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3 years ago

The measure of arc BCD is

Mathematics

1 answer:

makkiz [27]3 years ago

6 0

Answer:

m∠BCD = 140°

Step-by-step explanation:

ABCD is cyclic quadrilateral. A property of cyclic quadrilateral states that the opposite angles of it sum up to 180°. Here:

m∠A + m∠C =180° and m∠B + m∠D = 180°

So, m∠A + m∠C =180°

m∠A = 40° (given in the question)

40° + m∠C = 180°

m∠C = 180° - 40° = 140°

∴m∠C = m∠BCD = 140°

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Answer:

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Step-by-step explanation:

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3 years ago

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).

4 0

4 years ago

* WILL GIVE BRIANLIEST*(08.03)Consider the following set of equations:

cluponka [151]

The third choice is very useful. It's valid because two things that are both equal to 'y' are equal to each other, and it can be easily solved to find 'x'.

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3 years ago

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Please help meeeee I need correct asnwers

ycow [4]

Answer:

diameter = 12 cm

radius = 6cm

circumference = 12 $\pi$ cm ≈ 37.68 cm

area = 36 $\pi$ cm² ≈ 113.04 cm²

Step-by-step explanation:

r = radius

d = diameter

C = circumference

A = area

The diagram shows a circle with a diameter of 12 cm

Diameter

d = 12 cm

Radius

r = d/2

⇒ r = 12/2

⇒ r = 6 cm

Circumference

C = $\pi$ d

⇒ C = 12 $\pi$ cm

Area

A = $\pi$ r²

⇒ A = $\pi$ x 6²

⇒ A = 36 $\pi$ cm²

If you use $\pi$ = 3.14 then:

C = 37.68 cm

A = 113.04 cm²

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2 years ago

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tia_tia [17]

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3 years ago