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10 months ago

What is the value of x

Mathematics

2 answers:

valina [46]10 months ago

8 0

Answer:

x ≈ 19.2 units

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then

x² + 19² = 27²

x² + 361 = 729 ( subtract 361 from both sides )

x² = 368 ( take square root of both sides )

x = $\sqrt{368}$ ≈ 19.2 ( to the nearest tenth )

vivado [14]10 months ago

5 0

Answer:

x = 33

Step-by-step explanation:

$a {}^{2} + b {}^{2} = c {}^{2} \\ 27 {}^{2} + 19 {}^{2} = c {}^{2} \\ 729 + 361 = c {}^{2} \\ 1090 = c {}^{2} \\ \sqrt{1090 } = \sqrt{c {}^{2} } \\ c = 33$

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Need Help ASAP. Thank You.

bekas [8.4K]

Let, the number of hour, she can still watch the T.V. = x
Equation would be: x + 1.5 ≥ 5

Solving the equation:
x + 1.5 ≥ 5

Subtract 1.5 from both the sides,
x + 1.5 - 1.5 ≥ 5 - 1.5
x ≥ 3.5

In short, She can watch 3.5 hours more in that week

Hope this helps!

7 0

3 years ago

<img src="https://tex.z-dn.net/?f=3x%2B7%3D12-2x%3B1" id="TexFormula1" title="3x+7=12-2x;1" alt="3x+7=12-2x;1" align="absmiddle"

Igoryamba

Step-by-step explanation:

$3x + 7 = 12- 2x \\ 3x + 2x = 12 - 7 \\ 5x = 5 \\ x = \frac{5}{5} \\ x =1$

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2 years ago

A normally distributed population has mean 57,800 and standard deviation 750. Find the probability that a single randomly select

Stels [109]

Answer:

(a) Probability that a single randomly selected element X of the population is between 57,000 and 58,000 = 0.46411

(b) Probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000 = 0.99621

Step-by-step explanation:

We are given that a normally distributed population has mean 57,800 and standard deviation 75, i.e.; $\mu$ = 57,800 and $\sigma$ = 750.

Let X = randomly selected element of the population

The z probability is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

(a) So, P(57,000 <= X <= 58,000) = P(X <= 58,000) - P(X < 57,000)

P(X <= 58,000) = P( $\frac{X-\mu}{\sigma}$ <= $\frac{58000-57800}{750}$ ) = P(Z <= 0.27) = 0.60642

P(X < 57000) = P( $\frac{X-\mu}{\sigma}$ < $\frac{57000-57800}{750}$ ) = P(Z < -1.07) = 1 - P(Z <= 1.07)

= 1 - 0.85769 = 0.14231

Therefore, P(31 < X < 40) = 0.60642 - 0.14231 = 0.46411 .

(b) Now, we are given sample of size, n = 100

So, Mean of X, X bar = 57,800 same as before

But standard deviation of X, s = $\frac{\sigma}{\sqrt{n} }$ = $\frac{750}{\sqrt{100} }$ = 75

The z probability is given by;

Z = $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

Now, probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000 = P(57,000 < X bar < 58,000)

P(57,000 <= X bar <= 58,000) = P(X bar <= 58,000) - P(X bar < 57,000)

P(X bar <= 58,000) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ <= $\frac{58000-57800}{\frac{750}{\sqrt{100} } }$ ) = P(Z <= 2.67) = 0.99621

P(X < 57000) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{57000-57800}{\frac{750}{\sqrt{100} } }$ ) = P(Z < -10.67) = P(Z > 10.67)

This probability is that much small that it is very close to 0

Therefore, P(57,000 < X bar < 58,000) = 0.99621 - 0 = 0.99621 .

7 0

3 years ago

Are the irrational numbers closed under addition?

Arte-miy333 [17]

Answer:

Irrational numbers are not closed under addition.

Step-by-step explanation:

Irrational numbers are the numbers that cannot be expressed in the form of a fraction $\frac{x}{y}$ . In other words we can say that irrational number,s decimal expantion does not cease to end.

The closure property of addition in irrational numbers say that sum of two irrational number is always a rational number, But this is not true. It is not necessary that the sum is always irrational some time it may be rational.

This can be understood with the help of an example:

let (2+√2) and (-√2) be two irrational number. Their sum is (2+√2)+(-√2) = 2, which is clearly a rational number.

Hence, irrational numbers are not closed under addition.

4 0

3 years ago

A delivery truck drives three routes in one day. The first route is 1223 miles long, the second route is 1034 miles long, and th

avanturin [10]

Answer:

$Total = 38\frac{11}{12}\ miles$