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2 years ago

10

Mathematics

1 answer:

Zigmanuir [339]2 years ago

6 0

Answer:

The sum is 12276 .

Step-by-step explanation:

This expression can be written as:Σ10i=1(6×2n)=6×Σ10i=12n

The last expression is a sum of a finite geometrical sequence for which: a1=2,q=2,n=10. This sum can be calculated as:S10=2×1−2101−2=2×210−12−1=2×(210−1)==2×1023=2046So the value of the first expression is: 6×2046=12276

Mark me brainliest!!

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(High points) please solve both with explanation. I’ll give brainliest.

lawyer [7]

Answer:

$36\frac{9}{16}$

area: 136 cm

perimeter: 48 cm

Step-by-step explanation:

For the first one just subtract

$45\frac{1}{2}=\frac{91}{2}=\frac{364}{8}\\8\frac{7}{8}=\frac{71}{8}\\\frac{364}{8}-\frac{71}{8}=\frac{293}{8}\\\frac{293}{8}=\frac{586}{16}\\\\\frac{586}{16}-\frac{1}{16}=\frac{585}{16}=36\frac{9}{16}$

for the second one you just have to break it into smaller, more digestible pieces (work below)

7 0

3 years ago

According to a survey, 78% of residents in Summerville own a home. If 30 residents

rosijanka [135]

Answer:

0.1732 = 17.32% probability exactly 24 residents own a home.

Step-by-step explanation:

For each resident, there are only two possible outcomes. Either they own a home, or they do not. The probability of a resident owning a home is independent of any other resident. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

78% of residents in Summerville own a home.

This means that $p = 0.78$

30 residents are randomly selected:

This means that $n = 30$

Find the probability exactly 24 residents own a home.

This is P(X = 24).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 24) = C_{30,24}.(0.78)^{24}.(0.22)^{6} = 0.1732$

0.1732 = 17.32% probability exactly 24 residents own a home.

3 0

3 years ago

A projectile is fired from ground level with an initial speed of 550 m/sec and an angle of elevation of 30 degrees. Use that the

Nana76 [90]

Answer:

x (max) = 26760 m

y (max) = 3859 meters

V = 549.5 m/sec

Step-by-step explanation:

Equations to describe the projectile shot movement are:

a(x) = 0 V(x) = V(₀) *cos α x = V(₀) *cos α * t

a(y) = -g V(y) = V(₀) * sin α - g*t y = V(₀) * sin α *t - (1/2)*g*t²

a ) What is the range of the projectile. α = 30°

then sin 30° = 1/2 cos 30° = √3 /2 and tan 30° = 1/√3

x maximum occurs when in the equation of trajectory we make y = 0

Then

y = x*tan α - g*x / 2*V(₀)²*cos² α

x*tan α = g*x / 2* V(₀)²*cos² α

By subtitution

1/√3 = 9.8* x(max) / 2* (550)²*0.75

(1/√3) * 453750 / 9.8 = x (max)

x (max) = 453750 / 16.95 meters

x (max) = 26760 m

The maximum height is when V(y) = 0

We compute t in that condition

V(y) = 0 = V(₀) * sin α - g*t

t = V(₀) * sin α / g ⇒ t = 550* (1/2) / 9.8

t = 28.06 sec

Then h (max) = y(max) = V(₀) sin α * t - 1/2 g* t²

y (max) = 550* (1/2)*28.06 - (1/2)* 9.8 * (28.06)²

y (max) = 7717 - 3858

y (max) = 3859 meters

What is the speed when the projectile hits the ground

V = V(x) + V (y) and t = 2* 28.06 t = 56.12 sec

mod V =√ V(x)² + V(y)²

V(x) = V(₀) cos α = 550 * √3/2

V(x) = 475.5 m/sec V(x)² = 226338 m²/sec²

V(y) = 550*1/2 - 9.8* 56.12 ⇒ V(y) = 275 - 549.98

V(y) = - 274.98 V(y) ² =

V = √ 226338 + 75614 ⇒ V = 549.5 m/sec

7 0

3 years ago

In your sock drawer you have 5 blue, 7 gray, and 2 black socks. Half asleep one morning you grab 2 socks at random and put them

pentagon [3]

The question is incomplete! The complete question along with answers and explanation is provided below!

