Point M is the midpoint of PQ, and LM is the perpendicular bisector of PQ. Write a two-column proof to show that LP = LQ.

Answer: 8/3

Step-by-step explanation:

In this equation, x=-2

so

f(-2)=-1/6 (1/4)^(-2)

(1/4)^(-2)=4^2=16

f(-2)=-1/6 16

I am going to assume that it's (1/6)*(1/4)^x meaning:

f(-2)=16/6

=8/3

I hope I assumed correctly.

Answer:

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

Given function:

Find f(-2), by plugging in the value of x:

The statement "let c and d be disjoint compact subspaces of the Hausdorff space x and then there exist disjoint open sets u and v containing c and d, respectively." is proved.

Here we have given the let A and B be disjoint compact subspaces of the Hausdorff space X.

And we have to prove the statement.

According to the given question, let us consider that x be an arbitrary coordinate of A and here the points of x isn't in Y because A and B are disjoint.

Then according to Lemma 26.4 disjoint open sets Ux and Vx such that x Î Ux and Ux contain B.

Here the collection {Ux} is a covering of A by sets open in X.

And the finite collection of them {U1, ..,Un} covers A because A is compact.

Here the open set U = U1 U....U Un contains A and it is disjoint from

V = V1 I.....I Vn that contains B because it's the finite intersection of the corresponding open sets containing.

Therefore, here there exists disjoint open sets U and V containing A and B, respectively.

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The upper control limit is 16.4 if our desired confidence interval is 99.73%.

In statistics, a confidence interval describes the likelihood that a population parameter will fall between a set of values for a given percentage of the time.

Given 131 population

Standard deviation = 5

sample size = 11.

mean   = 131/11 = 11.9.

Determine the upper control limit if desired confidence interval is 99.73%

Confidence interval = sample mean ± margin of error

Upper limit  = sample mean + margin of error.

Margin of error = z* * population of standard deviation/[tex]\sqrt{n}[/tex]

Margin of error = 3.00 * 5/[tex]\sqrt{11}[/tex].

Value of z* for 99.73% confidence interval  is 3.00.

So margin of error = 4.5.

Upper limit  = 11.9 + 4.5

Upper limit  = 16.4

If we want a confidence level of 99.73%, the top control limit is 16.4.

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The required next term at the end of the sequence is 43.

Arithmetic progression is the series of numbers that have common differences between adjacent values are equal.

here,
1, 2, 4, 7, 12, 19, 30,
As
the sequence is the prime addition of the number, as.
1,
1 + 1 = 2
2 + 2 = 4,

4 + 3 = 7
7 +  5 = 12
12 + 7 = 19
19 + 11 = 30
30 + 13 = 43

Thus, At the end of the sequence, the required next term is 43.

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Answer:

19.9 m

Step-by-step explanation:

Cone: r= 1m Height= 2m (You will use the radius for the Cylinder)

1/3 x π x 1^2 × 2 = 2.0943951023932

2.0943951023932 x 2 = 4.1887902047864 (Just use the hundreths place if writing down.)

Cylinder: r= 1m Height= 5m

π x 1^2 x 5 = 5π = 15.707963267949

Now add both together then round to tenths.

4.1887902047864 + 15.707963267949 = 19.8967534727354

(Remember use hundreths place if writing down)

19.8967534727354 --> 19.9 m

By midpoint segment theorem DE=1/2BC for AD≅BD and AE≅EC of the triangle ABC.

A triangle is a three-sided polygon that consists of three edges and three vertices.

A line segment that connects two midpoints of the sides of a triangle is called a midsegment.

DE is the midsegment of AB and AC.

AD≅BD and AE≅EC.

The Midsegment Theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side.

DE=1/2BC

5=1/2(10)

5=5

Hence, DE=1/2BC for AD≅BD and AE≅EC of the triangle ABC.

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Answer:

y < 13x – 15

Step-by-step explanation:

13x – y < 15

–y < –13x +15

divide both sides by (–)

–(–y) < –(–13)x –(15)

y < 13x – 15

The data are statistically significant at level = 0.05, but not at level = 0.01.

