Identify the slope and y-intercept from the following equation.

The equation of a sine function given in accordance with the given specifications is y = 3sin[(2/3)x + π/8) - 2.

The trigonometric functions (also called circular functions, angle functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Given is the following specifications for a sine wave -

Amplitude: 3

Period: 3π

Phase Shift: π/8

Vertical Shift: -2

The general equation for sine wave is -

y = A sin(ωx + Ф) + k

Now, we know -

ω = 2π/T

ω = 2π/3π

ω = 2/3

And -

A = 3

Ф = π/8

k = - 2

y = 3sin[(2/3)x + π/8) - 2

Therefore, the equation of a sine function given in accordance with the given specifications is y = 3sin[(2/3)x + π/8) - 2.

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The given problem involves a student athlete's swim time and heart rate data for a random sample of 10 days. To analyze the data, we will first create a scatter plot by entering the data into a calculator. Then, using the regression function on the calculator, we can find the equation of the least-squares regression line and add it to the scatter plot. Lastly, we will interpret the slope and y-intercept of the regression line.

By entering the swim time and heart rate data into a calculator, we can create a scatter plot that represents the relationship between the two variables. Next, using the calculator's regression function, we can determine the equation of the least-squares regression line. This line represents the best fit to the data points and allows us to make predictions or analyze the relationship between swim time and heart rate.

Interpreting the regression line, the slope indicates the rate of change in the heart rate for each additional minute added to the swim time. For example, if the slope is 3.2, it means that for each additional minute added to the swim time, the heart rate will increase by 3.2 beats per minute.

The y-intercept represents the predicted heart rate when the swim time is zero. It indicates the baseline or starting point of the heart rate. For example, if the y-intercept is 120, it means that if the student is not swimming at all, their heart rate is predicted to be 120 beats per minute.

By interpreting the slope and y-intercept of the regression line, we can understand the relationship between swim time and heart rate and make predictions based on the data.

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Answer:

5 miles=8km

1miles=8/5=1.6km

57.5 miles=(57.5×1.6)km

=92km

Answer:

same way

3×3.14×4power 2= 37.68

Answer:

150.72

Step-by-step explanation:

V=πr²h

V=3.14·4²·3

V=3.14·16·3

V=50.24·3

V=150.72

Answer:

x = 5

Step-by-step explanation:

The small right triangle and the outer right triangle are similar, thus ratios of corresponding sides are equal, that is

\(\frac{3.5}{7}\) = \(\frac{2.5}{x}\) ( cross- multiply )

3.5x = 17.5 ( divide both sides by 3.5 )

x = 5

Answer:

I think the answer is 20

Step-by-step explanation:

6x3=18+2=20

Answer:

Kim now has 20 pet fish. This is because if you do (6 x 3) since you said Jan had 6 pet fish and Kim had 3 times as many meaning the six times the three. Then, Kim had got 2 more fish meaning she now had 20 fish in total. The (18 + 2).

Step-by-step explanation:

A. The linear equation is: y = 60x + 45

B. The graphed equation is shown in the attachment below.

A linear equation is defined as, y = mx + b, where the initial value = b; unit rate = m; x and y are the variables.

A. In this situation given, we have:

Substituting the values into y = mx + b, we would have the equation as:

y = 60x + 45

B. The graph of the equation is shown in the image attached below.

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the answer would be ...

f(x) = -5/2x + 4

We know this because the constant in this equation, 4, is the y-intercept!

This means that the number without the variable is where the line intersects the y-axis.

Additionally, the slope is called the "rise over run", but in this case it is negative. At the point, 4, on the y-axis, we go down 5 units (the numerator of the slope) and to the right by 2 units (the denominator).

We find ourselves at where the line intercepts the x-axis!

I hope my explanation isn't confusing and that it is helpful! If you have any questions or concerns, message me! :)

Answer:

The probability of an adult getting a NEG result and truly having tuberculosis is 0.01725, which is closest to option (A) 0.0373.

Let's use the following notation:

P(TB) represents the probability that an adult has tuberculosis, which is given as 0.05.

P(POS|TB) represents the probability that the test is positive given that an adult has tuberculosis, which is given as 0.746.

P(NEG|TB) represents the probability that the test is negative given that an adult has tuberculosis, which is 1 - P(POS|TB) = 0.254.

We are asked to find the probability of an adult getting a NEG result and truly having tuberculosis, which can be calculated using Bayes' theorem as follows:

P(TB|NEG) = P(NEG|TB) * P(TB) / P(NEG)

We can calculate P(NEG) using the law of total probability, which considers the two possible cases for an adult: having tuberculosis (TB) or not having tuberculosis (TB').

