2 3/4 divided by 1/2 ?

If the diameter of a circle changes from 18 cm to 6 cm, how will the circumference change?

omeli [17]

We know that

the length of a circumference=2*pi*r
for D1=18 cm--------------> r1=9cm
L1=2pi*9-------> 18pi cm

for D2=6 cm-----------> r2=3 cm
L2=2pi*3-------> 6pi cm

L2/L1----------> (6pi)/(18pi)---->1/3

the answer is the option A) multiplies by 1/3

6 0

3 years ago

Flora drew the following graph to answer the question. What was her mistake when she drew her graph?

slamgirl [31]

Answer:

She drew the graph too steep, if she is going down at a constant rate of 300 ft per hour, at 1 hour she would be at 2,700 ft. it would take her about 10 hours to get down the mountain.

7 0

2 years ago

A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test.

kompoz [17]

Complete Question

A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 40 girls and 40 boys in a community and gave them the standard memory test. The mean score for girls was 68 and the standard deviation of mean was 5.0. The mean score for boys was 66 and the standard deviation of mean was 5.0. What is the p-value and your conclusion at alpha 0.05

Answer:

The p-value is $p-value =0.073614$

The conclusion is

There is sufficient evidence to support the claim that there was no significant difference between boys and girls on a standard memory test

Step-by-step explanation:

From the question we are told that

The sample size of boys and girls is $n_1= n_2 = n = 40$

The standard deviation is $s_1= s_2 = s = 5$

The level of significance is $\alpha = 0.05$

The sample mean for boys is $\= x_1 =66$

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

$z = \frac{\= x_1 - \= x_2 }{ \sqrt{\frac{s_1 ^2 }{n_1} + \frac{s_2 ^2 }{n_1} } }$

=> $z = \frac{66 -68 }{ \sqrt{\frac{5^2 }{40} + \frac{5 ^2 }{40} } }$

=> $z = -1.789$

From the z table the area under the normal curve to the left corresponding to -1,789 is

$P(Z < -.1789 ) = 0.036807$

Generally the p-value is mathematically represented as

$p-value = 2 P(Z < -.1789 )$

=> $p-value = 2 * 0.036807$

=> $p-value =0.073614$

From the values obtained we see that $p-value < \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is sufficient evidence to support the claim that there was no significant difference between boys and girls on a standard memory test

3 0

2 years ago

What is 7.234 rounded to the nearest 10th

erma4kov [3.2K]

The answer would be 7.2 because the #in the hundredths place is less than 5

5 0

2 years ago

Read 2 more answers

20.

Mandarinka [93]

Answer:

a) e-0.03x(0.3-0.009x)

b) 33 hrs 20 min

c) 17.182

Step-by-step explanation:

Taking derivative of the above equation would give us the rate for change in donations :

hence

f'(x) = d/dx (0.3xe-0.03x)

using product rule of derivation where (uv)' = u'v +v'u

hence

f'(x) = (e-0.03x)d/dx(0.3x) + 0.3x*d/dx(e-0.03x)

= 0.3e-0.03x + 0.3x(-0.03)(e-0.03x)

f'(x) =0.3e-0.03x -0.009xe-0.03x

hence

a) rate of change in donations = e-0.03x(0.3-0.009x) taking exponent common

b) f'(x) = 0 according to statement

hence 0 = e-0.03x(0.3-0.009x)

0 = 0.3 - 0.009 x

which gives x = 33.33 hrs i.e after 33 hrs and 20 minutes rate of change of donations is 0.

c) donation level at the time is given by

f(x) = 0.3xe-0.03x

f(33.33) = 0.3 (33.33)e-0.03(33.33)

= 17.182

That is 17.182 thousand donations were made at that time.

5 0

3 years ago