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2 years ago

14

A group of students surveyed chose baseball and soccer as their favorite sport in the ratio 3:8

1 answer:

Anna [14]2 years ago

5 0

$3x-\ those\ who\ chose\ baseball\\8x-\ those\ who\ chose\ soccer\\\\
a)\\3x+8x=132\\\\
11x=132\ \ \ | divide\ by\ 11\\\\x=12\\\\
8x=8*12=96\\\\
96\ chose\ soccer.\\\\\
b)\\8x=56\ \ \ | divide\ by\ 8\\\\x=7\\\\
3x=3*7=21\\\\
21\ chose\ baseball.$

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What is the common ratio of the geometic sequence whose second and forth terms are 6 and 54, respectively?

Luda [366]

Answer:

C

Step-by-step explanation:

The n th term formula of a geometric sequence is

$a_{n}$ = a $r^{n-1}$

where a is the first term and r the common ratio

Using the second and fourth term, then

ar = 6 → (1)

ar³ = 54 → (2)

Divide (2) by (1)

$\frac{ar^3}{ar}$ = $\frac{54}{6}$ = 9

r² = 9 ⇒ r = $\sqrt{9}$ = 3 → C

7 0

2 years ago

Read 2 more answers

17. A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. Find

Pavlova-9 [17]

Answer:

$r = 3.74cm$

Step-by-step explanation:

Given

Hemisphere

$Radius = 7cm$

Cone

$Height = 49m$

Required

Determine the radius of the cone

First, we calculate the volume (V1) of the hemisphere.

$V_1 = \frac{2}{3}\pi r^3$

Substitute 7 for r

$V_1 = \frac{2}{3}\pi * 7^3$

$V_1 = \frac{2}{3}\pi * 343$

$V_1 = \frac{686}{3}\pi$

Volume (V2) of a cone is:

$V_2 = \frac{1}{3}\pi r^2h$

Because the lead is cast into a cone, then they have the same volume.

So, we have:

$\frac{686}{3}\pi = \frac{1}{3}\pi r^2h$

$686 = r^2h$

Substitute 49 for h

$686 = r^2 * 49$

Divide both sides by 49

$r^2 = \frac{686}{49}$

$r^2 = 14$

$r = \sqrt{14$

$r = 3.74cm$

<em>Hence, the radius of the cone is 3.74cm</em>

5 0

2 years ago

The points ????(0,0), ????(−4,1), ????(−3,5), and ????(1,4) are the vertices of parallelogram OABC Is this parallelogram a

gavmur [86]

Answer:

Yes, parallelogram OABC is a rectangle.

Step-by-step explanation:

The vertices of a parallelogram are O(0,0), A(-4,1), B(-3,5) and C(1,4).

A parallelogram is a rectangle if its any two adjacent sides are perpendicular to each other.

product of slopes of two perpendicular lines is -1.

Formula for slope is

$Slope=\dfrac{y_2-y_1}{x_2-x_1}$

Using the formula we get

$m_{OA}=\dfrac{1-0}{-4-0}=-\dfrac{1}{4}$

$m_{AB}=\dfrac{5-1}{-3-(-4)}=-\dfrac{4}{1}=4$

$m_{OA}\times m_{AB}=-\dfrac{1}{4}\times 4=-1$

It means OA is perpendicular to AB.

Since two adjacent sides are perpendicular, therefore the given parallelogram OABC is a rectangle.

6 0

2 years ago

24 POINTS!!!! help please. No work needed....

Mrrafil [7]

I’m more than happy to help you

8 0

3 years ago

Please help, refer to the picture for information.

aleksklad [387]

Answer:

b

Step-by-step explanation:

Using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (4, 1)

d = $\sqrt{(4+1)^2+(1-4)^2}$

= $\sqrt{5^2+(-3)^2}$

= $\sqrt{25+9}$ = $\sqrt{34}$ → b

5 0

2 years ago