I really need help with these questions:

Use basic identities to find the simplified expression-

1. (cos^2 x + sin^2 x) / (cot^2 x - csc^2 x)

2. cosine θ^2 / sine θ^2 + csc θ sin θ

Explanations would be greatly appreciated

Answer: 134.95 to be exact

you multiply the zscore with the standard deviation and add the mean

The formula for calculating the z-score:

z = (x - μ) / σ
Where

μ - mean

σ = standard deviation

The x-score that corresponds to a z-score of 2.33 is 134.95.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

Iq test scores are normally distributed:

Mean = 100

Standard deviation = 15
z-score = 2.33

The formula for calculating the z-score:

z = (x - μ) / σ

Where

μ - mean

σ = standard deviation

Now,

2.33 = (x - 100) / 15

Multiply 15 on both sides.

2.33 x 15 = x - 100

34.95 = x - 100

Add 100 on both sides.

34.95 + 100 = x

x = 134.95

Thus,

The x-score that corresponds to a z-score of 2.33 is 134.95.

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We would graph both equations: y = 4-x  and   y = 8-x^-1

The point on the graph where the lines cross is the solution to the system of equations.

using a graph tool

see the attached figure N 2

the solutions are the points

(-4.24,8.24)

(0.24,3.76)

Part A.  We have two equations:  y = 4-x   and   y = 8-x^-1

Given two simultaneous equations that are both to be true, then the solution is the points where the lines cross. The intersection is where the two equations are equal. Therefore the solution that works for both equations is when

4-x = 8-x^-1

This is where the two graphs will cross and that is the common point that satisfies both equations.

Part B

see the attached table

the table shows that one of the solutions is in the interval [-1,1]

Part C To solve graphically the equation 4-x = 8-x^-1

We would graph both equations: y = 4-x  and   y = 8-x^-1

The point on the graph where the lines cross is the solution to the system of equations.

using a graph tool

see the attached figure N 2

the solutions are the points

(-4.24,8.24) (0.24,3.76)

Final answer:

By establishing equations based on Pratap's rowing times upstream and downstream, we find that Pratap's rowing rate in still water is 5.5 miles per hour.

Explanation:

Finding Pratap's Rowing Rate in Still Water and the Current Rate

To calculate Pratap Puri's rowing rate in still water and the rate of the current, we need to set up two equations based on the information provided. We know that Pratap rowed 14 miles down a river in 2 hours and the return trip took 3 and a half hours.

Step-by-Step Solution

Let x be the rate at which Pratap can row in still water, and y be the rate of the current.

The downstream speed (with the current) is x + y, and the upstream speed (against the current) is x - y.

Using the formula distance = rate × time, for the downstream trip we have 14 = (x + y) × 2, and for the upstream trip 14 = (x - y) × 3.5.

Simplifying both equations gives us: 7 = x + y and 4 = x - y.

To find x, add the two equations to eliminate y, yielding 11 = 2x, or x = 5.5.

Therefore, Pratap's rowing rate in still water is 5.5 miles per hour.

Answer:

D - 45

Explanation:

Hope you have a great day!

The exponential function representing the relationship between the mass y of a radioactive sample in milligrams and t years since the start of the study is y = 200(1 - 0.054)^t.

The student is given a starting mass of a radioactive substance and the percentage of the mass that decays each year. To write an exponential function that models this situation, we consider the initial mass, which is 200 milligrams, and the decay rate, which is 5.4% per year. The relationship between the mass y and the time t in years can be represented by the formula y = 200(1 - 0.054)^t.

Using an exponential decay model, we understand that the amount of substance decreases by a certain percentage each year. To account for this, we raise the base (1 - 0.054) to the power of t, representing the number of years, which gives us the factor by which the original mass has reduced.

Answer:

Octagon

Step-by-step explanation:

It has 8 sides

[tex]\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a} [/tex]

a = 4

b = - 131

c = 480

Answer:

Face value of bond = $ 6000

Rate of interest =7.25 %

The Bond will mature in 5 years.

If the interest is semiannually , the rate of interest will reduce to half.

So, new rate of interest will be [tex]\frac{7.25}{2}=3.625[/tex]

Formula for simple interest

[tex]=\frac{\text{Principal}\times Rate \times time}{100}[/tex]

   Interest after 6 months will be

   [tex]=\frac{6000 \times 3.625 \times 1}{100}\\\\=60 \times 3.625\\\\=217.5[/tex]

So, interest that Randall will receive after six months = $ 217.50

Answer:

The correct answer is 3 1/24

Step-by-step explanation:

because I did all the math

Answer:

3 1/24

Step-by-step explanation:

To determine how many tickets Dan bought, we calculate the price per ticket from Amy's purchase as £3.50 each. Then we subtract Amy's payment from the total to find Dan's payment of £38.50, and finally, we divide Dan's payment by the price per ticket to find that Dan bought 11 tickets.

The question involves finding out how many tickets Dan bought for a concert, using the total amount paid by both Amy and Dan and the price Amy paid for her tickets.

First, we need to find out the price per ticket from the information provided about Amy's purchase:

Amy pays £24.50 for 7 tickets.

To find the price per ticket, we divide £24.50 by 7:

Price per ticket = £24.50 / 7 = £3.50

Next, we use the total amount paid to find out how much Dan spent:

Total amount paid by Amy and Dan = £63

Amount paid by Amy = £24.50

So, the amount paid by Dan = Total amount - Amount paid by Amy

Amount paid by Dan = £63 - £24.50 = £38.50

To find out how many tickets Dan bought, we divide the amount he paid by the price per ticket:

Number of tickets Dan bought = £38.50 / £3.50

Number of tickets Dan bought = 11 tickets

To find the distance from the plateau's base, use the tangent function with the given height and angle of elevation.

We can use trigonometry to determine the distance from the base of the plateau. The vertical height of the table (opposite side) is 70 m, and the elevation angle to the top of the plateau (theta) is 60 degrees. We can use the tangent function to find the distance (adjacent side) from the table's base: tan(theta) = opposite/contiguous. Solving for the space, we get: adjacent = contrasting/tan(theta). Plugging in the values, the distance from the plateau's base is approximately 40 m.

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Answer: [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

From the given picture, the total number of cards = 5

The number of red card = 2

Thus, the probability of drawing a red card P(red)=[tex]\frac{2}{5}[/tex]

Also, total number of digits on spinner = 8

Number of 1's=4

Thus, the probability of  spinning a 1 P( spinning 1)=[tex]\frac{4}{8}=\frac{1}{2}[/tex]

Since both the events of drawing a red card and spinning a 1 are independent events, therefore, the probability of drawing a red card and then spinning a 1=[tex]\text{ P(red)}\times\text{P( spinning 1)}=\frac{2}{5}\times\frac{1}{2}=\frac{1}{5}[/tex]

Answer:

All real numbers

Step-by-step explanation:

The domain of the function represented by f(x) = x + 1 is the all real numbers as there is only addition involved in the function so putting any number as input will not lead the function to infinity.

(3, -2)

Given equations are

d+e=1

-d+e=-5

We need to find d and e.

A system of equations is a set of one or more equations involving a number of variables

The system of equations are

d+e=1....(1)

-d+e=-5....(2)

d=1-e (from 1)

Substitute d in (2)

-(1-e)+e=-5

-1+e+e=-5

-1+2e=-5

2e=-5+1

2e=-4

e=-2

Now substitute value of e in (1)

d-2=1

d=1+2

d=3

Therefore the ordered pair for d + e = 1 and −d + e = −5 is (3, -2)

i.e value of d=3 and e=-2

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