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3 years ago

Which equations represent two vertical asymptotes of the function y = 3 cot(4∕3x)?

Mathematics

1 answer:

bezimeni [28]3 years ago

5 0

Answer:

A) x = 0 and x = 3π∕4

Step-by-step explanation:

cot 0° = oo (infinite)

4/3 x = 0

=> x = 0

cot 180° = oo (infinite)

4/3 x= 180

x = 3/4 × 180

= 135°

= ¾π

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Obesity is a risk factor for many health problems such as type 2 diabetes, high blood pressure, joint problems, and gallstones.

kodGreya [7K]

Answer:

a. A point estimate of the BMI for adults in the United States can be calculated from the sample mean, which has a value M=44.57.

b. The sample standard deviation is s=79.9507.

c. The 95% confidence interval for the BMI of adults in the United States is (26.18, 62.96).

Step-by-step explanation:

We start by calculating the sample mean and standard deviation of the BMI data:

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{75}(16.2+31.1+24.8+. . .+22.9)\\\\\\M=\dfrac{3343}{75}\\\\\\M=44.57\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{74}((16.2-44.57)^2+(31.1-44.57)^2+(24.8-44.57)^2+. . . +(22.9-44.57)^2)}\\\\\\s=\sqrt{\dfrac{473016.8667}{74}}\\\\\\s=\sqrt{6392.1198}=79.9507\\\\\\$

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=44.57.

The sample size is N=75.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{79.9507}{\sqrt{75}}=\dfrac{79.9507}{8.66}=9.232$

The degrees of freedom for this sample size are:

$df=n-1=75-1=74$

The t-value for a 95% confidence interval and 74 degrees of freedom is t=1.993.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=1.993 \cdot 9.232=18.39$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 44.57-18.39=26.18\\\\UL=M+t \cdot s_M = 44.57+18.39=62.96$

The 95% confidence interval for the BMI of adults in the United States is (26.18, 62.96).

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4 years ago

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inna [77]

2(3x + 2 + x) = 6x + 4 + 2x = 8x + 4

A and D have the same solutions

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3 years ago

Read 2 more answers

Find the coordinates of P that partitions segment AB , where A (2,3) and B (14,9), so that AP:PB is a 1:2 ratio. Also, find the

Paladinen [302]

For Point P, you need to recognize that a 1:2 ratio means that AP will be 1/3 of AB and PB will be 2/3 of AB.

So you need to find the change in the x-values, 14-2 = 12, and then add 1/3 of that change to the x-value of A.

Then you need to find the change in the y-values, 9-3 = 6, and then add 1/3 of that change to the y-value of A.

For the bisector, that's another way to say you'll split AB into two even pieces. For this, it's the same as what we just did, but you need to find 1/2 of the two respective changes (1/2 of the x-change and 1/2 the y-change).

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3 years ago

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iris [78.8K]

Answer: X(5x-1)

Hope this helps! ^^

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3 years ago

Does anyone know the answer to this question??

Step2247 [10]

C and then D because when you go outside and it’s cold then you know it’s cold

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