Solve the following equation for B over the interval [0,2pi]
, giving exact answers in radian units. If an equation has no solution, enter DNE. Multiple solutions should be entered as a comma-separated list.

Answer:

I didn't got the question well

Answer: 15

Step-by-step explanation:

we can  say 5x+55 and 2x+100 are corresponding angles and they are equal. so, 5x+55=2x+100

3x=45

x=15

Carlos needs to earn at least 16 points on the final quiz to earn at least a 90% average.

We have,

Let's start by finding the total number of points that Carlos can earn in the class:

Total points

= 5 quizzes x 20 points per quiz

= 100 points

If Carlos needs an average of 90% or greater, that means he needs to earn at least 90 points out of 100.

Total points earned.

= 18 + 19 + 17 + 20

= 74 points

To find the minimum score Carlos needs on the final quiz, we can set up an inequality:

(74 + x) / 5 ≥ 0.9

where x is the score on the final quiz.

Simplifying this inequality.

74 + x ≥ 90

x ≥ 16

Therefore,

Carlos needs to earn at least 16 points on the final quiz to earn at least a 90% average.

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Answer:

12

Step-by-step explanation:

you will have to divide $15 by $180 and when you do that your result should end up being 12, hope that helped

17/20 is the probability that their eyes are green or Hafzel.

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

The number of students having Green eyes =6

The number of students having Blue eyes =3

The number of students having Hafzel eyes =11

The total number of students=11+3+6

=20

The probability that their eyes are green is 6/20

The probability that their eyes are Hafzel is 11/20

The probability that their eyes are green or  Hafzel

6/20 + 11/20

= 17/20

Hence,  17/20 is the probability that their eyes are green or Hafzel.

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Answer:

slope  1/7

y intercept: (0, -67)

slope intercept form: y=1/7x - 61/7

Step-by-step explanation:

point slope form is

y+9=1/7 *(x+2)

Answer:  Oki should make 0 bags of her recipe, and Stephen should make 30 bags of his recipe.

For vertex (15,15):

3x + 4y = 120 --> 3(15) + 4(15) = 120 --> x = 15

3x + 2y = 90 --> 3(15) + 2y = 90 -->

Step-by-step explanation: A. To find the maximum number of bags of trail mix that Oki and Stephen can make together, we can use a system of inequalities to represent the constraints:

Let "x" be the number of bags of trail mix that Oki makes and "y" be the number of bags that Stephen makes. Then we have:

3x + 4y ≤ 120 (constraint on the number of cups of nuts)

3x + 2y ≤ 90 (constraint on the number of cups of dried fruit)

x ≥ 0 (non-negative constraint for Oki's bags)

y ≥ 0 (non-negative constraint for Stephen's bags)

B. To graph the feasible region, we can start by graphing the two constraint equations as lines:

3x + 4y = 120 (line A)

3x + 2y = 90 (line B)

We can find the x and y intercepts for each line:

For line A:

When x = 0, 4y = 120, y = 30 (y-intercept)

When y = 0, 3x = 120, x = 40 (x-intercept)

For line B:

When x = 0, 2y = 90, y = 45 (y-intercept)

When y = 0, 3x = 90, x = 30 (x-intercept)

Next, we can shade the region that satisfies all of the constraints. This region is below line A and to the left of line B, and is bounded by the x and y axes.

We can find the vertices of the feasible region by finding the intersection points of the two lines and the axes. These vertices are (0,0), (0,30), (15,15), and (30,0).

C. To find the maximum number of bags of trail mix that Oki and Stephen can make together, we need to evaluate the objective function at each vertex of the feasible region, and choose the vertex that maximizes the objective function.

The objective function is the total number of bags of trail mix:

z = x + y

Evaluating at the vertices:

Vertex (0,0): z = 0 + 0 = 0

Vertex (0,30): z = 0 + 30 = 30

Vertex (15,15): z = 15 + 15 = 30

Vertex (30,0): z = 30 + 0 = 30

The maximum value of the objective function occurs at vertices (0,30) and (15,15), where z = 30 bags of trail mix.

