In a survey of 420 people, 85% said they drink coffee

Svetradugi [14.3K]

The area ratio is 1:16 meaning that the old area is 1 while the new area is 16. So this is another way of saying "the area is multiplied by 16"

Take the square root of each part of the ratio of 1:16 and we get 1:4

So this is the scale factor. It tells us how the linear components of the circles relate to one another. If the circumference of the smaller circle is 1,then the larger circle has a circumference of 4.

Therefore, the circumference has been multiplied by 4

4 0

2 years ago

Complete the missing parts of the paragraph proof. Draw a perpendicular from P to AB. Label the intersection C. We are given tha

zvonat [6]

<span>1) We are given that PA = PB, so PA ≅ PB by the definition of the radius.

</span>When you draw a perpendicular to a segment AB, you take the compass, point it at A and draw an arc of size AB, then you do the same pointing the compass on B. Point P will be one of the intersections of those two arcs. Therefore PA and PB correspond to the radii of the arcs, which were taken both equal to AB, therefore they are congruent.

2) We know that angles PCA and PCB are right angles by the definition of perpendicular.

Perpendicularity is the relation between two lines that meet at a right angle. Since we know that PC is perpendicular to AB by construction, ∠PCA and ∠PCB are right angles.

3) PC ≅ PC by the reflexive property congruence.

The reflexive property congruence states that any shape is congruent to itself.

4) So, triangle ACP is congruent to triangle BCP by HL, and AC ≅ BC by CPCTC (corresponding parts of congruent triangles are congruent).

CPCTC states that if two triangles are congruent, then all of the corresponding sides and angles are congruent. Since ΔACP ≡ ΔBCP, then the corresponding sides AC and BC are congruent.

5) Since PC is perpendicular to and bisects AB, P is on the perpendicular bisector of AB by the definition of the perpendicular bisector.

<span>The perpendicular bisector of a segment is a line that cuts the segment into two equal parts (bisector) and that forms with the segment a right angle (perpendicular). Any point on the perpendicular bisector has the same distance from the segment's extremities. PC has exactly the characteristics of a perpendicular bisector of AB. </span>

6 0

2 years ago

Read 2 more answers

People tend to evaluate the quality of their lives relative to others around them (Frieswijk et al., 2004). In one study, resear

Alborosie

Answer:

Step-by-step explanation:

Hello!

Research.

n=9 frail elderly were interview and compared to a fictitious person who was worse off then the interviewee, a life-satisfaction score was determined for each person.

18, 23, 24, 22, 19, 27, 23, 26, 25

Assuming that the population average score is μ= 20, the researchers think that the elderly in the sample are more or less satisfied than others in the general population.

a. You have the information of one sample, assuming this sample has a normal distribution and each elderly interviewed is independent, then the t-test of choice is a one-sample t-test.

b. and c. If you say that the elderly are "more or less" satisfied than the others, this means that they are either as satisfied as to the general population or not satisfied as to the general population. Symbolically:

H₀: μ = 20

H₁: μ ≠ 20

This is a two-tailed test, meaning, you will have two critical regions.

d.

α: 0.05

Left critical value: $t_{n-1;/\alpha 2} = t_{8; 0.025}= -2.306$

Right critical value: $t_{n-1;1-\alpha /2} = t_{8;0.975} = 2.306$

e.

$t_{H_0}= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } } ~t_{n-1}$

X[bar]= 23

S= 3

$t_{H_0}= \frac{23-20}{\frac{3}{\sqrt{9} } }= 3$

f.

Considering that the calculated t-value is greater than the right critical value, the decision is to reject the null hypothesis, so using a significance level of 5% you can conclude that the average life-satisfaction score of the elderly is different than 20.

I hope it helps!

7 0

2 years ago

You can buy an 8-pack of paper towels for $7.92 or a 12-pack for $11.64. Which is the better buy?

goldfiish [28.3K]

Answer:

ill say the 8 pack

Step-by-step explanation:

8 0

1 year ago

The figure is made up of a cylinder and a cone.

Gnoma [55]

Answer:

51*pi or 160.221

Step-by-step explanation:

total volume = volume of a cone + volume of a cylinder

total volume = 1/3* pi*r^2* height(of cone) + pi* r^2 *height(of cylinder)

total volume = 1/3 * pi * 3^2 * 5 + pi * 3^2 * 4

total volume = 51*pi = 160.221

7 0

2 years ago