1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mars1129 [50]
3 years ago
13

Which postulate proves the two triangles congruent?

Mathematics
1 answer:
lorasvet [3.4K]3 years ago
3 0

Answer:

B) SAS

Step-by-step explanation:

Notice that there are two pairs of congruent sides, AC is congruent with ZX, and BC is congruent with YZ. Since there's one angle in each triangle that's congruent to each other, we can say B is the only true answer.

You might be interested in
The amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and standard deviation 13 mL. Supp
andreyandreev [35.5K]

Answer:

(a) X ~ N(\mu=63, \sigma^{2} = 13^{2}).

    \bar X ~ N(\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}).

(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is 0.0398.

(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is 0.2512.

(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.

Step-by-step explanation:

We are given that the amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and a standard deviation of 13 mL.

Suppose that 43 randomly selected people are observed pouring syrup on their pancakes.

(a) Let X = <u><em>amount of syrup that people put on their pancakes</em></u>

The z-score probability distribution for the normal distribution is given by;

                      Z  =  \frac{X-\mu}{\sigma}  ~ N(0,1)

where, \mu = mean amount of syrup = 63 mL

            \sigma = standard deviation = 13 mL

So, the distribution of X ~ N(\mu=63, \sigma^{2} = 13^{2}).

Let \bar X = <u><em>sample mean amount of syrup that people put on their pancakes</em></u>

The z-score probability distribution for the sample mean is given by;

                      Z  =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \mu = mean amount of syrup = 63 mL

            \sigma = standard deviation = 13 mL

            n = sample of people = 43

So, the distribution of \bar X ~ N(\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}).

(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < X < 62.8 mL)

   P(61.4 mL < X < 62.8 mL) = P(X < 62.8 mL) - P(X \leq 61.4 mL)

  P(X < 62.8 mL) = P( \frac{X-\mu}{\sigma} < \frac{62.8-63}{13} ) = P(Z < -0.02) = 1 - P(Z \leq 0.02)

                                                           = 1 - 0.50798 = 0.49202

  P(X \leq 61.4 mL) = P( \frac{X-\mu}{\sigma} \leq \frac{61.4-63}{13} ) = P(Z \leq -0.12) = 1 - P(Z < 0.12)

                                                           = 1 - 0.54776 = 0.45224

Therefore, P(61.4 mL < X < 62.8 mL) = 0.49202 - 0.45224 = 0.0398.

(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < \bar X < 62.8 mL)

   P(61.4 mL < \bar X < 62.8 mL) = P(\bar X < 62.8 mL) - P(\bar X \leq 61.4 mL)

  P(\bar X < 62.8 mL) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < \frac{62.8-63}{\frac{13}{\sqrt{43} } } ) = P(Z < -0.10) = 1 - P(Z \leq 0.10)

                                                           = 1 - 0.53983 = 0.46017

  P(\bar X \leq 61.4 mL) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } \leq \frac{61.4-63}{\frac{13}{\sqrt{43} } } ) = P(Z \leq -0.81) = 1 - P(Z < 0.81)

                                                           = 1 - 0.79103 = 0.20897

Therefore, P(61.4 mL < X < 62.8 mL) = 0.46017 - 0.20897 = 0.2512.

(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.

4 0
3 years ago
Maxine has a poster of her favorite ascertaining in her bedroom. The poster is 2.5 feet tall and 1.3 feet wide.what is the area
Archy [21]

Answer:

3.25 ft

Step-by-step explanation:

A = bh

A = (2.5)(1.3)

A = 3.25

4 0
3 years ago
Read 2 more answers
Helpppppppppppppppppppp
Tju [1.3M]

Answer:

the third option -24a^2b^12

Step-by-step explanation:

5 0
3 years ago
Between what two integers does 98 fall between
Nat2105 [25]

Answer: 99 and 97


Step-by-step explanation: If you make a numberline and write the numbers 90 through 100. 98 is in between integers 99 and 97.


8 0
3 years ago
What is the written form of 30.55
kirza4 [7]
Thirty and fifty-five hundredth.
4 0
3 years ago
Other questions:
  • Y=2x-1 4x+3y=27 what is the value of x
    5·1 answer
  • If the coordinates of point A are (8 , 0) and the coordinates of point B are (3 , 7), the y-intercept of is . If the coordinates
    5·1 answer
  • In Beijing in 2008, the Women's 3,000-meter Steeplechase became an Olympic event. What is this distance in kilometers? Quick ple
    7·1 answer
  • The label for a square box of pasta has an area of 16 in? What is the side length of the box?
    11·1 answer
  • Which inequality is true?
    9·2 answers
  • Which equation represents the line that is perpendicular to and passes through (-6,-9)?
    15·1 answer
  • .The diameter of a bike wheel is 27 inches. If the wheel makes 15 complete rotations, how far does the bike travel?
    7·1 answer
  • write the equaion of a line in slope-intercept form if the slope is 1/5 and the y-intercept is -9 explain please
    10·1 answer
  • Suppose f(x)=x^2 and g(x)=5x^2. Which steamy best compares the graph of g(x) with the graph of f(x)?
    10·1 answer
  • Which equation represents the line that is perpendicular to and passes through (-40,20)?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!