1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Marianna [84]
3 years ago
12

How many of the positive integer factors of 15552 are perfect squares?

Mathematics
2 answers:
Aleonysh [2.5K]3 years ago
8 0
Answer:

9 of the positive integer factors of 15552 are perfect squares
podryga [215]3 years ago
7 0

Answer: 9 integers factors

Step-by-step explanation:

Let's first find the factor of 15552

15552 / 2 = 7776

7776 / 2 = 3888

3888 / 2 = 1944

1944 / 2 = 972

972 / 2 = 486

486 / 2 = 243

273 / 3 = 81

81 / 3 = 27

27 / 3 = 9

9 / 3 = 3

3 / 3 = 1

Some of the factors of 15552 are:

2×2×2×2×2×2×3×3×3×3×3

4×4×4×9×9×3

4^2 × 9^2 × 4 × 3

The factor that are perfect square are:

4, 9, 16, 36, 64, 81, 144, 576, 1296

Therefore, 9 of the positive integer factors of 15552 are perfect squares.

You might be interested in
Annual starting salaries in a certain region of the U. S. for college graduates with an engineering major are normally distribut
defon

Answer:

0.8665 = 86.65% probability that the sample mean would be at least $39000

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean $39725 and standard deviation $7320.

This means that \mu = 39725, \sigma = 7320

Sample of 125:

This means that n = 125, s = \frac{7320}{\sqrt{125}} = 654.72

The probability that the sample mean would be at least $39000 is about?

This is 1 subtracted by the pvalue of Z when X = 39000. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{39000 - 39725}{654.72}

Z = -1.11

Z = -1.11 has a pvalue of 0.1335

1 - 0.1335 = 0.8665

0.8665 = 86.65% probability that the sample mean would be at least $39000

4 0
2 years ago
A torus is formed by rotating a circle of radius r about a line in the plane of the circle that is a distance R (> r) from th
jeyben [28]

Consider a circle with radius r centered at some point (R+r,0) on the x-axis. This circle has equation

(x-(R+r))^2+y^2=r^2

Revolve the region bounded by this circle across the y-axis to get a torus. Using the shell method, the volume of the resulting torus is

\displaystyle2\pi\int_R^{R+2r}2xy\,\mathrm dx

where 2y=\sqrt{r^2-(x-(R+r))^2}-(-\sqrt{r^2-(x-(R+r))^2})=2\sqrt{r^2-(x-(R+r))^2}.

So the volume is

\displaystyle4\pi\int_R^{R+2r}x\sqrt{r^2-(x-(R+r))^2}\,\mathrm dx

Substitute

x-(R+r)=r\sin t\implies\mathrm dx=r\cos t\,\mathrm dt

and the integral becomes

\displaystyle4\pi r^2\int_{-\pi/2}^{\pi/2}(R+r+r\sin t)\cos^2t\,\mathrm dt

Notice that \sin t\cos^2t is an odd function, so the integral over \left[-\frac\pi2,\frac\pi2\right] is 0. This leaves us with

\displaystyle4\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}\cos^2t\,\mathrm dt

Write

\cos^2t=\dfrac{1+\cos(2t)}2

so the volume is

\displaystyle2\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}(1+\cos(2t))\,\mathrm dt=\boxed{2\pi^2r^2(R+r)}

6 0
3 years ago
14 (OM) Radicals and Estimation (2 pts) Without a calculator, estimate the radical and explain how you estimated. Then using a c
Irina-Kira [14]

Q) Without a calculator, we must estimate the value of the following expression:

3-\sqrt[]{38}.

A) I estimate 3 - √38 to be approximately -3.2.

First, we estimate the value of √38. √38 is between √36 and √49, but close to √36 (since 38 is closer to 4 than it is to 9). Since √36 is 6, √38 is probably something like 6.1 or 6.2. Filling 6.2 in the expression and simplifying, we have this:

3-6.2=-3.2.

So, I expect the number 3 - √38 to be close to -3.2.

Using a calculator we find that: 3 - √38 ≅ -3.16, which it is approximately the result that we found.

Answer

Without a calculator we find that 3 - √38 ≅ -3.2.

5 0
1 year ago
a rental car agency charges $210.00 per week plus $0.15 per mile to rent a car. how many miles can you travel in one week for $2
max2010maxim [7]
$291-$210=$81
$81/0.15= 540 miles
I believe the answer is 540 mi.
7 0
3 years ago
Land's Bend sells a wide variety of outdoor equipment and clothing. The company sells both through mail order and via the intern
nata0808 [166]

Answer:

−35.713332 ; 0.313332

Step-by-step explanation:

Given that:

Sample size, n1 = 11

Sample mean, x1 = 79

Standard deviation, s1 = 18.25

Sample size, n2 = 18

Sample mean, x2 = 96.70

Standard deviation, s2 = 20.25

df = n1 + n2 - 2 ; 11 + 18 - 2 = 27

Tcritical = T0.01, 27 = 2.473

S = sqrt[(s1²/n1) + (s2²/n2)]

S = sqrt[(18.25^2 / 11) + (20.25^2 / 18)]

S = 7.284

(μ1 - μ2) = (x1 - x2) ± Tcritical * S

(μ1 - μ2) = (79 - 96.70) ± 2.473*7.284

(μ1 - μ2) = - 17.7 ± 18.013332

-17.7 - 18.013332 ; - 17.7 + 18.013332

−35.713332 ; 0.313332

3 0
2 years ago
Other questions:
  • Which measurement is most accurate to describe the length of a bee? 3 mm 2.2 cm 0.4 m 1 km
    6·1 answer
  • Solve algebra 2 bju press
    11·1 answer
  • 7(2b-5) + 3 = 10 ?????
    7·2 answers
  • Shane biked 1 mile less than three times the number of miles Lissette biked. Shane biked a total of 7 miles. Write an equation t
    6·1 answer
  • The Fratellis will be arrested if and only if the police believe Chunk. Question 9 options: 1) p ↔ q 2) p ∨ q 3) p → q 4) ~p 5)
    10·1 answer
  • Select the correct answer.<br> What is the value of X in the triangle?
    11·2 answers
  • Solve the simultaneous equations:<br><br> 5x+4y=5<br> 2x+7y=29
    11·1 answer
  • Felicia filled the bathroom sink with water. Is the amount more than
    10·1 answer
  • Solve the system by substitution.<br> 4x + 2y = 10<br> x − y = 13
    10·2 answers
  • Jesaria can jump rope 42 times in 20 seconds at this rate how many times can she jump rope in 2 minute
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!