Given-

H0: μ = 115

HA: μ ≠ 115

The sample mean = 120

The standard deviation = 25

Standard error of mean 2.5

Solution-

If  z = (xbar- μ ) / SE

Then the solution would be

z = (120-115) / 2.5

z = 2

P of the value = 2 P( z > 2) = 2(0.0228) = 0.0456 is the statistically significant level.

Therefore the answer is technically at .05 level of significance.

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Answer:

R = 0≤ y ≤ 800

D = 0≤ x ≤ 16

.

.

.

.

the 25th, 50th, and 75th percentile from the following list of 32 data are 25th percentile: 13 , 50th percentile: 21 , 75th percentile: 29.

To find the 25th percentile:

25th percentile: 25% of 32 = 8th number = 13

Count the total number of values in the data set, which is 32

Calculate 25% of 32, which is 8

Count 8 numbers from the beginning of the list and the 25th percentile is the 8th number, which is 13

To find the 50th percentile:

50th percentile: 50% of 32 = 16th number = 21

Count the total number of values in the data set, which is 32

Calculate 50% of 32, which is 16

Count 16 numbers from the beginning of the list and the 50th percentile is the 16th number, which is 21

To find the 75th percentile:

75th percentile: 75% of 32 = 24th number = 29

Count the total number of values in the data set, which is 32

Calculate 75% of 32, which is 24

Count 24 numbers from the beginning of the list and the 75th percentile is the 24th number, which is 29

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Answer:

81.74 cm²

Step-by-step explanation:

Use tan(x) to find x

tanθ = opposite/adjacent

tan(36) = x/15

15tan(36) = x

area of triangle = [tex]\frac{1}{2}[/tex]*b*h

[tex]\frac{1}{2}[/tex]*15tan(36)*15 = 81.74 cm² (2 d.p.)

After reducing the product in the lowest form and changing to mixed fraction , the answer is  [tex]3\frac{3}{4}[/tex]  .

In the question ,

it is given that ,

the two numbers are 2/8 and 15 ,

we have to find the product without using the calculator and express it in lowest form and then convert the improper fraction in to mixed fraction .

So , the product of 2/8 × 15  = 30/8

in lowest form it is 15/4 .

after converting the improper fraction 15/4  in mixed form ,

we get ,

15/4 = [tex]3\frac{3}{4}[/tex].

Therefore , the product of 2/8 × 15 is [tex]3\frac{3}{4}[/tex]  .

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The two events a and b are independent if and only if (a) Events a and b are independent  .

What are Independent Events ?

Two events A and B are said to be independents if the occurrence of event A does not affect the chance of occurrence of the other event B .

The probability of two independent events can be mathematically represented as  P(A and B) = P(A) × P(B) .

So, we can conclude that , Two events, a and b are independent if and only if Events a and b are independent  .

Therefore , the correct option is (a) .

The given question is incomplete , the complete question is

Two events, a and b are independent if and only if

Which of the following statements is true of a and b?

(a) Events a and b are independent

(b) Events a and b are not independent, but they are mutually exclusive

(c) Events a and b are not independent since and .

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Superman pro

Step-by-step explanation:

Superman pro

The value of the amount will be $721.40.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

500 dollar deposit for 20 years with a interest rate of 2%.

Now,

We know that;

The formula for amount is,

⇒ [tex]A = P (1 + r)^n^t[/tex]

Where, A is total amount, P is principle amount, r is interest rate.

Here, We have;

P = $500

t = 20 years

r = 2%

Substitute all the values, we get;

⇒  [tex]A = P (1 + r)^n^t[/tex]

⇒ [tex]A = 500 (1 + 0.02)^2^0[/tex]

⇒ A = 500 × 1.02²⁰

⇒ A = 500 × 1.44

⇒ A = $721.40

Thus, The value of the amount = $721.40

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All the possible values for the number 'x' will be less than or equal to 1,350.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The remainder of a number and 5 in addition to 25 is something like 45.

