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Romashka [77]
3 years ago
6

The picture below shows a box sliding down a ramp:

Mathematics
1 answer:
Gennadij [26K]3 years ago
4 0

Answer:

AC=15.1\ ft

Step-by-step explanation:

we know that

In the right triangle ABC

The function sine of angle 68 degrees is equal to divide the opposite side SB by the hypotenuse AC

so

sin(68\°)=\frac{AB}{AC}

substitute the values and solve for AC

sin(68\°)=\frac{14}{AC}

AC=\frac{14}{sin(68\°)}

AC=15.1\ ft

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A telemarketer is successful at getting people to donate money for her organization in 55% of all calls she makes. She must get
Tems11 [23]
An interesting twist to a binomial distribution problem.

Given:
p=55%=0.55 for probability of success in solicitation
x=4=number of successful solicitations
n=number of calls to be made
P(x,n,p)>=89.9%=0.899  (from context, it is >= and not =, which is almost impossible)

From context of question, all calls are assumed independent, with constant probability of success, so binomial distribution is applicable.

The number of successes, x, is then given by
P(x)=C(n,x)p^x(1-p)^{n-x}where
p=probability of success
n=number of trials
x=number of successesC(n,x)=\frac{n!}{x!(n-x)!}

Here we need n such that
P(x,n,p)>=0.899
given
x>=4, p=0.55, which means we need to find

Method 1: if a cumulative binomial distribution table is available, we can look up n=9,10,11 and find
P(x>=4,9,0.55)=0.834
P(x>=4,10,0.55)=0.898
P(x>=4,11,0.55)=0.939
So she must make (at least) 11 calls to make sure the probability of meeting her quota is 89.9% or more.

Method 2: using technology.
Similar to method 1, we can look up the probabilities directly, for n=9,10,11
P(x>=4,9,0.55)=0.834178
P(x>=4,10,0.55)=0.8980051
P(x>=4,11,0.55)=0.9390368

Method 3: using simple calculator
Here we need to calculate the probabilities for each value of n=10,11 and sum the probabilities of FAILURE S=P(0,n,0.55)+P(1,n,0.55)+P(2,n,0.55)+P(3,n,0.55)
so that the probability of success is 1-S.
For n=10,
P(0,10,0.55)=0.000341
P(1,10,0.55)=0.004162
P(2,10,0.55)=0.022890
P(3,10,0.55)=0.074603
So that
S=0.000341+0.004162+0.022890+0.074603
=0.101995
and Probability of getting 4 successes (or more) 
=1-S
=0.898005, missing target by 0.1%

So she will have to make 11 phone calls, bring up the probability to 93.9%.  The work is similar to that of n=10.
8 0
3 years ago
SAT question <br> Can someone explain to me what this is asking
frozen [14]

Answer:

B

Step-by-step explanation:

The vertex is the turning point of the parabola.

First find the zeros by equating y to zero, that is

(x - 6)(x + 12) = 0

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 12 = 0 ⇒ x = - 12

The vertex lies on the axis of symmetry which is situated at the midpoint of the zeros, thus

x_{vertex} = \frac{6-12}{2} = \frac{-6}{2} = - 3

Thus the x- coordinate of the vertex is x = - 3 → B

6 0
3 years ago
Латна монтаж на работа
Bezzdna [24]

Answer:

$183.75

Step-by-step explanation:

divide by 12 (hours)

147/12=12.25

multiply by 15 (hours)

12.25*15=183.75

Hope this helps! :)

4 0
3 years ago
How do you find the general solution for cos2A=cos^2A
eduard

Answer:

A =  0 +/- nπ radians ,  where n is an integer.

Step-by-step explanation:

cos 2A =  cos^2 A

Use the identity cos 2A = 2 cos^2 A -1  :

2cos^2 A - 1 = cos^2 A

cos^2 A = 1

Cos A = +/-1

When cos A = 1,  A = 0 +/- 2nπ radians.

when cos A = -1, A = π +/- nπ radians.

6 0
3 years ago
What is the answer to this hard question -5k - 19 = 5 -13k
Gwar [14]

You are trying to solve for k (get k by itself)

-5k - 19 = 5 - 13k       Add 19 on both sides

-5k - 19 + 19 = 5 - 13k + 19

-5k = 24 - 13k          Add 13k on both sides

-5k + 13k = 24 - 13k + 13k

8k = 24       Divide 8 on both sides

k = 3

3 0
3 years ago
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