Can you guys help me with the second one please :( .
I’ll mark you as a brainliest

Answer:

cscu – cotu = sinu/1 + cosu

1/sinu – cosu/sinu= sinu/1 + cosu

1 – cosu/sinu= (sinu)(1 – cosu) ÷ (1 + cosu)(1 – cosu)

1 – cosu/sinu= 1 – cosu/sinu

Hence Proved!!

-TheUnknownScientist 72

There are 90 ways that a coach can select a starting team of one center, two forwards, and two guards if the basketball team consists of three centers, five forwards, and three guards.

To determine the number of ways to select a starting team, we first need to choose one center out of three centers, which can be done in 3 ways.

Then we need to choose two forwards out of five forwards, which can be done in 5C2 ways, where 5C2 represents the number of combinations of 2 items that can be chosen from a set of 5 items.

Finally, we need to choose two guards out of three guards, which can be done in 3C2 ways.

Using the multiplication principle, the total number of ways to select a starting team is:

3 x 5C2 x 3C2 = 3 x 10 x 3 = 90

Therefore, there are 90 ways.

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For a line parallel to the x-axis and passing through the point (-2, -4), the equation is y = -4.

a. Since the line is parallel to the x-axis, it means the slope is 0. This is because the line does not have any vertical change (change in y) for a given horizontal change (change in x).

b. The y-intercept of the line parallel to the x-axis is the y-coordinate of any point on the line. In this case, the line passes through (-2, -4), so the y-intercept is -4.

c. The equation of the line can be written in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. Since the slope is 0 and the y-intercept is -4, the equation simplifies to y = -4. This means that for any value of x, the y-coordinate will always be -4, indicating a horizontal line parallel to the x-axis.

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Answer:

As far as I know

Mode: The most frequent number—that is, the number that occurs the highest number of times. Example: The mode of {4 , 2, 4, 3, 2, 2} is 2 because it occurs three times, which is more than any other number.

The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

We do not have enough evidence to conclude that the proportion of students being bullied at school has decreased at a 5% level of significance.

Hypothesis testing is a statistical method used to determine whether a hypothesis about a population parameter is supported by the data. In this case, the hypothesis is that the proportion of students being bullied at school has decreased.

The one-sample proportion test is a type of hypothesis test used to determine whether a proportion in a sample is significantly different from a known population proportion.

In this case, we are testing whether the proportion of students who reported being bullied in the sample of 75 sixth grade students is significantly different from the population proportion of 43%.

To test whether the proportion of students being bullied at school has decreased, we can use a hypothesis test with the null hypothesis that the proportion is still 0.43 and the alternative hypothesis that the proportion is less than 0.43.

Let p be the true proportion of students being bullied at school, then we have:

H₀ : p = 0.43

Hₐ : p < 0.43 (one-tailed test)

Using the sample data, we can calculate the sample proportion of students who reported being bullied at school:

=> \(\hat{p}\) = 30/75 = 0.4

We can use this to calculate the test statistic:

=> z = ( \(\hat{p}\)  - p) / √(p×(1 - p)/n) = (0.4 - 0.43) /√(0.43×0.57/75) = -0.81

At the 5% level of significance with a one-tailed test, the critical z-value is -1.645. Since our calculated test statistic (-0.81) is greater than the critical value, we fail to reject the null hypothesis.

Therefore,

We do not have enough evidence to conclude that the proportion of students being bullied at school has decreased at a 5% level of significance.

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Answer:

78

Step-by-step explanation:

Can you give me brainliest please

Answer:

Give somuchcringe321 brainliest

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

2 multiplied by 2 is 4. You have 2 of the 2's so it becomes 4.

Answer:4

Step-by-step explanation:

have a good day :)

The arc length of the curve x =\(y^4/4 + 1/8y^2\), for 1 <= y <= 5, is approximately 33.93 units.

To find the arc length of the curve, we use the formula for arc length integration. Given the equation x = \(y^4/4 + 1/8y^2\) and the interval 1 <= y <= 5, we want to determine the length of the curve within this range.

First, we differentiate the equation with respect to y to obtain dx/dy. In this case, dx/dy = \(y^3 + 1/4y\). Then, we use the formula for arc length:

L = ∫[a,b] \(\sqrt{(1 + (dx/dy)^2)}\) dy

Plugging in the values from the given interval, a = 1 and b = 5, we integrate the expression \(\sqrt{(1 + (y^3 + 1/4y)^2)}\) with respect to y. Evaluating this integral gives us the arc length of the curve within the specified interval, which is approximately 33.93 units.

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Answer:

3643750000

Step-by-step explanation:

Jasmine can run in one hour is 7.25 miles.

The formula of the unitary method is to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.

Given that,

Jasmine can run 4\(\frac{5}{6}\) miles in \(\frac{2}{3}\) of an hour.

