is (24, 7, 25) a Pythagorean triple?

Answer:

d. 260. is the answer.

Answer:

a) 0.1536 = 15.36% probability that exactly two of the four components last longer than 1000 hours.

b) 0.9728 = 97.28% probability that the subsystem operates longer than 1000 hours.

Step-by-step explanation:

For each component, there are only two possible outcomes. Either they fail in less than 1000 hours, or they do not. The probability of a component failing in less than 1000 hours is independent of any other component. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

One subsystem has four identical components, each with a probability of 0.2 of failing in less than 1000 hours.

Four components means that [tex]n = 4[/tex]

Probability of 0.2 of failling means that 1 - 0.2 = 0.8 probability of not failling, so [tex]p = 0.8[/tex]

a) Find the probability that exactly two of the four components last longer than 1000 hours.

This is [tex]P(X = 2)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{4,2}.(0.8)^{2}.(0.2)^{2} = 0.1536[/tex]

0.1536 = 15.36% probability that exactly two of the four components last longer than 1000 hours.

b) Find the probability that the subsystem operates longer than 1000 hours.

It will operate if at least two compoents last longer than 1000 hours. So

[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{4,2}.(0.8)^{2}.(0.2)^{2} = 0.1536[/tex]

[tex]P(X = 3) = C_{4,3}.(0.8)^{3}.(0.2)^{1} = 0.4096[/tex]

[tex]P(X = 4) = C_{4,4}.(0.8)^{4}.(0.2)^{0} = 0.4096[/tex]

[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.1536 + 0.4096 + 0.4096 = 0.9728[/tex]

0.9728 = 97.28% probability that the subsystem operates longer than 1000 hours.

Answer:

Yes

Step-by-step explanation:

yes, yes it does

Answer:

$25

Step-by-step explanation:

she received$12 five times

12×5=60 ...(1)

she earned$5 two times for yard work

5×2=10....(2)

(1)+(2).... 60+10=70

Bought dog food and ticket

30+15=45

70-45=25

Answer $25 is what she is left with at the end of the month

Answer:

She would have 5 dollars left

Step-by-step explanation:

Answer:

Speed = distance / time

= 6/3 =2 ft/sec

Time = distance / speed

= 60/2

= 30 seconds

(5x + 2) + (4x + 5)

= 5x + 2 + 4x + 5

= 5x + 4x + 5 + 2

= 9x + 7

The area of the entire surface will be 2160 feet Wide/Long.

Answer:

[tex] - 2x - 2x = 729 + 3 - 27 - 1 \\ [/tex]

[tex] - 4x = 704[/tex]

[tex]x = -704 \div 4 = -176[/tex]

Answer:

2nd answer choice :)

Step-by-step explanation:

The new figure produced is given below.

Option C is the correct answer.

A scale factor is defined as the ratio between the scale of a given original object and a new object,

We have,

Let the figure be in the first quadrant.

Now,

Rotation of 180-degree means,

The figure will be in the third quadrant.

Now,

Dilation with a factor of 1/2.

This means,

The figure will shrink by 1/2.

Thus,

The new figure is given below.

Learn more about scale factors here:

https://brainly.com/question/20759556

#SPJ5

Answer:

really!!?? thank you!!!  need one! ;w;

Step-by-step explanation:

Answer:

put it at 4.5

Step-by-step explanation:

put it at 4.5 because 20's square root is 4.472 but it says approximately so you need to round 4.472 to 4.5

Answer:

12 square units

Step-by-step explanation:

The area of a given figure is the measure of space occupied by the figure on a 2 dimensional plane.

Area of a triangle = [tex]\frac{1}{2}[/tex] x base x height

From the given grid, the following can be observed for triangle STU.

base SU = 6 units

height = 4 units

Thus,

area of triangle STU =  [tex]\frac{1}{2}[/tex] x base x height

                                  =  [tex]\frac{1}{2}[/tex] x 6 x 4

                                  = 3 x 4

area of triangle STU = 12 square units

The required area of triangle STU is 12 square units.

Answer:

x≥1

Step-by-step explanation:

Answer:

29π/12.

Step-by-step explanation:

Multiply by π/180

= 435π/180

= 29π/12 radians.

Answer:

11. 78

12. 4x² - 3x - 1

Step-by-step explanation:

11. Sum of n whole numbers = ½(n² + n)

Multiply

½*n² + ½*n

= n²/2 + n/2

To find the sum of the first 12 whole number, substitute 12 for n into the equation.

= 12²/2 + 12/2

= 144/2 + 12/2

= 72 + 6

= 78

12. Area of trapezoid = ½(a + b)*h

Where,

a = 5x - 4

b = 3x + 2

h = x + 1

Area = ½(5x - 4 + 3x + 2)*(x + 1)

Area = ½(8x - 2)*(x + 1)

Area = ½[8x(x + 1) -2(x + 1)]

= ½[8x² + 8x - 2x - 2]

Add like terms

= ½(8x² - 6x - 2)

= ½(8x²) - ½(6x) - ½(2)

= 4x² - 3x - 1

Answer:

Step-by-step explanation:

Answer:

Is Mary a guy?  :|  

Step-by-step explanation:

I did this by just a good guess  , not really the right way

2000*.45=900  ( 900 is the old savings)

2000*.2 =400   ( how much her salary went down by )

2000-400=1600 ( new salary )

1600*.45 = 720    ( 45% of new salary is new savings

900-720=180      ( change in savings is 180 , the amount the question asks for)

Mary's old salary was 2,000

Answer:

X Y

10 7

8 5

6 3

Step-by-step explanation:

Not much to explain - just put a number 3 smaller than X into column Y

The required table for the given rule can be completed as follows:

X Y

10 7

8 5

6 3

A linear relationship is a connection that takes the shape of a straight line on a graph between two distinct variables - x and y. When displaying a linear connection using an equation, the value of y is derived from the value of x, indicating their relationship.

The rule is given in the question, as follows:

y is 3 less than x

For each value of x in the first column, the corresponding value of y in the second column can be calculated by subtracting 3 from x.

For example, if x is 10, then y is 3 less than x, which is 7 (10 - 3 = 7).

Similarly, if x is 8, then y is 5 (8 - 3 = 5), and if x is 6, then y is 3 (6 - 3 = 3).

The table for the given rule can be completed as follows:

X Y

10 7

8 5

6 3

Learn about the linear relationship here :

https://brainly.com/question/11663530

#SPJ5

Answer:

I. p = 7

II. 17 litres

Step-by-step explanation:

I. Determination of the value of p

Mean = 17.7

p =.?

Let the number of litre be L

Let the number of motorist be M

Mean = summation LM / summation M

Summation of LM = (16×11) + (17×10) + (18×p) + (19×4) + (20×8)

= 176 + 170 + 18p + 76 + 160

= 582 + 18p

summation M = 11 + 10 + P + 4 + 8

= 33 + p

Mean = summation LM / summation M

17.7 = 582 + 18p / 33 + p

Cross multiply

17.7(33 + p) = 582 + 18p

584.1 + 17.7p = 582 + 18p

Collect like terms

584.1 – 582 = 18p – 17.7p

2.1 = 0.3p

Divide both side by 0.3

p = 2.1 / 0.3

p = 7

II. Determination of the median number of litre.

Let the number of motorist be M (i.e the frequency)

summation M = 11 + 10 + P + 4 + 8

p = 7

summation M = 11 + 10 + 7 + 4 + 8

summation M = 40

The median is the middle term i.e

Median = (summation M / 2)ᵀʰ motorist

Median = (40 / 2)ᵀʰ motorist

Median = 20ᵀʰ motorist

Considering the table in the question above, the 20ᵀʰ motorist has 17 litres.

Therefore, the median number of litres is 17 litres.

Answer:

The monthly service charge

Step-by-step explanation:.

Answer:

m=4

n=-6

The above is just a possible value you can come up with your own :D.

See below for an explanation.

Step-by-step explanation:

Here you are going to really know the exponent rules. But in jest, you basically need to know that m+n=-2 due to exponent rules.

So?

An example would be

m=4

n=-6

Why?

Because 4-6=-2!

Answer:

x is 44 because

3x+4+x=180

4x=180-4

4x=176

x=44

Answer:

your answer will be option B

Step-by-step explanation:

[tex]\frac{10}{12} =\frac{a}{38} \\\\a=\frac{(10) (38)}{12} \\\\=31.6[/tex]

Answer:

A prediction based on the data is reliable, because the means of the samples are close together.

Step-by-step explanation:

Test approved

The most accurate statement is A. A prediction based on the data is reliable, because the means of the samples are close together.

Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.

Given three data sets.

All the samples have 10 data points.

Number of data points = 10

Mean of sample 1 = 9.1

Mean of sample 2 = 9.4

Mean of sample 3 = 8.9

We can see that the mean of the three samples is so close to each other.

So the data is reliable.

Hence the option is A.

Learn more about Reliability of Data here :

https://brainly.com/question/19901862

#SPJ7

Answer:

A

Step-by-step explanation:

Khan Academy

Answer:

d. and e.

Step-by-step explanation:

i did the test

Option A and Option D represents the equation of area of rectangular piece which are A=4×[tex]2\frac{1}{2}[/tex] and A=4×5/2.

The area of Rectangle is length times of width.

Given that A rectangular piece of glass is shown.

The length is measured as 4 feet.

The width is measured as 2 and one-half feet.

We have to find the  equations can be used to find the area of the piece of glass.

Area=Length×width

Area=4 feet × 2 and one-half feet

=4×[tex]2\frac{1}{2}[/tex]

=4×5/2

Hence, Option A and Option D represents the equation of area of rectangular piece which are A=4×[tex]2\frac{1}{2}[/tex] and A=4×5/2.

To learn more on Area of Rectangle click:

https://brainly.com/question/20693059

#SPJ2