To determine how many of each type of recipe to make, we can substitute each vertex into the two constraint equations to find the corresponding values of x and y.

For vertex (0,30):

3x + 4y = 120 --> 3x + 4(30) = 120 --> 3x = -90 --> x = -30

3x + 2y = 90 --> 3(-30) + 2(30) = 90 --> y = 15

Therefore, Oki should make 0 bags of her recipe, and Stephen should make 30 bags of his recipe.

For vertex (15,15):

3x + 4y = 120 --> 3(15) + 4(15) = 120 --> x = 15

3x + 2y = 90 --> 3(15) + 2y = 90 -->

Answer:

5) \(y=\frac{7}{2}x\)

6) \(y=\frac{1}{4}x\)

Step-by-step explanation:

k in this equation represents the slope of the line. To find the slope of a line, pick 2 points that land perfectly on the grid and find the vertical and horizontal distance between them. The vertical distance is the 'rise', and the horizontal distance is the 'run'. Given those two numbers, you can calculate the slope:

\(k=\frac{rise}{run}\)

A more precise definition is:

\(k=\frac{y2-y1}{x2-x1}\)

5)

You can use whichever 2 points you want here. I'll use the 2 outermost points:

(x1, y1) = (2, 7)

(x2, y2) = (8, 28)

Now, to find the distance between them, subtract the position of the first point from the second point. Vertical distance first, subtract the y-coordinates:

\(28-7=21\)

The rise is 21.

Horizontal distance, subtract the x-coordinates:

\(8-2=6\)

Slope is 'rise over run' as I wrote above, so you can now write the slope and the equation of the line:

\(k=\frac{21}{6}\\\\k=\frac{7}{2}\\\\y=\frac{7}{2}x\)

6)

I'll pick the 2 outermost points again:

(x1, y1) = (8, 2)

(x2, y2) = (24, 6)

This time, I'll just plug all 4 values directly into the 2nd formula I wrote at the top.

\(k=\frac{y2-y1}{x2-x1}\\\\k=\frac{6-2}{24-8}\\\\k=\frac{4}{16}\\\\k=\frac{1}{4}\\\\y=\frac{1}{4}x\)

8.4 is the value of x in the equation 4x+8y=40, when y=0.8. Hence, option B is correct.

A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.

The given equation:

4x + 8y = 40

Substituting y = 0.8 into the equation, we get:

4x + 8(0.8) = 40

Simplifying:

4x + 6.4 = 40

Subtracting 6.4 from both sides:

4x = 33.6

Dividing both sides by 4:

x = 8.4

Thus, option B is correct.

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Answer:

(0,10)

Step-by-step explanation:

Answer:

(0,10)

Step-by-step explanation:

See picture

Mrs. Wu initially had $1062.40.

Let's break down the given information step by step:

1. Mrs. Wu spent 1/6 of her money on a dress and 2 blouses.

  Let's assume Mrs. Wu's total money is represented by the variable M. She spent 1/6 of M on the dress, which means she spent (1/6)M on the dress and the same amount on two blouses.

2. The dress cost 3 times as much as each blouse.

  Let's assume the cost of each blouse is represented by the variable B. Therefore, the cost of the dress would be 3B.

3. Mrs. Wu spent 3/4 of her remaining money on a watch.

  After spending on the dress and blouses, Mrs. Wu has (M - (1/6)M) = (5/6)M remaining. She spent 3/4 of this remaining money on a watch, which is (3/4) * (5/6)M = (15/24)M.

4. She spent $220.50 more on the watch than on the dress.

  The amount spent on the watch is (15/24)M, and the amount spent on the dress is (1/6)M. The difference between these amounts is $220.50.

To find the value of M, we can set up an equation:

(15/24)M - (1/6)M = $220.50

Simplifying the equation:

(15/24 - 1/6)M = $220.50

(5/24)M = $220.50

Multiplying both sides by (24/5):

M = $220.50 * (24/5)

M = $1062.40

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Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Answer:

304

Step-by-step explanation:

you don't know the relation of feet and inches ? or what is the problem ?

