A middle school has 200 boys and 300 girls enrolled in the seventh-grade. The principal randomly selects 45 seventh-grade students to take a lunch survey. How many of the seventh-grade students selected for the survey should the principal expect to be boys?

Answer:

abcd

Step-by-step explanation:

efg

Explanation is in the file

tinyurl.com/wpazsebu

Distance=√[{3-(-5)}²+{-3-(-4)}²]=√[{8}²+{1}²]=√[64+1]=√65

Distance=√65=8.06 (approx)

Answer:

the dimensions of the rectangle are 10 and 7.

Step-by-step explanation:

Given;

area of the rectangle, A = 70 m²

dimensions of the rectangle, = x - 11 and x - 8

The area of rectangle is calculated as;

A = L x B

70 = (x - 11)(x - 8)

70 = x² - 8x - 11x + 88

0 = x² - 8x - 11x + 88 - 70

0 = x² - 19x + 18

0 = x² - x - 18x + 18

0 = x(x - 1) -18(x - 1)

0 = (x - 18)(x - 1)

0 = x - 18     or    

0 = x - 1

x = 18 or 1

The dimensions of the rectangle are calculated as;

L = 18 - 11  = 7

B = 18 - 8 = 10

Therefore, the dimensions of the rectangle are 10 and 7.

Answer:

12. 524 in³ (3 sig. fig.)   13. 2000 cm³ (3 sig. fig.)

Step-by-step explanation:

12. Volume of sphere = (4/3)πr³

= 500/3π

= 524 in³ (3 sig. fig.)

13. Volume of cylinder = πr²h

= 7²π(13)

= 637π

= 2000 cm³ (3 sig. fig.)

Answer:

8a + ab + 5

Step-by-step explanation:

1. a + 7a+3ab-2ab-1+6

2. combine like terms

(a + 7a) + (3ab - 2ab) + (-1+6)

8a + ab + 5

Answer:

8a + ab + 5

Step-by-step explanation:

combine like terms. like term have same variables

a and 7a  ; 3ab and (-2ab) ; (-1) and 6 are like terms

a + 7a + 3ab - 2ab - 1 + 6 = 8a + ab + 5

Answer:

The population in 2015 will be 165 million.

Step-by-step explanation:

The exponential growth formula is given by:

[tex] f(t) = a(1 + r)^{\Delta t} [/tex]

Where:

a: is the initial population

r: is the rate of increase

Δt: is the time        

With the initial information we can find the rate:

[tex] 151 = 145(1 + r)^{1998-1990} [/tex]      

Using logarithm:                                    

[tex] ln(151) = ln(145) + 8[ln(1 + r)] [/tex]  

[tex] ln(1 + r) = \frac{ln(151) - ln(145)}{8} [/tex]                        

[tex] ln(1 + r) = 5.0683 \cdot 10^{-3} [/tex]          

Using exponential:          

[tex] e^{ln(1 + r)} = e^{5.0683 \cdot 10^{-3}} [/tex]

[tex] r = 5.081 \cdot 10^{-3} [/tex]        

Now, we can find the estimated population in 2015:

[tex] f(t) = 151(1 + 5.081 \cdot 10^{-3})^{2015-1998} [/tex]              

[tex] f(t) = 165 [/tex]              

Therefore, the population in 2015 will be 165 million.

I hope it helps you!

Answer:

27/sqrt9, 4^2 are the rational numbers

Step-by-step explanation:

All the other ones do not terminate, so this leaves these as the answers.

hope this helps!

Answer:

Let's talk through this a one step at a time.

*Since f(x) is concave-up with its vertex on the x-axis, we know f(x) ≥ 0.

*We also know that when we shift a function's domain by a positive number, we shift the function left and when we shift a function's domain by a negative number, we shift the function right. So f(x-5) is f(x) shifted to the right by 5.

*At this point, f(x-5) has its vertex at (5,0).

*When we negate f(x-5), the parabola becomes concave down yet the vertex remains at (5,0). Now we're at -f(x-5). At this point we have -f(x-5)≤0 with a range (-∞,0]

*If we add 2 to create g(x)=2-f(x-5), then we have a concave down parabola with its vertex shifted up by 2, at (5,2). So, g(x) is concave down with its vertex at (5,2). Hence

Answer:

Step-by-step explanation:

x² - 7x - 30 = 0

x² + 3x - 10x - 30 = 0

x ( x + 3 ) - 10 ( x + 3 ) = 0

( x - 10 ) ( x + 3 )

x = 10 , -3

Answer:

-3 and 10

Step-by-step explanation:

[tex]f(x)=x^2-7x-30[/tex]

1) Factor the equation

First, find two factors of -30 which has a sum of -7.

⇒ These two factors are 3 and -10.

Then, write the equation as a product of two binomials.

[tex]f(x)=(x+3)(x-10)[/tex]

2) Find the zeros

The zero product property states that any value, when multiplied by 0 will equal 0. Therefore, in this equation, either x+3 or x-10 must equal 0 for the function to equal 0:

x+3=0

x=-3

or

x-10=0

x=10

Therefore, the zeros of the function are -3 and 10.

I hope this helps!

Answer:

its 4

Step-by-step explanation:

I uploaded the answer to a file hosting. Here's link:

tinyurl.com/wpazsebu

Answer:

72/96

Step-by-step explanation:

Answer:

I have made it in above picture

Answer:

2 A.)

1) 3-4x+8x^2-6+2x-5x^2

2) 8x^2-5x^2-4x+2x+3-6

3) 3x^2-2x-3

B.) 3x-5-7x^2+2+6x^2+5x

Step-by-step explanation:

please mark brainiest

please give 5 stars

thank you

Answer:

The last one.

Step-by-step explanation:

If you can't see or there's something you don't understand you can ask:) Good luck and I hope it helps.

A) Always

In a perfect sphere the centre is an equal distance from any point from the surface.

THANK YOU!!

∝ Sidhdi

Answer:

x = 53

Step-by-step explanation:

x = 53 (Vertically Opposite Angles)

Answer:

B.20

Step-by-step explanation:

The line that is parallel to this line will have the same slope of this line, as the two will never intersect. They will run side by side. The line y = 2x - 5 is written in slope-intercept form, which is y = mx + b. The value of m represents the slope, and in this equation m = 2. Therefore, the line we are looking for will have a slope of 2 also.

That line should also be in slope-intercept form. We now know the value of m, but we also know the value of x and y. The ordered pair (8, 10) is a point on the line, and every ordered pair is in the form (x, y). Therefore, x = 8 and y = 10. We can plug those values into y = mx + b, along with m = 2. That gives us:

10 = 2(8) + b We need to solve for b.

10 = 16 + b

b = -6

Answer:

Polymomial with 4 terms i believe

Answer:

Sorry I don't know this language

Answer:

b,c,d

Step-by-step explanation:

if its 43x, none of the point is true.

if its 4/3x:

a. Not true 4/3(1) + 5 = 6 1/3

b. True 4/3(6) + 5 = 13

c. True 4/3(21) + 5 = 33

d. True 4/3(99) + 5 = 137

Answer:

Step-by-step explanation:

Answer:

200 feet

Step-by-step explanation: