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2 years ago

Point Z is equidistant from the vertices of ΔTUV.

Mathematics

2 answers:

Naily [24]2 years ago

4 0

Answer:

option C. Angle BTZ Is-congruent-to Angle BUZ

Step-by-step explanation:

nadya68 [22]2 years ago

3 0

Answer:

option C. Angle BTZ Is-congruent-to Angle BUZ

Step-by-step explanation:

Point Z is equidistant from the vertices of triangle T U V

So, ZT = ZU = ZV

When ZT = ZU ∴ ΔZTU is an isosceles triangle ⇒ ∠TUZ=∠UTZ

When ZT = ZV ∴ ΔZTV is an isosceles triangle ⇒ ∠ZTV=∠ZVT

When ZU = ZV ∴ ΔZUV is an isosceles triangle ⇒ ∠ZUV=∠ZVU

From the figure ∠BTZ is the same as ∠UTZ

And ∠BUZ is the same as ∠TUZ

So, the statement that must be true is option C

C.Angle BTZ Is-congruent-to Angle BUZ

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Gabi is working on another backyard project. She is building a fence to keep deer out of her garden. One side of her garden is a

nydimaria [60]

Answer:

length: 14 feet , width: 43 feet, or

length: 86 feet, width: 7 feet

Both solutions are valid.

Explanation:

1. First assumption is that the shape of the fence is rectangular.

2. Second, assum the length parallel to the wall measure y feet, so the other two lengths, y, together with x will add up 100 feet

2x + y = 100

3. The, the area of the fence will be:

length × width = xy = 600

4. Now you have two equation with two variables which you can solveL

Solve for y in the first equation: y = 100 - 2x

Substitute the value of y into the second equation: x (100 - 2x) = 600

5. Solve the last equation by completing squares:

Distributive property: 100x - 2x² = 600
Divide both sides by - 1: 2x² - 100x = - 600
Divide both sides by 2: x² - 50x = -300
Add the sequare of the half of 50 to both sides: x² - 50x + 625 = 325
Factor the left side: (x - 25)² = 325
Square root both sides: x - 25 = ± 18.028

Clear x: x = 25 ± 18.028
x = 43.028 ≈ 43 or x = 6.972 ≈ 7

Both values are valid,

If x = 43 , then y = 600/43 = 14

If x = 7, then y = 600/7 = 86

Thus, the lenght and width of the fence may be:

43 feet (width) and 14 feet (length), or

7 feet (width) and 86 feet (length).

3 0

2 years ago

A salesman normally makes a sale (closes) on % of his presentations. Assuming the presentations are independent, find the pro

Tamiku [17]

Answer:

$(a)\ 0.0864$

$(b)\ 0.096$

$(c)\ 0.24$

$(d)\ 0.936$

Step-by-step explanation:

Given

$p \to$ close

$q \to$ fail to close

$p = 60\%$

$p = 0.60$

First, calculate the value of q

Using complement rule

$q = 1 - p$

$q = 1 - 0.60$

$q = 0.40$

So, we have:

$p = 0.60$ and $q = 0.40$

Solving (a): Fails to close on the 4th attempt

This means that he closes the first three attempts. The event is represented as: p p p q

So, we have:

$Pr = p*p*p*q$

$Pr = p^3*q$

$Pr = 0.60^3*0.40$

$Pr = 0.0864$

Solving (b): He closes for the first time on the 3rd attempt

This means that he fails to close the first two attempts. The event is represented as: q q p

So, we have:

$Pr = q * q * p$

$Pr = q^2 * p$

$Pr = 0.40^2 * 0.60$

$Pr = 0.096$

Solving (c): First he closes is his 2nd attempt

This means that he fails to close the first. The event is represented as: q p

So, we have:

$Pr = q * p$

$Pr = 0.40 * 0.60$

$Pr = 0.24$

Solving (d): The first he close is one of his 3 attempts

To do this, we make use of complement rule

The event that he does not close any of his first three attempts is: q q q

The probability is:

$Pr = q*q*q$

$Pr = q^3$

The opposite is that the first he closes is one of the first three

So, we have:

$Pr' = 1- Pr$ --- complement rule

$Pr' = 1- q^3$

$Pr' = 1- 0.40^3$

$Pr' = 1- 0.064$

$Pr' = 0.936$

4 0

2 years ago

Which statement correctly describes the slope of the linear function that is represented by the data in the table? x y 8 –8 8 –4

spin [16.1K]

Answer:

Step-by-step explanation:

slope=change in y/change in x

one way is t pick 2 points, (x1,y1) and (x2,y2)

the slope is (y2-y1)/(x2-x1)

pick some points

(8,4) and (8,0)

slope=(0-4)/(8-8)=-4/0=undefined

the slope is undefined

there is no slope.

5 0

2 years ago

Read 2 more answers

a sports statistician claim that the mean winning times for boston marathon women's open division champions is at least 2.68 hou

GenaCL600 [577]

Answer:

We conclude that the mean winning times for Boston marathon women's open division champions is at least 2.68 hours.

Step-by-step explanation:

We are given that a sports statistician claim that the mean winning times for Boston marathon women's open division champions is at least 2.68 hours.

The mean winning time of a sample of 30 randomly selected Boston marathon women's open division champions is 2.60 hours. assume the population standard deviation is 0.32 hours.

Let $\mu$ = mean winning times for Boston marathon women's open division champions.

So, Null Hypothesis, $H_0$ : $\mu\geq$ 2.68 hours {means that the mean winning times for Boston marathon women's open division champions is at least 2.68 hours}

Alternate Hypothesis, $H_A$ : p < 2.68 hours {means that the mean winning times for Boston marathon women's open division champions is less than 2.68 hours}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean winning time = 2.60 hours

$\sigma$ = population standard deviation = 0.32 hours

n = sample of women's open division champions = 30

So, test statistics = $\frac{2.60-2.68}{\frac{0.32}{\sqrt{30} } }$

= -1.37

The value of z test statistics is -1.37.

Now, P-value of the test statistics is given by following formula;

P-value = P(Z < -1.37) = 1 - P(Z $\leq$ 1.37)

= 1 - 0.9147 = 0.0853

Since, P-value of the test statistics is more than the level of significance as 0.0853 > 0.05, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the mean winning times for Boston marathon women's open division champions is at least 2.68 hours.

6 0

2 years ago

Rational number 3 by 40 is equals to

kkurt [141]

Answer:

6/80, 9/120, 12/160 etc

8 0

2 years ago

Read 2 more answers