Please help me with my math!

Using distance between two points formula, a = 0

The distance between two points (x, y) and (x', y') is given by

d = √[(x' - x)² + (y' - y)²]

Now, If the distance between the points (0, 6) and (a, 0) is 6 units, to find the value of a,

Let

So, substituting the values of the variables into the equation, we have

d = √[(x' - x)² + (y' - y)²]

6 = √[(a - 0)² + (0 - 6)²]

⇒ √[a² + (- 6)²] = 6

√[a² + 36] = 6

Squaring both sides, we have that

a² + 36  = 6²

a² + 36  = 36

a² = 36 - 36

a² = 0

a = √0

a = 0

So, a = 0

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The question is incomplete. Here is the complete question

If the distance between (0, 6) and (a, 0) os 6 units. Find the value of a

​

Answer:

  (a, b) alternate interior angles at M and N, and at A and B are congruent

  (c) the triangles are congruent by SAS and by ASA (and MX = NX)

  (d) angles are no longer congruent, so the triangles are not congruent. The radii are given as congruent, but the chords cannot be shown congruent.

Step-by-step explanation:

Given same-size circles A and B, externally tangent to each other at X, each with chords MX and NX, you want to know what can be concluded if AM║BN, and what is unprovable if those segments are not parallel.

The circles being the same size means all the radii are congruent. This is shown by the single hash marks in the attached diagram.

Alternate interior angles where a transversal crosses parallel lines are congruent. If AM║BN, this means the angles marked with a single arc are congruent, and the angles marked with a double arc are congruent. These are the alternate interior angles at transversal MN and at transversal AB.

If AM║BN, in addition to the given congruences, we also know ...

∆AMX ≅ ∆BNX by SAS or ASA (take your pick).

If AM and BN are not parallel, MN is not a straight line through X, the angles at A and B are not congruent, and the angles at M and N are not congruent. (We assume segment AB still goes through X.)

__

Additional comment

Triangles MAX and NBX are isosceles, so their base angles are congruent. If X lies on MN, then AM and BN must be parallel, since the vertical angles at X will be congruent along with the other base angles at M and N. If AM and BN are not parallel, point X cannot lie on segment AB.

The probability of a bulb lasting for at most 540 hours is 0.7521, rounded to four decimal places.

The life of light bulbs is distributed normally. The variance of the lifetime is 225 and the mean lifetime of a bulb is 530 hours. Find the probability of a bulb lasting for at most 540 hours. Round your answer to four decimal places.

Using the z-score formula z = (x - μ) / σ, where x is the value in question (540 hours in this case), μ is the mean (530 hours in this case) and σ is the standard deviation (15 hours in this case), we can calculate the z-score:
z = (540 - 530) / 15
z = 10 / 15
z = 0.67
Using a z-table, we can look up the probability of a value being less than or equal to 0.67, which is 0.7521.
Therefore, the probability of a bulb lasting for at most 540 hours is 0.7521, rounded to four decimal places.

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Answer:

yes

Step-by-step explanation:

The expected count for women for the presence of aortic stenosis is 57.7. The correct option is D.

Aortic stenosis is a cardiovascular ailment that causes the aortic valve in the heart to narrow, reducing blood flow from the heart to the rest of the body. Aortic stenosis usually progresses gradually and, in the beginning, may not produce any symptoms.

The severity of aortic stenosis is divided into four categories, ranging from mild to severe. People who are asymptomatic may require monitoring, whereas those who are symptomatic may need to undergo surgery or other procedures.

The expected count for women for the presence of aortic stenosis in this question refers to the number of women who have this condition according to a particular study or statistic.

Therefore, the correct option is D.

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(a)The distribution of X (the average of the 49 races) follows a normal distribution with mean 146 minutes and standard deviation 11 minutes. (b)The probability of the average of the sample being between 144 and 149 minutes is 0.5854.(c)The 80th percentile for the average of these 49 marathons is 157.2 minutes.(d) The median of the average running times is 146 minutes.

Part(a) The distribution of X (the average of the 49 races) follows a normal distribution with mean 146 minutes and standard deviation 11 minutes. Part (b) The probability that the average of the sample will be between 144 and 149 minutes in these 49 marathons can be calculated using the z-score formula: z = (x - mean)/standard deviation
For x = 144, z = (144 - 146)/11 = -0.18
For x = 149, z = (149 - 146)/11 = 0.27,using the z-score table, the probability of the average of the sample being between 144 and 149 minutes is 0.5854 (0.4026 + 0.1828).

Part (c) The 80th percentile for the average of these 49 marathons can be calculated using the z-score formula: z = (x - mean)/standard deviation, For the 80th percentile, z = 0.84 (from z-score table). Therefore, x = 146 + (0.84 * 11) = 157.2 minutes. Part (d) The median of the average running times is 146 minutes. The median is the midpoint of the data which means half of the data is above the median and half of the data is below the median. Therefore, the median of the average running times is equal to the mean.

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When a data line on a graph slopes down as it goes to the right, it is depicting that the relationship between the variables on the graph is inverse.

An inverse relationship is a kind of correlation between two variables, in which one variable decreases while the other increases, or vice versa. An inverse relationship happens when one variable increases while the other decreases, or when one variable decreases while the other increases.

On a graph, when a data line slopes down as it goes to the right, this is an indication that the relationship between the variables on the graph is inverse. As the values of x increase, the values of y decrease. Therefore, we can conclude that there is an inverse relationship between x and y.

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We cannot use arccos (28/53) and arcsin (28/53) because they correspond to angle B, not angle A. Similarly, arctan (28/45) and arctan (45/28) do not give the measure of angle A.

The cosine function has an opposite known as the arccos function. It provides the angle whose cosine is the specified value. Try it. Drag any vertex of the triangle and watch how the angle C is determined using the arccos() function. Meaning: A 30 degree angle is one whose cosine is 0.866.

The inverse cosine function is the arccosine. The arccosine function's input values range from -1 to 1, matching the cosine function's output range of -1 to 1. So, for x=2, arccos x is undefined.

From the given figure, we can see that:

cos A = 28/53

sin A = 45/53

Therefore, the expressions that give the measure of angle A are:

(B.) arccos (45/53)

(D.) arcsin (45/53)

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The water level in the aquarium rises by (A) 0.25.

The volume of water in the aquarium before the rock is added is:

100 cm x 40 cm x 37 cm = 148000 cm^3

When the rock is added, its volume is 1000 cm^3, so the total volume of water and the rock is:

148000 cm^3 + 1000 cm^3 = 149000 cm^3

To find the new water level, we need to divide the total volume by the base area of the aquarium:

149000 cm^3 ÷ (100 cm x 40 cm) = 37.25 cm

Therefore, the water level rises by:

37.25 cm - 37 cm = 0.25 cm

So the answer is (A) 0.25.

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Your question is incomplete, but probably the complete question is :

An aquarium has a rectangular base that measures 100 cm by 40cm and has a height of 50cm. The aquarium is filled with water to a depth of 37 cm. A rock with volume 1000cm^3 is then placed in the aquarium and completely submerged. By how many centimeters does the water level rise?

(A) 0.25

(B) 0.5

(C)

(D)1.25

(E) 2.5

Answer:

Step-by-step explanation:

You can’t solve this equation as none of the numbers have the same coefficient to solve. If you wanted to solve for x and y, you will need two equations as there are two unknown variables in the equation and the only way to solve for x and y is to use simultaneous method which includes two equations.

Answer:

15

Step-by-step explanation:

Answer can only be found through estimation.

This means you have to do:

[tex]\frac{50*3}{\sqrt{100} }[/tex]

This will get you 15.