Let the number be 'x'. Then the inequality is given as,

x / (5 + 25) ≤ 45

x / 30 ≤ 45

x ≤ 1,350

All the possible values for the number 'x' will be less than or equal to 1,350.

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a) The probability that they actually use drugs, if an employee tests positive for drug use is 69%

b) The probability that a nondrug user will test positive for drug use twice in a row is 0.25%

c) The probability that someone who tests positive twice in a row is not a drug user is 23%

Based on past knowledge of circumstances that might be relevant to the event, Bayes' theorem estimates the likelihood of an event.

The theorem explains how a degree of belief, stated as a probability, should logically alter to account for the presence of relevant data using Bayesian probability interpretation.

The question state that

Pr(D) = 0.10

Pr(D') = 0.90

Pr (P/D) = 0.98 ( (2% False negatives means for drug users, 2% will get a negative result, so 98% will get positive result)

Pr(P/D') = 0.05

a) The probability that they actually use drugs, if an employee tests positive for drug use Pr(D/P) = Pr(D)*Pr (P/D) / Pr(D)*Pr (P/D)+Pr(D')*Pr(P/D')

⇒ Pr(D/P) = (0.10*0.98)/(0.10*0.98 + 0.90*0.05)

⇒ Pr(D/P) = 0.098/(0.098+0.045)

⇒ Pr(D/P) = 0.098/0.143

⇒ Pr(D/P) ≈ 0.6853

⇒ Pr(D/P) ≈ 69%

b) The probability that a nondrug user will test positive for drug use twice in a row Pr (P*2/D') = Pr(P/D')*Pr(P/D')

⇒ Pr (P*2/D') = 0.05*0.05

⇒ Pr (P*2/D') = 0.0025

⇒ Pr (P*2/D') = 0.25%

c) The probability that someone who tests positive twice in a row is not a drug user Pr (D'/P*2) = Pr(D')*Pr (P*2/D') / Pr(D')*Pr (P*2/D')+Pr(D)*Pr (P*2/D)

⇒ Pr (D'/P*2) = (0.90*.0.05²)/(0.90*0.05²+0.10*0.98²)

⇒ Pr (D'/P*2) = 0.00225/ 0.00225+0.09604

⇒ Pr (D'/P*2) = 0.00225/0.09829

⇒ Pr (D'/P*2) ≈ 0.2289

⇒ Pr (D'/P*2) ≈ 23%

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   The probability that the sample mean will be within ±5 of the population mean is 0.6826

If the population is normally distributed, the sample means will be normally distributed even with smaller samples. [This is known as the Central Limit Theorem, which states that when a large number of random samples are drawn from a population, the means of these samples will be normally distributed.]

Z=X-μ/σ

Given here, σ = 50 , μ =200 , σₓ = 5 , n = 100 ,                                                                      

                     z = 205-200/5    z = 195-200/5

we get z= ±1

From the z table, we get P( z= -1)  = 0.1587

From the z table we get P( z= 1)  = 0.8413

Thus the final answer is = 0.8413- 0.1587

                                        =  0.6826

Hence,  the probability that the sample mean will be within ±5 of the population mean is  0.6826

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The statement given in the question holds true . We get this result after analyzing the given data set .

Given , hypothesis is ,

Let d be any positive integer not equal to2 , 5 or 13 .

Show that one can find distinct a , b  in the set {2,5,13,d} such that ab-1 is not a perfect square.

Using the modular way to solve this question we get ,

d = 0 , 3 = | 4 |

Then , we get the result as ,

13d - 1 , which is not a perfect square.

d = 2|4|

we get , 2d -1

which again is not a perfect square.

Similarly after checking the value for all the possible cases , we will get the result that the hypothesis is correct.

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Answer:

sorry new don't understand the app

Since our test statistics ( 8.96 ) is less than the critical value ( 29.141 ),

there is no strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 millimeters.

