Find m∠ABD and m∠CBD given m∠ABC = 111∘

Using the expression 10 x 2/5 as an example, describe how to multiply a whole number by a fraction that is less than one.

Schach [20]

To multiply a whole number by a fraction less than one, you have to rewrite the whole number in the expression as a fraction by putting a one under it.
For example, in 10 x 2/5, you would rewrite the 10 to 10/1 x 2/5.
Then, you would multiply the top and bottom of the two fractions. In this case, it would be 10 x 2 and 1x5. This would result in 20/5.
Finally, you would simplify this fraction by dividing. The final answer is 4.

5 0

2 years ago

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Several years ago, 50% of parents who had children in grades K-12 were satisfied with the quality of education the students r

galina1969 [7]

Answer:

The 95% confidence interval for the proportion of parents that are satisfied with their children's education is (0.4118, 0.4618). 0.5 is not part of the confidence interval, so this represents evidence that parents' attitudes toward the quality of education have changed.

Step-by-step explanation:

We have to see if 50% = 0.5 is part of the confidence interval.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 1095, \pi = \frac{478}{1095} = 0.4365$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4365 - 1.96\sqrt{\frac{0.4365*0.5635}{1095}} = 0.4118$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4365 + 1.96\sqrt{\frac{0.4365*0.5635}{1095}} = 0.4612$

The 95% confidence interval for the proportion of parents that are satisfied with their children's education is (0.4118, 0.4618). 0.5 is not part of the confidence interval, so this represents evidence that parents' attitudes toward the quality of education have changed.

5 0

3 years ago

Which of the following ratios is equivalent to 24:36?

Ksju [112]

Answer:

D, 20:30

Step-by-step explanation:

At first glance, this does not seem like the correct ratio. But I'll spare you a long intro and get into it:

20:30: Divide both of them by 10

=2:3

2 x 12:3 x 12

24:36

Hope this helps!

4 0

3 years ago

Find the inner product for (7, 2) * (0, -2) and state whether the vectors are perpendicular.

Andrews [41]

Answer: A

Step-by-step explanation:

To find the inner product of two vectors (a,b) and (c,d) you would use the equation (a * c) + (b * d)

So for (7,2) and (0,-2) the inner product would be

(7 * 0) + (2 * -2)

= 4

The vectors are only perpendicular when the inner product is equal to 0. Since it is equal to -4 in this case, the vectors are not perpendicular.

A -4; no

3 0

3 years ago

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PLZ HELP, AND PLZ EXPLAIN

shutvik [7]

Answer:

C

Step-by-step explanation:

To make it easy let's start by organizing our information :

AC=12 AND BD=8
ABCD is a rhombus
K and L are the midpoints of sides AD and CD
we notice that the rhombus ABCD is divided into four right triangles

What do you think of when you hear a right triangle ?

The pythagorian theorem !

AC and BD are khown so let's focus on them .

If we concentrated we can notice that AB and BD are cossing each other in the midpoints . why ?

Simply because they are the diagonals of a rhombus .

ow let's apply the pythagorian theorem :

(AC/2)² + (BD/2)² = BC²
6²+4²=52
BC²= 52⇒ $\sqrt{52}$ =BC

Now we khow that : AB=BC=CD=AD= $\sqrt{52}$

This isn't enough . Let's try to figure out a way to calculate the length of KL wich is the base of the triangle

KL is parallel to AC
k is the midpoint of AD and L of DC

I smell something . yes! Thales theorem

KL/AC=DL/DC=DK/AD WE4LL TAKE OLY ONE

KL/12= $\sqrt{52}$ /2* $\sqrt{52}$
KL/12=1/2⇒ KL=6

Now we have the length of the base kl

Now the big boss the height :

notice that you khow the length of KL
BD crosses kl from its midpoint and DL = $\sqrt{52}$ /2

What I want to do is to apply the pythgorian thaorem to khow the lenght of that small part that is not a part of the height of the triangle . I will call it D

DL²=(KL/2)²+D²
52/4= 9+ D²
D² = 52/4-9 +4 SO D=2

now the height of the trigle is H= BD-D= 8-2=6

NOw the area of the triangle is :

A=(KL*H)/2 ⇒ A= (6*6)/2=18

THE ANSWER IS 18 SQ.UN

5 0

3 years ago