1 foot = 12 inches

so, if we would simply scale feet to inches (divide by 12), the length would be 32 inches.

32×12 / 12 = 32.

but it is 16 inches.

we notice the ratio of 32 to 16 (a factor of 2 between them), so we need another division by 2 to scale correctly.

therefore the scaling factor s = 1/12/2 = (1/12)/(2/1) = 1/24 on inches.

this scaling factor is the same for every dimension or axis.

the full size width is 38×12 inches.

so the scaled width of the room is therefore 38×12/24 = 38/2 = 19.

the floor area of the scanned room is then 16 × 19 = 304

Answer:

a

Step-by-step explanation:

A. The tallies are missing

(I think this can be the answer )

Answer:

B

Step-by-step explanation:

ik im late but i hope i helped anyone from 2022

Answer:

x>_-1

Step-by-step explanation:

x is such that x is greater or equal to -1

Answer:

-1+2x= 17

2x=18

x=9

Step-by-step explanation:

ans. 9

Answer:

its A) 9

Step-by-step explanation:

Answer:

plane

point

line

Step-by-step explanation:

Based on the options provided, the kinds of symmetry in a 2D number can be:

Therefore, the possible kinds of symmetry in a 2D number can be

plane symmetry,

point symmetry, or

line symmetry.

It will take 18.9 years for your investment to reach $1,500

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

Initial deposit = 500 dollars

Rate of growth = 6% per year

The above implies that the growth follows an exponential path

An exponential function that represents a growth function is represented as

A(n) = a * (1 + r)ⁿ

Where

A(n) = value of investment after nth year

a = Initial deposit = 500

r = rate of growth = 6%

Substitute the known values in the above equation, so, we have the following representation

A(n) = 500 * (1 + 6%)ⁿ

Evaluate the sum

A(n) = 500 * 1.06ⁿ

When the investment is 1500 grams, we have

500 * 1.06ⁿ = 1500

Divide both sides by 500

1.06ⁿ = 3

So, we have

n = log(3)/log(1.06)

Evaluate

n = 18.9

Hence, the number of years is 18.9

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Answer:

The answer is actually 18.3 Years

Step-by-step explanation:

I got it correct on the test :D

Answer:

The answer is "\(= \frac{\pi}{8}(15-41n^2 )\\\)".

Step-by-step explanation:

The radius = x

the value of height is= \(e^{-x}\)

The Formula for  the volume by the shell method:

\(\bold{V= \int\limits^b_a {(2\pi\ rad)(height)} \, dx }\)

   \(= 2\pi \int\limits^{In 16}_0 {xe^{-x}} \, dx\\\\\\= 2\pi {(e^{-x}[-x-1])}_{0}^{In 16}\\\\ = 2\pi {(\frac{1}{16} \times (15-41n^2 ))}\\\\ = \frac{\pi}{8}(15-41n^2 )\\\)

Answer: The set does not have a solution

Step-by-step explanation:

Adding Equations 1 & 3 we get 5x = 7. This gives x = 7/5

Putting this value of x in eq. 2 we get

-2y + 2z = -1-(7/5) or

2y - 2z = 12/5  or  5y - 5z = 6

Multiplying eq. 1 by 2  we get  

4x + 2y - 2z = 6

adding this with eq. 2 we get 5x = 5 or x = 1

As the common solution for x from equations 1&3 does not satisfy eq. 1&2 it comes out that the three equations do not have a common solution.

Same can be verified by using different sets of two equations also.

Answer:

1) 7/8     8/7

2) 4.4

3) 3.7

4) 2.8

Step-by-step explanation:

Length of bottom side of Figure A: 8 cm

Length of bottom side of Figure B: 7 cm

From Figure A to Figure B, the scale factor is 7/8.

7/8

8/7

5 × 7/8 = 35/8 = 4.375

4.4

3.2 × 8/7 = 3.657...

3.7

3.2 × 7/8 = 2.8

2.8

Answer:

sin(100°) = 0.985

sin(-100°) = -0.985

Step-by-step explanation:

In a unit circle, each point (x, y) on the circumference corresponds to the coordinates (cos θ, sin θ), where θ represents the angle formed between the positive x-axis and the line segment connecting the origin to the point (x, y).

