what are the 3 consecutive integers with a sum of 48

Answer:

120 ways

Step-by-step explanation:

To solve the question above, we use combination formula:

Where ;

nCr = n! / (n-r)! r!

10C7 = 10! / (10 - 7)! 7!

10C7 = 10! / 3! 7!

10C7 = (10 * 9 * 8) / 3 * 2 * 1

10C7 = 720 / 6

= 120 ways

Answer:

12.4m

Step-by-step explanation:

In order to solve this equation, we can use the length of a carriage as our unknown value (using the engine is a bit more difficult). The questions says that the whole train: 4 carriages and an engine = 86.8m

If we represent carriage length as 'x', we can write the following equation:

4x (length of 4 carriages) + (2/3)x (length of engine as it is 2/3 of a carriage) = 86.8m

4x+(2/3)x = 86.8

From here we can combine into one fraction:

[tex]4x+\frac{2}{3} x=\frac{14}{3}x[/tex]

So now our equation looks like this:

[tex]\frac{14x}{3}=86.8[/tex]

Now all we need to do is multiply both sides by 3 and then divide both sides by 14 to isolate and solve x:

[tex]\frac{14x}{3}*3=86.8*3\\ 14x=260.4\\\frac{14x}{14}=260.4/14\\ x=18.6\\[/tex]

Now that we know the carriage length, we can use it to find the engine length:

Engine length = 2/3 Carriage length

[tex]E=\frac{2}{3}x\\ E=\frac{2}{3} (18.6)\\E = 12.4m[/tex]

Hope this helped!

Length of a carriage = x

Length of four carriages = 86.8 m

Length of each carriage =

[tex]86.8 \div 4 \: m \\ = \: 21.7 \: m[/tex]

Length of one carriage = 21.7 m

Length of the engine =

[tex] = \frac{2}{3} x[/tex]

[tex] = \frac{2}{3} \times 21.7[/tex]

[tex] = 43.4 \: m[/tex]

[tex]43.4 \div 3 \: m \\ = 14.4666666667 \: m[/tex]

∴ The length of the engine is 14.4666666667 m .

Answer:

Negation: The product of any irrational number and any nonzero rational number is not irrational.

Step-by-step explanation:

(a)

Given statement: The product of any irrational number and any nonzero rational number is irrational.

Negation: The product of any irrational number and any nonzero rational number is not irrational.

(b)

Let if possible the product of any irrational number and any nonzero rational number is not irrational that is rational.

Let [tex]x[/tex] be an irrational number and [tex]y\neq 0[/tex] be a rational number.

[tex]xy=z[/tex] where [tex]z[/tex] is rational.

So,

[tex]xy=z\\x=\frac{z}{y}[/tex]

As quotient of two rational numbers is also rational, [tex]x[/tex] must be rational which is a contradiction to the fact that [tex]x[/tex] is irrational.

The probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X) is approximately 2.6092%.

Here,

Since the length of the pipes follows a uniform distribution on the interval [10 feet, 10.57 feet], the probability density function (PDF) for each pipe is:

f(x) = 1 / (10.57 - 10) = 1 / 0.57 ≈ 1.7544 for 10 ≤ x ≤ 10.57

Since the lengths of the pipes are independent, the joint probability density function (PDF) of X and Y is the product of their individual PDFs:

f(x, y) = f(x) * f(y) = 1.7544 * 1.7544 = 3.0805 for 10 ≤ x ≤ 10.57 and 10 ≤ y ≤ 10.57

Now, we want to find the probability that the second pipe (Y) is more than 0.11 feet longer than the first pipe (X).

Mathematically, we want to find P(Y > X + 0.11).

Let's set up the integral to calculate this probability:

P(Y > X + 0.11) = ∬[10 ≤ x ≤ 10.57] [y > x + 0.11] f(x, y) dx dy

We integrate with respect to x first and then with respect to y:

P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] ∫[10 ≤ x ≤ y - 0.11] f(x, y) dx dy

P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [∫[10 ≤ x ≤ y - 0.11] 3.0805 dx] dy

P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [3.0805 * (x)] from x = 10 to x = y - 0.11 dy

P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [3.0805 * (y - (10 - 0.11))] dy

P(Y > X + 0.11) = 3.0805 * ∫[10 ≤ y ≤ 10.57] (y - 9.89) dy

P(Y > X + 0.11) = 3.0805 * [(y² / 2) - 9.89y] from y = 10 to y = 10.57

P(Y > X + 0.11) = 3.0805 * [((10.57)² / 2) - 9.89 * 10.57 - (((10)² / 2) - 9.89 * 10)]

P(Y > X + 0.11) = 3.0805 * [((111.7249 / 2) - 104.9135 - (50 / 2 - 98.9)]

P(Y > X + 0.11) = 3.0805 * [(55.86245 - 104.9135 + 49.9)]

P(Y > X + 0.11) = 3.0805 * [0.84895]

P(Y > X + 0.11) ≈ 2.6092

Therefore, the probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X) is approximately 2.6092%.

To learn more on probability click:

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Answer:

y=5

x=10 and

z=2

Step-by-step explanation:

since they are equivalance then,

for

triangle ABC and triangle DFE

AB=DF,BC=FE and AC= DE

So, AB=DF

8y-20= 4y

or, y=5

Then, BC= FE

2x+5=x+15

or, x=10

and

AC=DE

3z+9=10z-5

or, z= 2

hope u got ut.

The triangles are parallel thus their sides are equal to each other peer to peer.

So ;

[tex]x + 15 = 2x + 5[/tex]

Subtract sides -5

[tex]x + 15 - 5 = 2x + 5 - 5[/tex]

[tex]x + 10 = 2x[/tex]

Subtract sides -x

[tex]x - x + 10 = 2x - x[/tex]

[tex]x = 10[/tex]

_________________________________

[tex]4y = 8y - 20[/tex]

Subtract sides -8y

[tex]4y - 8y = 8y - 8y - 20[/tex]

[tex] - 4y = - 20[/tex]

Negatives simplifies

[tex]4y = 20[/tex]

Divided sides by 4

[tex] \frac{4}{4}y = \frac{20}{4} \\ [/tex]

[tex]y = 5[/tex]

_________________________________

[tex]10z - 5 = 3z + 9[/tex]

Plus sides 5

[tex]10z - 5 + 5 = 3z + 9 + 5[/tex]

[tex]10z = 3z + 14[/tex]

Subtract sides -3z

[tex]10z - 3z = 3z - 3z + 14[/tex]

[tex]7z = 14[/tex]

Divided sides by 7

[tex] \frac{7}{7}z = \frac{14}{7} \\ [/tex]

[tex]z = 2[/tex]

_________________________________

And we're done....♥️♥️♥️♥️♥️

Answer:

6

Step-by-step explanation:

51 divided by 8.5

The measurement of ∠KNL   is 102°

First, you must set up an equation to find x.

[tex]5x+2=[3(x+14)[/tex]

Then, you must simplify both sides of the equation.

[tex]5x+2=3x+42[/tex]

Next, subtract 3x on both sides.

[tex]2x+2=42[/tex]

Then, subtract 2 on each side.

[tex]2x=40[/tex]

Next, divide 2 on each side.

[tex]x=20[/tex]

Now that we have the value of x, we can substitute it in for angle KNL.

[tex][3(20+14)][/tex]

[tex][3(34)][/tex]

[tex]102[/tex]

[tex]102[/tex]°

You would need 3/4 cups of water.

Answer:

Step-by-step explanation:

582×23≈600×20=12,000

Answer:

-7

Step-by-step explanation:

(-12)-(-5)

negative and negative make a positive

-12+5

= -7

Answer:

-7

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

yes the last person is correct

Step-by-step explanation:

Answer:

a = -6

Cov (2X+Y, 3X-4Z) = 30

Step-by-step explanation:

Key points:

Cov(2X, -3Y+2) = a⋅Cov (X,Y)

Cov (2X, -3Y) + Cov (2X, 2) = a⋅Cov (X,Y)

(2)⋅(-3)⋅Cov (X, Y) + 0 = a⋅Cov (X,Y)

-6⋅Cov (X, Y) + 0 = a⋅Cov (X,Y)

⇒ a = -6.

(c)

Suppose that X, Y, and Z are independent, with a common variance of 5, i.e. V (X) = V (Y) = V (Z) = 5

Cov (2X+Y, 3X-4Z) = Cov (2X, 3X) + Cov (2X, -4Z) + Cov (Y, 3X) + Cov (Y, -4Z)

                               = 6⋅Cov (X, X) - 8⋅Cov (X, Z) + 3⋅Cov (Y, X) - 4⋅Cov (Y, Z)

                               = (6 × 5) - 0 + 0 - 0

                               = 30

Thus, the value of Cov (2X+Y, 3X-4Z) is 30.

The value of a = -6. And, Cov (2X+Y, 3X-4Z) = 30.

Since

Cov (aX, bY) = a·b·Cov (X, Y)

Cov (X, X) = V (X)

Cov (X, a) = 0

In the case when X and Y are independent so Cov (X, Y) = 0.

Now

Cov(2X, -3Y+2) = a⋅Cov (X,Y)

Cov (2X, -3Y) + Cov (2X, 2) = a⋅Cov (X,Y)

(2)⋅(-3)⋅Cov (X, Y) + 0 = a⋅Cov (X,Y)

-6⋅Cov (X, Y) + 0 = a⋅Cov (X,Y)

a = -6.

(c)

here

Suppose that X, Y, and Z are independent, with a common variance of 5, i.e.

V (X) = V (Y) = V (Z) = 5

So,

Cov (2X+Y, 3X-4Z) = Cov (2X, 3X) + Cov (2X, -4Z) + Cov (Y, 3X) + Cov (Y, -4Z)

= 6⋅Cov (X, X) - 8⋅Cov (X, Z) + 3⋅Cov (Y, X) - 4⋅Cov (Y, Z)

= (6 × 5) - 0 + 0 - 0

= 30

Thus, the value of Cov (2X+Y, 3X-4Z) is 30.

Learn more about variance here: https://brainly.com/question/24138432

Answer: is 0.001

10^-3 = (1)/(10^3) move the negative exponent to the denominator (1)/(1000) simplify 10^3 in the denominator (1)/(1000) = 0.001

Step-by-step explanation:

Hope you have a great night

Answer: 0.001

Step-by-step explanation:

Answer:

i will

Step-by-step explanation:

Answer: The heaviest 19% of fruits weigh more than 753grams.

Step-by-step explanation:

Let X = fruit's weights that are normally distributed.

Given: [tex]\mu=720,\ \ \ \sigma=38[/tex]

To find : x such that P(X>x)=19%

i.e. P(X<x) = 81%  [100%-19%=81%]

i.e. P(X<x) = 0.81

[tex]P(\dfrac{X-\mu}{\sigma}<\dfrac{x-720}{38})=0.81[/tex]

Since, [tex]Z=\dfrac{X-\mu}{\sigma}[/tex] and from z-table the z value for p-value of 0.81 (one -tailed) = 0.8779

[tex]\dfrac{x-720}{38}=0.8779\\\\\Rightarrow\ x-720 =38\times0.8779\\\\\Rightarrow\ x-720 =33.36\\\\\Rightarrow\ x = 33.36+720=753.36\approx753[/tex]

Hence, the heaviest 19% of fruits weigh more than 753grams.

Answer:

Step-by-step explanation:

To write the value of three hundred and eighty two thousandths in words, we can follow the steps below:

Split the expression based on the place values

The statement is expressed as:

[tex]\frac{382}{1000}[/tex] = 0.382

three hundred thousandth = 0.300 (thousandth)

eighty thousandth= 0.080

two thousandth = 0.002

Add the values gotten

= 0.300 + 0.080 + 0.002

= (3*10⁻¹) + (8*10⁻²) + (2*10⁻³)

= 0.382

Answer:

NOM and POR

(so so sorry if it's wrong, I tried my best to help you but I had to look up an image of a angle like that but i hope you have a wonderful day, sorry again if i am wrong, i hope i help in a way, in i did not, sorry)

Answer:

4, 2.75, 1.5, 0.25, –1, . . .

Step-by-step explanation:

edge2020

Answer:

6.32455532034

is the square root of 40

Answer:

38.5

Step-by-step explanation:

17-19= -2

-2+156=154

154 divided by 4= 38.5

it should be 17 - 19 + 154 then divided by 4

so 38.5 cookies

Answer:

2

Step-by-step explanation:

Here, we have a mean of 50 and a standard deviation of 25, we now need to find out in terms of standard deviation how 0 is far from 50.

Firstly, we subtract 0 from 50

That gives 50. Now, we need to divide this difference by the standard deviation

That will be 50/25 and that makes it 2

So 0 is two deviations away from 50

Answer:

[tex]\theta = 56[/tex]

Step-by-step explanation:

Represent the angles with [tex]\theta[/tex] and [tex]\alpha[/tex]

Such that:

[tex]\theta = 22 + \alpha[/tex]

Since both angles are complementary, we have:

[tex]\theta + \alpha = 90[/tex]

Substitute [tex]\theta = 22 + \alpha[/tex]

[tex]22 + \alpha + \alpha = 90[/tex]

[tex]22 + 2\alpha = 90[/tex]

Collect Like Terms

[tex]2\alpha = 90 - 22[/tex]

[tex]2\alpha = 68[/tex]

[tex]\alpha = 68/2[/tex]

[tex]\alpha = 34[/tex]

Recall that:

[tex]\theta = 22 + \alpha[/tex]

[tex]\theta = 22 + 34[/tex]

[tex]\theta = 56[/tex]

Hence:

The larger angle is 56

3A=120 degrees (bcoz they are alternate exterior angles)

A= 40 degrees

5B= 120 degrees( bcoz they're alternate exterior angles)

B= 24 degrees

to find value of y I equalized

8+15=29/3 + y

y= 23-29/3

y=17/3

Answer/Step-by-step explanation:

Part A: In the table given above, every input value has exactly one output value. No input value gives two different output value. Therefore, the data in the table represents a function.

Part B: in the table given, when x = 4, y = 9. That is, f(4) = 9.

Given the relation f(x) = 2x - 8, to find what value it would give us, when x = 4, substitute x = 4 into the relation.

f(4) = 2(4) - 8 = 8 - 8

f(4) = 0

Therefore, the relation in the table has a greater value when x = 4.

Part C: using, f(x) = 2x - 8, when f(x) = 34, value of x would be calculated as shown below:

34 = 2x - 8

Add 8 to both sides

34 + 8 = 2x

42 = 2x

Divide both sides by 2

42/2 = x

21 = x

x = 21

Answer:

6

Step-by-step explanation:

I solved the equation, but you can't simplify 6.