what is the sum of this infinite geometric series? 2+ 2/5+2/25+2/125+..... ...?

The probability that Lucas is accepted to at least one of the two schools is 55%, while the probability that he does not get into either school is 45%.

The subject of the question is probability theory, which is a branch of mathematics. Lucas has a 0.4 chance of getting into Stanford, a 0.3 chance of getting into Cal-Poly, and a 0.15 chance of getting into both. These are independent probabilities because they do not affect each other.

a) To calculate the probability that he gets accepted to at least one of the schools, we add the probabilities of him getting into each school, and then subtract the probability of him getting into both (because we're double counting that scenario). So, that's 0.3 (for Cal-Poly) + 0.4 (for Stanford) - 0.15 (for both) = 0.55, or 55%.

b) In probability theory, the total probability of all possibilities is always 1. So, to find the probability that he doesn't get into EITHER school, we subtract the probability that he gets into at least one school from 1. So, 1 - 0.55 (the answer from part a) = 0.45, or 45%. So, there's a 45% chance that Lucas doesn't get accepted into either school.

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Answer:

The answer is ∠EGH.

Step-by-step explanation:

In order to determine the correct option, we have to know about adjacent angle.

Two angles are adjacent when they have a common side and vertex (corner point). So in this case, the adjacent angle must have GE or DG common side and the G vertex.

According to the options, the adjacent angle to ∠DGE is:

∠EGH

The other options are not adjacent angles because they do not have a common side.

Finally the correct option is ∠EGH.

Answer:

The absolute value parent function is symmetric with respect to the y-axis.  

The graphs of f(x) = 2|–x| and f(x) = 2|x| are identical because the absolute value of negative x is a reflection across the y-axis.  

If you substitute the three given points into both functions, they produce true statements.

Step-by-step explanation:

Answer:

6s-54

Step by step: Put the 6 in front of the s and then multiply 6*9. so the answer is 6s-54

The distributive property is used in mathematics to multiply a number by multiple numbers within parentheses. Using it for expression 6(s - 9) gives us 6s - 54.

The expression you need to simplify using the distributive property is 6(s - 9). The distributive property is a fundamental property in mathematics that allows you to multiply a singular number by multiple numbers within parentheses.

In case of the expression 6(s - 9), you'll simply need to distribute or multiply the number 6 to each term inside the parentheses.

6 x s and 6 x -9. Performing these will give us 6s - 54.

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Answer:

She need to drive more than 2000 miles for the first rental company to be a better deal .

Step-by-step explanation:

Case 1) One car rental company offers a flat rate of $35 per day plus $0.10 per mile

Let m be the no. of miles

She will need the car for 5 days.

So, total cost = [tex]35 \times 5 +0.10m=175+0.10m[/tex]

Case 2)  Another car rental company offers the same car for $25 per day plus $0.25 per mile.

Let m be the no. of miles

She will need the car for 5 days.

So, total cost = [tex]25 \times 5 +0.25m=125 +0.25m[/tex]

Now we are supposed to find How many miles would she need to drive for the first rental company to be a better deal?

So, [tex]175+0.10m <125 +0.25m [/tex]

[tex]175+125 <125 +0.25m-0.10m [/tex]

[tex]300 < 0.15m [/tex]

[tex]\frac{300}{0.15} < m [/tex]

[tex]2000 < m [/tex]

So, she need to drive more than 2000 miles for the first rental company to be a better deal

Final answer:

The lowest possible value for t as the median of the numbers 32, 64, 22, t, 41, 22, and 78 is 32. This value maintains the order when the numbers are arranged from lowest to highest for t to be the median.

Explanation:

To find the lowest possible value for t given that it is the median of the numbers 32, 64, 22, t, 41, 22, and 78, we first need to arrange the numbers in ascending order.

Since there are seven numbers, the median would be the fourth number when sorted.

To ensure t is the lowest possible median, we sort the remaining numbers excluding t. Thus, we have:

22, 22, 32, 41, 64, 78

The third value is 32, and the fifth value is 41, so for t to be the median, t must be greater than or equal to 32 but less than or equal to 41.

