Find all values of x in the interval [0, 2π] that satisfy the equation. 7 sin(2x) = 7 cos(x)

Answer:

arithmetic sequence formula: first term + (n - 1)common difference

9 + (n - 1)-2

9 + -2n + 2

= -2n + 11

Using the arrangements formula, it is found that 1680 arrangements can be made with these numbers.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

When there are repeated elements, repeating [tex]n_1, n_2, \cdots, n_n[/tex] times, the number of arrangements is given by:

[tex]A_n^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]

For the number 28535852, we have that:

Hence the number of arrangements is:

[tex]A_8^{3,2,2} = \frac{8!}{3!2!2!} = 1680[/tex]

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The standard form of the equation whose graph is the line through (1, -2) and (-5, 6) is 3y = -4x -2.

According to the question,

The standard form of the equation whose graph is the line through (1, -2) and (-5, 6). Now first to find slope of the equation using below formula,

Slope of the equation (m)= (change in y axis) / (change in x axis)

= (6- (-2))/(-5 - 1)

= 8/-6

=-(4/3)

Slope of the equation (m) = -4/3. whose graph is the line through (1, -2) and (-5, 6).Formula to find Standard form of the equation is y = mx + c.

-2 = -(4/3) 1 + c

c = -2 +(4/3)

c = -2/3

The standard form of the equation whose graph is the line through (1, -2) and (-5, 6) is 3y = -4x -2. y = -(4/3)x -(2/3).

⇒  3y = -4x -2.

Hence, the standard form of the equation whose graph is the line through (1, -2) and (-5, 6) is 3y = -4x -2.

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The behavior of the graph with the equation y=x66x5+50x3+45x2108x108 at each of its zeros will be as follows: two of them will resemble a quadratic function, while one of them will resemble a linear function.

This is further explained below.

Generally, a diagram that illustrates the relationship between variable quantities, usually consisting of two variables, with each variable being measured along one of a pair of axes that are intersected at right angles.

In conclusion, At each of its zeroes, the graph y=x66x5+50x3+45x2108x108 will exhibit one linear behavior and two behaviors that resemble quadratic functions.

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Answer:

approximately 2 lb

Step-by-step explanation:

Juan: 31/7

Ari: 19/3

Juan's fraction is close to 32/8 = 4

Ari's fraction is close to 18/3 = 6

6 - 4 = 2

Answer: approximately 2 lb

Answer:

See below

Step-by-step explanation:

237/50   =    4    R 37

37/20     =     1     R 17

17 / 10     =     1     R 7

7 / 1         =     7    R 0

4   50gm's      1     20gm       1   10gm       and   7    1g wts

The required number of weights used in chemical balance to weigh 237g is 4,1,1,7 respectively.

What is mathematical expression?

A mathematical expression expression in mathematical is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Here, it is given that :

A chemical balance needs to weigh 237g using weights of 50g, 20g, 10g and 1g.

Now, let us find the number of weights for each weight type :

For 50g weight the maximum number of weights needed will be 4 that is :

50g x 4 = 200g

Now, for 20g weight the maximum number of weights needed will be 1 that is :

20g x 1 = 20g

Now, for 10g weight the maximum number of weights needed will be 1 that is :

10g x 1 = 10g

Now, for 1g weight the maximum number of weights needed will be 7 that is :

1g x 7 = 7g

Adding all the weights we get :

200g + 20g + 10g + 7g = 237g;

which is the required weight and the number of weights used is 4,1,1,7 respectively.

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Answer:

40 apples

Step-by-step explanation:

x = (4·2)/(1/5) = 8/(1/5) = (8/1):(1/5) = (8/1)·(5/1) = 40/1 = 40 apples

It takes 10 apples to make a gram of fat. Multiply the 10 apples by 4 grams of fat to find that it takes 40 apples to make 4 grams of fat.

Answer:

your question is not correct i can not find the answer

Applying the central angle theorem, we have:

a. angle BAC.

b. arc BEC

c. arc BC

d. Measure of arc BEC = 260°

e. Measure of arc BC = 100°

According to the central angle theorem, the central angle that is suspended at the center of a circle by two line segments (usually radii) have a measure that is equal to the measure of the intercepted arc. That is:

Measure of central angle = measure of intercepted arc.

A major arc have a measure that is greater than 180 degrees or half a circle, while minor arcs have a measure that is less than 180 degrees or half a circle.

a. A central angle in the image given is: angle BAC.

b. One major arc in the given circle is arc BEC (greater than half a half a circle/180 degrees).

c. One minor arc in the given circle is arc BC (less than half a half a circle/180 degrees).

d. m∠BEC = 360 - 100

m∠BEC = 260°

m∠BEC = measure of arc BEC [central angle theorem].

