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Ivanshal [37]
3 years ago
12

Which shows the correct solution to the inequality StartFraction 7 over 10 EndFraction greater-than-or-equal-to 1 and StartFract

ion 5 over 8 EndFraction + p?
Mathematics
2 answers:
Flura [38]3 years ago
6 0

Answer:

the answer is c

Step-by-step explanation:

Lena [83]3 years ago
4 0

Answer:

The correct answer is p \geq  \frac{74}{80}

Step-by-step explanation:

An inequality compares two quantities unlike an equality. An inequality is written with either a greater than ( > ) or lower than ( < ) or greater than equal to (  ) or less than equal to (  ) signs. We solve the above given inequality to find the solutions of the unknown p. An inequality reverses if and only if we we multiply both sides with a negative quantity. Addition or subtraction does not change the sign in the inequality.

\frac{7}{10} \geq 1 + \frac{5}{8} + p\\\\\frac{7}{10} \geq \frac{13}{8} + p\\\\\frac{7}{10} - \frac{13}{8} \geq p\\\\\frac{-74}{80} \geq p\\p \leq \frac{-74}{80} \\p\geq \frac{74}{80}

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Where do the brackets go?
Firdavs [7]
(5+8)x(6-2)+5 The brackets go there because of the way the numbers are placed. (I added words because without them I could not post this answer.)
5 0
3 years ago
Solve using elimination.<br> 5x - 6y = 2<br> -5x - 5y = 20
s344n2d4d5 [400]

Answer:

x = -2, y =-2

Step-by-step explanation:

5x - 6y = 2

-5x - 5y = 20

Add the two equations together to eliminate x

5x - 6y = 2

-5x - 5y = 20

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

-11y = 22

Divide by -11

-11y/-11 = 22/-11

y = -2

Now we can find x

5x -6(-2) =2

5x +12 = 2

Subtract 12 from each side

5x +12-12 =2-12

5x = -10

Divide by 5

5x/5 = -10/5

x = -2

6 0
3 years ago
Use Green's Theorem to evaluate the line integral along the given positively oriented curve. ∫C (3y +5e√x)dx + (10x + 3 cos
elena-s [515]

By Green's theorem, the line integral

\displaystyle \int_C f(x,y)\,\mathrm dx + g(x,y)\,\mathrm dy

is equivalent to the double integral

\displaystyle \iint_D \frac{\partial g}{\partial x} - \frac{\partial f}{\partial y} \,\mathrm dx\,\mathrm dy

where <em>D</em> is the region bounded by the curve <em>C</em>, provided that this integrand has no singularities anywhere within <em>D</em> or on its boundary.

It's a bit difficult to make out what your integral should say, but I'd hazard a guess of

\displaystyle \int_C \left(3y+5e^{-x}\right)\,\mathrm dx + \left(10x+3\cos\left(y^2\right)\right)\,\mathrm dy

Then the region <em>D</em> is

<em>D</em> = {(<em>x</em>, <em>y</em>) : 0 ≤ <em>x</em> ≤ 1 and <em>x</em> ² ≤ <em>y</em> ≤ √<em>x</em>}

so the line integral is equal to

\displaystyle \int_0^1\int_{x^2}^{\sqrt x} \frac{\partial\left(10x+3\cos\left(y^2\right)\right)}{\partial x} - \frac{\partial\left(3y+5e^{-x}\right)}{\partial y}\,\mathrm dy\,\mathrm dx \\\\ = \int_0^1 \int_{x^2}^{\sqrt x} (10-3)\,\mathrm dy\,\mathrm dx \\\\ = 7\int_0^1 \int_{x^2}^{\sqrt x} \mathrm dy\,\mathrm dx

which in this case is 7 times the area of <em>D</em>.

The remaining integral is trivial:

\displaystyle 7\int_0^1\int_{x^2}^{\sqrt x}\mathrm dy\,\mathrm dx = 7\int_0^1y\bigg|_{y=x^2}^{y=\sqrt x}\,\mathrm dx \\\\ = 7 \int_0^1\left(\sqrt x-x^2\right)\,\mathrm dx \\\\ = 7 \left(\frac23x^{3/2}-\frac13x^3\right)\bigg|_{x=0}^{x=1} = 7\left(\frac23-\frac13\right) = \boxed{\frac73}

6 0
3 years ago
Consider the probability that at least 88 out of 158 software users will not call technical support. Assume the probability that
Nookie1986 [14]

Answer:

E(X) = 158*0.57 =90.06

And the standard deviation for the random variable is given by:

\sigma= \sqrt{158*0.57*(1-0.57)} = 6.223

And the distribution for the approximation is given by:

X \sim N (\mu = 90.06, \sigma = 6.223)

We can use the z score formula given by:

z = \frac{x -\mu}{\sigma}

And using the complement rule we got:

P(X \geq 88) = 1-P(X

And using the standard normal table we got:

P(X \geq 88) = 1-P(X

Step-by-step explanation:

Previous concepts  

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

Solution to the problem

Let X the random variable of interest, on this case we now that:  

X \sim Bin (n = 158, p =0.57)

The probability mass function for the Binomial distribution is given as:  

P(X)=(nCx)(p)^x (1-p)^{n-x}  

Where (nCx) means combinatory and it's given by this formula:  

nCx=\frac{n!}{(n-x)! x!}  

We want this probability:

P(X\geq 88)

Normal approximation

We need to check if we can use the normal approximation , the conditions are:

np =158*0.57 = 90.06>10

n(1-p) = 158*(1-0.57) = 67.94>10

Since we satisfy both conditions the normal approximation makes sense

The expected value is given by this formula:

E(X) = 158*0.57 =90.06

And the standard deviation for the random variable is given by:

\sigma= \sqrt{158*0.57*(1-0.57)} = 6.223

And the distribution for the approximation is given by:

X \sim N (\mu = 90.06, \sigma = 6.223)

We can use the z score formula given by:

z = \frac{x -\mu}{\sigma}

And using the complement rule we got:

P(X \geq 88) = 1-P(X

And using the standard normal table we got:

P(X \geq 88) = 1-P(X

4 0
3 years ago
A skier travels 4 seconds and cover 72 meters. how long will it take the skier to travel 360 meters?
d1i1m1o1n [39]
It should take 20 seconds for the skier to travel 360 meters.
4 0
3 years ago
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