In Rosettenville, a suburb of Johannesburg, South Africa, Robert Brozin and Fernando Duarte acquired the Chicken Land restaurant in 1987, launching Nando's.

The eatery was renamed Nando's in honor of Fernando. The restaurant incorporated influences from former Mozambican Portuguese colonists, many of whom had relocated to Johannesburg's southeast after their country gained independence in 1975. Expansion was an essential component of their vision from the beginning. Nando's had already grown from one restaurant in 1987 to four by 1990. It became increasingly difficult to implement a common strategy and decision-making became inefficient as new outlets were maintained as separate businesses.

In 1995, Nando's International Holdings (NIH) was established as a new international holding because managing this growingly complex global structure had become extremely challenging. The South African branch of Nando's Group Holdings (NGH) was successfully listed on the Johannesburg Stock Exchange on April 27, 1997. NGH was 54% owned by NIH, with the remaining 26% available to the general public and former joint venture partners. The main goals of the share offer and listing were to broaden the group's capital base and enable group restructuring.

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The 41st term of the sequence is 121.

In mathematics, a sequence is a list of numbers or objects that follow a certain pattern or rule. A sequence's terms are typically identified by subscripts, like a1, a2, a3,..., an, where n denotes the number of terms in the sequence.

Sequences can be arithmetic, geometric, or neither, depending on terms follow a static difference, constant ratio, or neither of these series, respectively. Algebra uses geometric sequences to represent exponential development or decay whereas arithmetic sequences are frequently employed to model linear connections.

The given sequence is 2 , 5 , 8 , ...

The common difference is:

d = 5 - 2 = 3

The nth term of a sequence is given as:

an = a1 + (n-1)d

Substituting the value we have:

an = 2 + (n-1)3

an = 3n - 1

a41 = 3(41) - 1 = 122 - 1 = 121

Hence, the 41st term of the sequence is 121.

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The expressions that are equivalent to (x-2)² is x² - 4x + 4. (option B)

Now, let's look at the expression (x-2)². This is a binomial expression that can be simplified by applying the rules of exponents. Specifically, we can expand this expression as follows:

(x-2)² = (x-2) * (x-2)

= x * x - 2 * x - 2 * x + 2 * 2

= x² - 4x + 4

So, the expression (x-2)² is equivalent to x² - 4x + 4.

However, the problem asks us to identify other expressions that are equivalent to (x-2)². To do this, we can use the process of factoring. We know that (x-2)² can be factored as (x-2) * (x-2). Using this factorization, we can rewrite (x-2)² as:

(x-2)² = (x-2) * (x-2)

= (x-2)²

So, (x-2)² is equivalent to itself.

Hence the correct option is (B).

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Complete Question:

Which expressions are equivalent to (x−2)²?

Select the correct choice.

A. (x + 2) (x - 2)

B. x² - 4x + 4

C. x² - 2x + 5

D. x² + x - 2x

Answer: 15

Step-by-step explanation:

13--2 = 13 + 2 = 15

Answer:

if it is perpendicular to eacha other I e 0

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

P of spade = 1/4

P of face cards = 3/13

{P = probability}

Step-by-step explanation:

•Total cards in a deck = 52

No. of spade cards in the deck = 13

therefore,

Probability of drawing a spade out of a deck of cards = 13/52 = 1/4

No. of face cards in a deck = 3×4 = 12 (joker,king,queen)

therefore,

Probability of drawing a face card out of a deck of cards = 12/52 = 3/13

Answer:

20%

Step-by-step explanation:0% of 4445=

Answer:

they bought 62 item from noodles and 51 items from hot chips

The point that partitions segment AB in a 1:4 ratio is (-1/2, -1).

What is Segment?

In geometry, a segment is a part of a line that has two endpoints. It can be thought of as a portion of a straight line that is bounded by two distinct points, called endpoints. A segment has a length, which is the distance between its endpoints. It is usually denoted by a line segment between its two endpoints, such as AB, where A and B are the endpoints. A segment is different from a line, which extends infinitely in both directions, while a segment has a finite length between its two endpoints.

To find the point that partitions segment AB in a 1:4 ratio, we need to use the midpoint formula to find the coordinates of the point that is one-fourth of the distance from point A to point B. The midpoint formula is:

((x1 + x2)/2, (y1 + y2)/2)

where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the segment.

So, let's first find the coordinates of the midpoint of segment AB:

Midpoint = ((-3 + 7)/2, (2 - 10)/2)

= (2, -4)

Now, to find the point that partitions segment AB in a 1:4 ratio, we need to find the coordinates of a point that is one-fourth of the distance from point A to the midpoint. We can use the midpoint formula again, this time using point A and the midpoint:

((x1 + x2)/2, (y1 + y2)/2) = ((-3 + 2)/2, (2 - 4)/2)

= (-1/2, -1)

So, the point that partitions segment AB in a 1:4 ratio is (-1/2, -1).

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Answer:

x=15

Step-by-step explanation:

use the side splitter theorem

(x-6)/x = 3/5 (cross-multiply)

3x=5(x-6) distributive property

3x=5x-30

2x = 30

x = 15

the variance of X is 9. b) Determine E [2X² - 20X +5]:

Using linearity of expectation, we can find E [2X² - 20X +5] as:

E [2X² - 20X +5] = 2E[X²] - 20E[X] + 5

by the question.

The number of ways to select the first 2 white chips is given by:

Number of ways = (6C2) (5C0) (3C0) = 15

The number of ways to select the third chip as blue given that the first 2 chips were white is given by:

Number of ways = (3C1) = 3

Therefore, the probability of selecting the third chip as blue given that the first 2 chips were white is:

P(The third chip is blue the first 2 were white) = Number of ways / Total number of ways = 3 / 350 = 0.0086 (rounded to 4 decimal places)

c) P(The fourth chip is blue the first 2 were white):

The number of ways to select the first 2 white chips is given by:

Number of ways = (6C2) (5C0) (3C0) = 15

The number of ways to select the third chip as non-white given that the first 2 chips were white is given by:

Number of ways = (8C1) = 8

The number of ways to select the fourth chip as blue given that the first 2 chips were white, and the third chip was non-white is given by:

Number of ways = (3C1) = 3

Therefore, the probability of selecting the fourth chip as blue given that the first 2 chips were white is:

P(The fourth chip is blue the first 2 were white) = Number of ways / Total number of ways = 8*3 / 350 = 0.0686 (rounded to 4 decimal places)

Suppose we have a random variable X such that E[X]= 7 and E[X²] =58.

a) Determine the variance of X:

The variance of X is given by:

Var[X] = E[X²] - (E[X]) ²

Substituting the given values, we get:

Var[X] = 58 - (7) ² = 9

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Answer: x = 6

Step-by-step explanation:

(7x+3)+85+50 = 180

(7x+3)+135 = 180

7x+3 = 180 - 135 = 45

7x = 45-3 = 42

x = 42 / 7 = 6

x = 6

Construct a triangle PQR with sides PQ=8cm, PR=5cm, and QR=6cm, then draw a circle passing through P, Q, and R. This circle is called the circumcircle of triangle PQR.

We draw a line segment PQ = 8 cm long. From point P, we draw a line segment PR = 5 cm long at an angle of 60 degrees to PQ. Then, we draw a line segment QR = 6 cm long joining points Q and R to complete the triangle. Next, we use a compass to draw a circle passing through points P, Q, and R. This circle is called the circumcircle or circumscribed circle of the triangle, which is the unique circle that passes through all three vertices of the triangle. The circumcircle has a special property that its center is equidistant from the three vertices of the triangle.

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the length of chord in the circle is 13.5 units.

According to Pythagoras' Theorem, the square of the hypotenuse side of a right-angled triangle equals the sum of the squares of the other two sides.The Perpendicular, Base, and Hypotenuse are the three angles that make up this triangle.