Measure of arc BEC = 260°

e. Measure of arc BC = m∠BAC [central angle theorem].

Measure of arc BC = 100°

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Answer:

  170

Step-by-step explanation:

The given relations can be used to write and solve an equation for the number of stickers Peter has.

Let p represent the number of stickers Peter has. That is twice as many as Joe, so Joe has (p/2) stickers. Joe has 40 more stickers than Emily, so the number of stickers Emily has is (p/2 -40).

The total number of stickers is 300:

  p +p/2 +(p/2 -40) = 300

  2p = 340 . . . . . . . . . . . . . . add 40, collect terms

  p = 170 . . . . . . . . . . . divide by 2

Peter has 170 stickers.

__

Additional comment

Joe has 170/2 = 85 stickers. Emily has 85-40 = 45 stickers.

We could write three equations in three unknowns. Solving those using substitution would result in substantially the same equation that we have above. Or, such a system of equations could be solved using a calculator's matrix functions, as in the attachment.

  p +j +e = 300

  p -2j +0e = 0

  0p +j -e = 40

If the third term of the aritmetic sequence is 126 and sixty fourth term is 3725 then the first term is 8.

Given the third term of the aritmetic sequence is 126 and sixty fourth term is 3725.

We are required to find the first term of the arithmetic sequence.

Arithmetic sequence is a series in which all the terms have equal difference.

Nth term of an AP=a+(n-1)d

[tex]A_{3}[/tex]=a+(3-1)d

126=a+2d--------1

[tex]A_{64}[/tex]=a+(64-1)d

3725=a+63d------2

Subtract second equation from first equation.

a+2d-a-63d=126-3725

-61d=-3599

d=59

Put the value of d in 1 to get the value of a.

a+2d=126

a+2*59=126

a+118=126

a=126-118

a=8

[tex]A_{1}[/tex]=a+(1-1)d

=8+0*59

=8

Hence if the third term of the arithmetic sequence is 126 and sixty fourth term is 3725 then the first term is 8.

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Answer:

42

Step-by-step explanation:

similar triangles

24/x = (24+8)/x+14

that looks complicated so we do

8/24 = 14/x

or

24/8 = x/14

3 = x/14

x = 3*14

x = 42

we test it with the first equation

24/42 = 32/56

simplify

4/7 = 4/7

true so 42 is correct

The attached figure represents the array for 237 x 43

The array is given as:

237 x 43

An array is represented as:

Row x Column

This means that:

Row = 237

Column = 43

i.e. the array has 237 rows and 43 columns

The numbers are large, so the cells would be small when the arrays are drawn

See attachment for the array

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Answer:

45:315

Step-by-step explanation:

Add up the ratio to get the total ratio.

1+7=8

Divide the 360 by the total ratio.

360÷8=45

The number 45 tells you how many times to multiply both sets of the ratio to get a total of 360.

1×45=45

7×45=315

so,

45:315

Hope this helped. Comment below if you need more assistance! :)

Answer:

12 walls

Step-by-step explanation:

Let's take everyone paints a different wall and there are no overlaps.

Given information from the question:

1.5 hours = 1 wall

1 hour =

[tex] \frac{1}{1.5} \\ = \frac{2}{3} walls[/tex]

per person.

From the information above, we can deduce:

6 people =

[tex] \frac{2}{3} \times 6 \\ = \frac{12}{3} \\ = 4 \: walls[/tex]

Since we know 6 people can paint 4 walls in an hour,

3 hours =

[tex]3 \times 4 \\ = 12 \: walls[/tex]

The most efficient measurements of the box should be 4cm long, 1cm wide and 2cm high so that its cost is $129.2

To calculate the measurements of the rectangular box we must take into account the following condition:

According to the above, we can establish that the most appropriate measurement for the bottom and top should be 1cm (width) × 4cm (length). Additionally we can establish that the height of the box would be 2cm.

To find the volume of the box we must use the following formula:

The areas of this box are:

The total price of this box is as follows:

Top and bottom:

Sides:

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Answer:

-5^x + 3x - 2.

Step-by-step explanation:

(f - g) (x) = f(x) - g(x)

=  -5^x - 4 - (-3x - 2)

= -5^x - 4 + 3x + 2

= -5^x + 3x - 2.

0.03607

Absolute value is the distance of a number from zero. Since distance is always positive, the absolute value is the same number but positive.

Please note, for this problem I have rounded to 5 decimal points because the answer is irrational.

Subtracting

There are 2 different ways to approach this problem. You can either estimate the square root of 5 or plug this question straight into a calculator.

First, we can estimate [tex]\sqrt{5}[/tex] and round to 5 decimal places.

Then, take this value and subtract.

Absolute Value

Now that we have solved the subtraction problem we have to find the absolute value. As stated above, the easiest way to find absolute value is to simply make the number positive. Since the answer is already positive, this is the final answer.

