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2 years ago

Which pair of triangles can be proven congruent by the HL theorem

Mathematics

2 answers:

Lelu [443]2 years ago

7 0

Answer: Third pair

Step-by-step explanation:

The HL theorem says that if the hypotenuse and a leg of one right triangle are equal to the hypotenuse and a leg of another right triangle, then the triangles are said to be congruent.

From the given pictures only third pair of triangles have hypotenuse and one leg are equal.

Then by HL theorem, the triangles in third pair are congruent.

lys-0071 [83]2 years ago

4 0

third one is your answer

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6785∆4 is a 6-digit number with one of its digit represented by ∆. What can be the value of ∆ if 6785∆4 is divisible by 9 ? pls

GREYUIT [131]

Answer: The /\ is 6. The number is 6.

Explanation: 678564 ÷ 9 = 75396

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2 years ago

The heights of students at a college are normally distributed with a mean of 175 cm and a standard deviation of 6 cm. One might

frosja888 [35]

Answer:

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 175cm

Standard deviation = 6 cm

Percentage of students below 163 cm

163 = 175 - 2*6

So 163 is two standard deviations below the mean.

By the Empirical rule, 95% of the heights are within 2 standard deviations of the mean. The other 100-95 = 5% are more than 2 standard deviations of the mean. Since the normal distribution is symmetric, 2.5% of them are more than 2 standard deviations below the mean(so below 163cm) and 2.5% are more than two standard deviations above the mean.

2.5% of the students have heights less than 163cm.

Out of 1000

0.025*1000 = 25

25 is the answer

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2 years ago

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Tiffany put a $1550 item on layaway by making a 20% down payment and agreeing to pay $120 a month. How many months sooner would

amid [387]

1550*0.8=1240

1240/120 = approximately 11 months to pay off

1240/180=approximately 7 months to pay off

11-7 =4

so it would be paid off 4 months sooner, so C is the answer

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2 years ago

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What does x and y equal to 2x-3y=-7 2x+y=13

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Step-by-step explanation:

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2 years ago

Assume that the ages for first marriages are normally distributed with a mean of 26 years and a standard deviation of 4 years. W

Snowcat [4.5K]

Answer:

0.7743

Step-by-step explanation:

Mean of age = u = 26 years

Standard Deviation = $\sigma$ = 4 years

We need to find the probability that the person getting married is in his or her twenties. This means the age of the person should be between 20 and 30. So, we are to find P( 20 < x < 30), where represents the distribution of age.

Since the data is normally distributed we can use the z distribution to solve this problem. The formula to calculate the z score is:

$z=\frac{x-u}{\sigma}$

20 converted to z score will be:

$z=\frac{20-26}{4}=-1.5$

30 converted to z score will be:

$z=\frac{30-26}{4}=1$

So, now we have to find the probability that the z value lies between -1.5 and 1.

P( 20 < x < 30) = P( -1.5 < z < 1)

P( -1.5 < z < 1 ) = P(z < 1) - P(z<-1.5)

From the z-table:

P(z < 1) = 0.8413

P(z < -1.5) =0.067

So,

P( -1.5 < z < 1 ) = 0.8413 - 0.067 = 0.7743

Thus,

P( 20 < x < 30) = 0.7743

So, we can conclude that the probability that a person getting married for the first time is in his or her twenties is 0.7743

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2 years ago