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2 years ago

If 10x + 2 = 7, what is the value of 2x?

Mathematics

2 answers:

Julli [10]2 years ago

6 0

For this case we have the following equation:

$10x + 2 = 7$

From here, we clear the value of x.

We have then:

$10x = 7-2\\10x = 5\\x = \frac {5} {10}\\x = \frac {1} {2}$

Then, we look for the value of 2x. We have then:

$2x = 2 \frac {1} {2}\\2x = \frac {2} {2}\\2x = 1$

Answer:

The value of 2x is given by:

$2x = 1$

Andrew [12]2 years ago

6 0

10x+2=7
10x=5
x=1/2
2(1/2)=1

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What are the possible numbers of positive real, negative real, and complex zeros of f(x) = −7x4 − 12x3 + 9x2 − 17x + 3?

madreJ [45]

Now, recall Descartes Rule of Signs. Check the picture below.

the +x part, gives us the positive Real zeros, and it depends on how many times the sign changes from term to term, notice in the picture, it changed 3 times, so the positive real ones are 3, or 3-2, namely 1, so 3 or 1.

the negative real ones, come from using -x as the argument on f(x), and as you can see in the picture, there was only 1 sign change, meaning the negative real zeros are only 1.

since, based on the fundamental theorem of algebra the polynomial has 4 roots at most then,

3 positive real ones, and 1 negative real one, no complex ones

or

1 positive real one, and 1 negative real one, and 2 complex ones

bear in mind that complex always come in pairs, never alone.

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2 years ago

A student estimates the weight of astronauts on the moon by multiplying their weight by the decimal 0.16666....what fraction can

Elden [556K]

Let $x = 1.66666...$ ....(1)

Multiply both sides of equation (1) by 10.

$10x = 1.666666....$ .... (2)

Multiply both sides of equation (1) by 100.

$100x = 16.66666....$ ... (3)

Subtract equation (2) from equation (3)

$100x - 10x = 16.66666...- 1.66666...$

$90x = 15$

$x= \frac{15}{90} = \frac{1}{6}$

Hence, the required fraction form is $\frac{1}{6}$ .... Answer.

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2 years ago

Read 2 more answers

Define four symbolic constants that represent integer 25 in decimal, binary, octal, and hexadecimal formats

stealth61 [152]

Answer:

1) Decimal $25= (25)_{10}$

2) Binary $25= (11001)_2$

3) Octal $25= (31)_8$

4) Hexadecimal $25= (19)_{16}$

Step-by-step explanation:

Given : Integer is 25

To find : Represent integer in decimal, binary, octal, and hexadecimal formats.

Solution :

1) Integer into decimal - To convert into decimal the base goes to 10.

So, $25= (25)_{10}$

2) Integer into binary - To convert into binary the base goes to 2, it form in 0 and 1 and we divide integer by 2.

Divide 25 by 2 and note down the remainders.

2 | 25

2 | 12 R=1 ←

2 | 6 R=0 ↑

2 | 3 R=0 ↑

2 | 1 → R=1 ↑

So, $25= (11001)_2$

3) Integer into octal - To convert into octal the base goes to 8 and we divide integer by 8.

Divide 25 by 8 and note down the remainders.

8 | 25

| 3 → R=1

So, $25= (31)_8$

4) Integer into hexadecimal - To convert into hexadecimal the base goes to 16 and we divide integer by 16.

Divide 25 by 16 and note down the remainders.

16 | 25

| 1 → R=9

So, $25= (19)_{16}$

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2 years ago

Customers are used to evaluate a preliminary product design. In the past, 95% of highly successful products received good review

Sever21 [200]

Answer:

a. 61.5%; b. About 61.8%; c. About 36.4%

Step-by-step explanation:

This is a kind of question that we can solve using the Bayes' Theorem. We have here all the different conditional probabilities we need to solve this problem.

According to that theorem, the probability of a selected product attains a good review is:

$\\ P(G) = P(G|H)*P(H) + P(G|M)*P(M) + P(G|P)*P(P)$ (1)

In words, the probability that a selected product attains a <em>good review</em> is an <em>event </em>that depends upon the sum of the conditional probabilities that the product comes from <em>high successful product</em> P(G|H) by the probability that this product is a <em>highly successful product</em> P(H), plus the same about the rest of the probabilities, that is, P(G|M)*P(M) or the probability that the product has a good review coming from a <em>moderately successful</em> product by the probability of being moderately successful, and a good review coming from a poor successful product by the probability of being poor successful or P(G|P)*P(P).

<h3>The probability that a randomly selected product attains a good review</h3>

In this way, the probability that a randomly selected product attains a good review is the result of the formula (1). Where (from the question):

P(G|H) = 95% or 0.95 (probability of receiving a good review being a highly successful product)

P(G|M) = 60% or 0.60 (probability of receiving a good review being a moderately successful product)

P(G|P) = 10% or 0.10 (probability of receiving a good review being a poorly successful product)

P(H) = 40% or 0.40 (probability of being a highly successful product).

P(M) = 35% or 0.35 (probability of being a moderately successful product).

P(P) = 25% or 0.25 (probability of being a poor successful product).

Then,

$\\ P(G) = P(G|H)*P(H) + P(G|M)*P(M) + P(G|P)*P(P)$

$\\ P(G) = 0.95*0.40 + 0.60*0.35 + 0.10*0.25$

$\\ P(G) = 0.615\;or\; 61.5\%$

That is, <em>the probability that a randomly selected product attains a good review</em> is 61.5%.

<h3>The probability that a new product attains a good review is a highly successful product</h3>

We are looking here for P(H|G). We can express this probability mathematically as follows (another conditional probability):

$\\ P(H|G) = \frac{P(G|H)*P(H)}{P(G)}$

We can notice that the probability represents a fraction from the probability P(G) already calculated. Then,

$\\ P(H|G) = \frac{0.95*0.40}{0.615}$

$\\ P(H|G) =\frac{0.38}{0.615}$

$\\ P(H|G) =0.618$

Then, the probability of a product that attains a good review is indeed a highly successful product is about 0.618 or 61.8%.

<h3>The probability that a product that <em>does not attain </em>a good review is a moderately successful product</h3>

The probability that a product does not attain a good review is given by a similar formula than (1). However, this probability is the complement of P(G). Mathematically:

$\\ P(NG) = P(NG|H)*P(H) + P(NG|M)*P(M) + P(NG|P)*P(P)$

P(NG|H) = 1 - P(G|H) = 1 - 0.95 = 0.05

P(NG|M) = 1 - P(G|M) = 1 - 0.60 = 0.40

P(NG|P) = 1 - P(G|M) = 1 - 0.10 = 0.90

$\\ P(NG) = 0.05*0.40 + 0.40*0.35 + 0.90*0.25$

$\\ P(NG) = 0.385\;or\; 38.5\%$

Which is equal to

P(NG) = 1 - P(G) = 1 - 0.615 = 0.385

Well, having all this information at hand:

$\\ P(M|NG) = \frac{P(NG|M)*P(M)}{P(NG)}$

$\\ P(M|NG) = \frac{0.40*0.35}{0.385}$

$\\ P(M|NG) = \frac{0.14}{0.385}$

$\\ P(M|NG) = 0.363636... \approx 0.364$

Then, the <em>probability that a new product does not attain a good review and it is a moderately successful product is about </em>0.364 or 36.4%.

8 0

2 years ago

Tony and Manuel were trimming the branches of a tree. Tony was using an 18 ft ladder and Manuel was using a 24 ft ladder. Both l

REY [17]

Answer:

9.33 feet = 111.96 inches

Step-by-step explanation:

If we have similar triangles, the rate between matching sides is the same.

So the length of the smaller ladder (18 ft) over the length of the taller ladder (24 ft) is equal to the distance from the bottom of the smaller ladder to the tree (7 ft) over the distance from the bottom of the taller ladder to the tree (x ft):

18 / 7 = 24 / x

x = 7 * 24 / 18

x = 9.33 feet

To find this measure in inches, we just need to multiply by 12:

x = 9.33 * 12 = 111.96 inches

3 0

2 years ago