Use trigonometric identities to solve the trigonometric equation sin(2∅)-cos(∅)=0 for 0≤∅≤2π. You must show all of your work analytically.

Answer:

2/3

Step-by-step explanation:

1 and 2 are taken away, therefore you have 3, 4, 5, and 6 left as options to roll. So the answer is 4/6 since there's 4 numbers, but simplified it's 2/3.

Answer:

There are six possible outcomes when rolling a die, each of which is equally likely. Of these six outcomes, three are greater than 2 (3, 4, 5) and three are not (1, 2, 6). Therefore, the odds in favor of rolling a number greater than 2 are 3 to 3, or simply 1 to 1. Alternatively, we could express this as a probability: the probability of rolling a number greater than 2 is 3/6, or 1/2, since there are three favorable outcomes out of a total of six possible outcomes.

Step-by-step explanation:

The mean absolute deviation is $106.6.

Given the table shows the amount Bill spent on 5 days last week.

DayAmount12622313126534To find the mean of the amount he spent: The formula for calculating the mean of a given set of values is mean=∑x/n where x represents the values, n represents the number of values, and ∑x represents the sum of the values.

Mean=total sum of values/total number of values Mean=(26+23+31+26+534)/5Mean=640/5Mean=128So,

the mean of the amount he spent is $128.To find the mean absolute deviation: The mean absolute deviation (MAD) is the average distance between each data value and the mean. MAD shows how much the data set deviates from the mean. The formula for calculating the MAD is MAD=∑|xi−m|/n where xi represents the values, m represents the mean, and n represents the number of values. So, the calculation for each day is:

Day Amount Absolute deviation from mean1 26 |128-26|=102 23 |128-23|=105 31 |128-31|=974 26 |128-26|=102 534 |128-534|=406

The sum of all absolute deviations is:

10+10+97+10+406=533The mean absolute deviation (MAD) is: MAD=533/5=106.6So.

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The length FE in the circle is 6 units

The arc AE has a measure of 64 degrees

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

The circle

Given that the lengths from the center to either chords are equal

This means that

FE = 6 units

For the other circle, we have

BC = 58 degrees

AB = ED

The arc AE is calculated as

AE = 180 - BC - ED

Where

AB = ED = BC = 58 degrees

So, we have

AE = 180 - 58 - 58

Evaluate

AE = 64

Hence, the arc AE is 64 degrees

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The differentiation of the given function f(x) = eˣ+6 is eˣ

The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.

Given is function f(x) = eˣ+6, we need to find the derivative of this function,

f(x) = eˣ+6

f'(x) = d / dx (eˣ+6)

= d(eˣ)/dx + d(6)/dx

Since, 6 is a constant and derivative of a constant is zero,

d(eˣ)/dx + d(6)/dx = d(eˣ)/dx + 0

Now, when we differentiate eˣ, we get eˣ itself,

Therefore,

d(eˣ)/dx = eˣ

Therefore, the differentiation of the given function f(x) = eˣ+6 is eˣ

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Answer:

Step-by-step explanation:

divide by R

Length of gz = 12 units

Length of ot = 14.4 units

Given,

Triangle EGD with centroid at Z .

Now,

As we know that centroid divides the line segment in the ratio 2:1 .

Firstly calculate the length of gz,

gu = 18 unit

gz:zu = 2:1

gz = 2/3  * 18

gz = 12 units .

Secondly calculate the length of ot,

zt = 4.8 units

oz:zt = 2:1

oz = 4.8 * 2

oz = 9.6 units

ot = 9.6+ 4.8

ot = 14.4 units

Hence with the centroid length of ot and gz can be found out .

