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3 years ago

Circle O is inscribed in square EFGH.

Mathematics

1 answer:

Citrus2011 [14]3 years ago

3 0

Answer:

D) 25.5 cm

Step-by-step explanation:

Circumference = pi × d

20 = 3.14 × d

d = 6.3694267516

Diameter = length of one side

Perimeter of the square = 4s

4(6.3694267516)

25.4777070064 cm

From the options, closest is 25.5

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in parallelogram ABCD, AC is diagonal, the measure <ABC is 40°, and the measure of <ACD IS 57°. what is the measure of &lt

Nutka1998 [239]

Answer: $\angle CAD = 83^\circ$ Option D

Step-by-step explanation:

In this question we use properties of parallelogram and angle sum property of a triangle.

In parallelogram ABCD

$\angle ABC=40^\circ$

As, we know that opposite angles of parallelogram are equal

Therefore,

$\angle ABC =\angle ADC =40^\circ$

Now, in triangle ADC

We know that sum of all the angles of a triangle is $=180^\circ$

$\angle ACD +\angle ADC +\angle DAC =180^\circ$

$57^\circ +40^\circ +\angle DAC =180^\circ$

$97^\circ + \angle DAC = 180^\circ$

Subtracting 97 from both sides we get

$\angle DAC = 180^\circ - 97^\circ$

$\angle DAC = 83^\circ$

Measure of $\angle CAD = 83^\circ$

3 0

3 years ago

Henry drove 60.2 miles in 7 days how many miles did he drive in 1 day?

igor_vitrenko [27]

Answer:

8.6

Step-by-step explanation:

60.2/7 =8.6

8 0

3 years ago

Read 2 more answers

A manufacturer of nails claims that only 4% of its nails are defective. A random sample of 20 nails is selected, and it is found

irakobra [83]

Answer:

The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.

Step-by-step explanation:

A manufacturer of nails claims that only 4% of its nails are defective.

At the null hypothesis, we test if the proportion is of 4%, that is:

$H_0: p = 0.04$

At the alternative hypothesis, we test if the proportion is more than 4%, that is:

$H_a: p > 0.04$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

4% is tested at the null hypothesis

This means that $\mu = 0.04, \sigma = \sqrt{0.04*0.96}$

A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective.

This means that $n = 20, X = 0.1$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.1 - 0.04}{\frac{\sqrt{0.04*0.96}}{\sqrt{20}}}$

$z = 1.37$

P-value of the test and decision:

Considering an standard significance level of 0.05.

The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.

Looking at the z-table, z = 1.37 has a p-value of 0.9147

1 - 0.9147 = 0.0853

The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.

7 0

3 years ago

Read 2 more answers

Y= -8/9 (x+1)+6 <br> convert to standard form

Trava [24]

Answer:

kl l

Step-by-step explanation:

3 0

2 years ago

Create a matrix for this system of linear equations, The determinant of the coefficient matrix is

marin [14]

Answer: The determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.

Step-by-step explanation: The given system of linear equations is :

$2x+y+3z=13~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x+2y=11~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\3x+z=10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

We are given to find the determinant of the coefficient matrix and to find the values of x, y and z.

The determinant of the co-efficient matrix is given by

$D=\begin{vmatrix}2 & 1 & 3\\ 1 & 2 & 0\\ 3 & 0 & 1\end{vmatrix}=2(2-0)+1(0-1)+3(0-6)=4-1-18=-15.$

Now, from equations (ii) and (iii), we have

$x+2y=11~~~~~\Rightarrow y=\dfrac{11-x}{2}~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)\\\\\\3x+z=10~~~~~~\Rightarrow z=10-3x~~~~~~~~~~~~~~~~~~~~~~~~~(v)$

Substituting the value of y and z from equations (iv) and (v) in equation (i), we get

$2x+y+3z=13\\\\\Rightarrow 2x+\dfrac{11-x}{2}+3(10-3x)=13\\\\\Rightarrow 4x+11-x+60-18x=26\\\\\Rightarrow -15x+71=26\\\\\Rightarrow -15x=26-71\\\\\Rightarrow -15x=-45\\\\\Rightarrow x=3.$

From equations (iv) and (v), we get

$y=\dfrac{11-3}{2}=4,\\\\z=10-3\times3=1.$

Thus, the determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.

3 0

3 years ago