Therefore, sin(100°) equals the y-coordinate of the point (-0.174, 0.985), so:

\(\boxed{\sin(100^{\circ}) = 0.985}\)

Similarly, sin(-100°) equals the y-coordinate of the point (-0.174, -0.985), so:

\(\boxed{\sin(-100^{\circ}) = -0.985}\)

In the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

The value of the sine of the angles is calculated by applying the following formula as follows;

The value of sin (100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, 0.985) as given on the coordinates of the unit circle.

sin (100) = 0.985

The value of sin (-100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, -0.985), as given on the coordinates of the circle.

sin (-100) = -0.985

Thus, in the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

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The solution of the given system of equations is (4, 7).

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of equations are y=3x-5 -------(I) and y=1/2 x+5 -------(II)

Substitute equation (I) in (II), we get

3x-5=1/2 x+5

3x-1/2 x=5+5

2.5x=10

x=4

Substitute x=4 in equation (I), we get

y=3(4)-5

y=7

So, solution is (4, 7)

Therefore, the solution of the given system of equations is (4, 7).

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Answer:

G. Carla, Brenda, Marci, Susan

Step-by-step explanation:

The time given for all participants are in decimals except for that of Marci and Carla which are given in the form of mixed fractions.

Convert the mixed fractions into decimals, then compare the figures together to do the ranking.

Marci = \( 46\frac{49}{50} = \frac{2,349}{50} = 46.98 \)

Carla = \( 46\frac{9}{10} = \frac{469}{10} = 46.9 \)

The first four finishers from the 1st to the 4th are:

1. Carla - 46.9

2. Brenda - 46.97

3. Marci - 46.98

4. Susan - 47.21

Answer:

16.44

Step-by-step explanation:

The mean is  2,071,798.33

The Median is 1,485,552

The range is 7,425,310

The standard deviation is given as 1961105.68

Mean = (Sum of all populations) / (Number of cities)

= (8,336,817 + 979,576 + 2,693,976 + 2,320,268 + 1,680,992 + 1,584,064 + 1,547,253 + 1,423,851 + 1,343,573 + 1,021,795 + 978,908 + 911,507) / 12

= 24,861,580 / 12

= 2,071,798.33

To find the median, we need to arrange the populations in increasing order and find the middle value. If we arrange these values, we get:

911,507, 978,908, 979,576, 1,021,795, 1,343,573, 1,423,851, 1,547,253, 1,584,064, 1,680,992, 2,320,268, 2,693,976, 8,336,817

Since there are 12 cities (an even number), the median would be the average of the 6th and 7th values:

Median = (1,423,851 + 1,547,253) / 2

= 1,485,552

The mode isn't applicable here as no city population repeats.

The range is the highest population minus the lowest population:

Range = 8,336,817 - 911,507

= 7,425,310

Standard deviation  =  (911507- 2068548.3333333)² +  (978908 - 2068548.3333333)² + (979576  - 2068548.3333333)²  + ( 1021795 -  2068548.3333333)² +  (1343573- 2068548.3333333)²  +( 1423851- 2068548.3333333)² + (1547253- 2068548.3333333)² +( 1584064- 2068548.3333333)² + (1680992- 2068548.3333333)² + ( 2320268- 2068548.3333333)²  +(2693976- 2068548.3333333)² +( 8336817 - 2068548.3333333)² / 12

= 46151226311869 / 12

=  3845935525989.1

\(standard deviation = \sqrt{ 3845935525989.1}\)

=  1961105.6896529

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Answer:

should have dded like variables first

Step-by-step explanation:

Answer:

X=6

Step-by-step explanation:

3x+2x-6=24

add 3x and 2x this gives 5x

5x-6=24

then add the 6 to 24

5x=30

then divide both sides by 5

then X=6

Answer:

The answer is (-4,1)

Step-by-step explanation:

Answer:

(-4,1)

Step-by-step explanation: