Given: cos(3x – 180°) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction, where 0 ≤ x < 180°

Which values represent the solutions to the equation?

{10°, 110°, 130°}
{20°, 100°, 140°}
{30°, 330°, 390°}
{60°, 300°, 420°}

Answer:

5,000,000

Step-by-step explanation:

10 x 10 x 10 x 10 x 10 x 10 = 1,000,000

1,000,000 x 5 = 5,000,000

Answer:

5 Mg

Step-by-step explanation:

The metric prefix associated with \(10^{6}\) is Mega (M).

This can be written as 5 Mg.

Answer:A=hbb

2

Step-by-step explanation:

If the sides of a triangle are given along with an included angle, the area of the triangle can be calculated with the formula, Area = (ab × sin C)/2, where 'a' and 'b' are the two given sides and C is the included angle. This is also known as the "side angle side " method.

Answer:

as it is a right angled triangle

we can find its 3rd side with the help of hypotenuse formula.

according to it

h² = a² + b²

here,

h = hypotenuse i.e. longest side of a right angled triangle

a = side

b = base

now,

a/q we have to find h (or hypotenuse) of the right angled triangle

h² = (12)² + (5)²

h = 144 + 25

h = 169

h² = √169 = 13

therefore, 3Rd side of the triangle is 13.

is most right answer

Step-by-step explanation:

Step-by-step explanation:

as it is a right angled triangle

we can find its 3rd side with the help of hypotenuse formula.

according to it

h² = a² + b²

here,

h = hypotenuse i.e. longest side of a right angled triangle

a = side

b = base

now,

a/q we have to find h (or hypotenuse) of the right angled triangle

h² = (12)² + (5)²

h = 144 + 25

h = 169

h² = √169 = 13

therefore, 3Rd side of the triangle is 13.

Hope this answer helps you dear!

• if you have any doubt plz point it out.

Answer:

x~11

Step-by-step explanation:

22:17=14:x

22/17=14/x

22x=17*14

22x=238

22x/22=238/22

x=238/22

x=10.818181818181818

x~11

As the test's p-value above the 0.05 level of significance, we cannot reject the hypothesis.

X=97.77 is the mean on the PDI.

a )

The population standard deviation of the PDI:S = 14-69

The PDI sample size is n=70.

The test statistic value is

=X -μ/б-√n

97.77 - 100/14.69√70

Z = - 1.27

The test's p-value is 1.

Value of p = 2p (z - 1.27).

=2 ( = NORMSDIST (-1.27) )

= - 2 (0.1020 )

p-value = 0.2041

Since , the p -value of the test is greater the the 0.05 level of significance, so we fail to reject hypothesis

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The logistic differential equation for the hyena population is given by:

dP/dt = r * P * (1 - P/K)

where P(t) is the hyena population at time t, r is the growth rate, and K is the carrying capacity.

We are given that:

P(t) = 40 + k * e^(-0.57t)

K = 200

To determine the value of k, we can plug in these values into the logistic differential equation and solve for k:

dP/dt = r * P * (1 - P/K)

dP/dt = r * P * (1 - P/200)

dP/dt = r/200 * (200P - P^2)

dP/(200P - P^2) = r dt

Integrating both sides, we get:

-1/200 ln|200P - P^2| = rt + C

where C is a constant of integration.

Using the initial condition P(0) = 40 + k, we can solve for C:

-1/200 ln|200(40+k)-(40+k)^2| = 0 + C

C = -1/200 ln|8000-480k|

Plugging in this value of C and simplifying, we get:

-1/200 ln|200P - P^2| = rt - 1/200 ln|8000-480k|

ln|200P - P^2| = -200rt + ln|8000-480k|

|200P - P^2| = e^(-200rt) * |8000-480k|

200P - P^2 = ± e^(-200rt) * (8000-480k)

Since the population is increasing, we choose the positive sign:

200P - P^2 = e^(-200rt) * (8000-480k)

Using the initial condition P(0) = 40 + k, we get:

200(40+k) - (40+k)^2 = (8000-480k)

8000 + 160k - 2400 - 80k - k^2 = 8000 - 480k

k^2 + 560k - 2400 = 0

(k + 60)(k - 40) = 0

Thus, k = -60 or k = 40. Since k represents a growth rate, it should be positive, so we choose k = 40. Therefore, the value of the constant k is option (A) 4.

For the second part of the question, the logistic equation that could model the growth in the graph is option (B) dM/dt = (20-M)*(M-50). This is because the carrying capacity is between 20 and 50, and the population growth rate is zero at both of these values (i.e. the population does not increase or decrease when it is at the carrying capacity).

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Answer:

5-60x

12x

Step-by-step explanation:

= 3/4x-1 - 1/3x-4

= 3/4x - 5 - 1/3x

= 9-60x-4

12x

= 5 - 60x

12x

Answer:

Drag and drop expressions to the boxes to correctly complete the statements.

After applying the distributive property, Gustavo's expression was 9w + 45.

After he used the commutative property, his expression was 45 + 9w.

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

I think this is correct hope this helps

To show the height of the cliff in meters using the given information, let's denote the height of the cliff as h, and the horizontal distance from point A to the base of the cliff as x.

1. Apply the tangent function to angle theta: tan(theta) = h/x.
2. Apply the tangent function to angle alpha: tan(alpha) = (h + k)/x.
3. Solve the first equation for x: x = h/tan(theta).
4. Substitute this expression for x in the second equation: tan(alpha) = (h + k)/(h/tan(theta)).
5. Multiply both sides by h/tan(theta): tan(alpha) * (h/tan(theta)) = h + k.
6. Simplify: h * tan(alpha)/tan(theta) = h + k.
7. Solve for h: h = k * tan(theta)/(tan(alpha) - tan(theta)).

So, the height of the cliff in meters is h = k * tan(theta)/(tan(alpha) - tan(theta)). In the sketch, draw a right triangle with angle theta at point A, the height h, and horizontal distance x.

Then, draw another right triangle with angle alpha at point A, the combined height (h+k), and the same horizontal distance x.

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Interpreting as: circle 8.5 inches.

Assuming

"circle"

is a geometric object

circle | radius 8.5 inches

Equation:

(x - x_0)^2 + (y - y_0)^2 = 72.

(assuming center (x_0, y_0))

Properties:

diameter | 17 inches

area enclosed | 227 in^2 (square inches)

circumference | 53.4 inches

answer is D. 17/C

Answer:

127x1

Step-by-step explanation:

127 is prime, so there are only 2 factors

The four numbers that satisfy the given conditions are 13, 13, 13, and 19.

Let's represent the three equal numbers as x. We know that one of the numbers is a multiple of 19, so we can write it as 19y, where y is a positive whole number.

According to the given information, the four numbers add up to 96:

x + x + x + 19y = 96

Since the three equal numbers are represented as x, we can simplify the equation:

3x + 19y = 96

To find the values of x and y, we need to use trial and error or solve the equation using a systematic approach.

Let's start by trying different values of y and see if we can find a combination that satisfies the equation:

For y = 1:

3x + 19(1) = 96

3x + 19 = 96

3x = 96 - 19

3x = 77

x = 77/3 (not a whole number)

For y = 2:

3x + 19(2) = 96

3x + 38 = 96

3x = 96 - 38

3x = 58

x = 58/3 (not a whole number)

For y = 3:

3x + 19(3) = 96

3x + 57 = 96

3x = 96 - 57

3x = 39

x = 39/3

x = 13

So, one of the numbers is 13, and the other three numbers (since they are equal) are also 13.

Therefore, the four numbers that satisfy the given conditions are 13, 13, 13, and 19.

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Answer:

for the first one, go left 10, then down 7, and you have your point. for the second one, go left 5, then down 9, and you have your point.

Step-by-step explanation:

for the x-axis, negative means backwards

for the y-axis, negative means down

Answer:

Step-by-step explanation:

1.step. i^25^i

2.step. Rewrite (i^4)6^i=i^4

3.step. Rewrite (i^2)^2

4.step. ((i^2)^2)^6i

5.step. i^2 as -1

6.step. ((-1)^2)^6i

7.step. Raise −1 to the power of 2

i^6i

8.step.One to any power is one.

i1

9.step.Multiply i by 1.

ix1=i

Let's see

On solving

So

length

Width

A rectangle has a length of (2x+1) units, a width of (x-7) units and an Area of 17 square units. Find the dimensions of the rectangle.

In this question we are provided with the length of a rectangle (2x + 1) units and the width of the rectangle (x - 7). It is also given that the area is 17 units². We are asked to calculate the length and width of the rectangle.

First we will find the value of x

We know,

\( \bull \: \small\boxed{ \rm{ Area_{(rectangle)} = Length × Width}}\)

Substituting the values we get

\( \small\sf{ (2x + 1 ) (x - 7) = 17}\)

\( \small\rm{ 2x( x - 7) + 1(x - 7) = 17}\)

\( \small\rm{ 2 {x}^{2} - 14x + 1(x - 7) = 17}\)

\( \small\rm{ 2 {x}^{2} - 13x - 7 = 17}\)

\( \small\rm{2 {x}^{2} - 13x - 7 - 17 = 0 } \)

\( \small\rm{2 {x}^{2} - 13x - 24 = 0} \)

\( \small\rm{x = \dfrac{13 + 19}{2 \times 2} } \)

\( \small\rm{ x = \dfrac{32}{4} = 8}\)

\( \small\sf{x = 8} \)

Now we will substitute the value of x

Length = (2x + 1) = 2 × 8 + 1 = 16 + 1 = 17 units

Width = (x - 7) = 8 - 7 = 1 units

Answer:

\(Base = 57\)

Step-by-step explanation:

Given

\(Length = 2x + 4\)

\(Base = 3x\)

\(Perimeter = 141\)

Required

Determine the length of the base

The perimeter of an isosceles triangle is:

\(Perimeter = 2*Length + Base\)

\(141 = 2 (2x + 4) + 3x\)

\(141 = 4x + 8 + 3x\)

Collect Like Terms

\(4x + 3x = 141 - 8\)

\(7x = 133\)

Divide both sides by 7

\(x = 19\)

To get the base, we substitute 19 for x in \(Base = 3x\)

\(Base = 3 * 19\)

\(Base = 57\)

The area enclosed by the curves can be found by integrating the difference between the upper and lower curves with respect to x within the given x-interval,

which is from -ln(4) to ln(4). To compute the area enclosed by the curves y = e^x, y = e^(-x), and y = 4, we need to find the x-values where these curves intersect.

Setting y = e^x and y = 4 equal to each other, we get:

e^x = 4

Taking the natural logarithm of both sides, we have:

x = ln(4)

Setting y = e^(-x) and y = 4 equal to each other, we get:

e^(-x) = 4

Taking the natural logarithm of both sides, we have:

-x = ln(4)

x = -ln(4)

The area enclosed by the curves can be found by integrating the difference between the upper and lower curves with respect to x within the given x-interval.

∫[ln(4), -ln(4)] (e^x - e^(-x) - 4) dx

Evaluating this integral will give us the area enclosed by the curves.

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Answer:

23

Step-by-step explanation:

the angles are equal to each other so we use the equation

6x-7=9x-22 and solve for x

step 1 subtract 6 from each side

-7=3x-22

step 2 add 22 to each side

3x=15

step 3 divide each side by 3

x=5

then to find the angle abd we plug in 5 to 9x-22

9x5=45

45-22=23 so angle abd=23

hope this helps (:

if you have any more questions feel free to ask

Standard Deviation: Is a measure of how spread out values are in a data set compared to the mean. It is calculated by finding the square root of the variance, which is the average of the squared differences from the mean.

