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2 years ago

15

1. & 2. In the diagram below, points A, B, and C are collinear. Answer each of the following questions. The figure shown bel

ow is not drawn to scale, meaning you cannot determine your answers by using your ruler.

1 answer:

Lana71 [14]2 years ago

6 0

Answer:

a) $\overline{AB}$ = 8 in

b) When the length of AC = $6\frac{1}{2}$ in. and BC = $3\frac{1}{2}$ in. $\overline{AB}$ = 10 in

c) When the length of AB = 10.2 in. and BC = 3.7 in. $\overline {AC}$ = 6.5 in

d) When the length of AB = $4\frac{3}{4}$ in. and BC = $3\frac{1}{4}$ in. in. $\overline {BC}$ = $1\frac{1}{2}$ in

Step-by-step explanation:

a) When the length of AC = 5 in. and CB = 3 in. we have;

The length of $\overline {AB}$ = AC + CB (segment addition postulate)

Therefore;

$\overline{AB}$ = 5 in. + 3 in. = 8 in.

b) When the length of AC = $6\frac{1}{2}$ in. and BC = $3\frac{1}{2}$ in. we have;

The length of $\overline {AB}$ = AC + CB (segment addition postulate)

Therefore;

$\overline{AB}$ = $6\frac{1}{2}$ in.+ $3\frac{1}{2}$ in. = 10 in.

c) When the length of AB = 10.2 in. and BC = 3.7 in. we have;

The length of $\overline {AC}$ = AB - BC (converse of the segment addition postulate)

Therefore;

$\overline {AC}$ = 10.2 in.+ 3.7 in. = 6.5 in.

d) When the length of AB = $4\frac{3}{4}$ in. and BC = $3\frac{1}{4}$ in. in. we have;

The length of $\overline {BC}$ = AB - AC (converse of the segment addition postulate)

Therefore;

$\overline {BC}$ = $4\frac{3}{4}$ in. - $3\frac{1}{4}$ in.= $1\frac{1}{2}$ in.

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Tanya [424]

Answer:

radius =1.1618m

Step-by-step explanation:

circumference of circle =7.3m

2πr=7.3

r=7.3/(2π)=1.1618m

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2 years ago

Please explain the misleading

Ede4ka [16]

There are more compact cars (4*10 = 40) compared to trucks (2*10 = 20); however, the pictogram might make it appear that there are more trucks because the individual truck icon is larger compared to an individual compact car icon.

To anyone giving this image a quick glance, they may erroneously conclude that there are more trucks since their eye would notice the trucks first. Also, the person might think there are more trucks because bigger sizes tend to correspond to more proportion.

In real life, a truck is larger than a compact car, but the icons need to be the same size to have the figure not be misleading.

A very similar issue happens with the mid-size cars vs the compact cars as well. The three mid-size car icons span the same total width as the compact cars do, indicating that a reader might mistakenly conclude that there are the same number of mid-size cars compared to compact ones (when that's not true either).

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2 years ago

Karl drove 617.3 miles. For each gallon of gas, the car can travel 41 miles. Select a reasonable estimate of the number of gallo

Hatshy [7]

Answer:

The number of gallons of gas Karl used is 15 gallons.

Option (C) is correct.

Step-by-step explanation:

As given

Karl drove 617.3 miles.

For each gallon of gas, the car can travel 41 miles.

i.e

1 gallons = 41 miles

$1\ miles = \frac{1}{41}\ gallons$

Now find out for the 617.3 miles.

Thus

$617.3\ miles = \frac{617.3}{41}\ gallons$

$617.3\ miles = 15.1\ gallons$

$617.3\ miles = 15\ gallons\ (Approx)$

Therefore the number of gallons of gas Karl used is 15 gallons.

Option (C) is correct.

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3 years ago

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the e

I am Lyosha [343]

Answer:

(a) The proportion of tenth graders reading at or below the eighth grade level is 0.1673.

(b) The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.198, 0.260).

Step-by-step explanation:

Let <em>X</em> = number of students who read above the eighth grade level.

(a)

A sample of <em>n</em> = 269 students are selected. Of these 269 students, <em>X</em> = 224 students who can read above the eighth grade level.

Compute the proportion of students who can read above the eighth grade level as follows:

$\hat p=\frac{X}{n}=\frac{224}{269}=0.8327$

The proportion of students who can read above the eighth grade level is 0.8327.

Compute the proportion of tenth graders reading at or below the eighth grade level as follows:

$1-\hat p=1-0.8327$

$=0.1673$

Thus, the proportion of tenth graders reading at or below the eighth grade level is 0.1673.

(b)

the information provided is:

<em>n</em> = 709

<em>X</em> = 546

Compute the sample proportion of tenth graders reading at or below the eighth grade level as follows:

$\hat q=1-\hat p$

$=1-\frac{X}{n}$

$=1-\frac{546}{709}$

$=0.2299\\\approx 0.229$

The critical value of <em>z</em> for 95% confidence interval is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

Compute the 95% confidence interval for the population proportion as follows:

$CI=\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

$=0.229\pm 1.96\times \sqrt{\frac{0.229(1-0.229)}{709}}\\=0.229\pm 0.03136\\=(0.19764, 0.26036)\\\approx (0.198, 0.260)$

Thus, the 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.198, 0.260).

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2 years ago

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qaws [65]

Answer:

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Step-by-step explanation:

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