\(\frac{2}{3}\) of an hour = 4\(\frac{5}{6}\) miles

                     = \(\frac{29}{6}\) miles

By using unitary method we will find the value of an hour.

1 hour = \(\frac{\frac{29}{6} }{\frac{2}{3} }\)

          =  \(\frac{29}{6}\) × \(\frac{3}{2}\)

          = \(\frac{29}{4}\)

1 hour  = 7.25 miles

Hence, Jasmine can run in one hour is 7.25 miles.

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The quadratic formula to solve second order linear homogeneous ODEs if it does not yield real roots. The given statement is false.

The quadratic formula can still be used to solve second-order linear homogeneous ODEs even if it does not yield real roots. When the roots of the characteristic equation are complex conjugates, we can use Euler's formula to express the general solution in terms of sine and cosine functions.

For example, suppose we have the second-order linear homogeneous ODE:

ay'' + by' + cy = 0

The characteristic equation is:

\(ar^2\) + br + c = 0

If the roots of this equation are complex conjugates, say r = α ± βi, we can use Euler's formula to write:

r = α ± βi = |r|e^(±iθ)

where |r| = sqrt(\(\alpha^2\) + \(\beta^2\)) and θ = arctan(β/α).

Then, the general solution can be written as:

y(t) = e^(αt)(C1 cos(βt) + C2 sin(βt))

where C1 and C2 are constants determined by the initial conditions of the ODE.

So, even if the roots of the characteristic equation are not real, the quadratic formula can still be used to obtain the roots, and the general solution can still be expressed in terms of real-valued functions.

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sin(01)=-32.70/13 I think

Answer:

Whichever one is only negatives.

Step-by-step explanation:

Whole numbers are integers that are only positive

Answer:

B. m-3=m+3

Step-by-step explanation:

Because the others have a solution such as 0 and -1.

And That would eliminate D

To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.

To compare the two quantities, you need to divide the number of giraffes by the number of penguins.

30 giraffes / 6 penguins = 5

This means that there are 5 times as many giraffes as penguins at the zoo.

There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.

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Therefore, the points on the ellipsoid where the tangent plane is parallel to the xy-plane are: (x, y, z) = (±2cosθ, sinθ, 0), z = 0 where θ is any angle between 0 and 2π.

To find the point(s) on the ellipsoid x^2/4 + y^2 + z^2/9 = 1 where the tangent plane is parallel to the xy-plane (z = 0), we need to find the gradient vector of the function F(x, y, z) = x^2/4 + y^2 + z^2/9 - 1, which represents the level surface of the ellipsoid, and determine where it is orthogonal to the normal vector of the xy-plane.

The gradient vector of F(x, y, z) is given by:

F(x, y, z) = <∂F/∂x, ∂F/∂y, ∂F/∂z> = <x/2, 2y, 2z/9>

At any point (x0, y0, z0) on the ellipsoid, the tangent plane is given by the equation:

(x - x0)/2x0 + (y - y0)/2y0 + z/9z0 = 0

Since we want the tangent plane to be parallel to the xy-plane, its normal vector must be parallel to the z-axis, which means that the coefficients of x and y in the equation above must be zero. This implies that:

(x - x0)/x0 = 0

(y - y0)/y0 = 0

Solving for x and y, we get:

x = x0

y = y0

Substituting these values into the equation of the ellipsoid, we obtain:

x0^2/4 + y0^2 + z0^2/9 = 1

which is the equation of the level surface passing through (x0, y0, z0). Therefore, the point(s) on the ellipsoid where the tangent plane is parallel to the xy-plane are the intersection points of the ellipsoid and the plane z = 0, which are given by:

x^2/4 + y^2 = 1, z = 0

This equation represents an ellipse in the xy-plane with semi-major axis 2 and semi-minor axis 1. The points on this ellipse are:

(x, y) = (±2cosθ, sinθ)

where θ is any angle between 0 and 2π.

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Answer:

Step-by-step explanation:

The standard form of an equation for a straight line is y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).

We can calculate the slope from the two given points, A(5,7) and B(9,-1).

Slope is Rise/Run, where Rise is the change in y and Run is the change in x.

From the two given points, starting at (5,7) and going to (9,-1):

Rise = (-1 -7) = -8

Run = (9-5) = 4

Rise/Run (slope) = -8/4 or -2

The equation becomes y = -2x + b

We can find b by entering either of the two given points and solving for b. I'll pick (5,7):

y = -2x + b

7 = (-2)*(5) + b

7 = -10 + b

b = 17

The equation is y = -2x + 17

Check this with a DESMOS graph (attached).

