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3 years ago

Which expression is equivalent to 5x + 10 y - 15

Mathematics

1 answer:

klasskru [66]3 years ago

5 0

The answer is the first one because you have to multiply the outsider five to the other numbers inside the parenthesis. You don't add them or subtract them because they don't have the same variable

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Two fair dice are rolled. Determine the following probability

VashaNatasha [74]

????????????????????????????????

8 0

3 years ago

If y varies inversely as x and y=23 when x=8 find y when x=4

valina [46]

<h2>INVERSE VARIATION</h2>

EQUATION: 

$y = \frac{k}{x}$

––––––––

First, find the constant of variation k using the formula k=xy.

$23 = \frac{k}{8}$

$k = (8)(23)$

$k = 184$

––––––––

Then, find y if x is equal to four using the formula y=184/x.

$y = \frac{184}{x}$

$y = \frac{184}{4}$

$y = 46$

Final Answer:

5 0

3 years ago

A man wants to test for diabetes. His family history shows that the probability of getting diabetes is 0.6. He decides to do a h

lesantik [10]

So,

The probability of the man having diabetes is 0.6 or 60%. Because we are figuring the probability BEFORE the test is taken that he has the disease, we can disregard the test and its accuracy rate. That rate is 60%, the probability of him having diabetes.

The correct option is D.

8 0

3 years ago

The hemisphere of radius r is made from a stack of very thin plates such that the density varies with height, r = kz, where k is

Papessa [141]

Answer:

M = ¼ k π R⁴

zG = 8/15 R

Step-by-step explanation:

Note: I'm using lower case r as the radius of each plate and upper case R as the radius of the hemisphere.

The mass of each plate is density times volume:

dm = ρ dV

Each plate has a radius r and a thickness dz. So the volume of each plate is:

dV = π r² dz

Substituting:

dm = ρ π r² dz

We're told that ρ = kz. Substituting:

dm = kz π r² dz

Next, we need to write the radius r in terms of the height z. To do that, we need to look at the cross section (see image below).

The height z and the radius r form a right triangle, where the hypotenuse is the radius of the hemisphere R.

Using Pythagorean theorem:

z² + r² = R²

r² = R² − z²

Substituting:

dm = kπ z (R² − z²) dz

We now have the mass of each plate as a function of its height. To find the total mass, we integrate between z=0 and z=R.

M = ∫ dm

M = ∫₀ᴿ kπ z (R² − z²) dz

M = kπ ∫₀ᴿ (R² z − z³) dz

M = kπ (½ R² z² − ¼ z⁴) |₀ᴿ

M = kπ (½ R⁴ − ¼ R⁴)

M = ¼ k π R⁴

Next, to find the center of gravity, we use the weighted average:

zG = (∫ z dm) / (∫ dm)

zG = (∫ z dm) / M

We already found M, we just have to evaluate the other integral:

∫ z dm

∫₀ᴿ kπ z² (R² − z²) dz

kπ ∫₀ᴿ (R² z² − z⁴) dz

kπ (⅓ R² z³ − ⅕ z⁵) |₀ᴿ

kπ (⅓ R⁵ − ⅕ R⁵)

²/₁₅ k π R⁵

Plugging in:

zG = (²/₁₅ k π R⁵) / (¼ k π R⁴)

zG = ⁸/₁₅ R

5 0

3 years ago

Given a term in a geometric sequence and the common ratio, find the explicit formula, a11=5120 ans r=-2

sweet-ann [11.9K]

Answer:

$U_n=5(-2)^{n-1}$

Step-by-step explanation:

Given a geometric sequence, the nth term of the geometric sequence is obtained by using the formula:

$U_n=ar^{n-1}$

If the eleventh term, $a_{11}=5120$

and the common ratio, r=-2.

Then:

$5120=a(-2)^{11-1}\\a=\frac{5120}{2^{10}} =5$

The explicit formula for the sequence is:

$U_n=5(-2)^{n-1}$

5 0

3 years ago