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2 years ago

12

There are 16 books on a shelf. 7 of these books are new. (a) What is the ratio of new books to used books? (b) What is the ratio

of all books to used books?

2 answers:

777dan777 [17]2 years ago

4 0

The answers are
a. 7:9
b. 16:7

ELEN [110]2 years ago

4 0

7 out of the 16 books are new, so 9 of them are used.

7:9 is the ratio of new books to old books.
16:9 is the ratio of all books to used books.

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Two people are standing on opposite sides of a hill. Person A makes an angle of elevation of 65° with the top of the hill and pe

8090 [49]

Answer:

Option 3. 71 ft. is the distance between B and top of the hill.

Step-by-step explanation:

Let the height of the hill is h ft and the distance of A from the hill be x ft and distance from B to hill is y.

It is given distance between A and B is 45 ft. ∠BAO = 65° and ∠ABO = 80°.

We have to find the distance of B from the top of the hill.

Now from ΔACO $tan 65 = \frac{h}{45-x} = 2.14$

$h=2.14(45-x)$

From ΔBCO $tan80 = \frac{h}{x} = 5.67$

h = 5.67x

Now h = 5.67x = 2.14(45-x)

5.67x = 96.3 - 2.14x

2.14x + 5.67x = 96.3

7.81x = 96.3

x = 96.3/7.81 = 12.33 ft

Therefore $cos80 = \frac{x}{OB}$

$0.174 = \frac{12.33}{OB}$

$OB = \frac{12.33}{.174}=70.86=71ft.$

Therefore 71 ft is the distance between B and the top of the hill.

3 0

3 years ago

The surface area of a given cone is 1,885.7143 square inches. What is the slang height?

kap26 [50]

Answer:

If $r >> h$ , the slang height of the cone is approximately 23.521 inches.

Step-by-step explanation:

The surface area of a cone (A) is given by this formula:

$A = \pi \cdot r^{2} + 2\pi\cdot s$

Where:

$r$ - Base radius of the cone, measured in inches.

$s$ - Slant height, measured in inches.

In addition, the slant height is calculated by means of the Pythagorean Theorem:

$s = \sqrt{r^{2}+h^{2}}$

Where $h$ is the altitude of the cone, measured in inches. If $r >> h$ , then:

$s \approx r$

And:

$A = \pi\cdot r^{2} +2\pi\cdot r$

Given that $A = 1885.7143\,in^{2}$ , the following second-order polynomial is obtained:

$\pi \cdot r^{2} + 2\pi \cdot r -1885.7143\,in^{2} = 0$

Roots can be found by the Quadratic Formula:

$r_{1,2} = \frac{-2\pi \pm \sqrt{4\pi^{2}-4\pi\cdot (-1885.7143)}}{2\pi}$

$r_{1,2} \approx -1\,in \pm 24.521\,in$

$r_{1} \approx 23.521\,in \,\wedge\,r_{2}\approx -25.521\,in$

As radius is a positive unit, the first root is the only solution that is physically reasonable. Hence, the slang height of the cone is approximately 23.521 inches.

3 0

2 years ago

100 POINTS AND BRAINLIEST IF RIGHT A survey asked 12 students how many portable electronic devices they have in their homes. The

Morgarella [4.7K]

Answer:

¾

Step-by-step explanation:

More than 3: 9

P(more than 3) = 9/12 = ¾

6 0

3 years ago

X3 + 2xsquared - x - 2 = (x + 6_)(x + 2_)(x + 4_)

Anon25 [30]

3345 because it’s squared

3 0

2 years ago

Could someone help me with this ASAP? thanks !

Maru [420]

<h3>Answer:</h3>

A. $6x^2$ +-5x+14x+-35

$6x^2$ +9x-35

B. $5x^4+-3x^3+10x^3+-6x^2$

$5x^4+7x^3-6x^2$

C. $25x^2+-20x+20x+-16$

$25x^2-16$

D. $x^4+-4x^2+-7x^2+28$

$x^4-11x^2+28$

$====================================$

Step-by-step explanation:

A. (3x*2x)+(3x*-5)+(7*2x)+(7*-5)

Multiply and simplify.

$6x^2$ +9x-35

B. ( $x^2*5x^2$ )+( $x^2*$ -3x)+(2x $*5x^2$ )+(2x $*-3x$ )

Multiply and simplify.

$5x^4+7x^3-6x^2$

C. $(5x*5x)+(5x*-4)+(4*5x)+(4*-4)$

Multiply and simplify.

$25x^2-16$

D. $(x^2*x^2)+(x^2*-4)+(-7*x^2)+(-7*-4)$

Multiply and simplify.

$x^4-11x^2+28$

I hope this helps!

But you should really do this yourself.

3 0

3 years ago