The answer of how to do the question

Which value, when placed in the box, would result in a system of equations with infinitely many solutions?

ira [324]

<span>For a system of equations to have infinitely many solutions, the equations have to be lineary dependent, (i.e. one of the equations is a multiple of the other equation). For the given equation to have infinitely many solutions, the second equation have to be a multiple of the first equation. The first equation can be rewritten as y - 2x = -5 The second equation is the first equation multiplied by 2, i.e. 2(y - 2x= -5) = 2y - 4x = -10 Therefore, the correct answer is -10 (option a).</span>

7 0

2 years ago

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Please help with finding the measure, pic attached

vekshin1

Answer:

B. 50°

Step-by-step explanation:

∠PLM+ ∠PML =60+70 =130°

So, ∠MPL = 180°-130°=50°

According to the opposite angle theorem,

∠ KPN = ∠MPL which is 50°

7 0

3 years ago

Need help please assist me find the area of a regular hexagon

garri49 [273]

Answer:

The area of the regular hexagon is $166.3\ units^{2}$

Step-by-step explanation:

we know that

The area of a regular hexagon can be divided into 6 equilateral triangles

so

step 1

Find the area of one equilateral triangle

$A=\frac{1}{2}(b)(h)$

we have

$b=r=8\ units$

$h=4\sqrt{3}\ units$ ----> is the apothem

substitute

$A=\frac{1}{2}(8)(4\sqrt{3})$

$A=16\sqrt{3}\ units^{2}$

step 2

Find the area of 6 equilateral triangles

$A=(6)16\sqrt{3}=96\sqrt{3}=166.3\ units^{2}$

7 0

2 years ago

When multiplying 4.73 by 2.1 how many decimal places will the product have

hichkok12 [17]

it would be 9.93300

so 3 decimal places because the zeros don't count

3 0

3 years ago

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Polly's Polls asked 1850 second-year college students if they still had their original major. According to the colleges, 65% of

suter [353]

Answer:

The probability that Polly's Sample will give a result within 1% of the value 65% is 0.6424

Step-by-step explanation:

The variable that assigns the value 1 if a person had its original major and 0 otherwise is a Bernoulli variable with paramenter 0.65. Since she asked the question to 1850 people, then the number of students that will have their original major is a Binomial random variable with parameters n = 1850, p = 0.65.

Since the sample is large enough, we can use the Central Limit Theorem to approximate that random variable to a Normal random variable, which we will denote X.

The parameters of X are determined with the mean and standard deviation of the Binomal that we are approximating. The mean is np = 1850*0.65 = 1202.5, and the standard deviation is √np(1-p) = √(1202.5*0.35) = 20.5152.

We want to know the probability that X is between 0.64*1850 = 1184 and 0.66*1850 = 1221 (that is, the percentage is between 64 and 66). In order to calculate this, we standarize X so that we can work with a standard normal random variable W ≈ N(0,1). The standarization is obtained by substracting the mean from X and dividing the result by the standard deviation, in other words

$W = \frac{X-\lambda}{\sigma} = \frac{X-1202.5}{20.5152}$

The values of the cummulative function of the standard normal variable W, which we will denote $\phi$ are tabulated and they can be found in the attached file.

Now, we are ready to compute the probability that X is between 1184 and 1221. Remember that, since the standard random variable is symmetric through 0, then \phi(-z) = 1-\phi(z) for each positive value z.

$P(1184 < X < 1221) = P(\frac{1184-1202.5}{20.5152} < \frac{X-1202.5}{20.5152} < \frac{1221-1202.5}{20.5152})\\ = P(-0.9018 < W < 0.9018) = \phi(0.9018) - \phi(-0.9018) = \phi(0.9018)-(1-\phi(0.9018))\\ = 2\phi(0.9018)-1 = 2*0.8212-1 = 0.6424$

Therefore, the probability that Polly's Sample will give a result within 1% of the value 65% is 0.6424.

Download pdf

4 0

3 years ago