The equation for the tangent plane is 12x - y + 4z - 56 = 0 and the equation for normal line is (x - 6)/12 = (32 - y) = (z - 2)/4

Finding the Equations for Tangent Plane and Normal Line:

The given function is,

f(x, y, z) = x² - y - z² = 0

∂f/ ∂x = 2x

∂f/ ∂y = -1

∂f/ ∂z = 2z

At given point (6, 32, 2),

∂f/ ∂x = 12

∂f/ ∂y = -1

∂f/ ∂z = 4

(a) The equation of tangent plane is given as follows,

(∂f/ ∂x)(x-x₁) + (∂f/ ∂y)(y-y₁) + (∂f/ ∂z)(z-z₁) = 0

12(x - 6) - 1(y - 32) + 4(z - 4) = 0

12x - 72 - y + 32 + 4z - 16 = 0

The required tangent plane is,

12x - y + 4z - 56 = 0

(b) The equation for normal line is given as,

(x-x₁) / (∂f/ ∂x) = (y-y₁) / (y-y₁) = (z-z₁) / (∂f/ ∂z)

(x - 6)/12 = (y - 32)/(-1) = (z - 2)/4

Thus, the required equation of normal line is,

(x - 6)/12 = (32 - y) = (z - 2)/4

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The histogram that correctly shows the data in the table is the histogram number four.

This a type of graph that allows people to visually represent data by using bars and gathering the data they have in different categories.

This data can be represented using ranges of temperature and the number o elements or substances in these ranges.

This data matches the fourth graph

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Explanation:(x)(x)=x^2 and(x)(x)(x)=x^3

Answer:

3rd grade

Step-by-step explanation:

Given that the values are different types (fractions, decimals, and percentages), it would be helpful to convert them to the same type of value.

Converting everything to percentages seems more convenient.

Since 61.24% is already a percentage, we simply have to convert 0.52, 25/36, and 0.5274444 (I wrote 0.5274 like this since the 4 is a repeating value).

To convert 0.52, we simply multiply by 100:

0.52 * 100 = 52%

For 25/36, we need to know its decimal form and multiply by 100 to find the percentage:

25 / 36 = 0.6944 * 100 = 69.44%

For 0.5274444, we also multiply by 100:

0.5274444 * 100 = 52.74444

Thus, we have 52% (2nd grade), 69.44% (3rd grade), 61.24% (4th grade), and 52.74444% (5th grade).

3rd grade has the highest portion of students

Answer:

0.7

Step-by-step explanation:

Each increment is 0.1, so count the approximate number of increments needed to get from the orange circle on the left and the one on the right and multiply by 0.1 to get the difference.

Step-by-step explanation:

M(x) = 4x^3 - 3

let M(x) = Y

Y = 4x^3 - 3...swap places of x & y.

X = 4y^3 - 3

look for x in terms of y.

4y^3 = x + 3

Y^3 = x + 3 / 4...put both sides under cube root.

y = ( x + 3 / 4 )^1/3

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

The straight angles are angles that form a straight line, and their measure = 180°

In the given figure, the Straight angles is :

[tex] \qquad \large \sf {Conclusion} : [/tex]

The probability that at least 11 of them graduated is 0.7739 if graduation rate is 92.5%.

Given that graduation rate is 95.2%.

We are required to find the probability that out of 12 selected candidates atleast 11 should be graduated.

Probability is basically the chance of happening an event among all the events possible. It cannot be negative. It lies between 0 and 1.

Probability=Number of items/ Total items.

Probability that atleast 11 will be graduated out of 12 selected candidates is as under:

It will be a binomial distribution.

So,

P(X>=11)=[tex]12C_{11}(0.925)^{11} (0.075)^{1} +12C_{12}(0.925)^{12} (0.075)^{0}[/tex]

=12*0.4241*0.075+1*0.3923

=0.3816+0.3923

=0.7739

Hence the probability that at least 11 of them graduated is 0.7739 if graduation rate is 92.5%.

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The number of specimens should be tested is 1352.

According to the statement

we have to given that the in testing of wine specimens, lead levels ranging from 47 to 660 parts per billion were recorded. and we have to find the number specimen should be tested.

so,

Using the uniform and the z-distribution, it is found that 1353 specimens should be tested.

For an uniform distribution of bounds a and b, the standard deviation is given by:

σ = [tex]\sqrt{\frac{(b-a^{2})}{12} }[/tex]

and put the values a= 50 and b= 700 then the

standard deviation is 187.64

And here the critical value become 1.6 then

We want the sample for a margin of error of 10, thus, we have to solve for n with the help of value of m is 100.

Then n is 1352.

So,  The number of specimens should be tested is 1352.

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Answer:

thanks for your support of the personal information on the direction of economics class