Complete the proof and rewrite the statements.
Given :
ABC is an isosceles triangle in which AC = BC
CD ⊥ AB
Prove : AD = BD
Statement Reason
i) AC = BC Given
ii) ԼCDA = _______ Right angle
iii) CD = CD Common side
iv) ΔADC ≅ Δ BDC _______ test
v) AD = BD CPCT

Answer:

1.33

Step-by-step explanation:

62 can only be subtracted from 82 once. So 82.46-62 would be 20.46. Since you can't subtract anymore you put a decimal point. 62x3=186 and 20.46-186=1.86 and you can subtract 186-186=0.

Answer:

z=0

50%

Step-by-step explanation:

Answer:

a) 0.18 = 18% probability a randomly chosen business customer flying with Global is on a jumbo jet.

b) 0.3 = 30% probability a randomly chosen non-business customer flying with Global is on an ordinary jet.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

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

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

Question a:

Event A: Jumbo

Event B: Business

60% of its capacity is provided on jumbo jets.

This means that [tex]P(A) = 0.6[/tex]

On jumbo jets, 30% of the passengers are on business

This means that [tex]P(B|A) = 0.3[/tex]

Desired probability:

We want to find [tex]P(A \cap B)[/tex], so:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(A \cap B) = P(B|A)P(A) = 0.6*0.3 = 0.18[/tex]

0.18 = 18% probability a randomly chosen business customer flying with Global is on a jumbo jet.

b) What is the probability a randomly chosen non-business customer flying with Global is on an ordinary jet?

Event A: Ordinary

Event B: Non-business

60% of its capacity is provided on jumbo jets.

So 100 - 60 = 40% are ordinary, which means that [tex]P(A) = 0.4[/tex]

On ordinary jets 25% of the passengers are on business.

So 100 - 25 = 75% are non-business, that is [tex]P(B|A) = 0.75[/tex]

Desired probability:

We want to find [tex]P(A \cap B)[/tex], so:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(A \cap B) = P(B|A)P(A) = 0.75*0.4 = 0.3[/tex]

0.3 = 30% probability a randomly chosen non-business customer flying with Global is on an ordinary jet.

Answer:

Below

Step-by-step explanation:

You can use this formula to calculate the volume of an object

     Volume = Mass / Density

Plugging everything in...

     Volume = 800g / 8 g/cm^3

                   = 100 cm^3

Hope this helps!

The volume of the boulder will be equal to 100 cubic centimeters.

A substance's density is defined as its mass per unit volume. The density in other words can be defined as the ratio of mass and volume. Its unit will be kg per cubic meter.

The volume is defined as the space occupied by an object in three-dimensional geometry.

It is given that an 800g boulder has a density of 8g/cm^3. The volume will be calculated by using the formula below:-

Volume = Mass / Density

Volume = 800g / 8 g/cm^3

             = 100 cm^3

Therefore, the volume of the boulder will be equal to 100 cubic centimeters.

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This question is solved applying the formula of the area of the rectangle, and finding it's width. To do this, we solve a quadratic equation, and we get that the cardboard has a width of 1.5 feet.

Area of a rectangle:

The area of rectangle of length l and width w is given by:

[tex]A = wl[/tex]

w(2w + 3) = 9

From this, we get that:

[tex]l = 2w + 3, A = 9[/tex]

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

In this question:

[tex]w(2w+3) = 9[/tex]

[tex]2w^2 + 3w - 9 = 0[/tex]

Thus a quadratic equation with [tex]a = 2, b = 3, c = -9[/tex]

Then

[tex]\Delta = 3^2 - 4(2)(-9) = 81[/tex]

[tex]w_{1} = \frac{-3 + \sqrt{81}}{2*2} = 1.5[/tex]

[tex]w_{2} = \frac{-3 - \sqrt{81}}{2*2} = -3[/tex]

Width is a positive measure, thus, the width of the cardboard is of 1.5 feet.

Another similar problem can be found at https://brainly.com/question/16995958

Answer:

y=0.5

Step-by-step explanation:

14y-6(y-3)=22

14y-6y+18=22

8y+18=22

8y=4

y=0.5

Then we check our work...

