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Question 2 Solve the equation (tan a + 2 sin a)/(tan a - 2 sin a) = 3 for 0°< 1< 180° Select your answer

The probability that the person will not die in the next year is 0.99635, the correct option is C.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that;

The probability that a person will die in the next year =100000

Now,

The probability that a person will die in the next year is given as 0.00001 (or 1/100000).

To find the probability that the person will not die in the next year, we can subtract the probability of dying from 1

Probability of not dying = 1 - Probability of dying

Probability of not dying = 1 - 0.00001

Probability of not dying = 0.99999

None of the options provided match this answer exactly, but the closest 0.99635.

Therefore, by the probability the answer will be 0.99635.

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The minimum sample size required to construct an 85% confidence interval with an error of no more than 0.07, given a mean of 5.4 energy drinks per week and a standard deviation of 0.7, is 58.

To determine the minimum sample size required to construct a 85% confidence interval with an error of no more than 0.07, we can use the formula:

n = (Z * σ / E)^2

where:
n = sample size
Z = Z-score for the desired confidence level (85% confidence level corresponds to a Z-score of approximately 1.44)
σ = standard deviation
E = margin of error

Given that the mean is 5.4 energy drinks per week and the standard deviation is 0.7, we can plug in the values:

n = (1.44 * 0.7 / 0.07)^2

Simplifying the equation:

n = (2.016 / 0.07)^2

n = 57.54

Therefore, the minimum sample size required to construct the specified confidence interval is 58.

DEATAIL ANS: The minimum sample size required to construct an 85% confidence interval with an error of no more than 0.07, given a mean of 5.4 energy drinks per week and a standard deviation of 0.7, is 58.

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Answer:

X = 2

AB = 39

CB = 27

Step-by-step explanation:

Since it's a parallelogram (two pairs of parallel sides), we can set each opposite side equal to each other. We know the equation for two opposite sides, side AD and side CB, therefore:

\(AD=CB\\14x-1=9x+9\\5x=10\\x=2\)

Now that we know x, we can solve the other equations:

\(12x+15=AB\\12*2+15=AB\\24+15=AB\\39=AB\)

And:

\(9*2+9=CB\\18+9=CB\\27=CB\)

Answer:

D

Step-by-step explanation:

W/-15=D

\(-\frac{W}{15}\)=D

Answer:

The answer to this question is A

The new coordinates will be C( 3 ,0),  D( 7,1) , E(2,4) , Option A is the correct answer.

When a object or a figure is reflected , it means an mirror image if the object is being created , the shape and size of the object remains same , Only the coordinates change on the basis of the axis used for Reflection.

The figure is given in the question.

The coordinates of the figure is

C( -3 ,0)

D( -7,1)

E(-2,4)

When reflection is done along any axis , the coordinates of the other axis change sign.

so in this case ( x,y ) -----> ( -x,y)

The new coordinates will be

C( 3 ,0)

D( 7,1)

E(2,4)

Therefore Option A is the correct answer.

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Equation of the line 'm' is 5x - 6y - 30 = 0.

According to graph,

A(6,0) and B(0,-5) lies on the line m.

Slope-intercept form -> y = mx + c

Putting B(0,-5) in slope-intercept form,

-5 = m(0) + c

 c = -5

Putting A(6,0) in slope-intercept form,

  0 = m(6) - 5

6m = 5

 m = 5/6

Putting the values of m and c in slope-intercept form,

 y = (5/6)x - 5

6y = 5x - 30

5x - 6y - 30 = 0

Hence, equation of the line is 5x - 6y - 30 = 0.

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Answer:

x = 50; 2x = 100

Step-by-step explanation:

x + 2x = 150

3x = 150

x = 50

2x = 2(50)

2x = 100

The vertex, focus, and directrix of the parabola 5x^2 + 16y = 0 are (0, 0), (-4/5, 0), and x = 4/5, respectively.

To find the vertex, focus, and directrix of the parabola with the equation 5x^2 + 16y, we can use the standard form of the equation for a parabola:

y = (1/4p)(x - h)^2 + k

where (h, k) is the vertex and p is the distance between the vertex and the focus or the vertex and the directrix.

Comparing the given equation to the standard form, we have:

5x^2 + 16y = 0
=> 16y = -5x^2
=> y = -(5/16)x^2

From this, we can determine that the vertex is at the origin (0, 0).

To find p, we can use the formula p = 1/(4a), where a is the coefficient of x^2. In this case, a = -5/16, so p = 1/(4*(-5/16)) = -4/5.