Given that;

H₀ : σ = 0.02

H₁ : σ > 0.02

The test statistics is;

X² = ( n-1 )s² / σ²  = ( 15 - 1)(0.016)² / (0.02)²

= 0.003584 / 0.0004

= 8.96

degree of freedom

df = n - 1 = 15 - 1 = 14

For right tailed test, critical value at 0.01 level of significance is 29.141.

Now since our test statistics ( 8.96 ) is less than the critical value (29.141 ),

Therefore, there is no strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 millimeters.

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Vanessa can buy a maximum of x oranges, where x is the number of oranges she can buy at the store. We can represent this mathematically as an inequality by letting x represent the number of oranges she can buy and setting it equal to the total amount of money she has minus the cost of the eggs divided by the cost of each orange:

x ≤ ($20 - $3) / $0.50

This inequality tells us that Vanessa can buy at most x oranges as long as the total cost of the oranges (x * $0.50) is less than or equal to the amount of money she has remaining after buying the eggs ($20 - $3).

In other words, Vanessa can buy at most x oranges as long as the total cost of the oranges is less than or equal to $17.50. This means she can buy at most 35 oranges, since 35 * $0.50 = $17.50. Therefore, the inequality that represents the maximum number of oranges Vanessa can buy is:

x ≤ 35.

The equation that represents a non linear function is y = x²   , the correct option is (a) .

In the question ,

four functions are given ,

we have to select the option that is non linear ,

we know that ;

A Linear Function is an equation in which the the highest degree of the equation is 1 , and the graph is a straight line .    and

A Non Linear Function ,is an equation in which the highest degree of the equation is more than 1 , and the graph is not a straight line .

So , from the given options

we can see that all the options have degree 1 except the equation y = x² which has highest degree 2 .

Therefore , The Non Linear Function is (a) y = x² .

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Answer:

Need more info please

Step-by-step explanation:

The value of the x is 3.26556.

What is the Intersecting Chord Theorem?

When two chords intersect each other inside a circle, the products of their segments are equal.

We have,

It is a little easier to see this in the diagram, each chord is cut into two segments at the point where they intersect.

One chord is cut into two line segments A(x+10) and B(x+1). The other is into segments C(x) and D(5x+1).

According to Intersecting Chord Theorem:

This theorem states that A×B is always equal to C×D no matter where the chords are.

A.B = C.D

(x+10) * (x+1) = (x) * (5x+1).

x² + x + 10x + 10 = 5x² + x

x² + x + 10x + 10 - 5x² - x = 0

-4x² + 10x + 10  = 0

using the Quadratic Formula where, a = -4, b = 10, and c = 10, we get

x=−0.765564

x = 3.26556

Hence, the value of the x is 3.26556.

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Answer:

43

Step-by-step explanation:

258 divided by 6 equals 43

Look below

Armando divided 6 and 258

258 is the bigger number, so we will keep that on the right, and then add the dividing symbol. Next, we will add the 6. That should look like this:

258÷6

then just put it on a calculator and you get the answer 43. hope that helps

The required equation for the variation of k is given as k = Fd² / xy.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Newton's Law of Universal Gravitation states that the gravitational attraction, f, between two objects with masses x and y is proportional to the product of their masses and inversely proportional to the square of their distance, d.
So,

F ∝ x × y - - - - (1)
And
F ∝ 1 / d² - - - - - (2)

Combining equations 1 and 2
F ∝ xy / d²
Or
F = kxy / d²

Now,
Formulate the above expression with subject to constant k.
K = Fd² / xy

Thus, the required equation for the variation of k is given as k = Fd² / xy.

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Ma'am there is nothing to solve...

:<

Answer:

Step-by-step explanation:

Yes there is literally nothing to solve:(

Proof:

Let's start of by solving for the length of AC, which is just the sum of lengths AB and BC, which is 10 + 3 = 13 units.

Because of our second given, AC ≅ EG, we know that EG is also 13 units in length. Also, from our first given, BC ≅ EF, we know that EF is 3 units.

We also know that the length of EG is the sum of lengths EF and FG so we can write the equation

EG = EF + FG

13 = 3 + FG

FG = 10 meaning FG is 10 units