14(0.5)-6((0.5)-3)=22

7-6(-2.5)=22

7+15=22

7+15 does equal 22, so this solution is correct.

The answer is d: As x gets closer to 3, the value of g gets closer to 4.

The limit of a function h of x as  x approaches the value a, written as [tex]\lim_{x \to a} h(x) = L[/tex] is the value the function h(x) approaches as x tends to the value "a", written as x → a. In this case, L.

Given the domain and range for function g are D(−∞, ∞) and R(−∞, ∞) and that the limit as x approaches 3 of the function g of x equals 4.

This implies that as x gets closer and closer to 3, the value of g gets closer and closer to 4.

Since the value g gets closer to is 3 as x gets closer to 4, we can write that the limit as x approaches 3 of the function g of x equals 4.

we can write this as

[tex]\lim_{x \to 3} g(x) = 4[/tex]

So, as x gets closer to 3, the value of g gets closer to 4.

So, the answer is d: As x gets closer to 3, the value of g gets closer to 4.

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Step-by-step explanation:

sec⁴B - sec²B = sec²B(sec²B - 1)

= (1 + tan²B)(tan²B)

= tan⁴B + tan²B

= Right-hand side (Proven)

Answer:

Since, mean of 200 items was 50 and number of items =200

So, mean =50

Also, we know mean = number of itemssum of items

∴50=200sum of items

Sum of items = 200×50=10000

Later on, it was discovered that the two items were misread as 92 and 8 instead of 192 and 88 respectively

Then  misread         instead         Correct item

             92                   192              192-92=100

              8                     88               88-8=80

∴ Correct sum of items =10000+180=10180

∴ Correct mean = number of items/sum of items

=10180/200 =50.9

Answer:

Hello,

203.6

Step-by-step explanation:

Sum of the item first= 50*200=10000

new sum is 10000+(192-92)+(88-8)=10180

New mean=10180/200=50.9

Answer:

The critical value is [tex]T_c = 2.5706[/tex].

The 90% confidence interval for the average net change in a student's score after completing the course is (9.04, 18.30).

Step-by-step explanation:

Before building the confidence interval, we need to find the sample mean and the sample standard deviation:

Sample mean:

[tex]\overline{x} = \frac{6+16+19+12+15+14}{6} = 13.67[/tex]

Sample standard deviation:

[tex]s = \sqrt{\frac{(6-13.67)^2+(16-13.67)^2+(19-13.67)^2+(12-13.67)^2+(15-13.67)^2+(14-13.67)^2}{5}} = 4.4121[/tex]

Confidence interval:

We have the standard deviation for the sample, so the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 6 - 1 = 5

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.5706, that is, the critical value is [tex]T_c = 2.5706[/tex]

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.5706\frac{4.4121}{\sqrt{6}} = 4.63[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 13.67 - 4.63 = 9.04.

The upper end of the interval is the sample mean added to M. So it is 13.67 + 4.63 = 18.30.

The 90% confidence interval for the average net change in a student's score after completing the course is (9.04, 18.30).

Answer:

16[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Answer:

16.25

Step-by-step explanation:

first do 12 -5 = 7. then 7/4 = 1.75 then 9+1.75 = 10.75 and finally 27-10.75= 16.25

Answer:

X = 28/3, or 9 1/3 or 9.3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

4 ther are 4 line symmetery

Answer:

two lines of symmetry

(a vertical and a horizontal)

Answer:

16

Step-by-step explanation:

hope this helps :)))))

Answer:

65% of 27.69 is 18.

Step-by-step explanation:

Formula = Number x 100

Percent = 18 x 100

65 = 27.69

Following shows the steps on how to derive this formula

Step 1: If 65% of a number is 18, then what is 100% of that number? Setup the equation.

18

65% = Y

100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

65Y = 18 x 100

65Y = 1800

Y = 1800

100 = 27.69

Answer:

45x=-44

x=-44/45

Step-by-step explanation:

is this a free question?