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Step 1: Write the dividend and divisor:

\(\sf\:\frac{{x^3 - 8x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 2: Divide the first term of the dividend by the first term of the divisor:

\(\sf\:\frac{{x^3}}{{x}} = x^2 \\ \)

Step 3: Multiply the divisor (x - 4) by the result (x^2):

\(\sf\:(x - 4) \cdot (x^2) = x^3 - 4x^2 \\ \)

Step 4: Subtract the result from the original dividend:

\(\sf\:(x^3 - 8x^2 + 6x + 41) - (x^3 - 4x^2) = -4x^2 + 6x + 41 \\ \)

Step 5: Bring down the next term from the dividend:

\(\sf\:\frac{{-4x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 6: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-4x^2}}{{x}} = -4x \\ \)

\(\sf\:(x - 4) \cdot (-4x) = -4x^2 + 16x \\ \)

\(\sf\:(-4x^2 + 6x + 41) - (-4x^2 + 16x) = -10x + 41 \\ \)

Step 7: Bring down the next term from the dividend:

\(\sf\:\frac{{-10x + 41}}{{x - 4}} \\ \)

Step 8: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-10x}}{{x}} = -10 \\ \)

\(\sf\:(x - 4) \cdot (-10) = -10x + 40 \\ \)

\(\sf\:(-10x + 41) - (-10x + 40) = 1 \\ \)

Step 9: There are no more terms to bring down, so the division is complete.

Step 10: Write the final result:

The quotient is \(\sf\:x^2 - 4x - 10\\\) and the remainder is 1.

Therefore, the division of \(\sf\:(x^3 - 8x^2 + 6x + 41) by (x - 4) \\\) is:

\(\sf\:(x^3 - 8x^2 + 6x + 41) ÷ (x - 4) \\ \) \(\sf\:= x^2 - 4x - 10 + \frac{{1}}{{x - 4}} \\ \)

The probability that a randomly selected point within the square falls in the red shaded square is 1/16

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event to occur is 1 and it is 100% in percentage.

Probability = sample space /total outcome

sample space is the area of the red shaded square and the total outcome is the big square.

Area of red shaded square = 1 × 1 = 1unit²

area of the big square = 4 × 4 = 16 units²

Therefore the probability that a point selected falls on the red shaded square

= 1/16

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Answer:

851,243,679,010

851,432,697,201

815,234,739,120

815,234,796,002

The data contained in the foodindustry file can be expressed mathematically by calculating the average sales per store for each restaurant chain.

This can be done by dividing the total sales of all stores in the chain by the total number of stores in the chain. Mathematically, this could be expressed as follows:

Average Sales per Store = Total Sales of all Stores / Total Number of Stores

For example, if a chain had 10 stores with a total sales of $100,000, the average sales per store would be $10,000 ($100,000/10). This calculation can be used to compare the performance of different restaurant chains, as well as to identify potential areas of improvement.

The data contained in the foodindustry file can be expressed mathematically by calculating the average sales per store for each restaurant chain, which is done by dividing the total sales of all stores in the chain by the total number of stores in the chain.

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Answer:

8 cans ÷ 3 rooms = 2.66 cans per room

11 rooms × 2.66 cans = 29.33 cans

So I need to purchase 30 cans for 11 rooms

Note that in the word problem above it is recommended to purchase at least 29 cans of paint to ensure sufficient coverage for all 11 rooms.

To determine the number of cans of paint needed to paint 11 rooms, we can set up a proportion using the given information.

If 8 cans of paint are needed to paint 3 rooms, we can set up the proportion  -

8 cans / 3 rooms = x cans / 11 rooms

To solve for x (the number of cans needed for 11 rooms), we can cross-multiply and solve for x  -

8 * 11 = 3 * x

88 = 3x

Divide both sides by 3  -

88 / 3 = x

x ≈ 29.33

Hence, it is recommended to purchase at least 29 cans of paint to ensure sufficient coverage for all 11 rooms.

