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Prove the value of the expression(s):
#1: (2^10+2^8)(2^5-2^3) is divisible by 60.
#2: (16^3-8^3)(4^3+2^3) is divisible by 63.
#3: (125^2+25^2)(5^2-1) is divisible by 39.

3 images will be provided if you do not understand what to do.

Answer:

Step-by-step explanation:

https://brainly.com/question/22157981

Answer:

8x5 equals 40.

Step-by-step explanation:

Answer:

8x5 is 40, hope that helped :)

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

you take the number 8 and then you add 4. and you find yourself with the answer 12

Answer:

17/15

Step-by-step explanation:

Find the GCF of the denominators

15

Convert the fractions

1/3 --->   5/15

4/5 --->  12/15

Add.

12/15 + 5/15 = 17/15

Answer:

[tex]r=\sqrt{\dfrac{3V}{\pi h}}[/tex]

Step-by-step explanation:

The volume of a cylinder is given by :

[tex]V=\dfrac{1}{3}\pi r^2h[/tex] .....(1)

Where

r and h are the radius and the height of the cylinder.

We need to solve the equation of r. Cross multiplying both sides in equation (1).

[tex]3V=\pi r^2h[/tex]

Dividing both sides by [tex]\pi h[/tex]. So,

[tex]\dfrac{3V}{\pi h}=\dfrac{\pi r^2h}{\pi h}\\\\r^2=\dfrac{3V}{\pi h}\\\\or\\\\r=\sqrt{\dfrac{3V}{\pi h}}[/tex]

So, the radius of the cylinder is equal to [tex]\sqrt{\dfrac{3V}{\pi h}}[/tex].

Answer:

c

Step-by-step explanation:

If the level of confidence falls to 90%, the length will likewise fall.

A confidence interval (CI) is a range of values that, with a particular level of certainty, is likely to encompass a population value. A population means that sits between an upper and lower interval is frequently stated as a percentage.

Let p be the proportion of students who gets at least 8 hours of sleep the previous night.

here, Sample size = n = 50

the 95% confidence interval for true proportion is,

P ± Zₐ/₂ * [tex]\sqrt{P{\frac{1-P}{n} }[/tex]

P ± 1.96 * [tex]\sqrt{P{\frac{1-P}{50} }[/tex]

95% confidence length = 2 *P ± Zₐ/₂ * [tex]\sqrt{P{\frac{1-P}{n} }[/tex]

= 2 * 1.96 * [tex]\sqrt{P{\frac{1-P}{50} }[/tex]   = 3.92 * [tex]\sqrt{P{\frac{1-P}{50} }[/tex]

For 90% confidence length =  2 *P ± Zₐ/₂ * [tex]\sqrt{P{\frac{1-P}{n} }[/tex]

= 2 * 1.645 * [tex]\sqrt{P{\frac{1-P}{50} }[/tex]   = 3.29 * [tex]\sqrt{P{\frac{1-P}{50} }[/tex]

Therefore, if the confidence level decreases to 90% then the length will also decrease.

Learn more about confidence intervals here:

https://brainly.com/question/24131141

#SPJ2

Answer:

<6

Step-by-step explanation:

Corresponding angles have the same matching corner when a transversal line crosses tow straight lines.

Thus, in the diagram given, the angle that has the same matching corner with <2 is the angle that corresponds to <2.

<6 has the same matching corner with <2.

Therefore, <6 corresponds with <2

Answer:

24.02 can i get brainliest

Step-by-step explanation:

Answer:

The height is 15

Answer:

is an attachment

test statistic = 9.87

p value is less than 0.01

Not all means of the three assembly methods are equal

Step-by-step explanation:

the anova table is an attachment

total number of methods = k = 3

number of observations n = 30

for treatment, df = 3-1 = 2

for error, df = 30 -3 (n-k) = 27

sst = 10800, sstr = 4560, sse = 10800-4560 = 6240

we find the mean of squares for error

sse/df of error = 6240/27 = 231.11

mean of squares for treatment = 4560/2 = 2280

test stat

F = 2280/231.11

= 9.8654

using f distribution table;

alpha = 0.05

df = 2 , 27

we get 3.35

h0; no difference in mean

h1; there is difference

9.87 > 3.35 so we reject H0, there is difference in means. all are not equal.

pvalue calculation

using excel,

FDIST(9.8654, 2, 27) = 0.0006078

p value is less than 0.01

we conclude that a. Not all means of the three assembly methods are equal

Answer:

show us a pic of the triangles

Step-by-step explanation:

Answer:

repost no pic

Step-by-step explanation:

Answer:20

Step-by-step explanation:

the other side is a mirror it would be 20 as well

Answer:

0.23

Step-by-step explanation:

If you convert 0.23 into a percent, it becomes 23%, which is more than 2.3%.

Hope that helps!

