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3 years ago

11

A coin is loaded so that the probability of getting heads is 3/4. If the coin is flipped twice, what is the probability of getti

ng heads twice?

2 answers:

USPshnik [31]3 years ago

6 0

The probability would be 9/16.
HOPE THIS HELPS! ^_^

Alisiya [41]3 years ago

5 0

The probability of the coin getting heads twice is 2/4

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A swimming pool has a rectangular base 10 ft long and 20 ft wide. The sides are 4 ft high, and the pool is half

Lostsunrise [7]

Answer:74880 ft.lb

Step-by-step explanation:

Given

Dimension of pool

base=10 ft

width=20 ft

height=4 ft

Pool is half filled

volume of Pool $=10\times 20\times 2=400 ft^3$

mass of water $=\rho \times volume$

mass $=62.4\times 400=24,960 lb$

This pool is in the form parallelepiped therefore average distance $=\frac{4+2}{2}=3$

Work $= 249600\times 3=74880 ft.lb$

7 0

3 years ago

Help me with these please

olchik [2.2K]

Step-by-step explanation:

(1) y = x e^(x²)

Take derivative with respect to x:

dy/dx = x (e^(x²) 2x) + e^(x²)

dy/dx = 2x² e^(x²) + e^(x²)

dy/dx = (2x² + 1) e^(x²)

Take derivative with respect to x again:

d²y/dx² = (2x² + 1) (e^(x²) 2x) + (4x) e^(x²)

d²y/dx² = (4x³ + 2x) e^(x²) + 4x e^(x²)

d²y/dx² = (4x³ + 6x) e^(x²)

Substitute:

d²y/dx² − 2x dy/dx − 4y

= (4x³ + 6x) e^(x²) − 2x (2x² + 1) e^(x²) − 4x e^(x²)

= 4x³ + 6x − 2x (2x² + 1) − 4x

= 4x³ + 6x − 4x³ − 2x − 4x

= 0

(2) y = sin⁻¹(√x)

sin y = √x

sin²y = x

Take derivative with respect to x:

2 sin y cos y dy/dx = 1

sin(2y) dy/dx = 1

dy/dx = csc(2y)

Take derivative with respect to x again:

d²y/dx² = -csc(2y) cot(2y) 2 dy/dx

d²y/dx² = -2 csc²(2y) cot(2y)

Substitute:

2x (1 − x) d²y/dx² + (1 − 2x) dy/dx

= 2 sin²y (1 − sin²y) (-2 csc²(2y) cot(2y)) + (1 − 2 sin²y) csc(2y)

Use power reduction formula:

= (1 − cos(2y)) (1 − ½ (1 − cos(2y))) (-2 csc²(2y) cot(2y)) + (1 − (1 − cos(2y))) csc(2y)

= (1 − cos(2y)) (1 − ½ + ½ cos(2y)) (-2 csc²(2y) cot(2y)) + cos(2y) csc(2y)

= (1 − cos(2y)) (½ + ½ cos(2y)) (-2 csc²(2y) cot(2y)) + cot(2y)

= (cos(2y) − 1) (1 + cos(2y)) csc²(2y) cot(2y) + cot(2y)

= (cos²(2y) − 1) csc²(2y) cot(2y) + cot(2y)

= -sin²(2y) csc²(2y) cot(2y) + cot(2y)

= -cot(2y) + cot(2y)

= 0

8 0

3 years ago

9 less than quotient of n and 5

Ber [7]

The correct answer is:
(n/5)-9

5 0

3 years ago

A cognitive psychologist wants to know whether memory performance is changed by old age. She randomly selects 7 elderly individu

defon

Answer:

$z = \frac{418.7-465.6}{\frac{53.6}{\sqrt{7}}}= -2.340$

Now we can calculate the p value with the following probability

$p_v =2*P(z$

If we use the commonly significance level of 0.05 we see that the p value is lower than these values we can conclude that the true mean is different from the value of 465.6 at 5% of significance

Step-by-step explanation:

Data provided

$\bar X=418.7$ represent the mean score on the standardized memory test

$\sigma=53.6$ represent the population standard deviation

$n=7$ sample size

$\mu_o =465.6$ represent the value that we want to verify

z would represent the statistic

$p_v$ represent the p value

System of hypothesis

We are interested to check if the memory performance for elderly individuals differs from that of the general population (mean different from 465.6), the system of hypothesis are then:

Null hypothesis: $\mu = 465.6$

Alternative hypothesis: $\mu \neq 465.6$

Since we know the population deviation we can use the z statistic from the z test for the true mean:

$z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$ (1)

Replacing the info given we got:

$z = \frac{418.7-465.6}{\frac{53.6}{\sqrt{7}}}= -2.340$

Now we can calculate the p value with the following probability

$p_v =2*P(z$

If we use the commonly significance level of 0.05 we see that the p value is lower than these values we can conclude that the true mean is different from the value of 465.6 at 5% of significance

6 0

4 years ago

Sasha runs 8 miles on Thursday, then runs 8 more miles on Friday, she ran 1/2 mile on Saturday. hHOW MANY MILES DID SHE RUN?

lesantik [10]

16 and a half of a mile she had ran altogether

8 0

3 years ago