Mean: The average value of a set of numbers. It is calculated by summing up all the numbers in the set and dividing the result by the total number of numbers in the set.

Distribution Curve: is a bell shaped curve that displays the mean with a line down the center of the curve and standards deviations within standard deviations.

See attached file for model of curve, from: https://commons.wikimedia.org/wiki/File:Standard_deviation_diagram.svg

Given the mean and standard deviation we can use a general rule to determine the population between the given lengths.

Generally in a normal distribution:

176 cm is 1 standard deviation less than the mean and 184 cm is 1 standard deviation greater than the mean. Using the general rules above, 68% of data falls between -1σ and +1σ. Therefore, the answer to this question would be B. 68%

Option (c) 26.7% of the global oceans are Marine Protected Areas (MPAs). Marine Protected Areas (MPAs) are designated areas in the oceans that are set aside for conservation and management purposes.

They are intended to protect and preserve marine ecosystems, biodiversity, and various species. MPAs can have different levels of restrictions and regulations, depending on their specific objectives and conservation goals.

As of the current knowledge cutoff in September 2021, approximately 26.7% of the global oceans are designated as Marine Protected Areas. This means that a significant portion of the world's oceans has some form of protection and management in place to safeguard marine life and habitats. The establishment and expansion of MPAs have been driven by international agreements and initiatives, as well as national efforts by individual countries to conserve marine resources and promote sustainable practices.

It is worth noting that the percentage of MPAs in the global oceans may change over time as new areas are designated or existing MPAs are expanded. Therefore, it is important to refer to the most up-to-date data and reports from reputable sources to get the most accurate and current information on the extent of Marine Protected Areas worldwide.

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Answer:

Cancellation it enables us to eliminate or get rid of one of the variables, so we can solve a more simplified equation.

Some textbooks refer to the elimination method as the addition method or the method of linear combination.

This is because we are going to combine two equations with addition!

Step 1

First, we align each equation so that like variables are organized into columns.

Step 2

Second, we eliminate a variable.

If the coefficients of one variable are opposites, you add the equations to eliminate a variable, and then solve.

If the coefficients are not opposites, then we multiply one or both equations by a number to create opposite coefficients, and then add the equations to eliminate a variable and solve.

Step 3

Thirdly, we substitute this value back into one of the original equations and solve for the other variable.

Example of how to apply the elimination method for solving systems of equations is attached.

Answer:

19.72

Step-by-step explanation:

Answer:

32 and 20

Step-by-step explanation:

x + y = 52

x - y = 12

2y = 40

y = 20

x = 32

Answer:

C

Step-by-step explanation:

Answer:

u

Step-by-step explanation:

it is undefined because its a vertical line.

Answer:

slope is undefined u

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (1, - 3 ) and (x₂, y₂ ) = (1, 0 )

m = \(\frac{0-(-3)}{1-1}\) = \(\frac{0+3}{0}\) = \(\frac{3}{0}\)

Since division by zero is undefined then the slope of the line is undefined

Answer:

There is one solution

Step-by-step explanation:

The solution is \(x=8\)

Explanation:

\(7(x-5)=x+13\)

\(7x-35=x+13\)

\(6x=48\)

\(x=8\)

Answer:

c

Step-by-step explanation:

The probability that the three friends are seated next to each other is 1/420

The total number of ways to seat the 7 people is 7! To find the number of ways to seat the three friends next to each other, we need to consider the number of ways to seat the other 4 people around them. So the number of favorable outcomes is 4!

The probability that the three friends are next to each other is then given by the ratio of the number of favorable outcomes to the total number of outcomes: (4!)/(7!) = 4!/5040 = 1/420.

So the probability that the three friends are seated next to each other is 1/420.

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Answer:

Elliott put 2.1 bags of birdseed in the feeders

Step-by-step explanation:

(5 1/2) - (3 2/5) = 2.1

I hope I helped! :)

Would appreciate Brainliest! ;)