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The equivalent expression of \(\sqrt{\frac{128x^5y^6}{2x^7y^5}}\) is \(\frac{8\sqrt y}{x}\)

The expression is given as:

\(\sqrt{\frac{128x^5y^6}{2x^7y^5}}\)

Divide 128 by 2

\(\sqrt{\frac{64x^5y^6}{x^7y^5}}\)

Apply the law of indices to the variables

\(\sqrt{\frac{64y^{6-5}}{x^{7-5}}}\)

Evaluate the differences

\(\sqrt{\frac{64y}{x^2}}\)

Take the square root of 64

\(8\sqrt{\frac{y}{x^2}}\)

Take the square root of x^2

\(\frac{8\sqrt y}{x}\)

Hence, the equivalent expression of \(\sqrt{\frac{128x^5y^6}{2x^7y^5}}\) is \(\frac{8\sqrt y}{x}\)

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Answer:

1000 klgram Sha bebe

And so many things I have to do whit a person do and every thing

Thank you

Answer:

11/7is your answer ....

Step-by-step explanation:

hope its help you

Answer:

4. Between 11:30 and 12:00, they did nothing. The graph didn't go up or down, it just stayed the same meaning they did nothing.

5. 5 miles an hour

Step-by-step explanation:

Based on the information given the new balance is $289.72.

First step is to calculate the finance charge

\(\text{Finance charge}=205.16\times(0.144\div12 \ \text{months})\)

\(\text{Finance charge}=205.16\times0.012\)

\(\text{Finance charge}=2.46\)

Second step is to calculate the New balance

\(\text{New balance}=205.16+2.46+82.10\)

\(\text{New balance}=\bold{\$289.72}\)

In conclusion, the new balance is $289.72.

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The expression with the correct coefficients in each block is given as follows:

20x³ + 0x² - 7x.

The functions in the context of this problem are defined as follows:

The operation is given as follows:

f(x)g(x) + h(x).

Hence, to obtain the resultant function, we apply the definitions into the operation and the simplify, applying the distributive property and combining the like terms, as follows:

4x(5x² - 4) + 9x = 20x³ - 16x + 9x = 20x³ - 7x.

As there is no x² term, the coefficient of zero multiplies the term x².

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To know the area of a figure, you would like to know its shape and estimations. The steps to take on how to draw a figure with the use of a ruler and a pencil is given below.

Begin by selecting the kind of figure you need to draw. Make use of a ruler to draw the sides of the figure. Make sure that the lines are straight and have the right length.

E.g. If the figure may be a rectangle or a parallelogram, you wish to create beyond any doubt that inverse sides are parallel to each other. If the figure is triangle, you would like to draw three lines that shows at three distinctive points. At last, name the sides and vertices of the figure.

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Answer:

y = 25x +100

He will collect 275 pounds in 7 weeks

It will take him 12 weeks.

Hope this helps!

Answer:

-20

Step-by-step explanation:

Simplify the real and imaginary parts of the expression.

The volume of the closet space = 207,936 in³

The volume of the one roll of toilet paper = 141.3in³

To calculate the volume of the closet, the formula that should be used is the formula for the volume of a rectangle = length×width×height.

Where;

length = 57 in

width = 57

height = 64

volume = 57×57×64 = 207,936 in³

The volume of the toilet paper with the shape of a cylinder would be = πr²h

where;

radius = diameter/2= 6/2=3in

height = 5 in

volume of cylinder = 3.14×3×3×5 =141.3in³

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Answer:

10 dollars

Step-by-step explanation:

5 + 5

Answer:

(3xy - 1)/3x = b

Step-by-step explanation:

make b the subject of formula

then simply it

did you get it

Answer:

b=Y-x/3

Step-by-step explanation:

Solve for b by simplifying both sides of the equation, then isolating the variable.

have a great day and thx for your inquiry :)

Answer:

(a) 100 fishes

(b) t = 10: 483 fishes

    t = 20: 999 fishes

    t = 30: 1168 fishes

(c)

\(P(\infty) = 1200\)

Step-by-step explanation:

Given

\(P(t) =\frac{d}{1+ke^-{ct}}\)

\(d = 1200\\k = 11\\c=0.2\)

Solving (a): Fishes at t = 0

This gives:

\(P(0) =\frac{1200}{1+11*e^-{0.2*0}}\)

\(P(0) =\frac{1200}{1+11*e^-{0}}\)

\(P(0) =\frac{1200}{1+11*1}\)

