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julia-pushkina [17]
2 years ago
5

Are the triangles similar? explain. please help

Mathematics
2 answers:
grin007 [14]2 years ago
5 0

Answer:

The triangles are similar.

Step-by-step explanation:

The reason for this is because they both share two pairs of angles that are the same: 40 degrees and 60 degrees. If these are equal, then that must mean the third angle for both triangles is also the same, making both triangles equal in proportion. Therefore, they must be similar.

MrRa [10]2 years ago
5 0

Answer:

Yes

Step-by-step explanation:

<u>(i) By AA similarity</u>

  • Both have two equal angles, 40° and 60°, therefore they can be defined as similar by AA similarity

<u>(ii) By SSS similarity</u>

  • AB/DC = 32/40 = 4/5
  • BC/EF = 24/30 = 4/5
  • AC/DF = 36/45 = 4/5
  • As the ratio of the sides of both triangles are equal, they are defined as similar by SSS similarity
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dsp73

Answer:

There are 60 total questions on the course exam.

Step-by-step explanation:

Given that:

Number of questions finished by Jasmine = 12

Percentage shown on the bar = 20%

The total number of questions will be 100%, therefore, 20% of the questions are equal to 12.

Let,

x be the total number of questions on the course exam

20% of x = 12

\frac{20}{100}x=12\\0.2x=12

Dividing both sides by 0.2

\frac{0.2x}{0.2}=\frac{12}{0.2}\\x=60

Hence,

There are 60 total questions on the course exam.

8 0
2 years ago
You recently took a statistics exam in a large class. The instructor tells the class that the scores were Normally distributed,
Lunna [17]

Answer:

b. the area to the right of 2

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X, which is also the area to the left of Z. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X, which is the area to the right of Z.

In this problem:

X = 96, \mu = 72, \sigma = 12

Z = \frac{X - \mu}{\sigma}

Z = \frac{96 - 72}{12}

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P(Z > 2), which is the area to the right of 2.

5 0
3 years ago
A huge ice glacier in the Himalayas initially covered an area of 454545 square kilometers. Because of changing weather patterns,
guajiro [1.7K]

We have been given that a huge ice glacier in the Himalayas initially covered an area of 45 square kilo-meters. The relationship between A, the area of the glacier in square kilo-meters, and t, the number of years the glacier has been melting, is modeled by the equation A=45e^{-0.05t}.

To find the time it will take for the area of the glacier to decrease to 15 square kilo-meters, we will equate A=15 and solve for t as:

15=45e^{-0.05t}

\frac{15}{45}=\frac{45e^{-0.05t}}{45}

\frac{1}{3}=e^{-0.05t}

Now we will switch sides:

e^{-0.05t}=\frac{1}{3}

Let us take natural log on both sides of equation.

\text{ln}(e^{-0.05t})=\text{ln}(\frac{1}{3})

Using natural log property \text{ln}(a^b)=b\cdot \text{ln}(a), we will get:

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-0.05t=\text{ln}(\frac{1}{3})

t=\frac{\text{ln}(\frac{1}{3})}{-0.05}

t=\frac{\text{ln}(\frac{1}{3})\cdot 100}{-0.05\cdot 100}

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t=-(0-\text{ln}(3))\cdot 20

t=20\text{ln}(3)

Therefore, it will take 20\text{ln}(3) years for area of the glacier to decrease to 15 square kilo-meters.

6 0
3 years ago
Round 80531 to the nearest thousand.
Iteru [2.4K]
That would be 8,1000
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3 years ago
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