plus the depth for half an hour to get the total depth, we can say that 16 men can dig 48m in 1.5 hours.

Step-by-step explanation:

(a) Let's start with the first pool. It has 3650 liters of water. For every minute, 27 liters are being drained. Thus, we can write its equation as 3650 liters - 27 liters per minute = end amount of liters. If we write minutes as m, we can say 3650-27m is our expression. Similarly, for the second one, we have 4166-39m as our answer

(b) For this, we just have to make the two expressions equal, so

4166-39m = 3650-27m

The solution is:

(a)

Amount of water in the first pool (in liters) = 3650 liters - 27 liters per minute * x minutes

Amount of water in the second pool (in liters) = 4166 liters - 39 liters per minute * x minutes

(b)

3650 liters - 27 liters per minute * x minutes= 4166 liters - 39 liters per minute * x minutes

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here, we have,

(a) With x being the minutes after which you want to calculate the amount of water in the pool, to calculate this amount of water you must subtract the water drained from the initial amount of water that the pool contains.

Knowing that, for example, the water from the first pool drains at a rate of 27 liters per minute, then after x minutes, the total water drained will be 27 liters per minute * x minutes. Then:

Amount of water in the first pool (in liters) =  3650 liters - 27 liters per minute * x minutes

Reasoning in the same way:

Amount of water in the second pool (in liters) = 4166 liters - 39 liters per minute * x minutes

(b)  Now want to know when the two pools would have the same amount of water.  If they have the same amount of water then you can express:

Amount of water in the first pool = Amount of water in the second pool

Replacing the expressions found in (a):

3650 liters - 27 liters per minute * x minutes= 4166 liters - 39 liters per minute * x minutes

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