The Pythagoras Theorem formula is as follows from the definition:

Hypotenuse² = Perpendicular² + Base²

c² = a² + b²

From the figure, the hypotenuse, x of both triangle are same as both of them are radius of circle.

According to Pythagoras theorem,

x²=6.3²+11.9²

x²=181.3

x=√181.3

x=13.5

Hence, the length of chord in the circle is 13.5 units.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The probability that x is less than 2 is approximately 0.4866. The probability that x is greater than 3 is approximately 0.3528. The probability that x is less than 5 is approximately 0.6321. The probability that x is between 2 and 5 is approximately 0.1455.

The given probability density function is an exponential distribution with a rate parameter of λ = 1/3. The formula for P(x < x_0) is the cumulative distribution function (CDF) of the exponential distribution, which is given by:

F(x_0) = ∫[0,x_0] f(x) dx = ∫[0,x_0] 1/3 * 4 * e^(-x/3) dx

a. Write the formula for P(x < x_0):

Using integration, we can solve this formula as follows:

F(x_0) = [-4e^(-x/3)] / 3 |[0,x_0]

= [-4e^(-x_0/3) + 4]/3

b. Find P(x < 2):

To find P(x < 2), we simply substitute x_0 = 2 in the above formula:

F(2) = [-4e^(-2/3) + 4]/3

≈ 0.4866

Therefore, the probability that x is less than 2 is approximately 0.4866.

c. Find P(x > 3):

To find P(x > 3), we can use the complement rule and subtract P(x < 3) from 1:

P(x > 3) = 1 - P(x < 3) = 1 - F(3)

= 1 - [-4e^(-1) + 4]/3

≈ 0.3528

Therefore, the probability that x is greater than 3 is approximately 0.3528.

d. Find P(x < 5):

To find P(x < 5), we simply substitute x_0 = 5 in the above formula:

F(5) = [-4e^(-5/3) + 4]/3

≈ 0.6321

Therefore, the probability that x is less than 5 is approximately 0.6321.

e. Find P(2 < x < 5):

To find P(2 < x < 5), we can use the CDF formula to find P(x < 5) and P(x < 2), and then subtract the latter from the former:

P(2 < x < 5) = P(x < 5) - P(x < 2)

= F(5) - F(2)

= [-4e^(-5/3) + 4]/3 - [-4e^(-2/3) + 4]/3

≈ 0.1455

Therefore, the probability that x is between 2 and 5 is approximately 0.1455.

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The mean (also called the arithmetic mean or average) is a measure of central tendency that represents the typical or average value of a set of data. The mean is calculated by summing up all the values in the data set and dividing by the number of values.

The mean of x is calculated by the following formula:

mean of x = ∑(x * P(x))

Where, ∑ = Summation operator

            x = Value of random variable  

            P(x) = Probability of the corresponding value of x.

Let's calculate the mean of x using the formula provided above.

mean of x = (-1 × 0.3) + (0 × 0.4) + (1 × 0.3)

                = -0.3 + 0 + 0.3  

                = 0

Therefore, the mean of x is 0.

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Answer: To fill out a table of equivalent ratios for Blake's lemonade recipe, we can use the ratio of lemons to cups of lemonade:

Lemons             Cups of Lemonade

3                        4

6                        8

9                        12

12                      16

15                      20

18                      24

To plot the points on a coordinate axes, we can use the Lemons as the x-coordinate and the Cups of Lemonade as the y-coordinate. The points would lie on a line that passes through the origin (0,0) and the point (12,16).

         |       *

 Cups of |    *     *

Lemonade  | *           *

         |________________

            Lemons

              0    12

The line represents the proportional relationship between the number of lemons and the amount of lemonade produced. As the number of lemons increases, the amount of lemonade produced increases proportionally.

Step-by-step explanation: