Forty families gathered for a fund-raising event. Suppose the individual contribution for each family is normally distributed with a mean and a standard deviation of $120 and $24, respectively. The organizers would call this event a success if the total contributions exceed $5,200. What is the probability that this fund-raising event is a success?

Step-by-step explanation:

3(x - 5) = 6

x - 5 = 2 (divide 3 on both sides)

x = 7 (add 5 on both sides)

The solution is x = 7.

3(x-5)=6

multiply 3 by x and -5

3x-15=6

add 15 on each side

it cancels out on the left nd on the right u get 21

so it would be

3x=21

divide by 3 on each side

X=7

Check:

3(7-5)=6

3(2)=6

6=6

Answer:

h = (A - 2πr²)/(2πr)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

A = 2πrh + 2πr²

Step 2: Solve for h

Answer:

[tex]c=2.25[/tex]

Step-by-step explanation:

[tex]4.5=2c\\2c=4.5\\c=4.5/2\\c=2.25[/tex]

Answer:

[tex]Time = 11\frac{2}{3}\ min[/tex]

Step-by-step explanation:

Given

[tex]Security\ A = 2\ mins, 20\ secs[/tex]

[tex]Security\ B = 1\ mins, 40\ secs[/tex]

Required

After how many minutes, will they round together

First, convert the given time to minutes

[tex]Security\ A = 2\ mins, 20\ secs[/tex]

[tex]Security\ A = 2\ mins+ 20\ secs[/tex]

[tex]Security\ A = 2\ mins+ \frac{20}{60}\ min[/tex]

[tex]Security\ A = 2\ mins+ \frac{1}{3}\ min[/tex]

[tex]Security\ A = 2\frac{1}{3}\ min[/tex]

[tex]Security\ B = 1\ mins, 40\ secs[/tex]

[tex]Security\ B = 1\ mins+ 40\ secs[/tex]

[tex]Security\ B = 1\ mins+ \frac{40}{60}\ min[/tex]

[tex]Security\ B = 1\frac{2}{3}\ min[/tex]

So, we have:

[tex]Security\ A = 2\frac{1}{3}\ min[/tex]

[tex]Security\ B = 1\frac{2}{3}\ min[/tex]

List out the multiples of the time of both security personnel take round.

[tex]Security\ A = 2\frac{1}{3}min,\ 4\frac{2}{3}min,\ 7min,\ 9\frac{1}{3}min,\ 11\frac{2}{3}min...[/tex]

[tex]Security\ B = 1\frac{2}{3}min,\ 3\frac{1}{3}min,\ 5min,\ 6\frac{2}{3}min,\ 8\frac{1}{3}min,\ 10min\ ,11\frac{2}{3}min,...[/tex]

In the above lists, the common time is:

[tex]Time = 11\frac{2}{3}\ min[/tex]

This implies that they go on round after [tex]11\frac{2}{3}\ min[/tex]

Answer:

x = -2

Step-by-step explanation:

5x + 2(x - 4) = 5x + x - 10

First, we need to to multiply out the parathesis in the equation:

5x + 2(x - 4) = 5x + x - 10

5x + 2x - 8 = 5x + x - 10

Next, we can combine "like terms" to simplify the equation further:

5x + 2x - 8 = 5x + x - 10

7x - 8 = 6x - 10

Now we can isolate the variable "x" to one side:

7x - 8 = 6x - 10

x - 8 = -10

x = -2

To check our work, we can replace x with -2 in our original equation:

5x + 2(x - 4) = 5x + x - 10

5(-2) + 2 (-2 - 4) = 5(-2) + -2 - 10

-10 + 2 (-6) = -10 -2 - 10

-22 = -22

I hope this helps!

-TheBusinessMan

Answer:

C. 3.33 moles

Step-by-step explanation:

Ammonia decomposes

[tex]2NH_3\rightarrow N_2+3H_2[/tex]

We have to find the moles of hydrogen formed in 2.22 moles of ammonia.

From the reaction

2 moles of ammonia gives 3 moles of hydrogen

1 mole of ammonia  produce hydrogen=3/2 moles

2.22 moles of ammonia produces hydrogen=[tex]\frac{3}{2}\times 2.22[/tex] moles

Number of moles of hydrogen formed by decomposition of 2.22 moles of ammonia

=[tex]\frac{6.66}{2}=3.33[/tex]moles

Hence, 3.33 moles of hydrogen are formed in 2.22 moles of ammonia.

Option C is true.

C. 3.33 moles

Answer:

Surface area = 70π cm²

Step-by-step explanation:

Surface area = πr² + πrl

Surface area = (π × 5 × 5) + (π × 5 × 9)

Surface area = (25π) + (45π)

Surface area = 70π cm²

Answer:

92/85

Step-by-step explanation:

Answer:

option 2

Step-by-step explanation:

x is going away from 7 in a positive direction which means greater than. the fact that it is just greater than not equal to means that there is a black circle instead of a filled in one because it excludes that number.

Answer:

Option 2

Step-by-step explanation:

If the inequality is "x > 7" it means that if it was to be represented on a number line, all values that "c" could possibly take would be located to the right (on the number line) of 7. Now there only two options that follow this statement, those options are options 2 and 4. But there is another thing we must understand. x must be larger than 7 (it can not be equal to 7), therefor option 2 is right since it follows the second statement  while option 4 would represent inequality "x ≥ 7".      

Answer:

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:

Your answer is A

Step-by-step explanation:

I hope I helped :)

Answer:

Step-by-step explanation:

3x - 3y = -3

2x - 6y = 2

-6x + 6y = 6

2x - 6y = 2

-4x = 8

x = -2

-4 - 6y = 2

-6y = 6

y = -1

(-2, -1)

Answer:

5935 base balls

Step-by-step explanation:

Volume of a cylinder : pi * r² * h

r = Radius, h = height = 6ft

Diameter = 4ft ; Radius = diameter / 2 = 4/2 = 2ft

V = π * 2^2 * 6

V = 75.398223 ft³

Diameter of baseball = 2.8 inches

2.8 inches = 2.8 × 2.8 * 2.8 = 21.952 in³ = 0.0127037 ft³

Hence,

75.398223 ft³ / 0.0127037ft³

= 5935.1370

= 5935 base balls

Answer:

Step-by-step explanation:

a₁ = -3 = (-1)¹×3

a₂ = 6 = (-1)²×2×3

a₃ = -28 = (-1)³×2²×7

a₄ = 72 = (-1)⁴×2³×3²

a₅ = -360 = (-1)⁵×2³×3²×5

a₆ = 2160 = (-1)⁶×2⁴×3³×5

That's as far as I got. I can predict that a₇ is a multiple of -32 and a₈ is a multiple of 64, but I don't see the pattern with the other factors.

Answer:

t = 10

Step-by-step explanation:

15 = 1.5 × t

15/1.5 = t

10 = t

the answer is,

541.42%

I think this is the answer.

Answer:

Step-by-step explanation:

Using first equation in the second gives you

x-3(-2x+1)=11

x+6x-3=11

7x-3=11

7x=14

x=2, making y=-2x+1 become

y=-2(2)+1

y=-4+1

y=-3 so the solution is the point

(2,-3)

Answer:

a) 24[tex]ft^2[/tex]

b) 52ft

Step-by-step explanation:

a)

This question asks to find the capacity of the container. This is essentially asking what the volume of the container is. This can be done by multiplying the length by the width by the height.

4 * 2 * 3

= 24

b)

This question is asking how much material was used to make the prism. This is essentially asking what the surface area of the prism is. This can be found by finding the area of all the sides of the prism and then adding it up. Since it is a rectangular prism, opposite faces are congruent, hence one only has to find the area of three faces, add it up, then multiply it by two to find the answer.

2 ( 4 * 2 ) + 2 ( 3 * 4 ) + 2 ( 2 * 3 )

= 2(8) + 2(12) + 2(6)

= 16 + 24 + 12

= 52

Answer:

First and last

Step-by-step explanation:

(4x - 7) (x + 3)

FOIL

4x^2 + 5x - 21

Answer:

The order of large fries costs $ 2.10, while each hamburger costs $ 3.25.

Step-by-step explanation:

Given that the cost of a hamburger is $ 1.15 more than an order of large fries, and Bill bought two hamburgers and an order of fries for a total of $ 8.60, to determine what is the price of each item, the following calculation must be performed:

X + X + 1.15 + X + 1.15 = 8.60

3X + 2.30 = 8.60

3X = 8.60 - 2.30

X = 6.30 / 3

X = 2.10

Thus, each order of large fries costs $ 2.10, while each hamburger costs $ 3.25.

Answer:

Step-by-step explanation:

I think that you want to know how many total pounds of beans do you have.

Well, to find this, simply find the LCM of 6 and 4. That is 12.

So convert the fractions to have a denominator of 12.

10/12, 9/12

Now add:

(10+9)/12 = 19/12 = 1 7/12

Answer:

https://geometryhelp.net/triangle-inequality-theorem/

Step-by-step explanation:

This is from that site. Visit it and you may find what you're looking for.

If we want to go from point A to point B, getting there through any intermediate point C, which is not on the straight line between A and B, is going to be longer. This should seem intuitively correct. But we will prove it formally.

Where do triangles come into this? Imagine that the line AB is a side of a triangle, ΔABC. Going from A to B is the straight, short way. Going there by first going to another point, C (which is the side AC) and then from C to B (which is the side CB) is going to be longer.

Answer:

it is reflected in the x-axis so y=0

Answer:

area of a square

= side × side

= 12 × 12

=144cm^2

Answer:

6j(5k+3)

Step-by-step explanation:

18j+30jk

Factor out 6.

6(3j+5jk)

Consider 3j+5jk. Factor out j.

j(3+5k)

Rewrite the complete factored expression.

6j(5k+3)

Answer:

(x+1)(x-6)

thats the ans :)