The equation of line AB is y= -2x +17

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

Points A(5, 7) and B(9, -1)

So, slope for the equation is

sloe= (-1 - 7)/ (9- 5)

slope = -8/ 4

slope= -2

Now, using slope- intercept form

y - b = m ( x- a)

y - 7= -2( x - 5)

y- 7 = -2x + 10

y= -2x + 17

Hence, the equation of line AB is y= -2x +17

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Answer:

y = 1/2x - 3

Step-by-step explanation:

Slope = -2

Slope of the perpendicular line: 1/2

b = -2 - (1/2)(2)

b = -3

Answer:

1st question's answer I don't know and 2nd question's answer is 37.1

Step-by-step explanation:

Mean= sum of all the terms/no. of terms

=12.5+38.3+16.3+2+145+8.5/6

=222.6/6

=37.1

The requirement f(x1) * f(x2) < 0 for choosing initial guesses x1 and x2 with opposite signs ensures the validity and convergence of certain numerical root-finding methods such as the bisection method or the regula falsi method.

The statement you provided is true for certain numerical methods used to find roots of equations, such as the bisection method or the regula falsi method. These methods are iterative and require an initial interval or range where the root is expected to be found. To ensure convergence and a valid solution, it is necessary to choose initial guesses x1 and x2 such that the function f(x) evaluated at those points have opposite signs, i.e., f(x1) * f(x2) < 0.

The rationale behind this requirement is based on the Intermediate Value Theorem, which states that if a continuous function f(x) changes sign over an interval [x1, x2], then there exists at least one root within that interval. By ensuring that f(x1) and f(x2) have opposite signs, we guarantee the existence of a root within the interval [x1, x2].

The bisection method works by repeatedly bisecting the interval and selecting a new subinterval that contains the root. At each iteration, the method narrows down the interval by halving it, based on the sign change observed in the function evaluations.

Similarly, the regula falsi (or false position) method also operates by iteratively refining the interval based on the linear interpolation between the function values at the endpoints. The method adjusts the interval based on the sign change of the function, converging to the root.

Both methods rely on the property of opposite signs to guarantee convergence and avoid getting stuck in a non-converging or incorrect solution. If the initial guesses do not satisfy the condition f(x1) * f(x2) < 0, it is possible that the method fails to converge or converges to a different root or solution.

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Answer:

They lost 8% of the games they played.

Step-by-step explanation:

If the total percent is 100% then we just subtract 92% from that, to get 8% left.

To solve the equation 3a² = -4a + 15 by factoring, we need to rewrite it in the form of a quadratic equation, set it equal to zero, and then factor it. The solutions to the equation 3a² = -4a + 15 are a = 5/3 and a = -3.

The equation 3a² = -4a + 15 can be rearranged as 3a² + 4a - 15 = 0. Now we can factor the quadratic expression.

To factor the quadratic expression, we need to find two numbers that multiply to give -45 and add up to +4. The numbers that satisfy these conditions are +9 and -5. So, we can write the equation as (3a - 5)(a + 3) = 0.

Setting each factor equal to zero, we have two possible solutions: 3a - 5 = 0 or a + 3 = 0.

Solving these equations, we find a = 5/3 or a = -3.

Therefore, the solutions to the equation 3a² = -4a + 15 are a = 5/3 and a = -3.

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The number of pastries baked by Katie is 40, and each pastry is shared by 5 people, making a total of 200 people served.

Let's define two variables to represent the number of pastries and the number of people per pastry:

p = number of pastries

pp = number of people per pastry

Then, the total number of pastries and the total number of people can be expressed as:

total pastries = p = 40

total people = p * pp = 200

We can solve for pp by dividing both sides by p:

pp = total people / p = 200 / 40 = 5

So, the algebraic expression to represent this situation is:

p = 40, pp = 5, total people = p * pp = 200

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Answer:

is it 17/5?

Step-by-step explanation:

Answer:

y = -3/4x -4

Step-by-step explanation:

y = -3/4x + b

-1 = -3/4(-4) + b

-1 = 12/4 + b

-1 = 3 + b

-4 = b

y = -3/4x -4

Answer:

650

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Part A: -1 and 2.5

Part B: The vertex is a minimum

Part C: tbh, I'm not quite sure about this part but just use parts A and B to answer :)

(you can also use the website desmos. com/calculator as a graphing calculator)

The average amount of trash collected is found to be 3 pounds.

Let the average amount of trash collected be 'x'.

As per the given conditions, equation form:

80*(1.5 + x ) = 360

Applying the Distributive Property:

120 + 80x = 360

Simplifying:

80x = 240

x = 240/80

x = 3

Thus, the average amount of trash collected is found to be 3 pounds.

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The complete question is attached.

The required GCF is 8.

The greatest common factor is that greatest number from the factors which divides the number completely.

For example take numbers 12 and 16.

The factors of 12 are 2×2×3.

And the factors of 16 are 2×2×2×2.

We can clearly see that the common factors are 2×2 which gives 4. So, 4 is the greatest common factor which divides both 12 and 16.

Here it is given to find the greatest common factor of 16 and 40.

Factors of 16 = 2×2×2×2

Factors of 40 = 2×2×2×5

We can see clearly the common factors are 2×2×2 which gives 8.

So, 8 is the greatest common factor.

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