-Sabrina

Answer: 6 5/7

Step-by-step explanation:

Answer:

Gavin will have to invest his money for 20 years to reach that sum of money.

Step-by-step explanation:

Given that Gavin invested $ 350 in an account paying an interest rate of 4.7% compounded continuously, assuming no deposits or withdrawals are made, to determine how long would it take to the nearest tenth of a year for the value of the account to reach $ 890 se you must perform the following calculation:

890 = 350 x (1 + 0.047 / 365) ^ X x 365

X = 20

Thus, Gavin will have to invest his money for 20 years to reach that sum of money.

Solution :

Here, we have 5 trails that corresponds to the 5 times the binary symbol is sent. On each trail, success is said to occur when the binary symbol is received correctly. The probability of a success is p = 1 - q = 0.9 and q = 0.1

Now if the 0 is being transmitted, then the 0 is sent 5 number of times and then we call the decoding a 0 success. Let the repeated transmission are independent. In this case, we have 5 trails. Let each repeated bit the receiver decodes as 1 a success, using the binomial probabilities. We using the [tex]$S_{k,5}$[/tex] to denote an event of [tex]$k$[/tex] successes in the 5 trails, then the probability k are decoded at the receiver is:

[tex]$P[S_{k,5}]=\binom{5}{k}p^k(1-p)^{5-k}$[/tex]

           [tex]$=\binom{5}{k}(0.9)^k(1-0.9)^{5-k}$[/tex]

           [tex]$=\binom{5}{k}(0.9)^k(0.1)^{5-k}$[/tex]    

Here, k = 1, 2, 3, 4, 5

The probability of the transmitted bit to be decoded correctly is:

[tex]$P[C]=P[S_{5,5}]+P[S_{2,5}]$[/tex]

         [tex]$=\binom{5}{3}(0.9)^5(0.1)^{0}+\binom{5}{4}(0.9)^4(0.1)^1$[/tex]

         [tex]$=(0.9)^5+5(0.9)^4(0.1)^1$[/tex]

         = 0.91854

The probability that the deletion occurs is

[tex]$P[D]=P[S_{3,5}]+P[S_{2,5}]$[/tex]

          [tex]$=\binom{5}{3}(0.9)^3(0.1)^{2}+\binom{5}{2}(0.9)^2(0.1)^3$[/tex]

         [tex]$=10(0.9)^3(0.1)^2+10(0.9)^2(0.1)^3$[/tex]

         = 0.081

The probability of an error is

[tex]$P[E]=P[S_{1,5}]+P[S_{0,5}]$[/tex]

          [tex]$=\binom{5}{1}(0.9)^1(0.1)^{4}+\binom{5}{0}(0.9)^0(0.1)^5$[/tex]

         [tex]$=5(0.9)^1(0.1)^4+(0.1)^5$[/tex]

         = 0.00046

Answer:

£2.10

Step-by-step explanation:

1.80 divided by .12 = .15

.15 times 7 = 1.05

1.05 divided by 3 = .35

.35 times 5 = 2.10

The cost of 5 pens will be £1.75

Since 12 pencils cost £1.80, the price of a pencil will be gotten by dividing £1.80 by 12. This will be:

= £1.80 / 12

= £0.15

A pencil costs £0.15

Since the ratio of the cost of a pen to the cost of a pencil is 7: 3, therefore, the cost of a pen will be:

= 7/3 × £0.15

= £0.35.

The cost of a pen is £0.35, therefore, the cost of 5 pens will be:

= £0.35 × 5

= £1.75

In conclusion, the cost of 5 pen is £1.75.

Read related link on:

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Answer:

Refer the attachment for explanation :

Gretchen has the highest ratio of blue and red marbles.

Hope it helps :)

Answer:

x=2

Step-by-step explanation:

x=2 i believe. i apologize if incorrect

Answer:

I don’t know how to solve the equation with algebra tiles but here’s the answer without using them

4x-3=5

Add 3 to both sides of the equation to balance it out

4x=8

Divide both sides by 4 to get

x=2

Answer:

51.04 ı think

Step-by-step explanation:

Answer:

she makes 51.04

Step-by-step explanation:

Answer:

It is (1,5) :)

Answer:

Substituton is like being a back up to anything and for anuone

Answer:

12.1875 or 195/16 or 12 3/16

Step-by-step explanation:

All you must do is multiply them by each other

hope this helps

Answer:

12.19 inches

Step-by-step explanation:

please mark brainliest

Answer:

A

Step-by-step explanation:

yyjvgyujjjjuyrcjkoiffffgy

Answer: $34.85

Step-by-step explanation: $41 x 15%= 34.85 before tax

Answer:

20

Step-by-step explanation:

Answer:

tom is 8 and becky is 18 now

Step-by-step explanation:

in two years becky would be 20 and tom will be 10

hope this helps