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grandymaker [24]
2 years ago
8

Noelle stands at the edge of a cliff and drops a rock. The height of the rock is given by the function f(x)-4.9x2 + 15, where c

is the number of seconds after noelle releases her rock.
Cesar, who is standing nearby on the ground, throws a rock straight up in the air. The height of Cesar’s rock is given by the function g(x)-4.9x2+10x, where x is the number of seconds after he releases his rock.

What is the height the money the two rocks are at the same level above ground.

Mathematics
1 answer:
Oxana [17]2 years ago
3 0
A graphing calculator shows the rocks are at the same height 1.5 seconds after they are released.

That height is 3.975 meters.

_____
f(x) = g(x)
-4.9x^2 +15 = -4.9x^2 +10x
15 = 10x . . . . . . . . . . . . . . . . . . add 4.9x^2
1.5 = x . . . . . . . . . . . . . . . . . . . divide by 10
f(1.5) = -4.9*2.25 +15 = 3.975

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A recent study found that 51 children who watched a commercial for Walker Crisps (potato chips) featuring a long-standing sports
hichkok12 [17]

Answer:

1

The claim is that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

2

The kind of test to use is a t -test because a t -test is used to check if there is a difference between means of a population

3

t  =  3.054

4

The p-value  is   p-value  =  P(Z >  3.054) = 0.0011291

5

The conclusion is  

There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

The test statistics is  

Step-by-step explanation:

From the question we are told that

   The first sample size is  n_1  =  51

    The first sample  mean is \mu_1  =  36

    The second sample size is  n_2  =  41

    The second sample  size is  \mu_2  =  25

     The first standard deviation is  \sigma _1  =  21.4 \  g

    The second standard deviation is  \sigma _2  =  12.8 \  g

  The  level of significance is  \alpha =  0.05

The  null hypothesis is  H_o  :  \mu_1 = \mu_ 2

The  alternative hypothesis is  H_a :  \mu_1 > \mu_2

Generally the test statistics is mathematically represented as

    t  =  \frac{\= x_1 - \= x_2}{ \sqrt{ \frac{s_1^2}{n_1}  + \frac{s_2^2}{n_2}  } }

=>   t  =  \frac{ 36 - 25}{ \sqrt{ \frac{ 21.4^2}{51}  + \frac{ 12.8^2}{41}  } }

=> t  =  3.054

The  p-value is mathematically represented as

     p-value  =  P(Z >  3.054)

Generally from the z table  

             P(Z >  3.054) =  0.0011291

=>   p-value  =  P(Z >  3.054) = 0.0011291

From the values obtained  we see that p-value  < \alpha so  the null hypothesis is rejected

Thus the conclusion is  

  There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

5 0
2 years ago
Rachel is bowling with her friends. her bowling ball has a radius of 4 inches. as she bowls she tracks the location of the finge
Goshia [24]

Question Continuation

The finger hole changes by 45 degrees.

Define a function, f, that gives the height of the finger hole above the ground (in inches) in terms of the angle of rotation (measured in radians) it has swept out from the 12 o'clock position.

Answer:

f(θ) = r(1 + cos(θ)) for 0 ≤ θ ≤ π/4

Step-by-step explanation:

Given

Let represent radius

r = 4 inches

Considering that she starts tracking the location when the finger hole is at the 12 o'clock; this means that the angle measurement at this point is 0°.

Let θ represent the angle

At 12 o'clock mark

θ = 0

When the finger hole changes by 45 degrees

θ = 45°

Convert 45° to radians

θ = 45° * π/180

θ = π/4

So, angle θ is such that θ∈[0, π/4]

This can be represented as

0 ≤ θ ≤ π/4

Calculating the measure of f(θ) in polar coordinates

When θ = 0, f(θ) = r (i.e. the current position of the bowl)

When θ = π/2, f(θ) = rcosθ

This is so because f(θ), being the function of the height is a measure of the radius* cos(θ)

Taking measurement of f(θ) from 0 to π/2

f(θ) = r + rcosθ

f(θ) = r(1 + cos(θ))

So, f(θ) = r(1 + cos(θ)) for 0 ≤ θ ≤ π/4

7 0
2 years ago
In general, after a group makes a reservation at a restaurant, they do not show up 20% of the time. If a restaurant has 8 reserv
sashaice [31]

Answer:

P(more than 2 don't show up)=0.2031

Step-by-step explanation:

Multiplication rule for independent events:

If two events A and B are independent then the multiplication rule state that:

P(A and B)= P(A) x P(B)

Find the probability that more than two do not show up:

The probability that the reservations at the restaurant do not show up is 0.20 (=20%) and there were 8 reservations.

P(more than 2 don't show up)= 1- P(less than or equal to 2 don't show up)

= 1-( P(none show up) +P(one don't show up)+P(two don't show up)

=1- ((0.8⁸) +₈ C₁ (0.2¹)x(0.8⁷)  +₈ C₂ (0.2²)x(0.8⁶)

=1- (0.1678 +0.3355+0.2936)= 1-0.7969

P(more than 2 don't show up)=0.2031

5 0
2 years ago
Lucia is making a 21.6 centimeter beaded string to hang in the window. She decides to put a green bead every 0.4 centimeters and
olasank [31]
21.6 ÷ 0.4 = 54 times for green
21.6 ÷ 0.6 = 36 times for purple

Together, 90 beads. Separately, 54 green and 36 purple.
3 0
2 years ago
Read 2 more answers
Let n be an integer in the conditional statement below.
statuscvo [17]

Answer:

The hypothesis is:   "The last digit of n is zero."

The conclusion is:   "n is divisible by five."

The converse is:   "If n is divisible by five, the the last digit of n is zero."

The contrapositive is:   "If n is not divisble by five, then n does not end in zero."

Step-by-step explanation:

I just took the test :)

5 0
2 years ago
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