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Vinvika [58]
3 years ago
13

James correctly answered 85% of the 60 problems on his math test. How many questions did James answer correctly❄️

Mathematics
1 answer:
harina [27]3 years ago
3 0

Answer:

James answered 51 questions correctly.

Step-by-step explanation:

1) Slide the decimal 2 places to the left in the percentage (85% = .85)

2) Multiply total by new decimal (60 x .85)

3) All done! (51)

Keep in mind that 100% is just 1 whole. Therefor 85% of one whole is .85. In this problem, 60 represents our whole.

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Let $a$ and $b$ be nonzero real numbers such that
algol [13]
<h3>Answer:   -7/2</h3>

=========================================================

Explanation:

Let's expand out (2 - 7i)(a + bi) using the FOIL rule

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7bi^2

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7b(-1)

(2 - 7i)(a + bi) = 2a + 2bi - 7ai + 7b

(2 - 7i)(a + bi) = (2a+7b) + (2bi-7ai)

(2 - 7i)(a + bi) = (2a+7b) + (2b-7a)i

We're told the result is purely imaginary. What this means is that the real part (2a+7b) is zero, while the imaginary part (2b-7a) is nonzero. If both are zero, then we have 0+0i = 0 which is purely real.

For example, the complex numbers 0-7i and 0+2i are purely imaginary.

Let's use the fact that 2a+7b must be zero to do the following steps:

2a+7b = 0

2a = -7b

a = -7b/2

a/b = -7/2 which is the final answer

We must check to see if 2b-7a is nonzero

2b - 7a = 2b - 7(-7b/2)

2b - 7a = 2b + 24.5b

2b - 7a = 26.5b

The result is nonzero if and only if b is nonzero. Luckily we're told b is nonzero at the top of the problem. So we don't have any worries that (2b-7a) is zero.

Therefore, (2a+7b) + (2b-7a)i will be purely imaginary with a/b = -7/2

------------------

A concrete example:

Let a = -14 and b = 4

a/b = -14/4 = -7/2

(2-7i)(a+bi) = (2-7i)(-14+4i) = 0 + 106i which is purely imaginary.

I'll let you do the steps in expanding that out using the FOIL rule.

4 0
1 year ago
Find the product: −5(−3)(−3)<br> A) −30<br><br> B) −45<br><br> C) 30<br><br> D) 45
morpeh [17]

Answer:

30

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
five times the difference of twice a number and three, decreased by the sum of the number and eight, equals thirteen
trapecia [35]
5x(2y-3)-(y+8)=13 I believe this is correct
7 0
3 years ago
g Two teams compete in the NBA (National Basketball Associa- tion) championshipseries. The team who wins four games out of seven
Firlakuza [10]

Answer: The required probability is 0.32.

Step-by-step explanation:

Since we have given that

Probability of winning team A over B = 0.7

Probability of losing team A over B = 0.3

Number of matches = 7"

So, using the "Binomial distribution" :

We get that

P(X=5)=^7C_5(0.7)^5(0.3)^2=0.32

Hence, the required probability is 0.32.

4 0
3 years ago
The sum of x and 10 is 5
Jobisdone [24]

Answer:

x=-5

Step-by-step explanation:

This is the sentance turned into an equation: x+10=5

Solved: x+10=5

x=5-10

x=-5

5 0
3 years ago
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