What are the solutions to the trigonometric equation on the
interval [0,2π)?
2cos2x=cosx
Select all correct solutions.
0
π6
π3
π2
2π3
5π6
π

Answer: C

The equation (b + 4r = 7) is a missing number equation, not representing log10. The equation (p- (7q + 1/2 r) would be correct, if the 7q were a 2q. The answer to the question would have to be C, (x / y^2 √z).

Hope this helps you!

Answer:

c

Step-by-step explanation:

you divide each side by four to get a=2.5 b=2.5 and c=3

Answer:

The answer is C.

Step-by-step explanation:

If this does not help you im sorry!

Have a good day!

The correct answer is

2 loaves of pumpkin bread and 6 loaves of banana bread. Option C.

For the solution for the Pumpkin bread:

4 eggs

3 1/2 cups of flour

Banana bread:

1 egg

1 (0.5) cups of flour

Available ingredients:

14 eggs

16 cups of flour

Assume 2 loaves of pumpkin bread and 6 loaves of banana bread

For the solution for the Pumpkin bread:

PB=4 eggs* 2

PB= 8 eggs

PB=3 *0.5 * 2

PB = 7 cups of flour

For the solution of the Banana bread:

BB =1 *6

BB= 6 eggs

For cups

BB= 1 (0.5) * 6

BB= 9 cups of flour

In conclusion, The solution of the Total used ingredients

I=8 + 6

I= 14 eggs

For cups

IC=7 + 9

IC= 16 cups of flour

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Answer:

C 2 loaves of Pb and 6 loaves of BB

Step-by-step explanation:

Answer:

y=6x

Step-by-step explanation:

if u times x by 6 you get the y number underneath

for example:

x=1

y=6

so 1×6=6

x=2

y=12

so 2×6=12

If Rachana randomly selects two mugs from the set, the probability that she gets two different mugs is 0.1556 or 15.56%.

To solve this problem, we can use the concept of combinations. Since there are 10 mugs in the set, there are 10 choose 2 = 45 ways to select two mugs without considering order.

Out of these 45 ways, we need to count the number of ways Rachana can select two different mugs. Since there are 3 different types of mugs, Rachana can choose any one of the three types for the first mug. There are 10 mugs in the set, out of which 3 belong to the chosen type. Therefore, the probability of choosing a mug of the chosen type is 3/10.

For the second mug, Rachana can choose from the remaining 9 mugs. Since she needs to choose a different type of mug, she can choose any one of the 2 remaining types. There are 7 mugs left from the other 2 types. Therefore, the probability of choosing a mug of a different type is (7/9) * 2/3 = 14/27.

Therefore, the probability of selecting two different mugs is the product of the probabilities of selecting a mug of the chosen type and a mug of a different type. This is given by (3/10) * (14/27) = 7/45, which is approximately 0.1556 or 15.56%.

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Complete question is:

Rachana has a set of ten mugs the set up is made of 3 different mugs. If Rachana randomly selects two mugs from the set, what is the probability that she gets two different mugs?

Answer:

c

Step-by-step explanation:

Answer:

68

Step-by-step explanation:

Hey your so polite and it’s appreciated! First mark other side of angle (right) as 28. 180-56 = 124. Since other side is smaller don’t make it equal. So it has to be higher than 61. So it’s 68! hope this helps !

Answer:

The next two times both buckets dump water at the same time are 4:54 P.M and 7:18 P.M.

Step-by-step explanation:

From the question, one bucket dumps water every 18 minutes, say bucket A;

and the other bucket dumps water every 16 minutes, say bucket B.

Also, It is currently 2:45 P.M. and both buckets dumped water 15 minutes ago,

that is, both buckets dumped water at 2:30 P.M.

For bucket A, the next times it will dump water will be:

2:48 P.M, 3:06 P.M, 3:24 P.M, 3:42 P.M, 4:00 P.M, 4:18 P.M, 4:36 P.M, 4:54 P.M, 5:12 P.M, 5:30 P.M, 5:48 P.M, 6:06 P.M, 6:24 P.M, 6:42 P.M, 7:00 P.M, 7:18 P.M, 7:36 P.M, 7:54 P.M, 8:12 P.M, 8:30 P.M etc.

For bucket B, the next times it will dump water will be:

2:46 P.M, 3:02 P.M, 3:18 P.M, 3:34 P.M, 3:50 P.M, 4:06 P.M, 4:22 P.M, 4:38 P.M, 4:54 P.M, 5:10 P.M, 5:26 P.M, 5:42 P.M, 5:58 P.M, 6:14 P.M, 6:30 P.M, 6:46 P.M, 7:02 P.M, 7:18 P.M, 7:34 P.M, 7:50 P.M etc.

From above, we observe that the next two times both buckets dump water at the same time are 4:54 P.M and 7:18 P.M.

Hence, the next two times both buckets dump water at the same time are 4:54 P.M and 7:18 P.M.

The required equation model is n + d = 30 which represents a jar containing n nickels and d dimes worth a total of $30. which is the correct answer would be an option (D).

A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

We have been given that a jar contains n nickels and d dimes worth a total of $30.

To determine the equation model that represents the given information.

As per the given information, the algebraic form is:

quantity of nickels + quantity of dimes = total worth

n + d = 30

Thus, the required equation model is n + d = 30 which represents a jar containing n nickels and d dimes worth a total of $30.

Hence, the correct answer would be option (D).

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Answer:

r = 8.2

Step-by-step explanation:

5r – 10 = –51

5r = –41

r = 8.2

The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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Okay, here we have this:

Considering the provided points and information, we are going to calculate the requested slope, so we obtain the following:

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

m=(6-5)/(4-1)

m=1/3

Finally we obtain that the slope of the line is 1/3.

The maximum value is 5 and the minimum value is -11.The maximum value is approximately 13.84 and the minimum value is -1040. The maximum value is approximately 0.8 and the minimum value is -0.333.

1. For f(x) = -2x - 1 over [-3, 5]:
  - Take the derivative of f(x) with respect to x: f'(x) = -2.
  - Set f'(x) equal to zero and solve for x: -2 = 0. There are no solutions, so there are no critical points.
  - Since the interval is finite, we evaluate f(x) at the endpoints:
    - f(-3) = -2(-3) - 1 = 5.
    - f(5) = -2(5) - 1 = -11.
  - Therefore, the maximum value is 5 and the minimum value is -11.

2. For f(x) = x³ - 4x + 10 over [-10, 10]:
  - Take the derivative of f(x) with respect to x: f'(x) = 3x² - 4.
  - Set f'(x) equal to zero and solve for x: 3x² - 4 = 0.
    - x = 2/√3 or x = -2/√3.
  - Since the interval is finite, we evaluate f(x) at the endpoints and critical points:
    - f(-10) = -10³ - 4(-10) + 10 = -1040.
    - f(-2/√3) ≈ 8.16.
    - f(2/√3) ≈ 13.84.
    - f(10) = 10³ - 4(10) + 10 = 960.
  - Therefore, the maximum value is approximately 13.84 and the minimum value is -1040.

3. For f(x) = x/(x^2 + 1) over [1, 4]:
  - Take the derivative of f(x) with respect to x: f'(x) = (x² + 1 - 2x²) / (x² + 1)².
  - Set f'(x) equal to zero and solve for x: (x²+ 1 - 2x²) / (x² + 1)² = 0.
    - x² + 1 - 2x² = 0.
    - -x² + 1 = 0.
    - x² = 1.
    - x = ±1.
  - Since the interval is finite, we evaluate f(x) at the endpoints and critical points:
    - f(1) = 1 / (1² + 1) ≈ 0.333.
    - f(-1) = -1 / (1² + 1) ≈ -0.333.
    - f(4) = 4 / (4² + 1) ≈ 0.8.
  - Therefore, the maximum value is approximately 0.8 and the minimum value is -0.333.

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Step-by-step explanation:

Taking the men first: there are 5 ways to form a 4-man committee out of 5 men.

Taking the women now: There are 20 ways to form a 3-woman committee out of 6 women.

Each of the 5 possible male groups can be combined with any of the 20 possible female groups.

So: 100.

Answer:

Step-by-step explanation:

Without an illustration, I can’t know the position of ∠2 to ∠1.

If the angles are adjacent then ∠2 = 180° - ∠1 = 130°.

Otherwise, ∠2 = ∠1 = 50°

Answer:

790 with a dash over the 9

Step-by-step explanation:

A graph of the linear equation y = -4x + 3 in slope-intercept form is shown in the image attached below.

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

First of all, we would rewrite the linear function in slope-intercept form by making y the subject of formula as follows;

4x + y = 3

y = -4x + 3

Next, we would use an online graphing calculator to plot the given linear function as shown in the graph attached below.

In conclusion, the slope of this linear function is equal to -4 and it does not represent a proportional relationship.

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The area of the region which is inside the polar curve r = 5 sinθ but outside r = 4 will be 3.75 square units.

When the two curves intersect then they bound the region is known as the area bounded by the curve.

The area of the region which is inside the polar curve r = 5 sinθ but outside r = 4 will be

Then the intersection point will be given as

\(\rm 5 \sin \theta = 4\\\\\theta = 0.927 , 2.214\)

Then by the integration, we have

\(\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214}[ (5 \sin \theta)^2 - 4^2] d\theta \\\\\\\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214} [25\sin ^2 \theta - 16] d\theta \\\\\\\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214} [ \dfrac{25}{2}(1 - \cos 2\theta ) - 16] d\theta \\\)

\(\rightarrow \dfrac{1}{2} [\dfrac{25 \theta }{5} - \dfrac{25 \cos 2\theta }{2} - 16\theta]_{0.927}^{2.214} \\\\\\\rightarrow \dfrac{1}{2} [\dfrac{25(2.214 - 0.927) }{5} - \dfrac{25 (\cos 2\times 2.214 - \cos 2\times 0.927) }{2} - 16(2.214 - 0.927]\\\)

On solving, we have

\(\rightarrow \dfrac{1}{2} \times 7.499\\\\\rightarrow 3.75\)

Thus, the area of the region is 3.75 square units.

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An equation for the boiling point of this liquid is y = -0.0015x + 215.55. Also, the boiling point of this liquid at 2500 ft is equal to 211.8°F.

In order to write an equation for the boiling point of this liquid, we would have to first calculate its slope because the relationship between altitude and the boiling point of this liquid is linear (direct proportion or proportional relationship).

Mathematically, the slope of any linear equation can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided about the altitudes and boiling points of this liquid, we have the following parameters:

Point (x, y) = (8500, 202.8)

Point (x, y) = (4200, 206.7)

Substituting the given points into the formula, we have;

Slope, m = (209.25 - 202.8)/(4200 - 8500)

Slope, m = 6.45/-4300

Slope, m = -0.0015

At point (8500, 202.8), the equation of this line is given by:

y - y₁ = m(x - x₁)

Where:

y - 202.8 = -0.0015(x - 8500)

y - 202.8 = -0.0015x + 12.75

y = -0.0015x + 12.75 + 202.8

y = -0.0015x + 215.55

Now, we can calculate the boiling point of this liquid at 2500 ft:

y = -0.0015(2500) + 215.55

y = -3.75 + 215.55

y = 211.8°F.

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Complete Question:

The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8500 ft, the liquid boils at 202.8°F. At an altitude of 4200 ft, the liquid boils at 209.25°F. Write an equation giving the boiling point b of the liquid, in degrees Fahrenheit, in terms of altitude a, in feet. What is the boiling point of the liquid at 2500 ft?

Answer:

Step-by-step explanation:

f(x) = x - 5 and g(x) = 5x

- f(x + 1) = - ( x + 1 - 5 ) = 4 - x

- 3g(x - 1 ) = - 3 [ 5 (x - 1)] = 15 - 15x

h(x) = 4 - x + 15 - 15x = 19 - 16x

h(3) = 19 - 16(3) = - 29

Linear expressions are expressions in which the highest power of the variable is 1.

Linear expressions 3x - 2 and 2x - 3 have a difference of 3x - 2

The given parameter is:

\(\mathbf{difference = x + 1}\)

Let one of the linear expressions be 2x - 3, and the other expression be y.

So, the difference would become

\(\mathbf{y -(2x -3) = x + 1}\)

Open bracket

\(\mathbf{y -2x +3 = x + 1}\)

Collect like terms

\(\mathbf{y = 2x + x + 1 - 3}\)

Evaluate like terms

\(\mathbf{y = 3x - 2}\)

Hence, 3x - 2 and 2x - 3 have a difference of 3x - 2

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Answer:

  x = 12

Step-by-step explanation:

The sum of the exterior angles of a convex polygon is 360°.

  (5x +4)° +(4x +9)° +(9x -6)° +(4x +1)° +(7x +4)° = 360°

  29x +12 = 360 . . . . . divide by °, collect terms

  29x = 348 . . . . . . . subtract 12

  x = 12 . . . . . . . . . divide by 29

Answer:

x=11.58

Step-by-step explanation:

The sum of an exterior angle of a polygon is 360°,

9x-6+4x+9+5x+4+7x+4+4x+1=360°

29x+24=360

29x=360-24

29x=336

x=336/29

x= 11.586

x=11.58

Hope it helps! :)

Solution

For this case we can do the following

7x^3 + 7x^2 +18

4x^3 -4x^2 - 4x - 2

_________________

11x^3 +3x^2 -4x +1

The total number of students in the college is expressed as: 5x

The parameters given are:

1/2 of the students who learn the flute also learn the violin.

3 times as many students learn the violin as learn the flute.

x students learn both the flute and the violin

Thus, the total who learn the flute = 2x

Number who learn only flute = x

Since 3 times as many students learn the violin as learn the flute. Then, 3x students only learn the violin.

Thus, total number of students at the college is:

x + x + 3x = 5x

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Complete question is:

Every student at a music college learns the flute, the violin, or both the flute and the violin. 1/2 of the students who learn the flute also learn the violin. 3 times as many students learn the violin as learn the flute. x students learn both the flute and the violin. Find an expression, in terms of x, for the total number of students at the college. Flute X Violin​

The area of the region enclosed by the curves is (3√3 - 13)/3.

To sketch the region enclosed by the given curves 4x+y^2=12, and x=y, we can begin by graphing the curves.

First, let's graph the curve 4x+y^2=12 by rewriting it in terms of y:

\(y^2 = 12 - 4x\)

This is a parabola that opens to the right and is centered at (3,0), with a width of 2√3.

Next, let's graph the line x=y, which passes through the origin at a 45-degree angle.

The region enclosed by the curves is the shaded region in the figure below:

To find the area of this region, we need to integrate with respect to x or y. Since the curves intersect at x=3, it's convenient to use vertical strips and integrate with respect to x.

The height of each strip is given by the difference between the y-coordinates of the parabola and the line at the corresponding x-value, which is:

y = √(12 - 4x) - x

The width of each strip is dx.

Thus, the area of the region is given by the integral:

S = ∫[0,3] (√(12 - 4x) - x) dx

We can simplify this integral by using the substitution u = 12 - 4x, du/dx = -4:

S = ∫[0,3] (√u - 3 + u/4) (-du/4)

S = ∫[0,12] (√u - 3 + u/4) (-du/4) (by extending the limits of integration)

S = [\(-u^{(3/2)/6} - 3u/4 + u^{2/32\)]_[0,12]

S = (3√3 - 13)/3

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===================================================

Explanation:

She starts off with $350 in savings. Then she adds on another $30 per week. After w of those weeks, she adds a total of 30w dollars. The w is just a placeholder for a number. For example, if w = 5, then 30*w = 30*5 = 150 dollars is added on top of the $350 already there.

Overall, the expression 30w+350 represents how much is in her savings after w weeks. Therefore, the equation Martina wants would be

s = 30w+350

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

For the second part, we'll plug w = 17 into that equation to find s

s = 30w+350

s = 30*17+350

s = 510+350

s = 860

Martina has $860 in her account after 17 weeks.

Answer:

(1,9)

Step-by-step explanation:

For a function, each x value has only one y value. 2, 3, and 4 are already used up.

(1,9)

Answer:

(1, 9)

Step-by-step explanation:

(1, 9) is the only possible answer,because the others have the same domain above the question, so they can't be a function

SOLUTION

Given the question, the following are the steps to solve the problem

Step 1: Write out the question

Step 2: Solve the expression in the first bracket

Step 3: Calculate the tangent of the result in step 2

Hence, the result from the evaluation of tan(sin^-1)(7/9) is approximately 1.2374

Answer:

v = 9

Step-by-step explanation:

-5 + v = 4

+5         +5

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

v = 9

To check just plug 9 in for v.

-5 + 9 = 4