Therefore, the vertex is (0, 0), the focus is (-4/5, 0), and the directrix is x = 4/5.

In conclusion, the vertex, focus, and directrix of the parabola 5x^2 + 16y = 0 are (0, 0), (-4/5, 0), and x = 4/5, respectively.

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The amount of interest that the customer will pay is given as follows:

$31.88.

The balance of an account after t periods is given as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are explained as follows:

Hence the interest accrued is given as follows:

I(t) = Prt.

The parameters for this problem are given as follows:

P = 2530.16, r = 0.00042, t = 30.

Hence the interest is given as follows:

I(30) = 2530.16 x 0.00042 x 30

I(30) = $31.88.

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h'(4) = 7. This means that the derivative of the function h(x) at x = 4 is equal to 7.The positive value of h'(4) indicates that at x = 4, the function h(x) is increasing, with a slope of 7.

To find h'(4), where h(x) = f(x) * g(x), we'll use the product rule of differentiation. The product rule states that the derivative of a product of two functions is given by the derivative of the first function times the second function, plus the first function times the derivative of the second function.

Given:

f(4) = 3

g(4) = 4

f'(4) = -2

g'(4) = 5

Let's differentiate h(x) using the product rule:

h'(x) = f'(x) * g(x) + f(x) * g'(x)

Substituting the given values at x = 4:

h'(4) = f'(4) * g(4) + f(4) * g'(4)

      = (-2) * 4 + 3 * 5

      = -8 + 15

      = 7

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Therefore, after using three-fourths of the rice in the box, 4 and 1/4 cups of rice remained.

To find the number of cups of rice that remained in the box, we need to calculate three-fourths (3/4) of the total amount of rice in the box.

The total amount of rice in the box is given as five and two-thirds cups. To work with a fraction, we can convert the mixed number to an improper fraction:

5 and 2/3 = (5 * 3 + 2) / 3 = 17/3 cups

Now, we can find three-fourths (3/4) of 17/3:

(3/4) * (17/3) = (3 * 17) / (4 * 3) = 51/12 = 4 and 3/12 = 4 and 1/4 cups

Therefore, after using three-fourths of the rice in the box, 4 and 1/4 cups of rice remained.

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The number of people who waited at least 6 minutes is given as follows:

50 people.

The height of each bin of the histogram represents the number of observations of the data-set in the desired interval.

The desired outcomes for this problem are given as follows:

Hence the number of people who waited at least 6 minutes is given as follows:

20 + 15 + 10 + 5 = 50 people.

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The differential dy is given by dy = (2x + 2)dx. Evaluating dy for x = 1 and dx = (1/2) gives dy = 3.

The differential dy represents the small change or infinitesimal variation in the dependent variable y. In this case, the function y is given by y = x² + 2x. To find the differential dy, we take the derivative of y with respect to x and multiply it by dx, the small change in x. The derivative of y with respect to x is 2x + 2, so the differential dy is given by dy = (2x + 2)dx.

To evaluate dy for specific values of x and dx, substitute the given values into the expression for dy. In this case, we are given x = 1 and dx = (1/2). Plugging these values into dy = (2x + 2)dx, we have dy = (2(1) + 2)(1/2) = 3.

The expression dy = (2x + 2)dx represents the differential of the function y = x² + 2x. It tells us how much y changes as x changes by a small amount dx. By substituting the given values x = 1 and dx = (1/2) into the expression, we find that dy = 3. This means that for a small change in x of (1/2), y changes by 3 units.

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Answer:

615,000

Step-by-step explanation:

Given that:

Whole number rounded to the nearest ten thousand is 620,000

Let x = the whole number

HTh__ TTh ____ Th ____ H ____ T ____ U

6_____ 2 ______ 0 ____ 0 ____ 0 ____ 0

The ten thousand digit is 0 ;

To round to the nearest 10 thousand, the thousand digit is rounded up to 1 and added to the ten thousand digit if it up to 5 or above and rounded down to 0 if below 5 with all subsequent digits(hundred, tens and unit) rounded to Zero..

Hence,

The whole number will could be range between :

615,000 - 619,999

Hence, the least possible value for the number is 615,000.

Answer:

C. (40 × 60 × 10) + (30 × 60 × 10) = V

Step-by-step explanation:

Picture of the cake can be found in the attachment below :

To solve, we resolve the cake into two distinct boxes :

The lower which is lateral sits parallel, whose volume, = (length * width * height) = (60 * 30 * 10)

And the other which sits vertically ;

Volume = (length * width * height) = (10 * 60 * 40)

Then, we add;

Overall volume:

(60 * 30 * 10) + (10 * 60 * 40)

The f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

To compute f′(a) algebraically for the given value of a, we use the following differentiation rule which is known as the Power Rule.

