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2 years ago

Is the origin Located at the point (1,1)

Mathematics

2 answers:

ddd [48]2 years ago

6 0

Answer:

No, the origin is Located at (0,0)

Evgen [1.6K]2 years ago

5 0

Answer:

Step-by-step explanation:

The origin is located at the center of a graph, at (0, 0)

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If x. 5x and 6x are the measures of the

max2010maxim [7]

Answer:

<em>Since one of the angles is 90°, the triangle is right.</em>

Step-by-step explanation:

<u>Angles in a Triangle</u>

The sum of angles in a triangle is 180°. We are given the angles are x, 5x, and 6x, thus:

x + 5x + 6x = 180

Simplifying:

12x = 180

Dividing by 12:

x = 180/12 = 15

x = 15°

5x = 75°

6x = 90°

Since one of the angles is 90°, the triangle is right.

6 0

2 years ago

Find the slope of the line.

lukranit [14]

Answer:

Step-by-step explanation:

slope = dy/dx

= 0/x

= 0

7 0

2 years ago

A geologist has collected 5 specimens of basaltic rock and 7 specimens of granite. The geologist instructs a laboratory assistan

MaRussiya [10]

The rocks are chosen without replacement, which means that the hypergeometric distribution is used to solve this question. First we get the parameters, and then we answer the questions. From this, we get that:

$E(X) = 5.25, Var(X) = 0.5966$
P(X < 6) = 0.9545
P(all specimens of one of the two types of rock are selected for analysis) = 0.2046.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The mean and the variance are:

$\mu = \frac{nk}{N}$

$\sigma^2 = \frac{nk(N-k)(N-n)}{N^2(N-1)}$

We have that:

5 + 7 = 12 rocks, which means that $N = 12$

9 are chosen, which means that $n = 9$

7 are granite, which means that $k = 7$

Question a:

$E(X) = \mu = \frac{9\times7}{12} = 5.25$

$Var(X) = \sigma^2 = \frac{9\times7(12-7)(12-9)}{12^2(12-1)} = 0.5966$

Thus:

$E(X) = 5.25, Var(X) = 0.5966$

Question b:

Since there are only 5 specimens of basaltic rock, at least 9 - 5 = 4 specimens of granite are needed, which means that:

$P(X < 6) = P(X = 4) + P(X = 5) + P(X = 6)$

In which

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 4) = h(4,12,9,7) = \frac{C_{7,4}*C_{5,5}}{C_{12,9}} = 0.1591$

$P(X = 5) = h(5,12,9,7) = \frac{C_{7,5}*C_{5,4}}{C_{12,9}} = 0.4773$

$P(X = 6) = h(6,12,9,7) = \frac{C_{7,6}*C_{5,3}}{C_{12,9}} = 0.3181$

Thus

$P(X < 6) = P(X = 4) + P(X = 5) + P(X = 6) = 0.1591 + 0.4773 + 0.3181 = 0.9545$

So P(X < 6) = 0.9545.

Question c:

5 of basaltic and 4 of granite: 0.1591 probability.

7 of granite is P(X = 7), in which

$P(X = 7) = h(7,12,9,7) = \frac{C_{7,7}*C_{5,2}}{C_{12,9}} = 0.0455$

0.1591 + 0.0455 = 0.2046, thus:

P(all specimens of one of the two types of rock are selected for analysis) = 0.2046.

A similar question is found at brainly.com/question/24008577

5 0

3 years ago

Find the cosine of R.

JulijaS [17]

Answer:

$cos(R) = \frac{\sqrt{15}}{5}$

Step-by-step explanation:

To find the cosine of <R, apply the following trigonometric ratio formula:

$cos(R) = \frac{adjacent}{hypotenuse}$

Adjacent = 3

Hypotenuse = √15

Plug in the values into the formula

$cos(R) = \frac{3}{\sqrt{15}}$

Multiply the numerator and denominator by √15 to rationalize.

$cos(R) = \frac{3 \times \sqrt{15}}{\sqrt{15} \times \sqrt{15}}$

$cos(R) = \frac{3\sqrt{15}}{(\sqrt{15})^2}$

$cos(R) = \frac{3\sqrt{15}}{15}$

$cos(R) = \frac{\sqrt{15}}{5}$

3 0

3 years ago

Judy lives in central city, where the tax rate is 3.9%. her property is assessed at $82,000. what is her tax?

coldgirl [10]

Her tax is $3198.
3.9/100=0.039.
0.039*8200=$3198.

8 0

2 years ago