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3 years ago

2. What is the external probability of rolling a 4

Mathematics

1 answer:

Nataly_w [17]3 years ago

6 0

Answer:

2. 1- Experimental probability of rolling a 4 = 40%

3. 2- Theoretical probability is 3% greater than experimental probability.

Step-by-step explanation:

Experimental probability of rolling a 4 = 100 × $\frac{8}{20}$

= 100 × 0.4

= 40%

Experimental probability of getting at least one tail = $\frac{72}{100}$

= 0.72

Theoretical probability of getting at least one tail = $\frac{3}{4}$

= 0.75

Theoretical probability is 3% greater than experimental probability.

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6x+7x^2 Factor the expression completely.

Anettt [7]

Answer:

x(6+7x)

Step-by-step explanation:

7 0

2 years ago

An investigator wants to estimate caffeine consumption in high school students. how many students would be required to estimate

astraxan [27]

We can solve this problem by referring to the standard probability distribution tables for z.

We are required to find for the number of samples given the proportion (P = 5% = 0.05) and confidence level of 95%. This would give a value of z equivalent to:

z = 1.96

Since the problem states that it should be within the true proportion then p = 0.5

Now we can find for the sample size using the formula:

n = (z^2) p q /E^2

where,

q = 1 – p = 0.5

E = estimate of 5% = 0.05

Substituting:

n = (1.96^2) 0.5 * 0.5 / 0.05^2

n = 384.16

<span>Around 385students are required.</span>

6 0

3 years ago

Find a parametrization of the line in which the planes x + y + z = -6 and y + z = -8 intersect.

rewona [7]

Answer:

L(x,y) = (2,-8,0) + (0,-1,1)*t

Step-by-step explanation:

for the planes

x + y + z = -6 and y + z = -8

the intersection can be found subtracting the equation of the planes

x + y + z - ( y + z ) = -6 - (-8)

x= 2

therefore

x=2

z=z

y= -8 - z

using z as parameter t and the point (2,-8,0) as reference point , then

x= 2

y= -8 - t

z= 0 + t

another way of writing it is

L(x,y) = (2,-8,0) + (0,-1,1)*t

6 0

3 years ago

(Photo attached) Trig question. I partially understand it, but not completely. Please explain! :) Thanks in advance.

aliya0001 [1]

Answer:

A = 2
B = 3

Step-by-step explanation:

You can start by recognizing 19/12π = π +7/12π, so the desired sine is ...

sin(19/12π) = -sin(7/12π) = -(sin(3/12π +4/12π)) = -sin(π/4 +π/3)

-sin(π/4 +π/3) = -sin(π/4)cos(π/3) -cos(π/4)sin(π/3)

Of course, you know that ...

sin(π/4) = cos(π/4) = (√2)/2

cos(π/3) = 1/2

sin(π/3) = (√3)/2

So, the desired value is ...

sin(19π/12) = -(√2)/2×1/2 -(√2)/2×(√3/2) = -(√2)/4×(1 +√3)

Comparing this form to the desired answer form, we see ...

A = 2

B = 3

5 0

3 years ago

The heat index I is a measure of how hot it feels when the relative humidity is H (as a percentage) and the actual air temperatu

PSYCHO15rus [73]

Answer:

a) $I(95,50) = 73.19$ degrees

b) $I_{T}(95,50) = -7.73$

Step-by-step explanation:

An approximate formula for the heat index that is valid for (T ,H) near (90, 40) is:

$I(T,H) = 45.33 + 0.6845T + 5.758H - 0.00365T^{2} - 0.1565TH + 0.001HT^{2}$

a) Calculate I at (T ,H) = (95, 50).

$I(95,50) = 45.33 + 0.6845*(95) + 5.758*(50) - 0.00365*(95)^{2} - 0.1565*95*50 + 0.001*50*95^{2} = 73.19$ degrees

(b) Which partial derivative tells us the increase in I per degree increase in T when (T ,H) = (95, 50)? Calculate this partial derivative.

This is the partial derivative of I in function of T, that is $I_{T}(T,H)$ . So

$I(T,H) = 45.33 + 0.6845T + 5.758H - 0.00365T^{2} - 0.1565TH + 0.001HT^{2}$

$I_{T}(T,H) = 0.6845 - 2*0.00365T - 0.1565H + 2*0.001H$

$I_{T}(95,50) = 0.6845 - 2*0.00365*(95) - 0.1565*(50) + 2*0.001(50) = -7.73$

8 0

3 years ago