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2 years ago

Line SU bisects angle RST. Which statement is NOT true?

Mathematics

2 answers:

bearhunter [10]2 years ago

8 0

Answer : The incorrect option is, (A) ∠RST = ∠RSU

Step-by-step explanation :

As we are given that, line SU bisects angle RST and SPUQ is a rhombus.

First we have to determine that ΔSQU and ΔSPU are congruent triangles.

Proof:

Side SU = Side SU (common side)

∠SQU = ∠SPU (In rhombus opposite angle are always equal)

∠RSU = ∠UST (angle bisector)

ΔSQU ≅ ΔSPU (By ASA congruency)

So, Side PS = Side QS

∠RST = ∠RSU this option is wrong because $\angle RSU=\frac{1}{2}\angle RST$

Thus, the incorrect option is, (A) ∠RST = ∠RSU

Lorico [155]2 years ago

5 0

In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.
so the answer is B

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Tags are placed to the left leg and right leg of a bear in a forest. Let A1 be the event that the left leg tag is lost and the e

Komok [63]

Answer:

0.75 = 75% probability that exactly one tag is lost, given that at least one tag is lost

Step-by-step explanation:

Independent events:

If two events, A and B, are independent, then:

$P(A \cap B) = P(A)*P(B)$

Conditional probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: At least one tag is lost

Event B: Exactly one tag is lost.

Each tag has a 40% = 0.4 probability of being lost.

Probability of at least one tag is lost:

Either no tags are lost, or at least one is. The sum of the probabilities of these events is 1. Then

$p + P(A) = 1$

p is the probability none are lost. Each one has a 60% = 0.6 probability of not being lost, and they are independent. So

p = 0.6*0.6 = 0.36

Then

$P(A) = 1 - p = 1 - 0.36 = 0.64$

Intersection:

The intersection between at least one lost(A) and exactly one lost(B) is exactly one lost.

Then

Probability at least one lost:

First lost(0.4 probability) and second not lost(0.6 probability)

First not lost(0.6 probability) and second lost(0.4 probability)

$P(A \cap B) = 0.4*0.6 + 0.6*0.4 = 0.48$

Find the probability that exactly one tag is lost, given that at least one tag is lost (write it up to second decimal place).

$P(B|A) = \frac{0.48}{0.64} = 0.75$

0.75 = 75% probability that exactly one tag is lost, given that at least one tag is lost

8 0

2 years ago

The square shown has a perimeter of 32 units. The square is rotated about line k.

Bad White [126]

A cylinder with a circumference of about 50 units is formed.

Step-by-step explanation:

Step 1:

The perimeter of the square is 32 units. The perimeter of a square is given by 4 times its side length.

$(4) sidelength = 32, sidelength = \frac{32}{4} = 8.$

So the side length of the square is 8 units.

If a square is rotated a cylinder will be formed. So the options with a cone are wrong as a cone is formed when a triangle is rotated.

Step 2:

To calculate the circumference of the cylinder, we multiply 2π with the radius. The radius is the same as the side length of the square. So r is 8 units.

The circumference of the cylinder $= 2\pi r = (2) (3.1415)(8) = 50.264.$

So the circumference of the cylinder is approximately equal to 50 units so the answer is the fourth option, a cylinder with a circumference of about 50 units.

4 0

2 years ago

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1. Keeping in mind the rules for significant digits, if we multiply 11.55 by 2.5, how many significant digits are we allowed to

kherson [118]

1. For multiplication and division), we first compare the number of significant figure (let's call it SF later in the problem) that the factors have. The product will have the least numbers between them. So, for the case of 11.55 x 2.5, 11.55 has 4 SF while 2.5 has 2. So we choose the smallest which is 2 for this case. Hence, the answer is B. 2. Using the same rules as mentioned in Item 1, we first compare the number of SF in the numbers give. 975.0321 has 7 SF while 0.0003 has 1 (all zeroes not following a counting number are not significant). We now solve for the quotient and round it off to 1 SF. (975.0321/0.0003) = 3250107. Rounding it off, we have 3000000 or 3 x 10⁶. Thus, the answer is D. 3. The rules for multiplication still apply even for more than two factors. So, let's first take note of the SF present in each factor as shown below. 0.00147 = 3 SF 8.314 = 4 SF 7.100 = 4 SF (zeroes after a counting number in the decimal place are considered significant) From this, we can see that the product must round off to 3 SF. Multiplying the three numbers, we have 0.00147 x 8.314 x 7.100 = 0.086773218 So, the product rounded off to 3 SF is 0.0868 or 8.68 x 10⁻². So, the answer must be C.

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2 years ago

A shipment of 7 television sets contains 2 defective sets. A hotel makes a random purchase of 3 of the sets. If x is the number

serg [7]

Answer:

The probability distribution is

X : 0 1 2

f(X) : 2/7 4/7 1/7

Step-by-step explanation:

Let x is the number of defective sets purchased by the hotel.

Total number of television sets = 7

Total number of defective television sets = 2

Since there are 2 defective television sets and hotel purchase 3 sets, So, X=0,1,2.

If X=0,

$P(X=0)=\frac{^5C_3}{^7C_3}=\frac{10}{35}=\frac{2}{7}$

If X=1,

$P(X=1)=\frac{^5C_2\cdot ^2C_1}{^7C_3}=\frac{10\cdot 2}{35}=\frac{4}{7}$

If X=2,

$P(X=2)=\frac{^5C_1\cdot ^2C_2}{^7C_3}=\frac{5\cdot 1}{35}=\frac{1}{7}$

The probability distribution is

X : 0 1 2

f(X) : 2/7 4/7 1/7

The probability histogram is shown below.

3 0

2 years ago

Jason places a mirror on the ground 40 feet from the base of a tree. He walks backwards until he can see the top of the tree in

MakcuM [25]

Given that the angle of incidence is equal to the angle of reflection, we can state tha the angle formed by the eyes of Jason with the mirror is equal to the angle formeb by the top of the three with the same mirror.

Then, you can write this similarity equation:

[height of the eyes of Jason] / [distance from the poistion of Jason to the image on the mirror] = [height of the tree / distance from the mirror to the base of the tree]

6feet / 8feet = x/40feet

x = 40feet *[6/8] = 30 feet.

Answer: 30 feet.

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2 years ago

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