\(P(0) =\frac{1200}{1+11}\)

\(P(0) =\frac{1200}{12}\)

\(P(0) = 100\)

Solving (a): Fishes at t = 10, 20, 30

\(t = 10\)

\(P(10) =\frac{1200}{1+11*e^-{0.2*10}} =\frac{1200}{1+11*e^-{2}}\\\\P(10) =\frac{1200}{1+11*0.135}=\frac{1200}{2.485}\\\\P(10) =483\)

\(t = 20\)

\(P(20) =\frac{1200}{1+11*e^-{0.2*20}} =\frac{1200}{1+11*e^-{4}}\\\\P(20) =\frac{1200}{1+11*0.0183}=\frac{1200}{1.2013}\\\\P(20) =999\)

\(t = 30\)

\(P(30) =\frac{1200}{1+11*e^-{0.2*30}} =\frac{1200}{1+11*e^-{6}}\\\\P(30) =\frac{1200}{1+11*0.00247}=\frac{1200}{1.0273}\\\\P(30) =1168\)

Solving (c): \(\lim_{t \to \infty} P(t)\)

In (b) above.

Notice that as t increases from 10 to 20 to 30, the values of \(e^{-ct}\) decreases

This implies that:

\({t \to \infty} = {e^{-ct} \to 0}\)

So:

The value of P(t) for large values is:

\(P(\infty) = \frac{1200}{1 + 11 * 0}\)

\(P(\infty) = \frac{1200}{1 + 0}\)

\(P(\infty) = \frac{1200}{1}\)

\(P(\infty) = 1200\)

The linear function that describes the distance (in miles) is therefore y = 65x + 80

We have to find the slope and the intercept in other to get the linear function

The data points are:

(1, 145) and (3, 275).

m = (y2 - y1) / (x2 - x1)

fixing the data points we have

m = (275 - 145) / (3 - 1)

= 130 / 2

= 65

y = mx + b

(1, 145):

145 = 65(1) + b

b = 145 - 65

= 80

y intercept is 80

The linear function is therefore y = 65x + 80

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The dimensions of the room are approximately 7 meters by 10.5 meters.

In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.

Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.

The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:

\(\text{Perimeter} = 2(\text{length} + \text{width})\)

Substituting the values we have for length and width, we get:

\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)

Simplifying the equation, we get:

\(\rightarrow35 = 2(2.5\text{x})\)

\(\rightarrow35 = 5\text{x}\)

\(\rightarrow\text{x}=\dfrac{35}{5}\)

\(\rightarrow\bold{x\thickapprox7}\)

So the width of the room is 7 meters.

To find the length, we can substitute x into the expression we have for the length:

\(\rightarrow\text{Length} = 1.5\text{x}\)

\(\rightarrow\text{Length} = 1.5(7)\)

\(\rightarrow\bold{Length=10.5}\)

So the length of the room is 10.5 meters.

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The value of k is 18.

If x + 2 is a factor of f(x) = x^3 + 5x + k, it means that when x = -2, the expression f(x) becomes zero.

Substituting x = -2 into f(x), we have:

f(-2) = (-2)³ + 5(-2) + k

= -8 - 10 + k

= -18 + k

Since f(-2) should equal zero, we have:

-18 + k = 0

k = 18

Therefore, the value of k is 18.

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Answer:

B:<

Step-by-step explanation:

You can solve this question with fractions. The way I did it was by changing both equations into fractions like this: 6÷7=6/1x1/7=6/7 and     7÷8=7/1x1/8=7/8. Since they don't have a common denomintor and you still dont know which fraction is bigger/smaller, we are going to find a common denominator which is 56. After converting both fractions, (6/7=48/56 and 7/8=49/56)  Now you can see that 7/8 is bigger than 6/7, which shows that 6÷7<7÷8.

Answer:

25.12

Step-by-step explanation:

The formula of the circumference of a circle is: C = 2(pi)(r)

Plug in 3.14 for pi and 4 for the radius.

C = 2(3.14)(4)

Multiply.

C = 25.12