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3 years ago

If triangle ABC is similar to triangle DEF, which statement is true about the two triangles?

1 answer:

6 0

Two figures are said to be congruent when they have the same shape and size or if one object is a mirror image of the other object. The triangles ABC and DEF are congruent since they are similar. They have equal lengths of the sides ad the angles should as well be equal with the two triangles.

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The port of South Louisiana, located along 54 miles of the Mississippi River between New Orleans and Baton Rouge, is the largest

Ksenya-84 [330]

Answer:

a) 0.7287

b) 0.9663

c) 0.237

d) 3.65 tons of cargo per week or more that will require the port to extend its operating hours.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 4.5 million tons of cargo per week

Standard Deviation, σ = 0 .82 million tons

We are given that the distribution of number of tons of cargo handled per week is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P( port handles less than 5 million tons of cargo per week)

P(x < 5)

$P( x < 5) = P( z < \displaystyle\frac{5 - 4.5}{0.82}) = P(z < 0.609)$

Calculation the value from standard normal z table, we have,

$P(x < 5) =0.7287= 72.87\%$

b) P( port handles 3 or more million tons of cargo per week)

$P(x \geq 3) = P(z \geq \displaystyle\frac{3-4.5}{0.82}) = P(z \geq −1.82926)\\\\P( z \geq −1.82926) = 1 - P(z < -1.829)$

Calculating the value from the standard normal table we have,

$1 - 0.0337 = 0.9663 = 96.63\%\\P( x \geq 3) = 96.63\%$

c)P( port handles between 3 million and 4 million tons of cargo per week)

$P(3 \leq x \leq 4) = P(\displaystyle\frac{3 - 4.5}{0.82} \leq z \leq \displaystyle\frac{4-4.5}{0.82}) = P(-1.829 \leq z \leq -0.609)\\\\= P(z \leq -0.609) - P(z < -1.829)\\= 0.271-0.034 = 0.237= 23.7\%$

$P(3 \leq x \leq 4) = 23.7\%$

d) P(X=x) = 0.85

We have to find the value of x such that the probability is 0.85.

P(X > x)

$P( X > x) = P( z > \displaystyle\frac{x - 4.5}{0.82})=0.85$

$= 1 -P( z \leq \displaystyle\frac{x - 4.5}{0.82})=0.85$

$=P( z \leq \displaystyle\frac{x - 4.5}{0.82})=0.15$

Calculation the value from standard normal z table, we have,

$P( z \leq -1.036) = 0.15$

$\displaystyle\frac{x - 4.5}{0.82} = -1.036\\x = 3.65$

Thus, 3.65 tons of cargo per week or more that will require the port to extend its operating hours.

8 0

3 years ago

Dominic and Terrell plan to start their weekend backpacking trip on Friday at 4:20 P.M, and return home on Sunday at 5:40 A.M. H

Aleonysh [2.5K]

I think the answer is 4.20 hours and minutes planning the last road trip .

6 0

3 years ago

2.5 hours travelled and 187 distance traveled in miles ( I have to find the unit rate)

Elena L [17]

Answer:

The first one is 75 and the second one is 81

Step-by-step explanation:

put 187.5 into calculator then divide it by the bottom number/denominator in this case 2.5 and then you get 75

put 303.75 into calculator then divide it by the denominator or 3.75 and you get an answer of 81

so 81 miles per hour

I really hope this helps!

8 0

3 years ago

Read 2 more answers

Helpppp!! i’m willing to give all my points and brainliest, especially w explanation!

Rainbow [258]

Here are the basic rules for a right triangle:
One angle is always 90° or right angle.

The side opposite angle 90° is the hypotenuse.

The hypotenuse is always the longest side.

The sum of the other two interior angles is equal to 90°.

The other two sides adjacent to the right angle are called base and perpendicular.

a quick way to find angle 1, is just to look at the figure. there seems to be bisecting angles, so angle FCE and angle 1 are congruent. (meaning angle 1 is also 34 degrees)

hope this helps! lmk.

8 0

2 years ago

A typical acoustic guitar has a range of three octaves. When the guitar is tuned to "concert pitch," the range of frequencies fo

AfilCa [17]

Given a variable, x, the compound ineaquality representing the range from a to b inclusive of the variable is given by

$a\leqx\leqb$
where a is the least value and b is the greatest value.

Thus, given a variable f, representing the frequencies for the three octaves of a <span>typical acoustic guitar.
</span>
Where the range of the frequencies is between 82.4 Hertz and 659.2 Hertz inclusive.

The complex inequality, representing <span>the range of frequencies for a guitar tuned to "concert pitch"</span> is given by

$82.4\leq f\leq659.2$

6 0

3 years ago