However, since we are looking for the lowest possible value of t, t would be 32, as this is the lowest it can be while still being the median of the sorted list.

Answer:

1 a 2 d 3b 4 c

Step-by-step explanation:

sorry it took me 6 years to get back to you

The first, fourth, and tenth terms of the arithmetic sequence A(n) = 12+(n-1)(3) are 12, 21, and 39 respectively.

The arithmetic sequence A(n) given by the rule A(n) = 12+(n-1)(3) represents the value of the nth term in the sequence. The first term of the sequence (n=1) can be found by substitifying n=1 into the equation, which will yield [tex]A(1)=12+(1-1)(3)=12.[/tex] The fourth term A(4) can be found similarly by substituting n=4 into equation resulting in [tex]A(4)=12+(4-1)(3)=21.[/tex]The tenth term A(10) can also be calculated in the similar manner giving [tex]A(10)=12+(10-1)(3)=39.[/tex] So, the first, fourth, and tenth terms of the arithmetic sequence are 12,21, and 39 respectively.

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According to Remainder Theorem for the polynomials, for every polynomial P(x) there exist such polynomials G(x) and R(x), that [tex] P(x)=(x\pm a)G(x)+R(x) [/tex].

When the polynomial in P(x) is divided by (x + a), then there exist such polynomials G(x) and R(x), that P(x)=(x+a)G(x)+R(x). Note that for x=-a:

Answer:

false

Step-by-step explanation:

The quotient is -3x² + 3x + 8.

To find the quotient when [tex]\(-3x^3 + 5x + 14\)[/tex] is divided by x - 2, we can use polynomial long division.

The dividend is [tex]\(-3x^3 + 0x^2 + 5x + 14\)[/tex] (since there is no [tex]\(x^2\)[/tex] term) and the divisor is x - 2.

1. Divide the first term of the dividend by the first term of the divisor: [tex]\(-3x^3 \div x = -3x^2\)[/tex].

2. Multiply the divisor by the result of step 1: [tex]\((-3x^2)(x - 2) = -3x^3 + 6x^2\).[/tex]

3. Subtract the result of step 2 from the dividend: [tex]\((-3x^3 + 0x^2 + 5x + 14) - (-3x^3 + 6x^2) = -6x^2 + 5x + 14\).[/tex]

4. Repeat the process with the new dividend [tex]\(-6x^2 + 5x + 14\)[/tex].

Continuing the division process, we find the quotient:

[tex]\[ \frac{-3x^3 + 5x + 14}{x - 2} = -3x^2 + 3x + 8 \][/tex]

So, the quotient is -3x² + 3x + 8.

Answer:

none there would be an answer if it was 3√7

Step-by-step explanation:

The expressions equivalent to 10x are 50x/5 and (50/5)x as they both simplify to 10x. The other options do not simplify to 10x. Hence option D and E are correct.

To determine which expressions are equivalent to 10x, we need to simplify each option. Let us consider the options one by one:

To solve this a simple division is required.

⇒ (50x/5x)= 10÷(1) = 10

⇒ 10 is not equivalent to 10x.

⇒ 100x - 10

This is not equivalent to 10x.

⇒  10 • 10x • 10 = 100x+10 (Not equivalent to 10x)

⇒ (50/5)x = 10x (Equivalent to 10x)

The correct answers are D and E, both of which simplify to 10x.

1/4 divided by 5 results into '0.05'

Given that we need to find 1/4 divided by 5

Thus let the required answer be denoted as "A"

Thus using basic definitions of divisions and fractions we can find out the resultant value

[tex]A=\frac{\frac{1}{4} }{5} \\A=\frac{1}{4*5} \\A=\frac{1}{20}[/tex]

Thus '1/20' is  the required answer

Now the resultant value can also be simplified to get a decimal value

[tex]A=\frac{1}{20} \\A=\frac{1}{2*10} \\A=\frac{1}{2} *\frac{1}{10} \\A=0.5*0.1\\A=0.05[/tex]

Thus '0.05' is the final answer