P(NEG) = P(NEG|TB) * P(TB) + P(NEG|TB') * P(TB')

= 0.254 * 0.05 + 0.7653 * 0.95

= 0.7352

Now we can substitute the values into Bayes' theorem:

P(TB|NEG) = 0.254 * 0.05 / 0.7352

= 0.01725

Therefore, the probability of an adult getting a NEG result and truly having tuberculosis is 0.01725, which is closest to option (A) 0.0373.

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Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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Answer: 7c + 2

Step-by-step explanation:

Combine like terms hope this helps

Answer:

A, 4

B, 0

Step-by-step explanation:

gcf = 4

32-28 = 4 (4-4) = 4(0) = 0

can i get brainliest?

Answer: a4 b0

Step-by-step explanation:

gcf = 4

32-28 = 4 (4-4) = 4(0) = 0

Let x be the number of quarters and y be the number of nickels in the piggy bank;

Since there are 63 coins in the piggy bank, then we have;

Also, 20nickels is 1 dollar and also 4 quarters is 1 dollar.

Since there is $12.55 in the piggy bank, we have;

Then, we substitute equation 3 in equation 2, we have;

Hence, the number of quarters in the piggy bank is 47

Answer:

Step-by-step explanation:

Alright so the step that comes first is adding two to both sides.

Let me show you,

Step 1

-b-2<8  Add 2 to both sides

-b<10

Then you divide the sides by -1

-b<10

b>-10

Answer:

5/6

Step-by-step explanation:

Answer:

20(4+3)

Step-by-step explanation:

GCF of 80 and 60 = 20

20*4=80

20*3=60

20(4+3)

hope this helps! :)

Answer:

b

Step-by-step explanation:

Answer:

14 cm

All you have to do is add the four sides up and you're good to go! :)

Answer:

The answer is 14

Step-by-step explanation:

perimeter - means to add . You add all the sides

area - means multiplication . You multiply the two numbers on the bottom so for an example is this was area the answer would've been (A-10)

Answer:

see step by step explanation

Step-by-step explanation:

part a: x=1/72  because there are 72 x's in the one so 1/72

part b: x=1/70 because there are 70 x in 1 so x = 1/70

Answer:

(7^2)^0

Step-by-step explanation:

The Zero rule property states that anytime you multiple an exponent by 0 it always equals 1. So, if you multiply the equation by 0 it will equal one.

Answer:

(2/3, 8/3)

Step-by-step explanation:

Using the line segment equation we get: (x,y)=(-6+2/3(4-(-6)), -4+2/3(6-(-4))=(2/3,8/3)

Answer:

Full Answer

Step-by-step explanation:

(-2,0)

Answer:2.6

Step-by-step explanation:

Answer:

2.6

Step-by-step explanation:

Answer:

89.9°

Step-by-step explanation:

h=324324324 meters

x=545454 meters

θ=tan⁻¹(h/x)=89.9°

Hope, this helps you.

Answer:

80.5 degrees - khan academy

Step-by-step explanation:

Jesus Christ your savior loves you!

We can expect 76 teenagers to say yes whether they  preferred watching shows over the internet, rather than through cable.

To calculate the expected number of teenagers who would prefer watching shows over the internet, rather than through cable:

73%, which is equivalent to 0.73 prefer watching shows over the internet. (Given)

Total number of teenagers surveyed is 104. (Given)

Expected number of teenagers who prefer watching shows over the internet =

= 0.73  × 104

= 75.92

Since it is a discrete variable we cannot have a fractional part of a teenager, we need to round the solution to the nearest whole number. Rounding 75.92 to the nearest whole number gives us 76.

Therefore, we can expect 76 out of the 104 teenagers surveyed to say yes, they prefer watching shows over the internet, rather than through cable.

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Answer:

y=20-5x/2

Step-by-step explanation:

Answer:

y=2.5x+10

Step-by-step explanation:

trust me lol

Step-by-step explanation:

y/8=-10-5

y/8=-15

y=15×8

y=120

Answer: 2800

Step-by-step explanation:

From the question, we are informed that during the winter season, the number of visitors that came to a theme park decreased by 700 to 2,100.

Therefore, the theme park's population at the beginning of the winter season will be gotten by adding 700 and 2100. This will be:

= 700 + 2100

= 2800

Answer:

Option D

Step-by-step explanation:

In order to find the answer to this question you need to multiply the precent by the number and then divide by one-hundred.

\(32=19\)

\(32\times19=608\)

\(608\div100=6.08\)

\(6.08=6\)

\(=6\)

Hope this helps.

Answer:

i hope it helps

Step-by-step explanation:

area= inside of figure

area of triangle= 1/2 base*height

perimeter= sum of all sides

perimeter of triangle= a+b+c

Answer:

A= 8.25 m  P≈ 16.2 m

Step-by-step explanation:

Answer:

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

We have a repeating decimal 4.6(1).

Let's express it as a GP:

Fund the sum of infinite GP, with the first term of a = 0.01 and common ratio of r = 0.1:

Add 4.6 to the sum:

Hence the fraction is 4 11/18.