This states that:If f(x) = xn, where n is any real number, then f′(x) = nxⁿ⁻¹This is valid for any value of x.

Therefore, we can differentiate f(x) = −7x + 5 with respect to x using the power rule as follows:

f(x) = −7x + 5

⇒ f′(x) = d/dx (−7x + 5)

⇒ f′(x) = d/dx (−7x) + d/dx(5)

⇒ f′(x) = −7(d/dx(x)) + 0

⇒ f′(x) = −7⋅1 = −7

Hence, the derivative of f(x) with respect to x is -7.Now, we evaluate f′(a) when a = −6 as follows:f′(x) = −7 evaluated at x = −6⇒ f′(−6) = −7

Therefore, f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

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The area of the shaded region is 96ft²

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m².

The area of a parallelogram is expressed as base × height

The area of parallelogram = 12× 12

= 144ft²

The area of the rectangle = l×w

= 8×6

= 48 ft²

The area of the shaded region = area of parallelogram - area of rectangle

area of the shaded region = 144-48

= 96ft².

Therefore the area of the shaded region is 96ft²

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Answer:

1/3 of a cup

Step-by-step explanation:

Just do (2 2/3)/8

Answer:

5 drinks will be americanos

Step-by-step explanation:

2:8  (2/8)

simplify

1:4  (1/4)

divide 20 by 4

5:20

The number of next 20 drinks which may be Americanos is 5.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given that,

Total drinks sold = 8

Number of drinks that is Americanos = 2

Probability of finding Americano = 2/8 = 1/4

If the total number of drinks next is 20,

Number of Americanos expected = Probability of Americanos × Number of drinks

= 1/4 × 20

= 5

Hence the number of Americanos expected is 5.

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T probability of rolling doubles after 45 tosses is 0.156

To do this, we enter the data values in a graphing calculator.

From graphing calculator, we have the following summary:

The regression equation is

y = bx + a

Where

b = SP/SSX = 1375/8250 = 0.16667

a = MY - bMX = 8.7 - (0.17*55) = -0.46667

So, we have:

y = 0.16667x - 0.46667

Approximate

y = 0.167x - 0.467

When the number of tosses is 45, we have:

y = 0.167 * 45 - 0.467

Evaluate

y = 7.048

Approximate

y = 7

45 tosses gives 7 doubles.

So, the probability is:

P = 7/45

Evaluate

P = 0.156

Hence, the probability of rolling doubles after 45 tosses is 0.156

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Answer:

16.25

Step-by-step explanation:

Answer:

48.75

Step-by-step explanation:

A representative sample based on the hospital scenario is option A

A subset of a larger population that accurately reflects the traits, diversity, and distribution of the total population is referred to as a representative sample.

Due to time, financial, or logistical limitations, it is frequently not possible or practical to investigate an entire population when conducting research or gathering data. In these situations, researchers choose a representative sample from which to deduce generalizations about the total population.

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Answer:

Step-by-step explanation:

Sorry I can't explain how it is done. It is very difficult to explain on paper.

Answer:

Step-by-step explanation:

(2x + 1/3x)³

= (7/3x)³

= 343/27 x³

Answer:

C. 15800 to spare

Step-by-step explanation:

All you have to do is add up the total money he has to spend  money, then you add up the total cost, and subtract the total money he has to spend by the total cost, and you're left with he has 15,800 left to spare. ;)

He should make a loan from the investors about 4.6%..

To determine the volume or chance of commodity in terms of 100, use the chance formula. Per cent simply means one in a hundred. With the chance formula, a number between 0 and 1 can be expressed. A number that's expressed as a bit of 100 is what it is. It's substantially used to compare and determine rates and is represented by the symbol.

Total quantum plutocrat Korey have

= Saving plutocrat heritage plutocrat

= $,500$,000

= $,500

Total quantum of charges

= Store Fixtures amount + Computer and Cash Register amount + Inventory  amount +Rent amount + Insurance amount

=  $2700 + $1200 + $17400 +$10800 + $3000

= $35100

So, Fund taken through loans and investor

= Total quantum of charges -Total quantum plutocrat Korey have

= $ 35100-$ 33500

= $ 1600

and, the percentage is

= 1600 x 100 / 35100

= 4.6%

He should make a loan from the investors about 4.6%.

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