In your sock drawer you have 5 blue, 7 gray, and 2 black socks. Half asleep one morning you grab 2 socks at random and put them on. Find the probability you end up wearing the following socks. (Round your answers to four decimal places.)

a) 2 blue socks

b) no gray socks

c) at least 1 black sock

d) a green sock

e) matching socks

Answer:

a) P(2 blue socks) = 0.1099 = 10.99%

b) P(no gray socks) = 0.2307 = 23.07%

c) P(at least 1 Black sock) = 0.2748 = 27.48%

d) P(green sock) = 0%

e) P(Matching socks) = 0.3516 = 35.16%

Step-by-step explanation:

Given Information:

5 Blue socks

7 Gray socks

2 black socks

Total socks = 5 + 7 + 2 = 14

a) The probability of wearing 2 blue socks

P(2 blue socks) = P(B1 and B2)

P(B1) = no. of blue socks/total no. of socks

P(B1) = 5/14 = 0.3571

Now there are 4 blue socks remaining and total 13 socks remaining

P(B2|B1) = 4/13 = 0.3077

P(B1 and B2) = 0.3571*0.3077 = 0.1099 = 10.99%

b) The probability of wearing no gray socks

5 Blue socks + 2 black socks = 7 socks are not gray

P(no gray socks) = P(Not G1 and Not G2)

P(Not G1) = no. socks that are not grey/ total no. of socks

P(Not G1) = 7/14 = 0.5

Now there are 6 socks remaining that are not gray and total 13 socks remaining

P(Not G2 | Not G1) = 6/13 = 0.4615

P(Not G1 and Not G2) = 0.5*0.4615 = 0.2307 = 23.07%

c) The probability of wearing at least 1 black sock

5 Blue socks + 7 Gray socks = 12 socks are not black

P(at least 1 Black) = 1 - P(Not B1 and Not B2)

P(Not B1) = no. socks that are not black/ total no. of socks

P(Not B1) = 12/14 = 0.8571

Now there are 11 socks remaining that are not black and total 13 socks remaining

P(Not B2 | Not B1) = 11/13 = 0.8461

P( Not B1 and Not B2) = 0.8571*0.8461 = 0.7252

P(at least 1 Black) = 1 - P( Not B1 and Not B2)

P(at least 1 Black) = 1 - 0.7252 = 0.2748 = 27.48%

d) The probability of wearing a green sock

There are 0 green socks, therefore

P(Green) = 0/14 = 0%

e) The probability of wearing matching socks

P(Matching socks) = P(2 Blue socks) + P(2 Gray socks) + P(2 Black socks)

P(2 Blue socks) already calculated in part a

P(2 Blue socks) = P(B1 and B2) = 0.1099

For Gray socks

P(G1) = no. of gray socks/ total no. of socks

P(G1) = 7/14 = 0.5

Now there are 6 gray socks remaining and total 13 socks remaining

P(G2 | G1) = 6/13 = 0.4615

P(2 Gray socks) = P(G1 and G2) = 0.5*0.4615 = 0.2307

For Black socks

P(B1) = no. of black socks/ total no. of socks

P(B1) = 2/14 = 0.1428

Now there is 1 black sock remaining and total 13 socks remaining

P(B2 | B1) = 1/13 = 0.0769

P(2 Black socks) = P(B1 and B2) = 0.1428*0.0769 = 0.0110

P(Matching socks) = P(2 Blue socks) + P(2 Gray socks) + P(2 Black socks)

P(Matching socks) = 0.1099 + 0.2307 + 0.0110 = 0.3516 = 35.16%

7 0

3 years ago

Simplify

UNO [17]

Answer:

3x²(y-1)

Step-by-step explanation:

Rewrite the expression as 5x²y+4x²y-6x²y-3x². Combining like terms, we get 3x²y-3x². Now, we can factor out 3x² to get 3x²(y-1)

3 0

2 years ago