A jar contains 25 gray, 7 pink, and 22 orange marbles. A marble is drawn at random.<br> P(not gray).

Un cono ha l'area laterale di 255 pigreco cm^2, l'apotema di 17 cm e pesa 900 pigreco g. Calcola il peso specifico del materiale

valkas [14]

Answer:

The specific weight is $1.5\frac{g}{cm^{3}}$

Step-by-step explanation:

The question in English

A cone has a lateral area of 255 pi cm^2, an apothem of 17 cm and weighs 900 pi g. It calculates the specific weight of the material of which it is composed

step 1

Find the radius of the cone

we know that

The lateral area of a cone is equal to

$LA=\pi rl$

we have

$LA=255\pi\ cm^{2}$

$l=17\ cm$

substitute the values

$255\pi=\pi r(17)$

Simplify

$255=r(17)$

$r=255/(17)=15\ cm$

step 2

Find the height of the cone

Applying the Pythagoras Theorem

$l^{2} =r^{2} +h^{2}$

substitute the values and solve for h

$17^{2} =15^{2} +h^{2}$

$h^{2}=17^{2}-15^{2}$

$h^{2}=64$

$h=8\ cm$

step 3

Find the volume of the cone

The volume of the cone is equal to

$V=\frac{1}{3}\pi r^{2}h$

substitute the values

$V=\frac{1}{3}\pi (15)^{2}(8)$

$V=600\pi\ cm^{3}$

step 4

Find the specific weight

Divide the mass by the volume

$\frac{900\pi }{600\pi}=1.5\frac{g}{cm^{3}}$

4 0

3 years ago

5 3/11 as a decimal rounded to the nearest hundredth

valentinak56 [21]

Answer:

5.27

Step-by-step explanation:

3 divided by 11 is 0.272727272727272727 or 0.27

add 5 and 0.27

5 0

2 years ago

Read 2 more answers

Starting in the 1970s, medical technology allowed babies with very low birth weight (VLBW, less than 1500 grams, about 3.3 pound

cluponka [151]

Answer:

The test statistic value using the VLBW babies as group 1 is z=-2.76±0.01 and the P-value for the test (±0.0001) is 0.0030.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of persons with normal birth weight that graduates from high school is significantly greater than the proportion of persons with very low birth weight that graduates from high school.

Then, the null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0$

The significance level is 0.05.

The sample 1 (VLBW group), of size n1=244 has a proportion of p1=0.77049.

$p_1=X_1/n_1=188/244=0.77049$

The sample 2 (control group), of size n2=247 has a proportion of p2=0.79757.

$p_2=X_2/n_2=197/247=0.79757$

The difference between proportions is (p1-p2)=-0.02708.

$p_d=p_1-p_2=0.77049-0.79757=-0.02708$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{188+197}{244+247}=\dfrac{385}{491}=0.988$

The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.988*0.012}{244}+\dfrac{0.988*0.012}{247}}\\\\\\s_{p1-p2}=\sqrt{0.00005+0.00005}=\sqrt{0.0001}=0.0098$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.02708-0}{0.0098}=\dfrac{-0.02708}{0.0098}=-2.76$

This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):

$P-value=P(t$

As the P-value (0.0030) is smaller than the significance level (0.05), the effect issignificant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of persons with normal birth weight that graduates from high school is significantly greater than the proportion of persons with very low birth weight that graduates from high school.

3 0

3 years ago

How do you earn $120 from his job yesterday. Today he expects to earn 15% less than yesterday and tomorrow he expects to earn 15

Ilya [14]

They took tax from his work

5 0

3 years ago

Which statements correctly use the properties of exponents to simplify? Check all that apply.

defon

The first one, second, and third

9 0

3 years ago

Read 2 more answers

A jar contains 25 gray, 7 pink, and 22 orange marbles. A marble is drawn at random. P(not gray).