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2 years ago

Point P is in the interior of ∠OZQ. If m∠OZQ = 125 and m∠OZP = 62, what is m∠PZQ?

Mathematics

1 answer:

aev [14]2 years ago

3 0

Answer:

Step-by-step explanation:

If point P is in the interior of ∠OZQ, then ∠OZQ = ∠OZP+∠PZQ. Given m∠OZQ = 125 and m∠OZP = 62, to get m∠PZQ, we will substitute the value of the angles given into the expression above as shown;

∠OZQ = ∠OZP+∠PZQ.

125 = 62 + ∠PZQ.

subtract 62 from both sides;

125 - 62 = 62 + ∠PZQ -62

63 = ∠PZQ

<em>Hence the angle m∠PZQ is 63°</em>

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Assuming that the Chinese population continues to grow at the same rate, how many years until the population reaches 1.5 billion

faltersainse [42]

Answer:

29 years

Step-by-step explanation:

The population of the Chinese people is 1.3 bn, and they grow at a rate of 0.49% per year. To get the number of years it requires to reach 1.5 bn, we use this method

after x years, the population will be

1.3 * 1.0049^x

so you just need to solve

1.3 * 1.0049^x = 1.5

1.0049^x = 1.5/1.3

x log 1.0049 = log(1.5/1.3)

x = log(1.5/1.3)/log(1.0049)

x = 0.062 / 0.002122

x = 29.25 years

Therefore, at the rate of 0.49%, the Chinese population of 1.3bn needs 29 years to clock 1.5 bn

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2 years ago

Workers have packed 1,400 glasses in 7 boxes. If they pack 3 more boxes, how many glasses will they have packed in all?

11111nata11111 [884]

1box = 1400/7 = 200

200×3=600

1400+600=2000

8 0

2 years ago

Read 2 more answers

One semester in a chemistry class, 14 students failed due to poor attendance, 23 failed due to not studying, 15 failed because t

BlackZzzverrR [31]

Answer:

(a) 16 students failed for exactly two of the three reasons.

(b) 7 students failed because of poor attendance and not studying but not because of not turning in assignments.

(c) 14 students failed because of exactly one of the three reasons.

(d) 3 students failed because of poor attendance and not turning in assignments but not because of not studying.

Step-by-step explanation:

We are given that one semester in a chemistry class, 14 students failed due to poor attendance, 23 failed due to not studying, 15 failed because they did not turn in assignments, 9 failed because of poor attendance and not studying, 8 failed because of not studying and not turning in assignments, 5 failed because of poor attendance and not turning in assignments, and 2 failed because of all three of these reasons.

As shown in the diagram attached below, a Venn diagram represents the situation given in the question;

In the diagram below, 2 in represents purple color represents the number of students failed because of all three of these reasons.

7 represents the number of students who failed because of poor attendance and not studying but not due to not turning in assignments.

6 represents the number of students who failed because of not studying and not turning in assignments but not due to poor attendance.

3 represents the number of students who failed because of poor attendance and not turning in assignments but not due to not studying.

2 in red color represents the number of students who failed only due to poor attendance.

8 in red color represents the number of students who failed only due to not studying.

4 in red color represents the number of students who failed only due to not turning in assignments.

(a) The number of students who failed because of exactly two of the three reasons = 7 + 6 + 3 = 16 students.

(b) The number of students who failed because of poor attendance and not studying but not because of not turning in assignments = 9 - 2 = 7 students.

(c) The number of students who failed because of exactly one of the three reasons = 2 + 8 + 4 = 14 students.

(d) The number of students who failed because of poor attendance and not turning in assignments but not because of not studying = 5 - 2 = 3 students.

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2 years ago

To control pollination, pollen-producing flowers are often removed from the top of corn in a process called detasseling. The hou

____ [38]

Answer: <u>Last option</u>

$Z_ {13} = 0.5,\ Z_ {17} = 2.5$

Step-by-step explanation:

The z-scores give us information about how many standard deviations from the mean the data are. This difference can be negative, if the data are n deviations to the left of the mean, or it can be positive if the data are n deviations to the right of the mean.

To calculate the Z scores, we calculate the difference between the value of the data and the mean and then divide this difference by the standard deviation.

$Z = \frac{x- \mu}{\sigma}$ .

Where x is the value of the data, μ is the mean and σ is the standard deviation

In this case :

μ = 12 $/h

$\sigma$ = 2 $/h

We need to calculate the Z-scores for $x = 17$ and $x = 13$

Then for $x = 17$ :

$Z_{17} = \frac{17-12}{2}$ .

$Z_{17} = 2.5$

Then for $x = 13$ :

$Z_{13} = \frac{13-12}{2}$ .

$Z_{13} = 0.5$

Therefore the answer is:

$Z_ {13} = 0.5,\ Z_ {17} = 2.5$

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2 years ago

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this squared based pyramid is cut horizontally at a height of 15cm to leave this frustum base area=10cm

scoundrel [369]

Answer:

583.33 cm³

Step-by-step explanation:

From the image attached, the total height (H) of the pyramid is 30 cm, the height of the frustrum (h) = 15 cm, the Frustrum base = lower base = B = 10 cm . To find the length of the upper base (b), we use:

$\frac{b}{H-h}=\frac{B}{H}\\ b=(H-h)\frac{B}{H}\\b=(30-15)\frac{10}{30}=5\\b=5\ cm$

The volume of the frustrum is given by:

$V=\frac{1}{3}h(B_1+B_2+\sqrt{B_1B_2} )\\ Where\ B_1\ is \ the\ area \ of\ the\ upper\ base= 5cm*5cm=25cm^2\\B_1\ is \ the\ area \ of\ the\ lower\ base= 10cm*10cm=100cm^2\\V=\frac{1}{3}(10)(25+100+\sqrt{25*100} )=583.33\\V=583.33\ cm^3$

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2 years ago