Answer:

what's the problem!?......

angle CDT is the opposite angle of ADN

and the segment DF=FN, so AD= AN

and thats why angle FAN= angle FAD

here, Angle FAN =60,

therefore, FAD=60, and AFD = 90 so angle ADN must be 30 degree

and the opposite of ADN is CDT, and the opposite angles are equal.

Hope u got it.

Answer:

±5i

Step-by-step explanation:

sqrt(-25)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(-1) sqrt(25)

±i 5

±5i

Step-by-step explanation:

Answer: D) 2 ohms and 2 ohms

Answer:

width: 3

Step-by-step explanation:

Given a length l and a width w, we can say that the perimeter is equal to

2 * l + 2 * w. Then, we also know that the perimeter is 27 plus its width, so

2 * l + 2 * w = 27 + w

and the length is 4 times its width, so length = 4 * width = l = 4 * w

We therefore have the two equations

2 * l + 2 * w = 27 + w

l = 4 * w

What we can do is plug 4* w for l in the first equation and solve from there. We thus have

2 * ( 4 * w) + 2 * w = 27 + w

8 * w + 2 * w = 27 + w

10 * w = 27 + w

subtract w from both sides to isolate the w and its coefficient

9 * w = 27

divide both sides by 9 to isolate w

w = 3

l = 4 * w = 12

Therefore, the width is 3 and the length is 12

Answer:

A

Step-by-step explanation:

f(x) = 1/(x-3)+7

f(x)-7=1/(x-3)

x=1/(f(x)-7)+3

f^-1(x)=1/(x-7)+3, where x≠7

The correct answer is option (a)  [tex]f^{-1}(x)= \frac{1}{x-7} +3[/tex] where [tex]x\neq 7[/tex].

The domain of a function is the complete set of possible values of the independent variable

Given [tex]f^{}(x)= \frac{1}{x-3} +7[/tex]

Let

[tex]y= \frac{1}{x-3} +7[/tex]

⇒y-7= 1/x-3

⇒x-3 =1/y- 7

⇒ [tex]x= \frac{1}{y-7} +3[/tex]

hence option a is correct

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Answer:

Abdul's tank can hold 27 gallons of gas.

Step-by-step explanation:

Given that Abdul's gas tank is 1/3 full, and after he buys 12 gallons of gas, it is 7/9 full, to determine how many gallons can Abdul's tank hold the following calculation must be performed:

1/3 = 0.3333

7/9 = 0.7777

0.777 - 0.333 = 0.444

0.444 = 12

1 = X

12 / 0.444 = X

27 = X

Therefore, Abdul's tank can hold 27 gallons of gas.

The 95% confidence interval is (8.3%,17.7%), and the correct option is C.

------------------------------------------

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

------------------------------------------

13% of a sample of 200 students do not like ice cream.

This means that [tex]\pi = 0.13, n = 200[/tex]

------------------------------------------

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

------------------------------------------

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.13 - 1.96\sqrt{\frac{0.13*0.87}{200}} = 0.083[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.13 + 1.96\sqrt{\frac{0.13*0.87}{200}} = 0.177[/tex]

------------------------------------------

As a percentage:

Thus, the 95% confidence interval is (8.3%,17.7%), and the correct option is C.

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Step-by-step explanation:

28000 ÷ 100

=280

280 × 5

=1400

Step-by-step explanation:

jlejej

are u using chrome os

Answer:

90

Step-by-step explanation:

Angle Formed by Two Chords= 1/2(SUM of Intercepted Arcs)

105 = 1/2 (120+x)

210 = 120+x

Subtract 120 from each side

210-120 = x

90 =x

The value of  Intercepted Arcs x will be 90. so option C is correct.

If the considered circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting(dividing in two equal parts) the line segment AB.

Or

|AC| = |CB|

Angle Formed by Two Chords= 1/2 (Sum of Intercepted Arcs)

105 = 1/2 (120+x)

210 = 120+x

Subtract 120 from each side;

210-120 = x

90 =x

Hence, the value of  Intercepted Arcs x will be 90. so option C is correct.

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Mercury will sink

(sorry if Im wrong)

Answer:

Sink.

Step-by-step explanation:

Mercury is a quicksilver and hence will sink.